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Chaos and ComplexityScientific Perspectives on Divine Action



A Series on "Scientific Perspectives on Divine Action"

First Volume

Quantum Cosmology and the Laws of Nature:

Scientific Perspectives on Divine Action

Edited by Robert John R ussell , Nan cey M urphy, and C. J . Isham

Second Volume

Chaos and Complexity:

Scientific Perspectives on Divine Action

Edited by Robert John Russell , Nancey Murphy, and Arthur R. Peacocke

Future Scientif ic TopicsEvolutionary and Molecular Biology

Neurobiology and Brain Research

Quantum Physics and Quantum Field Theory

Jointly published by the Vatican Observatory and

The Center for Theo logy and the Natural Sciences

Robert John Russell, General Editor of the Series

Supported in part by a grant from

the Wa yne and Gladys Valley Founda tion.



Chaos and ComplexityScientific Perspectives on Divine Action

Robert John RussellNancey MurphyArthur R. Peacocke

Editors

Vatican Observatory

Publications,

Vatican City State

The Center for Theology

and the Natural Sciences,

Berkeley, California

S E C O N D E D I T I O N

2 0 0 0



Robert John Russell (General Editor) is Professor of Theology and Science inResidence, Graduate Theological Union, Berkeley, California, and Founder and

Director of the Center for Theology and the Natural Sciences.

Nancey Murphy is Associate Professor of Christian Philosophy, Fuller Theological

Seminary, Pasadena, California.

Arthur R. Peacocke is currently Director of the Ian Ramsey Centre, Oxford,

England, Warden Emeritus of the Society of Ordained Scientists, and formerly

Dean of Clare College, Cam bridge, England.

About the cover: the image on the cover of this volume is a graphic depiction of

a Rossler attractor: the simplest case for a chaotic attractor. The image is taken

from "Chaos" by James P. Crutchfield, et al. , reprinted in this volume by

permission of Scientific American.

Copyright © 1995 by the Vatican Observatory Foundation

SECOND EDITION

Copyright © 1997 by the Vatican Ob servatory F ou nd ation

Copyright © 2000 by the Vatican Observatory Foundation

Distributed (except in Italy and Vatican City State) by

The Universi ty of Notre Dame Press

Notre Dame, Indiana 46556

U.S .A.

Distributed in Italy and Vatican City State by

Libreria Editrice Vaticana

V-0 0120 Cit ta del V aticano

Vatican City State

ISBN 0-268-008 12-4 (pbk. )

V A T I C A N P R E S S



A C K N O W L E D G M E N T S

The editors with to express their gratitude to the Vatican Ob servatory and the

Center for Theology and the Natural Sciences for co-sponsoring this research.

Particular appreciation goes to George Coyne and Bill Stoeger, whose leadership

and vision made this series of conferences possible.

Editing for this volume began with an initial circulation of papers for critical

responses be fore the conference in 1993, and continued with extensive interactions

between editors and authors after the conference. The editors want to express their

gratitude to all the participants for their written responses to pre-conference drafts

and for their enthusiast ic discussions during the conferen ces.

Regarding this volume, special thank s go es to G reg M aslow e, C TN S Editing

Coordinator, who devoted meticulous attention and long hours to every stage in the

preparation of the camera-ready m anu script of this volu m e. His effort ensured the

quality of the final manuscript and made it possible for us to meet our deadline for

publication in 1995. Thanks also goes to George Coyne for overseeing printing,

jacket design, and distribution, and to Karen Cheatham and Lisa Dahlen for their

help in hosting the conference at the GTU and their prel iminary work on this

manuscript. One of us (RJR) wishes to express special personal thanks to NanceyMurphy for the enormous effort she put into edit ing this volume, and to Wesley

Wildman for the pleasure of co-authoring with him.

Th e Center for Theology and the Natural Sciences w ishes to ackn ow ledge the

generous support of the W ayne and Gladys Valley F oun dation . The recent renew al

of their initial grant continues to make our on-going collaboration with the Vatican

Observatory possible . A second grant from the Valley Foundation, also recently

renewed, has supported the production of this volume.

The editors wish to thank the following for their generous permission to

reprint articles in this volume:

Chaos by James P. Cruthfield, J . Doyn e Farmer, N orman H. Packard, and Robert

S. Shaw: From Scientific A merican 225, no. 6 (December 1986): 46-57. Reprinted

by permission.

Understanding Complexity by Bemd-Olaf Kuppers : From Emergence or

Reduction? , ed. An sgar Beckerman n, Hans Flohr, and Jaegw on Kim (Berl in:

Walter de Gruyter, 1992), 241-256. Reprinted by permission of the author.

Chan ce and Law in Irreversible Thermo dynam ics, Theoretical Biology, and

Theology by Arthur R. Peacocke: From Philosophy in Science 4 (1990): 145-180.

© 1990 by the Pachart Foundation dba Pacha rt Pu blishing Ho use and reprinted by

permiss ion.



T A B L E O F C O N T E N T S

Introduction

Robert John Russell

I. SCIENTIFIC B A C K G R O U N D : C H A O S A N D C O M P L E X I T Y

Chaos

James P. Crutckfield, J. Doyne Farmer,Norman H. Packard, and Robert S. Shaw

Chaos: A Mathematical Introduction with Philosophical Reflect ions

Wesley J. Wildman and Robert John Russell

I I . C HAOS , C OM P L E XI T Y, AND T HE P HI L OS OP HY OF L I F E

Unders tanding Complexi ty

Bernd-Olaf Kiippers

Chaos, Probability, and the Comprehensibili ty of the World

Michael Heller

Chance and Law in Irreversible Thermodynamics,

Theoret ical Biology, and TheologyArthur R. Peacocke

I I I . C HAOS , C OM P L E XI T Y, AND DI VI NE AC T I ON

The Metaphysics of Divine Action

John Polkinghorne

The Discovery of Chaos and the Retrieval of the Trinity

Denis Edwards

Divine Providence and Instrumental i ty: Metaphors for

Time in Self-Organizing Systems and Divine Action

Stephen Happel



Reflections on Chaos and God's Interaction with the Worldfrom a Trinitarian PerspectiveJiirgen Moltmann 205

The God of Nature

Lang don Gilkey 211

IV . A L T E R N A T IV E A PPR O A C H E S T O D IV IN E A C T IO N

Gaps for God?Willem B. Drees 223

Describing God's Action in the World in Light

of Scientific Knowledge of Reality

William R. Stoeger 239

God's Interaction with the World: The Implications of

Deterministic "Chaos" and of Interconnected and

Interdependent Complexity

Arthur R. Peacocke 263

Particular Providence and the God of the Gaps

Thomas F. Tracy 289

Divine Action in the Natural Order: Buridan's Ass

and Schrodinger 's Cat

Nancey Murphy 325

Ordinary and Extraordinary Divine Action:

The Nexus of Interaction

George F.R. Ellis 359

L IST O F C O N T R IB U T IN G PA R T IC IPA N T S 3 97

INDEX 399



I N T R O D U C T I O N 1 1

Robert John Russell

1 Background to the Volume

In August, 1993, twenty scholars, with cross-disciplinary expertise in physics,cosmology, biology, philosophy of religion, philosophy of science, philosophicaland systematic theology, history of theology, and history of science, met for aweek-long conference at the Center for Theology and the Natural Sciences (CTNS)

in Berkeley, California. The purpose of the conference was to explore theimplications of chaos and complexity in physical, chemical, and biological systemsfor philosophical and theological issues surround ing the top ic of div ine a ction. Th eresulting papers form the contents of this volu m e. The c onf eren ce was the secondof a series of five such research con feren ces planned fo r the decade of the 1990son theology, philosophy, and the natural sciences. The overarching goal of theseconferences is to contribute to constructive theological research as it engagescurrent research in the natural sciences, and to id entif y and cr itiqu e the philo sop hi-cal and theological elements that m ay be pre sent in ongo ing research in the n aturalsciences.

The conferences are jointly sponsored by the Vatican Observatory andCTNS. The Vatican Observatory is housed in the Papal Palace in the picturesquetown of Castel Gandolfo, poised overlooking Lake Albano thirty miles southeastof Rome. Since 1935 it has been the site of basic research in both observational andtheoretical astronomy. It is also here that Pope John Paul II resides during thesummer. CTNS is an affiliate of the Graduate Theological Union (GTU) inBerkeley, California. CTNS sponsors and conducts a variety of research, teaching,

and public service programs in the interdisciplinary field of theology and science.Facilities for the conference were provided by the GTU, a consortium of nineRoman Catholic and Protestant seminaries and a graduate school of religionlocated just north of the campus of the University of California, Berkeley.

This series of conferences grew out of the initiative of Pope John Paul II,who, in 1979, called for an interdisciplinary collaboration of scholars to seek a"fruitful conc ord betw een science and faith, betw een the Chu rch and the world. . . (which) honors the t ru th of fa ith and of s c i e n c e . . . R e s p o n d i n g to thi s ca ll ,

the Vatican Observatory held a number of events culminating in a major

international conference at the Observatory in September, 1987. The resultingpublication, Physics, Philosophy and Theology: A Com mon Quest for Understand-

1Discourses of he Popes from Pius XI o John Paul II o the Pontifical Academy ofSciences (Vatican City State: Pontificia Accadcm ia Scientiarum , 1986 ), Scripta Varia 66, 73-

84 .



K U 1 3 E K 1 J U H I N K U S S E L L

ing,2 includes a message by the Pope on the relations between the church and thescientific com mu nities. This was the first m ajo r Pontific al statem ent on scien ce andreligion in three decades. It was reprinted, together with nineteen responses by

scientists, philosophers, and theologians, in John Paul II on Science and Religion:Reflections on the New View From Rom e?

Based on this work, George Coyne, Director of the Vatican Observatory,proposed a m ajor new initiative: a series of five confere nces fo r the deca de of the1990s. The goal would be to expand upon the research agenda begun in 1987 bymoving into additional areas in the physical and biological sciences. Coyneconvened a meeting at the Specola in June, 1990, to plan the overall direction ofthe research, out of which a long-term steering committee was formed with NanceyMurphy, Associate Professor of Chris t ian Philosophy, Fuller Theological

Seminary, Bil l Stoeger, Staff Astrophysicis t and Adjunct Associate Professor,Vatican Observatory Research Group, Steward Observatory, and myself asmem bers . Coyne then invited CTN S to co-sponsor the decade of research. C TN Swas able to accept this offer through the generous support of the Wayne andGladys Valley Foundation.

Th e first conferen ce in the series was held in September, 1991 at the VaticanObservatory in Castel Gandolfo. It resulted in the publication of Quantum

Cosm ology and the Law s of Nature: Scientific Perspectives on Divine Action.4

Future conferences will take up issues in evolutionary and molecular biology,including the study of self-organizing systems; the mind-brain problem; and topicsin quantum physics and quantum field theory.

2 Guiding Theme: Scientific Perspectives on Divine Action

A major issue in the way research is carricd out in the field of theology and scienceregards the role science ought to play. Too often science tends to set the agenda for

the research with little if any initiative taken by theology. From the beginning itwas the clear intention of the steering committee that our research expand beyondthis format to insure a two-way interaction between scientific and theologicalresearch program s. In order to achieve this goal we d ecided on a two-fo ld strategy.First, we searched for an overarching theological topic to them atize th e entire seriesof conferences. The topic of divine action, or Go d's action in and interaction withthe world, was quickly singled out as a promising candidate. Clearly it permeatesthe discussions of theology and science in both philosophical and systematiccontexts, and it allows a variety of particular theological and philosophical issues

to be pursued under a general umbrella.

Robert John Russell, William R. Stoeger, and George V. Coyne, eds. (Vatican City

State: Vatican Observatory, 1988).

Russell, Stoeger, and Coyne, eds. (Vatican City State: Vatican Observatory, 1990).4 Russell, Nancey Murphy, and C.J. Isham, eds. (Vatican City State: Vatican

Observatory, 1993; Berkeley, CA: Center for Th eolo gy and the Natural Sciences , 1993) .



I N T R O D U C T I O N 3

Next, we organized a series of individual conferences around specific areasin the natural sciences. W e cho se qua ntum cosm olog y, th e origin and status of thelaws of nature, and foundational issues in quantum physics and quantum field

theory to build on areas of research begun in Physics, Philosophy and Theology.We also chose chaos and complexity, biological evolution, molecular biology,genetics , creative self-organization, and the mind-brain problem to extend ourresearch into areas treated less directly in Physics, Philosophy a nd Theology.

The overall research methodology for the series of conferences wasconsidered as well . I t was agreed that papers for each conference would becirculated several times in advance of the conference for critical written responsesfrom all part icipants . Revis ions would be read in advance of the conference tomaximize the critical discussion of the papers during the event. Post-conference

revisions would be carefully reviewed by the volume editors in light of thesediscussions. W e agreed to hold regional pre-conferences in Berkeley and Rome toprovide an introduction for participants to relevant technical issues in science,philo sop hy , and theology and to foster joint research and collaboration am ongpart icipants prior to the conference. An organizing committee would guide thepreparation fo r, procedures o f, and editorial process following each con ference.

Since the topic of God's action in the world was chosen as the guidingtheological th em e for the confe renc es, a brief introduction to the topic is in order

here. Port ions of the following are drawn from the Introduction published inQuantum Cosmology and the Laws of Nature.

3 Overview of Divine Action: Historical and Contem porary Perspectives

3 .1 Biblical and Traditional Perspectives

The notion of God's acting in the world is central to the biblical witness. From the

call of Abraham and the Exodus from Egypt to the birth, ministry, death andraising of Jesus and the founding of the church at Pentecost, God is represented asmaking new things happen. Through these "mighty acts," God creates and saves;the themes of creation and redemption are intim ately linked in Biblical the olo gie s.5

^ h e ordering of the relation between redem ption and creation theologies in the history

of Israel is the subject of debate. It has long been held that the Exodus experience served as

the basis for Hebrew faith in God the creator, a positio n dev elop ed by G erhard von Rad (OldTestament Theology, 2 vols . [Ne w York: Harper & Ro w, 1957 -65], 1:138; and dem, TheProblem of the Hexateuch [New York: McGraw-Hill , 1966], 131-43). This view was

frequently incorporated in standard treatments of the doctrine of creation. See, e.g., Langdon

Gilkey, Maker of Heaven and Earth (Garden City, NY: Doubleday, 1959), 70. Recent

scholarship, how ever, has questioned this view , raising the possibility that creation theo logy

actually perm eates the historical development of Israel. See, e.g., Claus Westerman, Creation(Philadelphia: Fortress Press, 1974); Bem hard A nde rson , ed., Creation in he Old Testament

(Philadelphia: Fortress Press, 1984); and R.J. Clifford, "Creation in the Hebrew Bible," in



4 ROBERT J O H N R U S S E L L

Rather than seeing divine acts as occasional events in what are otherwise entirelynatural and historical processes, both the Hebrews and the early Christiansconceived of God as the creator of the world and of divine action as the continuing

basis of all that happens in nature and in history.6

The view that God works in and through all the processes of the worldcontinued to be held throughout Patristic and Medieval times, as even a cursoryreading of such theologians as Augustine and Tho m as Aq uinas d em onstrate s. He reGod was understood as the first cause of all events; all natural causes are secondaryor instrumental causes through which God works. In addition, God was thoughtto act immediately in the world through miracles, without using or by surpassingfinite causes. This view of divine action led to such problematic issues as doubleagency—can a single and unified event issue sim ultaneously fro m two fre e agents

(e.g., God and human agents) each of which is sufficient to accomplish the event?How does an infinite agent (God) preserve the finite freedom of a creaturely agentwhen they act together? Finally it lead to the problem of theodicy—if God acts inall events and God is good, why is there so much evil in the world?

The conviction that God acts universally in all events, and that God and freehuman agency can act together in specific events, was maintained by the ProtestantReformers and the ensuing Protestant orthodoxy. John Calvin, for example, arguedthat Go d is in absolute control over the world and at the same time maintained thathumans are responsible for evil dee ds. 7 In general, the topic of divine agen cy wastreated as part of the doctrine of providence and formulated in terms of divinepreservation, concurrence, and government. Questions about human freedom andthe reality of evil were seen more as problems requiring serious theologicalattention than as reasons for abandoning belief in God's universal agency.

The rise of modern science and modern philosophy in the seventeenthcentury led many to reject the traditional views of divine action, especially beliefin miracles. Although Isaac Newton argued for the essential role of God in relationto the metaphysical underpinnings of his mechanical system, and in this way

defended the sovereignty of God in relation to nature,8

Newtonian mechanics

Physics, Philosophy and Theology, 151-70. For a recent theological discussion of the

relation between creation, redemption, and natural science, see Ted Peters, "Cosmos as

Creation," in Cosmos as Creation, ed. Ted Peters (Nashv i l le: Ab ingdo n Press , 1989), 45-

113.

6 Se e, e.g., Gen. 45:5; Job 38:2 2-3 9:3 0; Ps. 148: 8-10; Is. 26:1 2; Phil . 2:1 2-1 3; 1 Cor.

12:6; 2 Cor. 3:5.

7 See, e .g . , John Calvin, The nstitutes II, iv, 2.

N e w to n 's m echanics and his system of the world led to profou nd philoso phic al issue s

through his introduction of absolute space and absolute time to ground the distinction

between uniform and accelcrated motion, as well as to important theological reconstructions

of the relation of God to nature in terms of the divine sensorium and the design of the

universe. See E.A. Burtt, The Metaphysical Foundations of Modern Science (Garden City,

NY: Doubleday, 1954). Michael Buckley has argued that the reliance on Newtonian science

as a foundation for theology, and the abandonm ent of the "Go d hyp othesis" thereafter, were




seemed to depict a causally closed universe with little, if any, room for God'sspecial action in specific events. With the ascendancy of deism in the eighteenthcentury, the scope of divine agency was limited to an initial act of creation.

Moreover, David Hume and Immanuel Kant raised fundamental questionsconcerning the project of natural theology, challenged belief in miracles, undercutmetaphysical speculation about causality and design, and restricted religion to thesphere of m orali ty.

Given this backg roun d, as w ell as the rise of the historical-critical approac hto the Bible, theology in the nineteenth century underwent a fundamentalquestioning not only of its contents and structure, but even of its method. Theresponse of Friedrich Schleiermacher (1768-1834) was to understand religion asneither a know ing (the activity of pure reason) n or a doing (the ac tivity of prac ticalreason) but as grounded in an entirely separate domain, the "feeling of absolutedependence." Theological assertions can only have as their basis the immediate

assert ions of rel igious self-consciousness . Schleiermacher understood God'srelation to the world in terms of universal divine im m anen ce. By m iracle we m ean" . . . sim ply the religious nam e for event. Every event, even the mo st natural andusual, becom es a m iracle, as soon as the religious view of it can be the dominant."9

3.2 The "Travail" of Divine Action in the Twentieth Century

Protestant theology in the first half of the twentieth century was largely shaped byKarl Barth. In his rejection of nineteenth-century liberal theology, Barth turned tothe sovereignty of the God who is "wholly other" and stressed God's initiatingaction in our redem ption . "Th e Gospel is . . . not an event, nor an experience, noran emo tion— how ever delicate! . . . [I]t is a com mu nication w hich presum es faithin the living God, and which creates that which it presumes."1 0 But do Barthian

principal causes of the rise of atheism in the West. See Michael J. Buckley, At he Originsof Modern Athesm (N ew Have n, CT: Yale University Press, 198 7). For a brief historical

account see Ian G. Barbour, ssues in Science and Reigion (New York: Harper Torchbook,

1966), chap. 3. One can also argue that the concept of inertia played an important role in

deflecting attention away from the view of God as acting ubiquitously to sustain nature in

being. See Wolfhart Pannenberg, 'Theo logical Qu estions to Scientists," in The Sciences andTheology n heTwentieth Century, ed. A.R. Peacocke (Notre Dame, IN: University of Notre

Dame Press , 1981), 3-16, esp. 5-6.

9Friedrich Schleiermacher, On Reigion: Speeches to its Cultured Despisers (New

York: Harper Torchbook, 1958), 88. In a long discussion in The Christian Faith(Edinburgh: T&T Clark, 1968), he wrote: 4 4[A ]s regards the miraculous . . . we shou ld

abandon the idea of the absolutely supernatural because no single instance of it can be

kn ow n by us. . . ."(#4 7.3, 183) For .an excellen t analysis of Schleiermacher and other

important developments in the nineteenth century see Claude Welch, Protestant Thoughtin he Nineteenth Century, 2 vol. (New Haven, CT: Yale University Press, 1972).

10 Karl Barth, The Epistle to he Romans 6th ed. (London: Oxford University Press,

1968), 28.



6 R O B E R T JO H N R U S S E L L

neo-orthodoxy and the ensuing "biblical theology" movement of the 1940s and1950s succeed in producing a credible interpretation of God's acts?

In a well-known article written in 1961, Langdon Gilkey forcefully argued

that they do not.1 1

According to Gilkey, neo-orthodoxy is an unhappy compositeof biblical/orthodox language and liberal/modern cosmology. It attempts todistance itself from liberal theology by retaining biblical language about Godacting through wondrous events and by viewing revelation as an objective act, notjust a subjective perception. Yet, like liberalism, it accepts the m odern p rem ise thatnature is a closed causal continuum, as suggested by classical physics. The resultis that, whereas orthodoxy used language univocally, neo -ortho dox y uses lang uag eat best analogically. In fact, since its language has been emptied of any concretecontent, its analogies devolve into equivocations. "Thus the Bible is a book

descriptive not of the acts of God but of Hebrew religion.. . . [It] is a book of theacts Hebrews believed God might have done and the words he [sic] might havesaid had he done and said them — but of course we recognize he did no t ."1 2

Thus, a " two-language" s trategy sets in: neo-orthodox theologians usebiblical language to speak confessionally about God's acts, but they use secularlanguage when speaking historically or scientifically about "what actuallyhappened." Similarly, the insistence that revelation presupposes faith founderswhen on e challenges the possibility of God acting in the even t in w hich faith origi-

nates. Thus, neo-orthodoxy, and with it much of contemporary theology, involvesa contradict ion between orthodox language and l iberal cosmology.

3 .3 Current Approaches to Divine Action

In the wake of these problems, several approaches to divine action are beingexplored in current literature. The following lists a few of the more pro m inent one sas suggested in part by a major anthology on divine action edited by Owen Thomasin 1983. 1 3

"Langdon B. Gilkey, "Cosmology, Ontology, and the Travail of Biblical Language,"

The Journal of Reigion 41 (1961): 194-205.1 2Ibid., 198.1 3See Owen C. Thomas, ed., God's Activity in he World: The Contemporary Problem

(Chico, CA: Scholars Press, 1983). A ccording to Thom as, only process and n eo-Th om istic

theologies offer full-blown metaphysical theories. They are therefore superior to the personal

action approach with its limited analogies, and these are all preferable to liberal, uniform

action and two-perspectives theologies, which offer neither theories nor analo gies. In a more

recent publication, Ian Barbour offers a lucid description and creative comparison of the

problem of d ivine action in classical theism, process theism, and their alternatives, including

several types of personal agency models. See Barbour, Reigion in an Age of Science, T he

Gifford Lectures 1989- 1991 , vol. 1 (San Francisco: HarperS an Fra ncisco, 19 90) , cha p. 9 . Se e

also Pcacocke, Theology for a Scientific Age: Beng and Becoming—Natural and Divine(Oxford: Ba<il Blackwell, 1990; and second enlarged edition, London: SCM Press, 1993

and reprinted, Minneapolis: Fortress Press, 1993), chap. 9; and Thomas F. Tracy, ed.. The




3 3 . 1 Neo-Thomism Here traditional Thomistic distinctions between primary andsecondary causality, characteristic of both Roman Catholicism and Protestantorthodoxy, have been modified in l ight of the work of Kant. Advocates include

Bernard Lonergan, Joseph Mareschal, Jacques M aritain, and Karl Ra hn er. R elatedworks are those of Austin Farrer and Eric M ascall. Re cent contributors to theologyand science from a neo-Thomistic perspective include W. Norris Clarke, ErnanMcMullin, and Bil l Stoeger. 1 4

3 3 2 Process Theology Process philosophy represents a fund am ental shift awayfrom Aris totel ian metaphysics . Based on the metaphysics of Alfred NorthWhitehead, process theology rejects the traditional conception of divine action interms of primary and secondary causes. Instead, Go d is seen as acting persuasively

in all events, though never exclusively determining their character, since each"actual occasion" also includes an irreducible element of genuine novelty as wellas its response to the influence to the past. Representatives include Charles Birch,Jo hn Co bb , Jr ., David Griffin, Charles Hartshorne, and Schubert Ogden . IanBarbour endorses a process perspective in a nuanced way, calling for a "social orinterpersonal analogy" of divine action, and provides a balanced assessment of thestrengths and weaknesses of other approaches. 1 5

3 3 3 Uniform Action Here God is thought of as acting uniformly in all events inthe world. Distinctions in meaning and significance are due entirely to humaninterpretation. Th is view is found in the writ ings of Gordon Ka ufm an and M auriceWiles .

3 3 . 4 Personal Agent Mo dels

3 . 3 . 4 . 1 Literal Divine Action Some philosophers of religion, notably WilliamAls ton,16 have questioned the assumption that the causal determinism of all natural

events by other natural events prevents us from speaking of God, literally, as apersonal agent who brings about particular states of affairs at particular times andplaces. First, he holds that there is no sufficient reason to adopt strict naturalisticcausal determinism. Second, he argues that deterministic laws hold only for closed

God Who Acts: Philosophical and Theological Explorations (University Park, PA: Penn-

sylvania State University, 1994).

1 4 S e e their articles in Physics, Philosophy and Theology.1 5Barbour echoes Thomas Tracy's objections to viewing "the world as the body of

God" since the universe lacks bodily unity and an environment (see section 3.3 .4.2 belo w) .

H e also believes that embodiment would fail to provide adequately for the independence of

God and the world. See Barbour, Reigion in an Age of Science, 259.

16William P. Alston, Divine Nature and Human Language (Ithaca: Cornell University

Press, 1989). See also, dem, "Divine Action, Human Freedom, and the Laws of Nature,"

in Quantum Cosmology, 185-207.



8 RO B E R T JO H N RUS S E L L

systems and we need not su ppose that all system s are closed to outside in fluenc es(including divine ones).

3 .3 .4 .2 Embodiment and Immanentist Models The analogy of God: world::mind:body has been explored in differing ways by such authors as ArthurPe a c o c k e , 1 7 G race Jantzetf, and Sallie McFd&ue. Pe aco cke stresses theimmanence of God in the world and views the universe as dynamic and inter-connected, suggesting biological and fem inine analog ies for divine agency . T heseanalogies counteract the tendency of traditional language both to stress God'stranscendence and to neglect God's immanence with respect to creation. Peacockeadopts a panentheistic approach wh ich com bines the languag e of im m anen ce withtranscendence in speaking about G od 's relation to crea tion .2 0 Jantzen proposes thatthe entire unive rse is G o d ' s body. God is immediately aware of all events in nature,and acts both universally throughout nature and particularly in unique events.Moreover, all of God's acts are basic or direct acts, analogous to the direct acts weperform when we move our own bodies . She recognizes that the embodimentmodel raises several problems, including the problem of evil, the relation of God'saction to the laws of nature, and the significance for the divine life if the universehas a finite past and/or future, but suggests important responses to each of these.McFague employs embodiment models to view "God as mother, lover and friend.

. . ."2 1

She admits, however, that the embodiment model suggests that God is atrisk, being vulnerable to the sufferings of nature.

3 .3 .4 .3 Non-Embodiment Thomas Tracy rejects both the claim that personalagency requires embodiment and that the world is like an organism. Instead hedevelops a conception of God as a non-embodied agent. 2 2 Tracy sees himself ascombining aspects of classical and process theism.

1 7P e a c o c k e , Creation and the World of Science (Oxford: Clarendon, 19 79), 142ff.,

207; and dem, Intimations of Reality (Notre Dame, IN: University of Notre Dame Press,

198 4), 6 3f f., 76. Se e also section 4.2 of his paper, "G od's Interaction with the World," in

this volume.

18Gr ace Jantzen, God's World, God's Body (Philadelphia: Westminster Press, 1984).1 9Sal l i e McFague, Modes of God: In an Ecological Nuclear Age (Philadelphia:

Fortress Press, 1987), 69-78; and dem, The Body of God: An Ecological Theology (Minne-

apolis: Fortress Press, 1993 ). S ee also, idem , "M odels of G od for an Eco logic al, Evo lution-

ary Era: God a s M other of the Universe," in Physics, Philosophy and Theology, 249-271 .

^According to panentheism, "the world is regarded as being . . . 4 within' God, but the

being of G od is regarded as not exhausted by, or subsumed within, the world" (Pe acock e,

Creation and the World of Science, 207 ). See also Theology for a Scientific Age n. 75, p.

370-2 .2 1M c F a g u e , Modes of God, 71.2 2

T racy , God, Action and Embodiment (Grand Rapids, MI: Eerdmans, 1984).




3.3.4.4 Interaction Models Many of the objections to embodiment models citedabove have been used by supporters of one or another form of an interactionmodel. John Polkinghorne argues that a clue to God's interaction with the world

can come from examining how humans interact with the world. He turns toquantum physics and chaos theory to suggest how the combination of lawlikebehavior with openness and flexibility in nature makes human and, in somepreliminary way, divine agency conceivable. 2 3

335 Assessment Ow en Thomas returned to the problem in 1991, with this rathercaustic comment:

Theologians continue to talk a great deal about God's activity in the world,and there continue to be only a very few who pause to consider some of the

many problems involved in such talk. 2 4

According to Thomas, the question of double agency still remains "the key issuein the genera l problem. . . Z '2 5 How can we assert coherently that both divine andcreaturely agen ts are fully active in one u nified event? A fter evaluating the currentstate of the discussion, Thomas's position is that one must either follow theprimary/secondary path of traditional theism or the process theology approach. Heasserts that if there is another solution to the problem , he has not heard of it, andconcludes that this question should be a major focus of future discuss ions . 2 6

3 .4 Working Typology of Theological Positions on Divine Action in Light o f

Science

The following working typology (see Figure 1) presents a correlation of varioustheological views with the types of claims their proponents tend to make aboutdivine action, including new developm ents in light of scie nce. It is mea nt prim arilyas a fram ew ork to gu ide the reader in interpreting the varieties of positions takenin the papers in this volume. It is presented here in its current form as work in

progress. Its heuristic nature should be underscored, as well as the fact that, likeany typology, it represents an abstraction from the extant literature; actual authorsmay hold differing positions at various places in their writings.2 7

The upper portion of the table includes five positions frequently found inhistorical and contemporary theology regarding divine action. It serves as a

^John Polkinghorne, Science and Providence (Boston: Shambhala, 1989). See also,

idem, 'The Laws of Nature and the Laws of Physics," in Quantum Cosmology, 437 -448 .

See also Reason and Reality: The eationship between science and theology (Philadelphia:

Trinity Press International, 1991), chap. 3.

2 4 Thomas, "Recent Thought on Divine Agency," in Divine Action, ed. Brian

Hebblethwaite and Edward Henderson (Edinburgh: T&T Clark, 1990), 35-50.2 5Ibid. , 46.2 6Ib id . , 50 .2 7 Since its inception in 1991, the typology has been developed further through

discussion with a number of scholars including Nan cey M urphy and Thom as Tracy.



10 R O B E R T JO H N R U S S E L L

backdrop to the current discussion s in theology and science, as foun d in the lowe rportion of the table.

For completeness, the table begins with the possibility that no events are

God's acts; this is obviously the position of atheism which denies God's veryexistence.

A second position is that God acts only "in the beginning,"2 8 creating theuniverse and the laws of nature. After this, the universe runs entirely on its ownaccording to the laws of nature. This is the deist option. If science could show thatthere was no beginning , the deis t view w ould be seriously underm ined.

According to a third view, it is the existence of the universe as such, and notprimarily its beginning, that requires explanation in terms of God's action. Thus,God acts not only in the beginning to create the universe (if indeed there was a

beginning); more importantly, God acts uniformly in al l events throughout thehistory of th e univ erse to sustain its exis tence mo men t by mo m ent. This me ans thatwithout God's continuous action the universe would simply cease to exist, sincematter does not contain its own sufficient principle of existence. Whether the lawsof nature prescribe or merely describe the regularities of natural processes (i.e. ,whether causal efficacy is contained in the laws governing nature or in natureitself). God is required as the ground of natural (secondary) causality and theprimary cause of every event in the universe. Still , on this view, no events are

special acts of God in any sense. W e are calling this view "g arde n-v ariety the ism ,"although pantheism could also fall into this category.

A fourth view is held by those who agree with thcists that God acts both inthe beginning (if there was one) and that God acts uniformly in all events.However, they add the further claim that certain events in nature and history canbe said to be special acts of God, but only in a subjective sense: they are seen as

revealing something special about the character or intentions of God even thoughGod does not really act differently in an objective way in these events. We call thisthe "liberal" view. In recent work in which a much more dynamic conception of

the universe has com e to prevail over the older, static cosmo logy , G od 's action insustaining the universe has often been seen as God's "continuous creation" of theuniverse. Those who view the universe in these more dynamic terms and speakabout continuo us creation are often eager to attribute special sig nificanc e to w hatappears to be the occasional appearance of genuine novelty, even if they agree thatall events are in fact uniformly caused by God through the unfolding realizationsof the potentialities of nature represen ted by the laws of nature.

Finally, it is possible to hold that there are events that in some objective senseare special acts of Go d. When we call these events "sp eci al" w e do so as a resp on seto G od 's initiative, an acknow ledgm ent of what Go d is doin g to bring them abo ut.It has most often taken the form of intervention : God perfo rm s such acts byintervening in or suspending the laws of nature. We will call this the "traditional"

"Assuming there was one, such as Big Bang cosmology supports! For a detailed

discussion of Jie scientific, philosophical, and theological com plexity of this assumption,

see Quantum Cosmology.



Creation Uniform Divine Action Objectively Special Divine Actionreation

Sustenance Subjectively

Special

Interventionist Non-Interventionist

Creation

Sustenance Subjectively

Special

Interventionist

Apparent with religious

presuppositions

Apparent without religious

presuppositions

Atheism

Deism X

'Theism' X X

'Liberal' X X X

'Traditional' X X X X

Theology and Science:

X X X X ?1) Top-Down or Whole-

Pait (e.g., mind/brain, non-

linear thermodynamics)

X X X X ?

(2 ) Bottom-Up (e.g.,

quantum indeterminacy)

X X X X ?

(3 ) Lateral Amplification

(e.g., chaos)

X X X X ?

(4 ) Primary/ Secondary X X X ? ?

Figure 1: Working Typology of Divine Action



12 ROBERT JOHN RUSSELL

view. Note that the traditional view usually includes the theist's claim that theexistence of the universe, both its continued sustaining in being and its beginning(if it had o ne), is a prod uct of G od 's action.

Much of the current discussion in th e field of theology and science regardingdivine action now turns on the question whether there are objectively special divineacts that are neither interventions nor suspensions of the laws of nature. We willcall these < 4non-interventionist" views. Among non-interventionists, it is still anopen question whether these events are objectively perceptible as special, that is ,whether they would be seen as God's acts by anyone present regardless of theirprior religious presuppositions, or whether it is precisely these presuppositionswhich allow observers to recognize that God has objectively acted in a special wayin the event in question.

Among those who opt for objectively special divine action, some authorsdistinguish between direct and indirect divine acts, or equivalently between basicand non-ba sic divine acts. The argum ent he re is that if God acts indirectly th roughsecondary causes to achieve an objectively special act, there has to be at least onedirect or basic act somewhere that initiates the chain of events the outcome ofwhich we call God's (indirect, objectively special) act. This is a logical point, andnot a theological point: if an agent is to do something indirectly, at some point theagent has to do something directly which eventuates in the indirect act. This issue

is related to the problem of the "causal joint."We should note that it is possible to affirm objectively special divine actswithout deciding whether these acts are themselves direct acts or are the indirectresult of other, perhaps hidden, direct acts of God. On the one hand, the specialevent in question may be seen as the direct act of God. On the other hand, most ofthe current argumen ts tend to see it as an indirect act of G od , that is, as the pro duc tof secondary causes stemming from a direct act of God located elsewhere. But ifthis is the case, then the question in turn bec om es: W here is this "elsew her e," thatis, where is the real domain of God's direct or basic act?

In surveying the continuing conversations with scholars in theology andscience, it has become clear that there are four distinct non-interventionist

approaches to this question, though combinations of them are also viable: (1) "top-down" or "whole-part" causality; (2) "bottom-up" causality; (3) what we might call"lateral" causality, and (4) "prim ary/s eco nda ry" cau sality. First of all , then, som edescribe divine action in terms of "top-down" or "whole-part" causality. Here, alocalized, special event in the world is viewed as the indirect result of God actingdirectly in one of two ways: either in a top-do w n way fr om a higher level in na tur e(using such analogies as "mind/brain"), or in a whole-part way starting either at the

physical boundaries or environment of the system (an analogy here is theformation of vortices in a liquid heated in a container), or, ultimately, at theboundary of the universe as a whole. The second, or "botto m -up ," app roach view sa special event in the macroscopic w orld as the indirect result of a direct act of Godat the quantum mechanical level, amplified by a stream of secondary causes linkedin a bottom-up way. This view p resupp oses that quantu m uncertainty be given anontological interpretation, namely that of indeterminism.

Seme authors in theology and science have pointed to a third non-interven-

tionist option, which w as of particular impo rtance at the 1993 con feren ce. The y




stress the "supple" and "subtle" nature of chaotic and complex systems in physics,meteorology, biology, and so on, focusing on their vulnerability to minute changesin their environm ent and their ability to a m plify these effects (the analogy here is

the "butterfly effect"). Since this view is entirely restricted to the classical level,2 9

involving a chain of events within a group of phenomena encompassed within asingle epistemic level (e.g., classical physics), we can call this view "lateral"causality. Perhaps, then, chaos and complexity would offer a new, non-interven-tionist understanding of God's objectively special action in nature, or at leastsuggest that new, holistic laws of nature might be indicated, which in turn couldlead to new insights into divine action.

Fourth, some authors are committed to accounts of divine action that workstrictly within the distinctions between primary and secondary causality. These

authors see no need to speak in terms of objectively special divine acts, with thepossible exception of miracles.

4 Chaos and Com plexity: Brief Introduction to the Scientific Them es of This

Volume

Am ong the many facets of our intellectual landscape inherited from the Enlighten-

ment, the "received view " from physics is that of nature as a ma chine . The unive rseis governed by a set of deterministic equations discovered by New ton at the closeof the seventeenth century. By the eighteenth century, most scientists wereconvinced that these equations would allow the exact prediction of the future stateof the world given precise know ledge of its present state and all relevant forces. AsPierre Simon M arquis de Laplace put it succinctly, to on e of sufficient intelligence"nothing would be uncertain and the future, as the past, would be present to itseyes." 30 In such a world, there would b e little need— or po ssibility— for G od to actin special events, as the biblical witness recounts. Notice that Laplace used

predictability as a criterion for evaluating the applicability of Newtonian physicsto the world and its confirmation in his own work on the stability of planetaryorbits against perturbations then served as a warrant in support of a metaphysicsof causal determinism.

W e are now , however, faced with a fundamental challenge to this "equation"between determinism and predictability. Though severe problems in predicting theactual course of events were kn ow n to exist fro m the outset— even the three-b ody

2 9 It is possible to appeal to quantum mechanics in order to introduce indcterminism

into the problem in terms of the initial- cond itions which are then amp lified by chao tic

dynam ics, but this m ov e (1) is challenged, in turn, by the apparent lack of "quantum chaos,"

and (2) effectively changes this approach into the previous one, viz., "bottom-up" cau sality.

For comments on "quantum chaos" see the papers by Crutchfield, et al.; and Wesley

W ildman and Robert Russell , both in this v olum e.

Pierre Simon Marquis de Laplace, A Philosophical Essay on Probabilities 6th ed.,

trans. F.W. Truscott and F.L. Emory (New York: Dover, 1961), 4.



14 ROBERT JOHN R USSELL

problem in Newtonian gravity defied an analytic solution—recent discoveries inso-called "chaotic dynamic systems*' have complicated the problem of predictionto the extreme. These chaotic systems now seem ubiquitous in nature; they areknow n to occur throughout hydrodynamics and plasma phy sics, and to pe rvad e thedomains of physics , meteoro logy, ch emistry, biology, evolution, and cosm ology.Chaotic systems are typically governed by simple, non-linear, deterministicequations. Thus, their future states are in principle entirely determined by theirpresent state and the fo rces acting on them , and in this sense they are p redictable.Nevertheless in many cases the future states appear to be random. Moreover, evenif we start with a chaotic equation in hop es of m ode ling the s yste m 's b ehav ior, theunusual properties of these equ ations and ou r ina bility to s pec ify their initial states

with infinite precision means that we will eventually lose the ability to predict thisbehavior. Chaotic systems thus embo dy elements of both d eterm inism , predictabil-ity, and unpredictability, even when they are treated entirely within the domain ofclassical physics. W hat, then, are the philosophical and m etaphysical implicationsof chaos, and do chaotic systems, in turn, shed any light on the topic of divineaction?

5 The Present Publication: Sum mary

These broad scientific, philosophical, and theological themes surface in nuancedand interwoven patterns in the essays included in this volume. Section I introducessom e of the basic mathem atical and scientific issues in the subjects of chaos andcomplexity. Section II deals with related issues in the p hiloso ph y of na ture . SectionIII focuses on the implications of chaos and complexity for the problem of divineaction. The authors in Section IV develop alternative proposals regarding divineaction, most of which were pursued after the authors concluded that chaos theoryis not helpful to the problem.

5.1 Scientific Background : Chaos and Com plexity

We begin with a previously published paper by James P. Crutchfield, J. Doyne

Farmer, Norman H . Packard, and Robert S. Shaw. Their pap er is reprinted hereto give a broad introduction and background to the science of chaos andcomplexity.

Until recently scientists assumed that natural phenomena such as the weather

or the roll of the dice could in principle be predictable given sufficient informationabout them. Now we know that this is impossible. "Simple deterministic systemswith only a few elements can generate random behavior." Though the future isdetermined by the past, small uncertainties are amplified so radically by chaoticsystems that, in practice, their behavior rapidly becomes unpredictable. Still thereis "order in chaos," since elegant geometrical forms underlie and generate chaoticbehavior. The result is "a new paradigm in scientific m od elin g" wh ich both limitspredictability in a fundamental way and yet extends the domain in which naturecan be at least partially predictable.




They then raise philosophical questions based on the mathematical analysis andconclude with possible theological implications.

The logistic equation is a simple, quadratic equation or " ma p ," x ^ = k x B ( l -

xj, which iteratively generates a sequences of states of the system represented bythe variable x. Th e tuning con stant k represents the influence of the environmenton the system. O ne starts from an initial state x̂ and a specified valu e for the tuningconstant k to genera te x^ Substituting Xj back into the map generates x 2 , and so on.Although incredibly simple at face value, the logistic map actually displaysremarkably complex behavior, much of which is still the focus of active scientificresearch.

The behavior of the iterated sequence produced by the logistic map can bedivided into fiv e regime s. The constant k determines which regime the seq uen ceoccupies as well as much of the behavior within that regime. In Regime I, thesequence converge s to 0. In Regime II, the sequence converges on a single po sitivelimit which depends on k. In Regime III, bifurca tions set in and increase in powersof two as k increases. Moreover, the initial conditions have a significant permanenteffect on the system in the form of "phase shifts." Chaos sets in in Regime IV.Here chaotic sequences are separated by densely packcd bifurcation regions andthere is maximal dependence on initial conditions. For most values of k, thesequenc es seem to fluctuate at random and the periodic points found in pre vious

regimes appear to be absent. Nevertheless, for almost all values of k we actuallyfind highly intricate bifurcation structures, and the sequences fall within broadbands, suggesting an underlying orderliness to the system. Finally in Regime V,chaos is found on the Cantor subset of x.

There is no universally accepted mathematical definition of chaos capturingall cases of interest. D efin ing chao s simp ly as randomness pro ves too vag uebecause this term acquires new and more precise shades of meaning in themathematics of chaos theory. D efinin g chaos in terms of sensitive de pen de nce oninitial conditions (the butterfly effect) results in the inclusion of many maps that

ot he rw ise display no chaotic behav ior. The definition adopted here requires achaotic m ap to meet three conditions: mixing (the effect of repeated stretching andfolding), density of periodic points (a condition suggesting orderliness), andsen sitiv e depe nde nce. Interestingly, in the case of the logistic m ap and m anysimilar chaotic maps, mixing is the fundamental condition, as it entails the othertwo.

The paper also addresses the question of the predictability of chaotic systems.On the one hand, a chaotic system such as the logistic map is predictable inprinciple, since the sequence of iterations is generated by a strict governingequ ation . On the othe r han d, chao tic system s are "eventually un pre dic tab le" inpractice, since most values of the initial conditions cannot be specified precisely,and even if they could, the inform ation ne cessa ry to specify them cannot be storedphysically. Yet these systems are also "temporarily predictable" in practice, sinceone can predict the amount of time which will elapse before mathematicalcalculations will cease to m atch the state of the system . This leads to a defin itionof 'chaotic randomness ' as a tertium quid between strict randomness (as in oneco m m on interpretation of quantum physics), and the complete absen ce of

randomness .



INTRODUCTION 17

What implications does mathematical chaos have for a philosophy of nature?It is superficial to say that the mathematical determinism of chaotic equationsrequires metaphysical determinism in nature, because of complexities in the

experimental testing of the mathematical models used in chaos theory. Inpar ticu lar, it m ay be very difficu lt to distinguish phcn om enolo gically betwe enchaos, sufficiently complicated periodicity, and strict randomness, even thoughthese are entirely distinct m athem atically. Th ere are additional practical limitationsto the testing of chaotic models of natural systems, including sensitivity to theeffects of the environm ent (such as heat noise or long-rang e interactions), and thefact that the development of the physical system eventually out paces even thefastest calculations.

Two philosophical conclusions are drawn from this. On the one hand, the

causal whole-part relations between environment and system, the causalconnnectedness implied in the butterfly effect, and the fact that much of theapparent randomness of nature can now be brought under the umbrella of chaos,are best seen as supporting evidence for the hypothesis of metaphysical determin-ism. On the other hand, how ever, there are profo und cpistemic and explan atorylimitations on the testing of chaos theory due to the peculiar nature of chaoticrandom ness. In this sense, chaos theory plac cs a fun da m ent al and un expe cted newlimit on how well the hypothesis of metaphysical determinism can be supported.

On the basis of these philosophical conclusions, what relevance docs chaostheory have for theology? On the one hand, it will be "bad news" to those whosimply assume that nature is open to the free actions of God and people, andparticularly bad news to those who mistakenly appeal to chaos theory to establishthis. O n the other han d, chaos theory will be irrelevant to theo logia ns op eratingwith a supervening solution to the problem of divine action, such as Kant's , thatis able to affirm human freedom and divine action even in the presence of strictm etaphysical determ inism . At still another level chaos theory is "goo d new s" tothe theological project and "bad ne w s" for "polem ical detcrmin ists." Due to the

fundamental, new limitation in the testability of chaos theory, one can never fullyexclude the possibility that classical physics as we now have it , including chaostheory, will be replaced by a better model of the world at the classical level whichallows for divine causali ty in some way. This "opens a window of hope forspeaking intelligibly about special, natural-law-conforming divine acts, and it is awindow that seems to be impossible in principle to close."

The article includes an extended bibliography of textbooks, key technicalarticles, experimental applications, useful introductions and surveys, and selectedworks on chaos theory and theology.

5 .2 Chao s, Com plexity, and the Philosophy of Nature

The three papers in this section take up issues in the philosophy of nature whichrelate in various ways to the topics of chaos or complexity.

According to the paper by Bernd-Olaf Kuppers reprinted here, thereductionistic research program "is based on the central working hypothesis thatall biological phenomena can be explained totally within the framework of physics

and chemistry." It assumes that there is no essential difference between non-living




and living matter; life arises as a "quasi-continuous" transition requiring noadditional epistemic principles other than those of physics and chemistry.Restrictions in our current understanding are merely the result of the complexity

of the problem and its com putab ility. Epistem ic reductionism leads to on tologicalreductionism in which "life is nothing but a complex interplay of a large numberof atoms and molecules." Even consciousness must ultimately be reducible tophysical laws.

To counter this program, some biologists and philosop hers of science appealto "emergence" and "downward causation," claiming that genuinely novelpropert ies and processes arise in highly complex phenomena. According to thisview, physics is a necessary part of the explanation but it cannot provide asufficient explanation on its own. Kuppers summarizes the claims of emergenceand downward causation, respectively, as follows: "(1) The whole is more than thesum of its parts. (2) The whole determines the behavior of its parts."

Since these concepts seem "vague and mysterious" to scientists in physicsand biology, Kuppers focuses here on a general problem concerning the transitionfrom the non-living to th e living: can we adequately characterize the emergence oflife in terms of the concept of complexity. Kuppers thinks not, since non-livingsystems may themselves be extraordinari ly complex. In addit ion, one may findevidence of emergence even within a field, such as within physics, and not just

between fields .In a similar way, those suppo rting intratheoretical reduction (e.g., red uction-ism within physics) frequently appeal to "bridge laws," while defenders ofemergence deny their availability and their fruitfulness. Arguments such as thesealso apply to the question of downward causation. In Kuppers ' opinion, bothemergence and downward causation are to be found within physics . Since no4<non-physical princ iple" is involved, ap parently, in the transition to life, K uppe rsconcludes that "both (em ergen ce and dow nw ard causation) m ust be thou ght of ascharacteristics of self-organizing matter that appear at all levels when matter

unfolds its complexity by organizing itself." Still, there are examples of biologicalsystems, such as the DNA macromolecule, which are immensely more complexthan complex physical systems. Do they point to a limitation in physical methodor in the reductionistic research program, or will physics undergo a paradigm shiftas it seeks to encompass these phenomena within its domain?

To understand these questions better, Kuppers begins by distinguishingbetween laws and initial or boundary conditions in physical theory. His centralclaim is that "the com plexity of a system or a phe nom eno n lies in the co mp lexity. . . of i ts boun dary cond it ions." Following the analysis of Michael Polanyi,

Kuppers argues that in a human construction, such as a complex machine, thedesign, or boundary conditions, governs the physical processes but cannot be de-duced from them. In this way a machine, by its structure and operation, is anemergent system, a whole which is "neither additive nor subtractive," whosepropert ies cannot be reduced to those of i ts components , and whose boundaryconditions represent a form of downward causation. A similar case can be madefor a living organism.

Now the question becomes, what determines the boundary condit ions? For

a machine, the answer is a blueprint. For the living organism, however, the



INTRODUCTION 19

"blueprint" lies in the o rga nism 's g eno m e w hich, in contrast to the m achine, is aninherent part of the living system. Kupp ers then distinguishe s c om plex fro m sim plesystems in terms of both their sensitivity to small changes in their boundary

conditions and the uniqueness of these conditions, given all possible physicallyequivalent condit ions.

The concept of boundary conditions thus becomes the key to understandingthe paradigm shift that is occurring within physics regarding the problem ofcomplex phenomena. This shift is not of the Kuhnian type, with its revolutionarychan ge in the fundam ental laws and the theoretical fram ew ork of a field. Insteadit is an "internal shift of emphasis" within the given explanatory structure of theparadigm. As Kuppers sees it , the shift of emphasis within the reductionisticresearch program consists in the move to regard the boundary conditions of

complex phenomena as that which needs explanation. He calls this shift ofemphasis the **paradigm of self-organization." It entails a sequence of explanations,in which boundary conditions at one level (such as the boundary conditions of theDNA molecule) are explained by those of another level (such as the randomm olecu lar structures), wh ich themse lves need explanation. In effect, the nestedstructures found in living matter are reflected by the nested structures of theparadigm of self-organization.

Finally, Kuppers points out that biological self-organization is only possible

in the context of non-equilibrium physics. Still , though the existence of specificboundary condit ions can be understood within the framework of physics , theirdetailed physical structure cannot be deduced from physics. "The fine structure ofbiological boundary conditions reflects the historical uniqueness of the underlyingevolutionary pro cess" and these, by definition, transcend the powers of natural lawto describe.

'T h e eternal my stery of the world is its com prchensibility." Th is is, of co urse,Albert Einstein's famous claim, and it serves as the point of departure for Michael

H e l l e r 's paper. According to Heller, this mystery is present in our prescientific

cognition, but it reveals itself in full light only when one contemplates whatEugene Wigner called " the unreasonable effectiveness of mathematics in thenatural sciences." It is not a priori self-evident that the world should be "algorith-mically compressible," that is , that many of its phenomena should be captured bya few mathematical formulae.

There have been attempts to neutralize this wonder by reducing allregularities in the universe to the blind game of chance and probability. Hellerbriefly reviews two such attempts: the so-called chaotic gauge program and AndreLinde's chaotic inflation in cosmology. If complete anarchy is the only law ofnature ("laws from no laws"), then the fu nd am enta l rationality of the world is lost.The problem is important from a theological point of view. At the most fundamen-tal level, God's action in the world consists in giving the world its existence andgiving it in such a way that eve rythin g that exists p articipate s in its rationality, thatis, is subject to the mathematically expressible laws of nature. If the ideology of the"pur e gam e of chanc e and probab il i ty" turns out to be correct, then G od 's act ionseems to be in jeopard y.

Heller responds by arguing that such attempts to neutralize the "mystery of

comprchensibility" lead us even deeper into the problem. Probability calculus is



2 0 ROBERT JOHN RUSSELL

as much a mathematical theory as any other, and even if chan ce and probab ility lieat the core of everything, the important philosophical and theological problem

remains of why the world is probabilistically comprehensible. The probab ilisticcomp ressibility of th e world is a special instance of its mathem atical com pressibil-ity. Heller clarifies this point by rem inding u s that there are two kind s of elem ents(in the Greek sense of this word) in the universe—the cosmic elements, such asintegrability, analyticity, calculability, predictability; and the chaotic elements, suchas probability, randomness, unpredictability, and various stochastic properties. Thechaotic elements are in fact as "mathematical" as the cosmic ones. If the cosmicelements provoke the question of w hy the world is m athem atical, the same is trueof the chaotic elements. In this vie w , cosmos and chaos are not antagonistic forces

but rather two components of the same Logos immanent in the structure of theuniverse.

Arthur Peacocke's topic in this reprint is the general relationship betweenchance and law in thermodynamics and biology, and its implications for belief inGod as creator.

Chance may be the means for actualizing the possibilities of the world, butit need not be seen as a metaphysical principle opp osed to ord er or u nde rcu tting th emeaning of life. Chance actually has two quite distinct meanings: it can refersimply to our ignorance of the processes which underlie an event, or it can refer to

unpredictable intersections of previously unrelated causal chains. Recendy, theinterplay between chance and law has come to be seen as crucial to the origin anddevelopment of life, particularly through the work of Jacques Monod in molecularbiology and Ilya Prigogine in irreversible therm ody nam ics and theoretical biolog y.As Monod emphasizes, evolution depends on chance, in the sense of twoindependent causal chains, operating in living organisms: one is at the geneticlevel, including chan ges in the nucleo tide b ases of DN A; the other is at the levelof the organism, including interactions between the organism expressing thesechanges and its environment. Chance also arises here in the sense that we cannotnow (nor may we ever be able to) specify the mechanisms underlying geneticmutations.

Though agreeing with him this far , Peacocke challenges both Monod'sgeneralization of the role of chance from the context of evolution to include all ofhuman culture, and his subsequent conclusion to the meaningless of life. Instead,Peacocke sees chan ce as the me ans by which all possibilities fo r the organizationof matter are explored in nature.

Peacocke then turns to irreversible thermo dyna m ics and theoretical b iology .

Thermodynamics is "the science of the possible" which prescribes how nature canbehave. Classical thermodynamics, with its focus on systems in equilibrium,centers on the second law of increasing entropy in closed systems. Through thestatistical thermodynamics of Boltzmann this came to be seen as increasingdisorder or random ness in closed systems. Ho w, the n, do living organism m aintainthemselves in a high state of organization and a low state of entropy, given thesecond law? The answer, as Peacocke po ints out, is that living systems are open totheir environment. By exchanging energy and matter with it they can decrease inentropy as long as there is an increase in the net environm ental entropy.



INTRODUCTION 21

But does thermodynamics help us to understand how more complexorganisms com e to be in the first place? Th e answ er co m es only with the extensionof classical thermodynamics, first to linear, and then to non-linear, irreversibleprocesses involved in what are called dissipative structures. According toPrigogine, if fluctuations in these non-linear, non-equilibrium structures areamplified, they can change the structures and result in new, more ordered states.Th e answer also includes the key role played by m ultiple and relatively stable stratain the hierarchy of biological complexity. These intermediate strata enhance therate of evolution of more complex organisms from very s imple ones, in effectdirecting evolution towards increased complexity. In essence, the evolution ofchemical, pre-biological, and biological complexity is seen as probable, perhaps

even inevitable, although the particular path taken in nature is unpredictable. Still,detailed kinetic and dynamic requirements, as well as thermodynamic ones, mustbe met for evolution to occur.

Peacocke then turns briefly to theological reflections. God is creator of theworld through a timeless relation to it in two ways. God is totally other than theworld, its transcendent ground of being. God is also immanent in the world,continuously creating all that is through its inbuilt evolutionary processes. Theseprocesses, revealed by the natural sciences, are in fact God's action in the world,and eventually include the evolution of humanity. Thus, all-that-is is in God, but

God is "m ore" than nature and humanity. The complex interplay of law and chan ceis itself "written into creation by the creator's intention and purpose," to emerge intime by the explorations of nature. Here Peacocke suggests the metaphor of Godas a musical composer and nature as G od 's c om position , perha ps like a rich fug ue.

But does this metaphor carry deistic overtones, as H. Montefiore claims? Notaccording to D. J . Bartholom ew, who sees chance as conducive to the productionof a world in which freedom can operate purposefully. Still, the best response tothe charge of deism, as Peacocke emphasizes, is to see God's action as immanentwithin natural processes. Moreover, as Rustum Roy points out, the interplay ofchance and law in nature means that we should accept a similar interplay aschara cteristic of G od 's creativity in hum an life and society, and we should becritical of belief in a God who "intervenes in the natural nexus for the good or illof individuals and societies." Peacocke concludes that just as it takes a stream tohave eddies, it is the existence of th e universe, flow ing as it does tow ards overallincreasing entropy, that is required if there are to be eddies of biological life.

5 .3 Chaos, Com plexity, an d Divine Action

Five essays comprise this section, each focusing on issues in philosophicaltheology relating to the problem of divine action in light of the sciences and thephilosophical arguments contained in the preceding material.

In "The Metaphysics of Divine Action," John Polkinghorne notes that anydiscussion of agency requires the adoption of a metaphysical view of the nature ofreality. He claims that there is no "deductive" way of going "from epistemologyto ontolo gy," but the strategy of critical realism is to m ax im ize the co nn ectio n. Th isleads most physicists, he claims, to interpret Heiscnbcrg's uncertainty principle as




implying an actual indeterminacy in the physical world, rather than an ignoranceof its detailed workings.

Polkinghorne is crit ical of physical reductionism, which makes unsubstanti-

ated and implausible claims for the explanatory power of the idea of self-organizing systems. Moreover, i t focuses strictly on the generation of large-scalestructure rather than the tem poral o penn ess nece ssary to acc om m oda te agen cy. Atheological appeal to divine primary causality is too vague to yield an understand-ing of providential action. We need not be stymied by the problem of the "causaljoint" that makes this pos sible. To p-dow n causality is a valuab le idea, but i t is notunproblematic and its plausibili ty depends upon exhibiting intrinsic gaps in thebottom -up descript ion in order to affo rd it room fo r m aneu ver.

Polkinghorne bel ieves that such gaps might originate from indeterminate

quantum events. How ever, there are problems about am plifying their effects, andthe idea also leads to an episodic account of divine agency. Polkinghorne prefersan approach based upon interpreting the un predictabilit ies of chao tic dyn am ics (inaccord w ith the strategy of critical realism) as indicating an ontological open nessto the future whereby "active information" beco m es a m odel for hum an and divineagency. He interprets sensitivity to small triggers as indicators of the vulnerabilityof chaotic systems to environmental factors, with the consequence that suchsystems have to be discussed holistically. It is not supposed, however, that such

triggers are the local mechanism by which agency is exercised.The resul ting metaphysical conjec ture Polkinghorne cal ls a com pleme ntarydual-aspect monism , in which mind and ma tter are opp osite poles or phase s of thesingle stuff of created reality. This scheme is antireductionist, stressing instead acontextualist approach in which the behavior of parts depends on the whole inwhich they participate. Polkinghorne then discusses some of the consequences ofadopting this point of view, including the insight that divine agency has its ownspecial characteristics and that God's knowledge of the world of becoming will betruly temporal in character.

Denis Edwards begins by pointing to a major shift in science: the oldworldview is giving way to a new paradigm of an open and self-organizinguniverse. Similarly, in systematic theology the old c onc ept of G od as the individu alSubject is giving way to a relational, dynamic, trinitarian concept of God.

The first part of Edwards' paper explores the general concept of divine actionfrom the perspective of what many are calling a "retrieved" trinitarian theology. Inthe W est, trinitarian theolog y as inherited from August ine and Aquinas emphasizedan individual and psycholog ical m odel of the Trinity rather a com m unitarian one.It focused on divine unity rather than three persons, a nd on div ine bein g rathe r than

divine love. The newer trinitarian theology builds instead on the writings ofRichard of St . Victor and Bonaventure. Edwards out l ines a theology of divineaction which understands the Trinity as a communion of mutual relationshipswhich are dynamic, ecstat ic, and fecund. He argues that the universe is God'strinitarian self-expression, that there are "proper" roles for the trinitarian personsin creation, and that divine interaction with creation is characterized by thevulnerability and liberating power of love.

The second part of the paper asks what this trinitarian theology of divineaction has to say about particular divine actions, such as the incarnation, the Holy



INTRODUCTION 23

Spirit , and divine providence. Edwards explores these questions by assessing theviews of John Polkinghorne and Arthur Peacocke. He finds both s ignificantagreements as well as some disagreements between them, part icularly over the

issue of whether the unpredictability of chaotic systems points towards anontological indeterminism in nature.

Edwards ' reflect ions can be summarized in the form of s ix s tatements: (1)The trinitarian God works in and through the processes of the universe, throughlaws and boundary condit ions, through regulari t ies and chance, through chaoticsystems and the capacity for self-o rgan ization. (2) This trinitarian Go d allows for,respects, and is responsive to, the freedom of human persons and the contingencyof natural processes, but is not necessarily to be denied a knowledge of futurecontingent events. (3) We must take into account not only the divine action of

continuous creation, but also particular or special divine acts. (4) If God is actingcreatively and responsively at all tim es and also in particu lar wa ys, the n this seem sto demand action at the level of the whole system as well as at the everyday levelof events, and at the quantum level. (5) Particular divine acts are always experi-enced as mediated through created realities. (6) The unpredictability, openness, andflexibility discovered by co ntem pora ry science is significant for talk of particulardivine action because it prov ides the basis for a worldview in which d ivine actionand scientific explanation are understood as mutually compatible, but it is not

possible or appropriate to attempt to identify the "causal joint" between divineaction and created causality.

According to Stephen Happel, Christian theology in the thought of ThomasAquinas has a coherent understanding of the interaction between God and creation.By developing a clear theory of transcendence and of universal instrumentality,Aquinas was able to articulate the basic ways in which inanimate, animate, andhuman secondary causes cooperate or conflict with the divine act of love for theuniverse (i.e. , providence). These terms can be transposed into an historicalontology and a language of mutual mediation such that all levels of reality have

their relative autonomy. Contemporary science, with its analysis of self-organizingsystems, provides an understanding of the regularities and contingencies ofinanimate and animate created realities. Its language permits us to understand howan open, flexible universe can provide the conditions for cooperation with oneanother and with divine action without conflict or violence to the integrity ofcreation.

H app el's analysis is basically op timistic. It is born of a religious convictionthat though the cosmos (whether human or non-human) is f lawed and fini te , i tsinternal logic is not vitiated, malicious, or deceptive. Images, the body and the non-verbal are no more (and no less) prone to sin than reason. Within the temporalbeing of "nature," self-organizing, living, self-conscious beings can engage withtheir environments in a cooperative way. Ultimately, Happel argues that self-conscious creatures may learn that cooperating with the ultimate environment, anunfa thom able Other, will not do violence to their own com plex teleonomies.

The Christian claim, h ow eve r, goes further. It maintains that this mysteriousenveloping environment is involved in a mutual self-mediation with creation.When one is in love, one mediates oneself in and through an other who is

discovering, planning, negotiating his or her personal identity in and through




oneself. That is mutual self-mediation. Christians claim that they are not merelyprojecting themselves abstractly into an alien environm ent to m ediate them selves,but that the Other has chosen out of love to mediate the divine subjectivity in and

through natural self-organization (because God is ul t imately a community ofmutual self-mediation). Th e story of the Christ could hav e b een qu ite different thanit was. Jesus could have mediated himself in som e othe r f ash ion , but he did no t. H echose to offer his life for others in self-sacrificing generosity. In this action, heoperated as though neither the natural nor the human e nvironm ent nor God werean enemy. In loving creation, entrusting his own life to others, even in death, faithclaims that there is here a divine love. This is what Happel has called elsewhere the"double dative of presence." We are present to the divine who in that samemovement is present to us. What we discover in this fragile and s tumbling process

of mediating ourselves and our world is an antecedent lover and friend.In his paper, Ju rg en M olt m an n firs t describes f ive m odels of the G od-wo rld

relation: (1) According to the Thomistic model, God is the causa prima of theworld. God also acts through the causae secundae which serve as God'sinstruments. (2) The interaction model postulates a degree of reciprocal influencebetween God and the world. This mo del can include the Thom istic mo del, but notvice versa. (3) The whole-part model, taken from biological systems theory,emphasizes that the w hole is m ore than and different from its parts. In com plex and

chaotic systems this difference shows up in the form of top-down causality. Thewhole-part model is more inclusive than the previous models and sheds light onGod's indirect effect upon the world as a whole. (4) The model of life processesemphasizes the open character of biological systems. The present state of a livingsystem is constituted by its fixed past and its open future or, more generally, bywhat can be called tradition and innovation. H ere th e wo rld p roc ess is ope n to Go das its transcendental future. (5) Finally, Moltmann considers two central theologi-cal models: creation and incarnation. Here God creates by a process of self-limitation (or tzitzum). The limitation on God's omnipresence creates a habitation

for the world; the limitation on God's omniscience provides the world with anopen future. God's self-limitation allows God to be present within the worldwithout destroying it . Moltmann believes this model is the most inclusive of thef ive .

Moltmann next offers three comments on how these models function incurrent theological discussions about chaotic, complex and evolutionary systems.

(1) He is critical of the interaction model, seeing it as a theistic model inwhich God is the absolute Subject who may intervene at will in nature. In themodern period it was replaced by two even more problematic models: deism and

pantheism. In their place Moltmann commends to us a trinitarian model in which"God the Father creates through the Logos/Wisdom in the power of the HolySpirit God not only transcends the world but is also imm anent in the w orld ."

According to this model God acts upon the world through God's presence in andperichoresis with all things.

(2) Next Moltmann discusses eschatology, the new creation of all things. ForMoltmann the future is not a state of completion but a process of continuingopenness, in which all finite creatures will participate in G od 's u nendin g and open

eternity even as God participates in their temporality. The openness of chaotic,



INTRODUCTION 25

complex, and evolutionary systems is suggestive of this vision, and seemsinconsistent with a future conceived of as co m p le te d .4 T h e future of the world canonly be imagined as the openness of all finite life systems to the abundance of

eternal life. In this way they can participate in the inexhaustible sources of life andin the divine creative ground of being."

(3) Finally Moltmann asks whether the universe as a w hole s hou ld b e thou gh tof as an open system. The growth of possibilities for such systems, theirundetermined character, and their dependence on an influx of energy suggest thatthe universe itself might be open to energy. "In this case the world would be a4system open to God* and God a 'Being open to the world. '"

L a ng do n G i l ke y 's paper considers two questions: whether nature'sprocesses suggest the existence of a God, and if so, what sort of God. However, he

emphasizes that the traces of God that may be found in nature are not the mainsource of religious belief; for Christians, God is encoun tered primarily in history.

Science, including chaos theory, provides a picture of reality that combinesboth order and novelty; the ascending order can well be described as an order ofincreasing value. Reflection on this scientific picture of reality, along with thewider data of human experience (history) leads to ontology or metaphysics—theeffort to understand the structure of being qua being. This level of reflection iscrucial for both the scientist and the theologian. For the scientist it provides the

rational grounding for science itself. Metaphysics is crucial for the theologian,since '"proofs" of any sort for the existence of God are always conditional upon aparticular metaphysical structuring of experience.

Consequently, the aspects of nature suggested by the sciences must berepresented in ontological categories. Beyond and through the abstractions of thescientific understanding of nature, nature's reality has manifested itself as power,

as spontaneity or life, as order, and as implying a redemptive principle, a strangedialectic of sacrifice, purgation, redemption, and rebirth. In nature each of theseappear as vulnerable and ambiguous as well as creative. Each of these characteris-

tics, therefore, raises a "limit question," and thus represents a trace of God. Forexample, what is the deeper, more permanent power that makes possible thetransitory appearance of power in nature? 'God' is the name for that ever-continuing source of power. To know God truly is to know God's presence in thepower, life, order, and redemptive unity of nature; to know nature truly is to kno wits mystery, depth, and ultimate value—to know it as an image of the sacred.

5 .4 Alternative Approaches to Divine Action

The six authors in this section are skeptical of the fruitfulness of chaos theory forthe problem of divine action, and are pursuing alternative app roa che s. T he f irst pa rtof this section deals with general issues, the second with specific issues, includingthe potential relevance of other topics in science beyond those of chaos andcomplexi ty .

Willem B. Drees argues that theories of chaotic and complex systems havemade it clearer than ever before that a naturalistic explanation of the world ispossible, even in light of the lack of pred ictability of these system s. The se theo ries

have effectively closed certain gaps in our understanding of nature. He is therefore




critical of Polk ingho rne's suggestion that the unpredictab ility of natural p roce ssesprovides a potential locus for divine action. Po lking hor ne sugge sts that G od bring sabout an input of information into the world without an input of energy. Dreesclaims that this is inconsistent with quantum physics and thermodynamics. Inaddition, Polkinghorne seems to interpret the unpredictability of chaotic systemsas a sign of intrinsic openness, but this ignores the real meaning of deterministicchaos. Moreover, discarding the theory of deterministic chaos would be inconsis-tent with the very critical realism that Polkinghorne promotes.

How ever, denying any such gaps within natural pro cesses n eed n ot fo rec loseall options for a religious view of reality. In fact Drees claims that science raisesrel igious questions about nature as a whole and about the most fundamental

structures of reality. To m ak e his case, he distinguishes betw een tw o conc eption sof explanation in contemporary philosop hy of science . Ontic view s of explan ationconsider an event explained if it is understood as a possible consequence of acausal mechanism. Epistemic views of explanation consider phenomena and lawsexplained if they are seen as part of a wider framework. Hence if one adopts anepistemic view of explanation the framework itself still requires an explanation.Along these lines, Peacocke and others have argued for divine action on the wholeof natural reality: God could cause specific events in nature via "top-down" or"wh ole-part" causation. Drees, however, rejects the attempt to extrapolate fr om the

context of nature as environment to the concept of God as the world 's environ-ment .

Given the various problems with at tempts to envisage God's act ion in theworld, Drees prefers to understand the world as God's act ion. Whatever s trengthexplanations have, there always remain limit questions about reality and aboutunderstanding which allow us to develop a religious interpretation of "secularnatural ism."

The approach to divine action taken by Will iam Stoeger is to accept withcritical seriousness our present and projected knowledge of reality from thesciences, philosophy and other disciplines, including theology which has alreadydeveloped in response to the sciences. By "critical seriou sness," S toeger m ean s thatthis knowledge, though critically assessed by the disciplines themselves, byphilosophy and by the other human sciences, does indeed indicate something aboutthe realities it talks about. Stoeger then integrates these results into a roughlysketched theory of God's action. Implicit here is the methodological problem ofhow the languages of science and theology are to be integrated.

Next Stoeger employs a philosophical presupposition which he calls a

"weakly critical realist" stance. Included are elements of Aristotelianism andThom ism, particularly the notions of primary and second ary c ausality. T hes e seemto him m ore adequate to both the scientific and the theological data. They also leadto fewer difficulties in explicating the essential diff eren ces betw een God and G o d 'screation, the relationships between them, and the ideas of divine immanence andtranscendence. Stoeger uses the term ' law' in the context of both physical pro-cesses and free human actions to mean any pattern, regularity, process, orrelationship, and its description. 4 Law' is thus used to describe or explain order. Itdoes not necessari ly imply determinism.



INTRODUCTION 27

Stoeger concludes this section by saying that there are aspects of divineaction which we are able to understand better by letting science and theologycritically interact. There are other aspects which seem thoroughly resistant to our

understanding, part icularly the nexus between God and the secondary causesthrough which God acts , or between God and the direct effects of divine action,such as creatio ex nihib. The analog of human agency is of som e limited h elp here .How ever, the principal b arrier is that we could only kn ow the critical nexus if w eourselves w ere divine, or if God revealed such know ledge to us .

Turning to the problem of God's act ion, Stoeger argues that i f God actsthrough secondary causes i t would seem to require the injection of information,and therefore energy, fro m outside the physical system . Tho ugh we cann ot r ule o utsuch injections, they have never been observed and are unattractive from many

points of view. Some scholars try to evade this problem by al lowing God toinfluence events at the quantum level. Stoeger admits that this is a solution, andmay in fact be the case, but he finds i t unattractive. God's working throughsecondary causes is almost always a function of God's invitation, or response, topersons. To locate such divine action at the quantum level r em ove s it fr om the levelof the personal. It is also unclear whether its intended effects can surface at thelevel of the complex and the personal.

Stoeger provides no a nsw er to this issue, but he believes that the fra m ew ork

he has established m ay m ov e us in th e right direction. Either there is some injectionof information and energy at the level of personal relationships, or God workswithin what is already given to make the recipient more receptive to what isavailable. Stoeger prefers the lat ter , though something of the former may beinvolved as well. TTie difficulty with higher regularities subsuming those at thelower-level is that we usually experience the lower level laws as constraining whatcan be done on a higher level while not being supplanted by them. Neverthelessthere is a great deal left under determined by the lower-level constraints withinwhich agents , including God, can function.

Accord ing to Arthur Peacocke , the long-established aim in science ofpredicting the future macroscopic states of natural systems has recently come to berecognized as unattainable in practice for those systems capable of manifesting"deterministic chao s." Th e possibility of prediction h as a lso bee n closely assoc iatedwith the conviction that there is a causal nexus which scientific procedures willunam biguously ascertain. In this paper, Peacocke surveys the applicability of theseconcepts with respect to relatively simple, dynamic, law-obeying systems; tostatistical properties of asse m blies; to New tonian system s wh ich are determ inisticyet unpredictable; and to "chaotic" and "dissipative" systems. In doing so he alsoanalyzes the limitations to predictability stemming from quantum theory.

Chaotic and dissipative systems prove to be unpredictable in practice,primarily because of the nature of our knowled ge of the real nu m ber s, and possib ly(and more problematically) because of quantum uncertainties . The notion ofcausality still proves to be applicable to these systems in an unambiguous, even ifonly in a probabilistic, fashion. How ever, for m any s ignificant interconnected andinterdependent complex systems the concept of causali ty scarcely seemsapplicable, since whole-part constraints operate, whereby the state of a system-as-

a-whole influences what occurs among its constituents at the microscopic level.




Peacocke acknowledges that in the past this phenomenon has also, perhaps

somewhat misleadingly, been denoted by himself and others as "downward" or

"top-down" causation , in particular in relation to evolution and to the brain-bod y

relation.Peacocke then considers how to conceive of God's relation to the world in

the light of modifications in the scientific concepts of predictability and causalitywhich the phenomena of deterministic chaos and dissipative systems on the onehand, and of "wh ole-part co nstrain ts" on the other hand, hav e induc ed. Con sider-ation of the form er has to take acco unt of the possible, and as yet unclear, effe ctsof quantum uncertainty on chaotic and dissipative systems. Peacocke concludesthat, whatever is decided about those effects, the unpredictabilities for us of no n-linear chaotic and dissipative systems do not, as such, help us in the problem ofarticulating more coherently and intelligibly how God interacts with the world,illuminating as they are concerning the flexibilities built into n atural pro cesse s. Th ediscussion is based in part on the assumption that God logically cannot know thefuture, since it does not exist for God to know.

However, Peacocke argues that the notion of "whole-part constraints" ininterconnected and interdependent systems does provide a new conceptualresource for modeling how God might be conceived of as interacting with andinfluencing events in the world. This is particularly true in conjunction with a

prime exemplification of the whole-part constraint in the unitive relation of thehuman-brain-in-the-human-body—in fact , this model of personal agency is thebiblical and traditional mo del for Go d 's ac tion in the w orld . He ev oke s the notio nof a flow of information as illuminating this 4 whole-part ' interaction of God withthe world, which could then be conceived of as a com m unication by God to thatpart of the world (nam ely, humanity) capable of discovering G od 's me anings.

Thomas Tracy's paper takes up a persis tent modern problem in relat ingscientific descriptions of the world as a natural order and theological claims aboutdivine action. Do some traditional ways of speaking about divine action require

"gaps" in the causal order and the refo re incom pleteness in scientific ex planation s?This appears to be the case, for example, if we claim that God acts in the world atparticular times and places to affect the unfolding course of events. Must this kindof theological claim compete with scientific descriptions of the world, so that wecannot both explain an event scientifically and affirm that it as a particular divineaction?

Tracy considers three strategies which reply to these questions. The firstavoids conflict between scientific and theological claims by insisting that, strictlyspeaking, God does not act in history but rather enacts history as a whole. Its

paradigmatic modern development comes from Friedrich Schleiermacher, whoholds that every ev ent both stands in a relat ion of absolute dependence upo n G od 'simmediate agency and is integrated into a complete system of natural causes. Onthis account, particular events can be singled out as acts of God only in the sensethat they especially evoke in us a recognition of God's universal activity, or playa distinctive role in advancing divine purposes "built into" the causal processes ofnature. This eliminates any risk of conflict between science and theology, but itdoes so at the cost of im posing significant limits on the claims that can be m ade,for example, about the person and work of Christ, about the divine-human



INTRODUCTION 29

interaction, and about human freedom and the problem of evil. Tracy considers acontemporary and widely influential version of this strategy developed by GordonKaufman. Unfortunately, Kaufman's proposal , Tracy argues, leaves us with a

series of questions about how God can be understood to enact history withoutacting in history.

The second strategy affirms that God does act in the world to affect thecourse of events, but holds that this does not require any gaps in the causal struc-tures of nature. There are at least two recent proposals that take this form. BrianHebblethwaite contends that God acts in and through the causal powers ofcreatures, so that the whole network of created agencies is "pliable, or flexible, tothe providential hand of God" without any gaps in the natural order. This leavesthe crucial puzzle unsolved, however; for if God affects the course of events once

they are underway, then an explanation of those even ts that a ppe als strictly to o therfini te causes must be incomplete . John Compton has suggested another way topursue this second strategy. Just as we routinely describe certain movements of thehuman body both as a series of physical events and as intentiona l a ction, so w e candescribe events in the world both as part of a causally complete natural order andas acts of God. Compton's proposal hinges on the claim that the language we usein discussing physical events, on the one hand, and intentional actions, on theother, are not interdependent. But this claim, Tracy argues, cannot be sustained

even within the terms of Compton's own discussion. These two versions of thesecond strategy, then, are undone by internal inconsistencies.

Th e third strategy grants that theologically m otivate d talk of partic ular div ineaction carries with it a commitment to the causal incompleteness of the naturalorder, and then argues that this is at least consonant with contemporary physicaltheory. Tw o key issues must be addressed b y any such p ropo sal. First, a case mu stbe made that the natural sciences now describe a world whose causal structure is"open" in certain respects. Second, it must be shown that this openness is relevantto the theological concern with divine action. Tracy argues that chaos theory, for

all its pow er to demo nstrate the limits of predictability, docs not p rov ide the need edopenness, since it presupposes an unbroken causal determinism. More promisingare interpretations of quantum mechanics that acknowledge the role in nature ofindeterministic chance. With regard to the second question, Tracy contends thatsuch chance (whether at the quantum level or elsewhere) will be theologicallyinteresting if the determination of such events by God can make a macroscopicdifference. If so, then God could affe ct the course of events withou t disrupting thestructures of nature, since they will provide for both novelty and regularity in theworld .

The essay concludes by exploring God's relation to indeterministic chance:must we say that God determines all events left undetermined by secondarycauses? God might, Tracy argues, choose not to determine some events, andthereby (contra Einstein) play dice with the universe.

Nancey Murphy directs our attention away from chaos and complexity tothe arena of quantum physics. In her paper, Murphy argues that the problem ofdivine action will be solved by nothing less than a revised metaphysical theory ofthe nature of matter and of natural causes. Her proposal is that we view the causal

pow ers of created entities as inherently incom plete. No even t occ urs with out div ine




participation but, apart from creation ex nihilo, God never acts except by means of

cooperation with created agents. Her paper attempts to show how this account can

be reconciled with contemporary science, focusing on divine action at the quantum

level.First Murphy proposes criteria, derived from both theology and science,

which any satisfactory theory of divine action must meet. She claims that it mustallow for objectively special divine acts, yet not un dercut ou r scien tific picture ofthe law-like regularity of many natural processes. Then she surveys changes inmetaphysical views of m atter and causation from ancient to modern philosoph y.The historical survey is intended to put in question current metaphysicalassumptions about the nature of matter and of natural causes, as a prelude toconsidering the consequences of recent developments in science for thesemetaphysical issues.

M urphy 's proposal is that any adequate account of div ine action m ust inclu dea "bottom-up" approach: if God is to be active in all events, then God must beinvolved in the mo st basic of natural events. Current science suggests that this mostbasic level is quantum phenomena. It is a bonus for theology that we find ameasure of indeterminacy at this level, since it allows for an account of divineaction wherein God has no need to overrule natural tendencies or processes. Thiscooperation rather than coercion is in keeping with God's pattern of respecting the

integrity of other higher-level creatures, especially human creatures.Consequences of this proposal are spelled out regarding the character ofnatural laws and regarding God's action at the macroscopic level. One of theseconsequences is that the "laws of nature" must be descriptive, rather thanprescriptive; they represent our human perceptions of the regularity of God'saction. In the end, she replies to some of the objections that have been raisedagainst theories of divine action based on quantum indeterminacy and explainshow the essay's proposal meets the criteria of adequacy set out in the beginning.

In "Ordinary and Extraordinary Divine Action," George Ellis intends to

elaborate the conclusions reached by Tracy, Murphy, and others concerning therole of quantum indeterminacy in a contem porar y un derstandin g of divine action.He claims that some account of special divine action is necessary if the Christiantradition is to make sense. However, there are two important constraints to bereckoned with. O ne is that an ideal account of divine action must not conflict witha scientific understanding of nature; the other is that some explanation must begiven of why a God capable of special action would not exercise that abilityregularly to oppose evil and ameliorate suffering.

Ellis' analysis focuses on the nature of bottom-up and top-down causation in

hierarchical systems. It is predicated upon the assumption that chaotic dynamicsdoes not provide the required openness in physical systems. Furthermore, hisanalysis of top-down causation convinces him that this concept alone does notprovide for an adequate account of divine action. He disting uish es be twe en gen erictop-dow n causation, in which boundary co ndit ions produce a global effect uponall the entities in a system, and spe cific top-down causation, w hich inv olves localinteractions v ith elements of the lower-level system. Special divine actions wouldseem to entail the latter. However, specific top-down causation seems to require,

in turn, that there be an intrinsic openness or ind eterm inacy at the verv lowe st level




of the hierarchy of com plex ity. Thu s, a study of the possibilities for divine actionvia top-down causation leads inevitably to a consideration of divine action at thequantum level .

Ellis takes God's action to be largely through the ordinary created processes.Go d initiates the laws of physics, establishe s th e initial condition s f or the univ erse,

and sustains the universe and its processes, which in turn result in the emergenceof hi gh er levels of order, including, finally, fre e hu m an being s. Special divineaction focuses on providing to human beings int imations of God's wil l for theirsocial lives. Thus, the prob lem of the m ode of divine action is largely a questionof how God might communicate directly with those who are open to revelat ion.Ellis speculates that quantum events in the brain (directed by God) might beamplified to produce revelatory thoughts, images, and emotions. If it is supposedthat God has adequate reason to restrict divine action to a combination of ordinaryaction (in and through n atural p rocesses) and rev elation (such as the Resu rrection

of Christ) then the problem of evil does not take on the same dimensions as it doeswhen it is assumed that God might freely intervene in any sort of process at anytime.

Finally, Ellis addresses the question of support for his view. He claims thatwhile individual moves made in the paper (such as the focus on divine action at thequantum level) may not appear to be justified, the combined constraints imposedby the need to make sense of the Christian tradition and by science actually limitthe possible acceptable positions quite se verely ; thus, the v iew herein presen ted is,in Ellis ' opinion, highly credible relative to the broad range of data.



I

SCIENTIFIC BACKGROUND:

CHAOS AND COMPLEXITY



C H A O S

James P. Crutchfield, J . Doyne Farmer, Norman H. Packard,

and Robert S. Shaw

There is order in chaos: randomn ess has an underlying geom etric form .Chaos imposes fundamental limits on prediction, but it also suggests causal

relationships where none were previously suspected.

Th e great pow er of science lies in the ability to relate cause and effect. On thebasis of the laws of gravitation, for exam ple, eclipses can be predicted thousan dsof years in advance. There are other natural phenomena that are not as predictable.Although the movem ents of the atm osph ere obey the laws of phy sics just as mu chas the movements of the planets do, weather forecasts are still stated in terms ofprobabilities. The weather, the flow of a mountain stream, the roll of the dice allhave unpredictable aspects. Since there is no clear relation between cause andeffect, such phenom ena are said to have random elem ents. Yet until recently there

was little reason to doubt that precise predictability could in principle be achiev ed.It was assu me d that it was on ly necessary to gather and process a sufficient amountof information.

Such a viewpoint has been altered by a striking d isco very : sim ple dete rm inis-t ic systems with only a few elements can generate random behavior. Therandomness is fundamental; gathering more information d oes not m ake it go aw ay.Randomness generated in this way has come to be called chaos.

A seeming paradox is that chao s is deterministic, generated by fixed rules thatdo not themselves involve any elements of chance. In principle the future is

completely determined by the past, but in practice small uncertainties are amplified,so that even though the behavior is predictable in the short term, it is unp redictablein the long term. There is order in chaos: underlying chaotic behavior there areelegant geometric forms that create randomness in the same way as a card dealershuffles a deck of cards or a blender mixes cake batter.

The discovery of chaos has created a new paradigm in scientific modeling.On o ne hand, it implies new fun dam ental limits on the ability to mak e prediction s.On the other hand, the determinism inherent in chaos implies that many randomphenomena are more predictable than had been thought. Random-lookinginformation gathered in the past and shelved because it was assumed to be toocomplicated can now be explained in terms of simp le laws. Ch aos allow s order tobe found in such diverse systems as the atmosphere, dripping faucets, and thehe art The result is a revolution that is affecting m any differe nt branches of science.

What are the origins of random behavior? Brownian motion provides aclassic example of randomness. A speck of dust observed through a microscopeis seen to move in a continuous and erratic jiggle. This is owing to the bombard-ment of the dust particle by the surrounding water molecules in thermal motion.



36 CRUTC HFIELD, ET AL.

Because the water molecules are unseen and exist in great number, the detailedmotion of the dust particle is thoroughly unpredictable. Here the web of causal

influences among the subunits can become so tangled that the resulting pattern ofbehavior becomes quite random.

The chaos to be discussed here requires no large number of subunits orunseen influences. The existence of random behavior in very simple systemsmotivates a reexamination of the sources of rando m ness eve n in large sys tem s suchas weather.

What makes the motion of the atmo sph ere so m uch h arder to anticipate thanthe motion of the solar system? Both are made up of many parts, and both aregoverned by Newton 's second law, F-ma, which can be view ed as a simp le

prescription for predicting the future. If the forces F acting on a given mass m areknow n, then so is the acceleration a. It then follo w s fro m the rules of calculus thatif the position and velocity of an object can be m easu red at a given instant, th ey aredetermined forever. This is such a pow erful idea that the eighteenth -century Frenc hmathematician Pierre Simon de Laplace once boasted that given the position andvelocity of every particle in the universe, he could predict the future for the rest oftim e. A lthou gh there are several obv ious practical difficulties to achievingLaplace's goal, for more than 100 years there seemed to be no reason for his not

being right, at least in principle. The literal application of Laplace's dictum tohuman behavior led to the philosophical conclusion that human behavior wascompletely predetermined: free will did not exist.

Twentieth-century science has seen the downfall of Laplacian determinism,for two very different reasons. The first reason is quantum mechanics. A centraldogma of that theory is the Hcisenberg uncertainty principle, which states thatthere is a fundamental limitation to the accuracy with which the position andvelocity of a particle can be mea sured . S uch un certainty gives a good explanationfor some random phenom ena, such as radioactive decay. A nuc leus is so small that

the uncertainty principle puts a fun dam ental limit on the k now ledge of its m otion,and so it is impossible to gather enough information to predict when it willdisintegrate.

The source of unpredictability on a large scale must be sought elsewhere,however. Some large-scale phenomena are predictable and others are not . Thedistinction has noth ing to do with quantum mechan ics. The trajecto ry of a baseball,for example, is inherently predictable; a fielder intuitively makes use of the factevery time he or she catches the ball. Th e traje cto ry of a flyi ng ba lloon with the airrushing out of it, in contrast, is not predictable; the balloon lurches and turns

erratically at times and places that are impossible to predict. The balloon obeysNe wto n's laws just as much as the baseball docs; then why is its behavior so muchharder to predict than that of the ball?

The classic example of such a dichotomy is f luid motion. Under somecircumstances the motion of a f luid is laminar—even, s teady, and regular—andeasily predicted from equations. Under other circumstances fluid motion isturbulent— uneven, unsteady, and irregular— and difficult to predict. Th e transitionfrom laminar to turbulent behavior is familiar to anyone who has been in an



C H A O S 37

airplane in calm weather and then suddenly encountered a thunderstorm. Whatcauses the essential difference between laminar and turbulent motion?

To understand fu lly why that is such a riddle, imag ine sitting by a m oun tainstream. The water sw irls and sp lashes as though it had a mind of its own, movingfirst on e way and then another. Nevertheless, the ro cks in the stream bed are firm lyfixed in place, and the tributaries enter at a nearly constant rate of flow. WTiere,then, does the random motion of the water come from?

The late Soviet physicist Lev D. Landau is credited with an explanation ofrando m fluid motion that held sw ay for man y years , nam ely that the mo tion of aturbulent f luid contains many different, independent oscillations. As the fluid isma de to mov e faster, causing it to become m ore turbulen t, the oscillations enter the

motion one at a time. Although each separate oscillation may be simple, thecomplicated combined motion renders the flow impossible to predict .

La nd au's theory has been disproved, how ever. Random behav ior occurs evenin very simple systems, without any need for complication or indeterminacy. TheFrench mathematician Henri PoincarS realized this at the turn of the century, whenhe noted that unpredictable, "fortuito us" phenom ena may occur in systems wh erea small chan ge in the present causes a mu ch larger c han ge in the future. The notionis clear if one thinks of a rock poised at the top of a hill. A tiny push one way oranother is enough to send it tumbling down widely differing paths. Although the

rock is sensitive to small influences only at the top of the hill, chaotic systems aresensitive at every point in their motion.

A simple example serves to illustrate just how sensitive some physicalsystems can be to external influences. Imagine a game of billiards, somewhatidealized so that the balls move across the table and collide with a negligible lossof energy. With a single shot the billiard player sends the collection of balls intoa protracted sequence of collisions. The player naturally wants to know the effectsof the shot. For how long could a player with perfe ct control over his or her strokepredict the cue ball 's trajecto ry? If the player igno red an effect even as minusculeas the gravitational attraction of an electron at the edge of the galaxy, the predictionwould become wrong after one minute!

The large growth in uncertainty comes about because the balls are curved,and small differences at the point of impact are amplified with each collision. Theamplification is exponential: it is compounded at every collision, like thesuccessive reproduction of bacteria w ith unlimited space and foo d. An y effect, nomatter how small, quickly reaches macroscopic proportions. That is one of thebasic properties of chaos.

It is the exponential amplification of errors due to chaotic dynamics thatprovides the second reason for Laplace 's undoing. Quantum mechanics impliesthat initial measurements are always uncertain, and chaos ensures that theuncertainties will quickly overwhelm the ability to make predictions. Withoutchaos Laplace might have hoped that errors would remain bounded, or at leastgrow slowly enough to al low him to make predict ions over a long period. Withchaos, predictions are rapidly doomed to gross inaccuracy.

The larger framework that chaos emerges from is the so-called theory ofdynamical systems. A dynamical system consists of tw o par ts: the no tions of a state



38 CRUTCHFIELD, ET AL.

(the essential information about a system) and a dy nam ic (a ru le that d escrib es howthe state evolves with time). The evolution can be visualized in a state space, anabstract construct wh ose coordinates are the com pon ents of th e state. In g enera l the

coordinates of the state space vary with the context; for a mechanical system theymight be position and velocity, but for an ecological model they might be thepopulations of d ifferent species .

A good example of a dynamical system is foun d in the simp le pen dulu m . Allthat is needed to determine its motion are two variables: position and velocity. Thestate is thus a point in a plane, whose coordinates are position and velocity.N ew ton's laws provide a rule, expressed mathematically as a differential equation,that describes how the state evolves. As the pendulum swings back and forth thestate m oves along an "orbit," or path, in the p lane . In the ideal ca se of a fric tion lesspendulum the orbit is a loop; failing that, the orbit spirals to a point as thependulum comes to rest .

A dynamical system's temporal evolution may happen in ei ther continuoustime or in discrete time. The former is called a flow, the latter a mapping. Apendulum m oves continuously fro m one state to another, and so it is described bya continuous-time flow. The number of insects born each year in a specific areaand the time interval between drops from a dripping faucet are more naturallydescribed by a discrete-time mapping.

F i g u r e 1 : STATE SPACE is a useful concept for visualizing the behavior of a

dynamical system. It is an abstract space whose coordinates are the degrees of freedom of

the system's motion. The motion of a pendulum {top), for example, is completely

determined by its initial position and velocity. Its state is thus a point in a plane whose

coordinates are position and velocity {bottom). As the pendulum swings back and forth it

follows an "orbit," or path, through the state space. For an ideal, frictionless pendulum the

orbit is a closcI curve {bottom lefi)\ otherwise, with friction, the orbit spirals to a point

{bottom right).



C H A O S 39

To find how a system evolves from a given initial state one can employ thedynam ic (equations of motion) to m ov e increm entally along an orb it. This m ethod

of deducing the system 's behavior requires com putational effort proportional to thedesired length of tim e to follow the orbit. For simple systems such as a frictionlesspendulum the equations of motion may occasionally have a closed-form solution,w hic h is a fo rm ula that expresses any fu tur e state in terms of the initial state. Aclosed-form solution pro vides a short cut, a simp ler algorithm that needs o nly theinitial state and the final time to predict the future without stepping throughintermediate states. With such a solution the algorithmic effort required to followthe motion of the system is roughly independent of the time desired. Given theequations of planetary and lunar motion and the earth's and moon's positions and

velocities, for instance, eclipses may be predicted years in advance.

Success in finding closed-form solutions for a variety of simple systemsduring the early development of physics led to the hope that such solutions existfor any m echanical system . Unfo rtuna tely, it is now kno wn that this is not true ingeneral . The unpredictable behavior of chaotic dynamical systems cannot beexpressed in a closed-form solution. Conseq uently there are no possible short cutsto predicting their behavior.

The state space nonetheless provides a powerful tool for describing the

behavior of chaotic systems. The usefulness of the state-space picture lies in theability to represent behavior in geometric form. For example, a pendulum thatmoves with friction eventually c om es to a halt, which in the state space m eans theorbit approaches a poin t. Th e point does not mov e— it is a fixed poin t— and sinceit attracts nearby orbits, it is known as an attractor. If the pendulum is given a smallpush, it returns to the same fixed-point attractor. Any system that comes to restwith the passage of time can be characterized by a fixed point in state space. Thisis an example of a very general phenomenon, where losses due to friction orviscosity, for examp le, cau se orbits to be attracted to a sm aller region of the state

space with lower dimension. Any such region is called an attractor. Roughlyspeaking, an attractor is what the behavior of a system settles down to, or isattracted to.

Some systems do not come to rest in the long term but instead cycleperiodically through a sequence of states. An example is the pendulum clock, inwhich energy lost to friction is replaced by a m ainspring or weigh ts. The pen dulu mrepeats the same motion over and over again. In the state space such a motioncorresponds to a cycle, or periodic orbit. No matter how the pendulum is setswinging, the cycle approached in the long-term limit is the same. Such attractorsare therefore called limit cycles. Another familiar system with a limit-cycleattractor is the heart.

A system may have several attractors. If that is the case, different initialconditions may evolve to different attractors. The set of points that evolve to anattractor is called its basin of attraction. The pendulum clock has two such basins:small displacements of the pend ulum from its rest position result in a return to re st;with large displacements, however, the clock begins to tick as the pendulumexecutes a stable oscillation.



Figure 2: CHAOTI C ATTRAC TORS are fractals: objects that reveal more detail as

they are increasingly magnified. Chaos naturally produces fractals. As nearby trajectories

expand they must eventually fold over close to one another for the motion to remain finite.

This is repeated again and again, generating folds within folds, ad infinitum. As a result

chaotic attractors have a beautiful microscopic structure. Michel Henon of the Nice

Observatory in France discovered a simple rule that stretches and folds the plane, moving

each point to a new location. Starting from a single initial point, each successiv e poin t

obtained by repeatedly ap plying He non 's rule is plotted. The resulting geom etric form (a)provides a simple exam ple of a chaotic attractor. Th e sm all bo x is m agn ified by a factor of

10 in b. By repeating the pro cess (c, d) the m icrosco pic structure of the attractor is rev ealed

in detail.



C H A O S 41

The next most complicated form of attractor is a torus, which resembles thesurface of a dou ghn ut. This shape describes m otion m ade up of two independent

oscillations, sometimes called quasi-periodic motion. (Physical examples can beconstructed from driven electrical oscillators.) The orbit winds around the torus instate space, one fre que ncy determined by how fast the orbit c ircles the doug hnutin the short direction, the other regulated by h ow fas t the o rbit circles the lo ng wa yaround. Attractors may also be higher-dimensional tori, since they represent thecombination of more than two oscil la t ions.

The important feature of quasi-periodic motion is that in spite of itscomplexity it is predictable. Even though the orbit may never exactly repeat itself,i f the frequencies that make up the motion have no common divisor, the motion

remains regular. Orbits that start on the torus near one another remain near oneanother, and long-term predictability is guaranteed.

Until fairly recently, fixed po ints, limit cycles, and tori were the on ly kno wnattractors. In 1963 Edward N. Lorenz of the M assachu setts Institute of Tech nolo gydiscovered a concrete example of a low-dimensional system that displayedcomplex behavior. Motivated by the desire to understand the unpredictability ofthe weather, he began with the equations of motion for fluid flow (the atm osp herecan be considered a fluid), and by sim plifyin g them he obtained a system that had

just three degrees of freedom. Nevertheless the system behaved in an apparentlyrandom fashion that could not be adequately characterized by any of the threeattractors then known. The at tractor he observed, which is now known as theLorenz attractor, was the first example of a chaotic, or strange, attractor.

Employing a digital computer to s imulate his s imple model, Lorenzelucidated the basic mechanism responsible for the randomness he observed:microscopic perturbations are amplified to affect ma croscopic beha vior. Tw o orbitswith nearby initial conditions diverge exponentially fast and so stay close togetherfor only a short time. The situation is qualitatively different for nonchaotic

attractors. For these, nearby orbits stay close to one another, small errors remainbounded and the behavior is predictable.

The key to understanding chaotic behavior l ies in understanding a s implestretching an d folding operation, which takes place in the state space. Exponentialdivergence is a local feature: because attractors have finite size, two orbits on achaotic attractor cannot diverge exponentially forever. Consequently the attractormust fold over onto itself. Although orbits diverge and follow increasinglydifferent paths, they eventually must pass close to one another again. The orbits ona ch aotic attractor are shuffled by this process, much as a deck of cards is shuffledby a dealer. The randomness of the chaotic orbits is the result of the shufflingprocess. The process of stretching and folding happens repeatedly, creating foldswithin folds ad infinitum. A chaotic attractor is, in other words, a fractal: an objectthat reveals m ore detail as it is increasingly m agn ified [see Figure 2 ].

Chaos mixes the orbits in state space in precisely the same way as a bakermixes bread dough by kneading i t . One can imagine what happens to nearbytrajectories on a chaotic attractor by placing a drop of blue food coloring in thedough. The kneading is a combination of two actions: rolling out the dough, in



42 CRUTCHFIELD, ET A L.

Figure 3: A CHAOTIC ATTRACTOR has a much more complicated structure thana predictable attractor such as a point, a limit cycle, or a torus. Observed at large scales, a

chaotic attractor is not a sm ooth su rface but one w ith folds in it. The illustration shows the

steps in making a chaotic attractor for the simplest case: the Rttssler attractor {bottom). First,nearby trajectories on the object must "stretch,** or diverge, exponen tially (top); here thedistance between neighboring trajectories roughly doubles. Second, to keep the objectcompact, it must 4fo ld " back onto itself (middle): the surface bends onto itself so that the twoends meet The Rdssler attractor has been observed in many systems, from fluid flows o

chemical reactions, illustrating Einstein 's maxim that nature prefers simple forms.



C H A O S 4 3

which the foo d coloring is spread out, and folding the dough over. At first the blobof food coloring simply gets longer, but eventually it is folded, and afterconsiderable t ime the blob is s tretched and refolded many t imes. On closeinspection the dough consists of many layers of alternating blue and white. Afteronly 20 steps the initial blob has been stretched to more than a million times itsoriginal length, and its thickness has shrunk to the molecular level. The blue dyeis thoroughly mixed with the dough. Chaos works the same way, except thatinstead of mixing doug h it m ixes the state space. Inspired by this pic tur e of m ixing ,Otto E. ROssler of the University of Tubingen created the simplest example of achao tic attractor in a flow [see Figure J ] .

W hen observations are m ade on a physical system , it is impo ssible to sp ecify

the state of the system exactly owing to the inevitable errors in measurement.Instead the state of the system is located not at a single point but rather within asmall region of state space. Although quantum uncertainty sets the ultimate size ofthe region, in practice different kinds of noise limit measurement precision byintroducing substantially larger errors. The small region specified by a measure-ment is analogous to the blob of blue dye in the dough. Locating the system in asmall region of state space by carrying out a measurement yields a certain amountof information about the system . The m ore accura te the m easure m ent is, the m oreknowledge an observer gains about the system's state. Conversely, the larger the

region, the m ore uncertain the observer. Since ne arb y po ints in no nc hao tic system sstay close as they evolve in time, a measurement provides a certain amount ofinformation that is preserved with time. This is exactly the sense in which suchsystems are predictable: initial measurements contain information that can be usedto predict future behavior. In other words, predictable dynamical systems are notparticularly sensitive to measurement errors.

The stretching and folding operation of a chaotic attractor systematicallyremoves the initial information and replaces it with new information: the stretchma kes small-scale uncertainties larger, the fold bring s wid ely sep arated traje ctor iestogether and erases large-scale information. Thus, chaotic attractors act as a kindof pum p bringing microscopic fluctuations up to a m acrosc opic exp ression . In thislight it is clear that no exact solutio n, n o sh ort cu t to tell the future, can exist. Aftera brief time interval the uncertainty s pec ified by the initial m easu rem ent cov ers theentire attractor and all predictive pow er is lost: there is simply no causal connectionbetween past and future.

Chaotic attractors functio n locally as noise amp lifiers. A sm all f luct uatio n du eperhaps to thermal noise will cause a large deflection in the orbit position soon

afterward. But there is an important sense in which chaotic attractors differ f romsimple noise amplifiers. Because the stretching and folding operation is assumedto be repetitive and continuous, any tiny fluctuation will eventually dominate themotion, and the qualitative behavior is independent of noise level. Hence chaoticsystems cannot directly be "quieted," by lowering the temperature, for example.Chaotic systems generate randomness on their own without the need for anyexternal random inputs . Random behavior comes from more than just theamplification of errors and the loss of the ability to predict—it is due to thecom plex orbits generated by s tretching and folding.



4 4 CRUTCH FIELD, ET AL.

It should be noted that chaotic as well as nonchaotic behavior can occur indiss ipationless , energy-conserving systems. Here orbits do not relax onto anattractor but instead are confined to an energy surface. Dissipation is, however,important in man y if not mo st real-world system s, and on e can exp ect the c onc eptof attractor to be generally useful.

Low-dimensional chaotic attractors open a new realm of dynamical systemstheory, but the question remains of whether they are relevant to randomnessobserved in physical systems. The first experimental evidence supporting thehypothesis that chaotic attractors un derlie rando m m otion in fluid flow wa s ratherindirect . The experiment was done in 1974 by Jerry P. Gollub of HaverfordCollege and Harry L. Sw inney of the U niversity of Texas at A ustin. The evid ence

was indirect bec ause th e investig ators f oc use d not on the attractor itself bu t ratheron statistical properties ch aracterizing th e attractor.

The system they examined was a Couette cell, which consists of twoconcentric cylinders. The space between the cylind ers is filled w ith a fluid, and oneor both cylinders are rotated with a fixed angular velocity. As the angular velocityincreases , the fluid shows progressively more complex flow patterns , with acomplicated t ime dependence. Gollub and Swinney essential ly measured thevelocity of the fluid at a given spot. As they increased the rotation rate, theyobserved transitions from a velocity that is constant in time to a periodically

varying velocity and finally to an aperiodically varying velocity. The transition toaperiodic motion was the focus of the exp eriment.

The experiment w as designed to distinguish between two theoretical picturesthat predicted diff ere nt scenarios for the behavior of the fluid as the rotation ra teof the fluid was varied. The Landau picture of random fluid motion predicted thatan ever higher number of independent fluid oscillations should be excited as therotation rate is increased. The associated attractor would be a high-dimensionaltorus. The Landau picture had been challenged by D avid R uelle of the Institut desHautes Etudes Scientifiques near Paris and Floris Takens of the University ofGroningen in the Netherlands. They gave m athem atical a rgum ents suggesting thatthe attractor associated with the Landau picture would not be likely to occur influid motion. Instead their results suggested that any pos sible high -dim ensio nal torimight give way to a chaotic attractor, as originally postulated by Lorenz.

Gollub and Swinney found that for low rates of rotation the flow of the fluiddid not change in time: the underlyin g attractor w as a fixed point. A s the rotationwas increased the water began to oscillate with one independent frequency,correspon ding to a lim it-cycle attractor (a periodic orbit), and as the rotation wa s

increased still further the oscillation took on two independent frequencies,corresponding to a two-dimensional torus attractor. Lan da u's theory predicted thatas the rotation rate w as further increased the pattern would continue: more distinctfrequencies would gradually appear. Instead, at a critical rotation rate a continuousrange of frequencies suddenly appeared. Such an observation was consistent withLo renz ' "deterministic nonperiodic flow," lending credence to his idea that chaoticattractors underlie fluid turbulence.

Although the analysis of Gollub and Swinney bolstered the notion thatchaotic attractors migh t underlie som e random motion in fluid fl ow , their wo rk w as



C H A O S 45

by no means conclusive. One would like to explicitly demonstrate the existence inexperimental data of a simple chaotic attractor. Typically, however, an experimentdoes not record all facets of a system but only a few. Gollub and Swinney couldnot record, for example, the entire Couette flow but only the fluid velocity at asingle point. The task of the investigator is to "reconstruct" the attractor from thelimited data. Clearly that cannot always b e don e; if the attractor is too c om plica ted,something will be lost. In some cases, however, it is possible to reconstruct thedynamics on the basis of limited data.

A technique introduced by us and put on a firm m athem atical fo und ation byTakens mad e it possible to reconstruct a state space and look fo r chaotic attracto rs.The basic idea is that the evolution of any single component of a system is

determined by the other components with which it interacts. Information about therelevant components is thus implicitly contained in the history of any singlecomponent To reconstruct an "equivalent" state space, one simply looks at a singlecomponent and treats the measured values at fixed time delays (one second ago,two seconds ago and so on, for example) as though they were new dimensions.

The delayed values can be viewed as new coordinates, defining a single pointin a multidimensional state space. Repeating the procedure and taking delaysrelative to different times generates many such points. One can then use othertechniques to test whether or not these points lie on a chaotic attractor. Although

this representation is in many respects arbitrary, it turns out that the importantproperties of an attractor are preserved by it and do not depend on the details ofhow the reconstruction is done.

The example we shall use to illustrate the technique has the advantage ofbeing familiar and accessible to nearly everyone. Most people are aware of theperiodic pattern of drops emerging from a dripping faucet. The time betweensuccessive drops can be quite regular, and more than one insomniac has been keptawake waiting for the next drop to fall. Less familiar is the behavior of a faucet ata somewhat higher flow rate. One can often find a regime where the drops, whilestill falling separately, fall in a never repeating patter, like an infinitely inventivedrumm er. (This is an experim ent easily carried ou t personally; the faucets withoutthe little screens work best.) The changes between periodic and random-seemingpatterns are reminiscent of the transition b etw een lam inar an d turbule nt flu id flow .Could a simple chaotic attractor underlie this randomness?

The experimental study of a dripping faucet was done at the University ofCalifornia at Santa Cruz by one of us (Shaw) in collaboration with Peter L. Scott,Stephen C. Pope, and Philip J. M artein. The first form of the experime nt consisted

in allowing the drops from an ordinary faucet to fall on a microphone andmeasuring the time intervals between the resulting sound pulses. By plotting thetime intervals between drops in pairs, one effectively takes a cross section of theunderlying attractor. In the periodic regime, for example, the meniscus where thedrops are detaching is moving in a smooth, repetitive manner, which could berepresented by a limit cycle in the state space . But th is sm ooth m otion is ina ccessi-ble in the actual experiment; all that is recorded is the time intervals between thebreaking off of the individual drops. This is like applying a stroboscopic light toregular m otion around a loop. If the timing is right, one sees only a fixed po int.



4 6 CRUTCHFIELD, ET AL.

The exciting result of the experiment was that chaotic attractors were indeedfou nd in the nonp eriodic regime of the dripp ing faucet. It could have been the case

that the randomness of the drops was due to unseen influences, such as smallvibrations or air currents. If that was so, there would be no particular relationbetween one interval and the next, and the plot of the data taken in pairs wouldhave shown only a featureless blob. The fact that any structure at all appears in theplots shows the random ness ha s a determ inistic unde rpinnin g. In particular, m anydata sets show the horsesh oe like shape that is the signature of the simple stretchingand folding process discussed above. The characteristic shape can be thought ofas a "snapshot" of a fold in progress, for exam ple, a cross section partway aroundthe Rossler attractor shown in Figure 2. Other data sets seem more complicated;

these may be cross sections of higher-dimensional attractors. The geometry ofattractors above three dimensions is almost completely unknown at this time.

If a system is chaotic, how chaotic is it? A measu re of chaos is the " en trop y"of the mo tion, which roughly speaking is the average rate of stretching and folding,or the average rate at which information is produced. Another statistic is the"dim ens ion" of th e attractor. If a system is simple, its behavior should be describedby a low-dim ensional attractor in the state space, such as the examples given in thisarticle. Several num bers m ay be required to specify the state of a more complicated

system, and its corresponding attractor would therefore be higher-dimensional.The technique of reconstruction, combined with measurements of entropyand dimension, makes it possible to reexamine the fluid flow originally studied byGollub and Swinney. This was done by members of Swinney's group incollaboration with two of us (Crutchfield and Farmer). The reconstructiontechnique enabled us to make images of the underlying attractor. The images donot give the striking demonstration of a low-dimensional attractor that studies ofother systems, such as the dripping faucet, do. Measurements of the entropy anddimension reveal, however, that irregular fluid motion near the transition in

Couette flow can be described by chaotic attractors. As the rotation rate of theCouette cell increases so do the entropy and dimen sion of th e un derly ing attrac tors.

In the past few years a growing number of systems have been shown toexhibit randomness due to a simple chaotic attractor. Among them are theconvection pattern of fluid heated in a small box, oscillating concentration levelsin a stirred- chemical reaction, the beating of chicken-heart cells and a largenumber of electrical and mechanical oscillators. In addition computer models ofphenomena ranging from epidemics to the electrical activity of a nerve cell tostellar oscillations have been shown to possess this simple type of randomness.There are even experiments now under way that are searching for chaos in areasas disparate as brain waves and economics.

It should be emphasized, however, that chaos theory is far from a panacea.Many degrees of freedom can also make for complicated motions that areeffectively random. Even though a given system may be known to be chaotic, thefact alone does not reveal very much. A good example is molecules bouncing offone another in a gas. Although such a system is known to be chaotic, that in itselfdoes no t m ake prediction of its behavior easier. So many particles are involved that



C H A O S 47

all that can be hoped for is a statistical description, and the essential statisticalpropert ies can be derived w ithout taking chaos into acc ount .

There are other uncharted q uestion s for w hich th e role of chaos is u nkn ow n.What of constantly changing patterns that are spatially extended, such as the dunesof the Sahara and ful ly developed turbulence? I t is not clear whether complexspatial patterns can be usefully described by a single attractor in a single statespace. Perhaps, though, experience with the simplest attractors can serve as a guideto a more advanced picture, which may involve ent ire assemblages of spat ial lymobile deterministic forms akin to chaotic attractors.

T h e existenc e of chaos af fec ts the scientific m etho d itself. Th e classicapproach to verifying a theory is to make predict ions and test them against

experimental da ta. If the phen om ena are chaotic, howev er, long-term predict ionsare intrinsically impossible. This has to be taken into account in judging the meritsof the theory. The process of verifying a theory thus bec om es a m uch m ore delica teoperation, relying on statistical and geometric properties rather than on detailedpredict ion.

Chaos brings a new challenge to the reductionist view that a system can beunderstood by breaking i t down and studying each piece. This view has beenprevalent in science in part because there are so many systems for which thebehavior of the whole is indeed the sum of its parts. C hao s dem onstrates , h ow eve r,

that a system can have complicated behavior that emerges as a consequence ofsimple, nonlinear interaction of only a few components.

Th e problem is becoming acute in a wide range of scientific disciplines, fromdescribing microscopic physics to modeling macroscopic behavior of biologicalorganisms. The ability to obtain detailed knowledge of a system's structure hasundergone a tremendous advance in recent years, but the ability to integrate thisknow ledge has been stymied by the lack of a proper conce ptual fram ew ork withinwhich to describe qualitative behavior. For example, even with a complete map ofthe nervous system of a simp le organ ism , such as the nem ato de studied by SidneyBrenner of the Universi ty of Cambridge, the organism's behavior cannot bededuced. Similarly, the hope that physics could be complete with an increasinglydetai led understanding of fundamental physical forces and const i tuents isunfounded. The interaction of components on one scale can lead to complex globalbehavior on a larger scale that in general cannot be deduced from knowledge of theindividual components.

Chaos is often seen in terms of the limitations it implies, such as lack ofpredictabi l i ty . Nature may, however, employ chaos construct ively. Through

amplification of small fluctuations it can provide natural systems with access tonovelty. A prey escaping a pre da tor 's attack could u se chaotic flight control as anelement of surprise to evade capture. Biological evolution demands geneticvariabi l i ty; chaos provides a means of structuring random changes, therebyproviding the possibili ty of putting variability under evolutionary control.

Even the process of intellectual pro gress relies on the injection of new ideasand on new wa ys of connecting old ideas. Innate creativity ma y hav e an unde rlyingchaotic process that selectively amplifies small fluctuations and molds them intomacroscopic coherent mental states that are experienced as thoughts. In some cases



48 CRUTCHFI ELD, ET AL.

the thoughts may b e decisions, o r w hat are perceived to be the exercise of w ill. Inthis light, chaos provides a mechanism that allows for free will within a worldgoverned by determinis t ic laws.



C H A O S: A M A T H E M A T IC A L IN T R O D U C T IO NW IT H PH IL O SO PH IC A L R E FL E C T IO N S

Wesley J. Wildman and Robert John Russell

1 Introduction

There is a simple quadratic equation often used to illustrate chaos, the so-called logistic map:

*nH =kx„( 1 ~X n)

Here, xn is the nh

num ber in a sequence and Jo0. The logistic map

is called an iterative map, because each number in the sequence is generatedby applying the map to the previous number in the sequence. So, for example,i f x 0 and k are stipulated, x } = A jc 0 ( 1 - jc 0) , x 2 = 1 —jc,), and so on.

This primary aim of this essay is, using the logistic map, to explain what'chaos' means. We focus on the logistic map for two reasons. Firstly, this mapdisplays most of the features of the broad class of chaotic dynamical systems:

the transit ion from regular to apparently random behavior, period-doublingbifurcation cascades, the influence of attractors, and the underlying character-istics of a fractal. A certain lack of generality is inevitable due to the discrete,one-dimensional character of the dynamical system obtained by iterating thelogis t ic map. The mathematics of the one-dimensional case is much s impler,however, and simplicity is a compelling virtue in an introductory essay.

Secondly, the logistic map has been specifically singled out in many ofthe papers in previous science and religion publications that discuss the possi-ble philosophical and theological implications of chaos (see the bibliography

for examples). Our tour of the logistic map will involve showing that the be-havior of the logistic map is more complex than this tradition of discussion inthe science-religion specialization has sometimes supposed. This is important,we hold, because clarity about the mathematics of chaos is essential for suchphilosophical and theological reflections to be relevant.

While the bulk of this paper is an introduction to the mathematics ofchaos, we also intend to make a small contribution to debates surrounding thephilosophical and theological import of chaos theory. This subsidiary goalinvolves treatment of the themes of unpredictabil i ty, randomness, determin-ism, chaos in nature, and divine action.

1.1 About Technical Ma terial

Th e logistic map , with its parab olic graph (see F igure 1 and Fig ure 2), is oneof the simplest possible equations, familiar to high school students of mathe-matics. Yet, under iteration, it produces an extraordinarily complex chaoticdynamical system. In fact, mathematicians are intensively engaged in trying to



5 0 WE S L E Y J . WIL DMAN AND RO B E RT JO H N RUS S E L L

f ind out more about the dynamical system this quadratic map produces. Mostof this mathematical labor lies well beyond the scope of an introductory papersuch as this one. The aim here is to introduce the mathematics of chaos, how-

ever, so technical material cannot be avoided entirely.We have tried to present the mathematical results as accessibly as possi-

ble, avoiding any indication of how they are obtained, in order to minimizetechnical language. The technical parts that remain have been flagged in thetext by means of a vertical bar in the right margin, such as the one that accom-panies this paragraph. We have also divided the mathematical material intobite-s ized pieces , making i t easier for non-mathematicians to maintain a senseof the flow of the discussion. In the final analysis, how ever, non-m athem aticalreaders will have to make their own decisions about which parts to skim, and

which to read more carefully. On the other hand, mathematically informedreaders will be frustrated by the absence of proofs, and so we refer them to thebibliography for more details. This is the double problem facing essays intro-ducing technical subjects, and we have tried to steer a middle way between thediverse expectations of the science and religion audience.

1.2 About Graphs

There are a number of different kinds of figures included in this paper, all ofwhich have been generated by the authors. One type of graph is called a'cobweb diagram,' and appears in Figure 1, Figure 2, and elsewhere. It illus-trates the process of iteration by overlaying the logistic map's parabolic shapewith a plot of xn+ against xn for several values of n. Another type is called a' time series plot. ' It graphs the sequence of values produced by iterations ofthe logistic map against the number of iterations completed. In such graphs,the vertical axis records the value, xm and the horizontal axis the iteration, n.This type offers a way to visualize what will soon be defined as the orbits of

the logistic map. Other types will be explained when they are used.

1.3 About References

The material in section 2 is available in a number of sources, and these sourcesinclude more on almost every topic than can be covered here. Rather than cit-ing a source for every piece of information, therefore, we have appended ashort bibliography to this paper. The papers and books listed there are organ-ized according to relevant topics and annotated where appropriate .

2 The Logistic Ma p

Figure 1 illustrates the first few numbers in the sequence produced by iteratingthe logis t ic map for k= 1, beginning from x 0=0.5 . To unders tand the d iagram,follow the l ine from x0 up to the parabola, and then left to the vertical axis; thepoint at which tne line meets the vertical axis is jc, . Th e d iagon al line helps to

locate xx on the horizontal axis. Now the second iteration begins, with x

2 lo -



C H A O S : A M A T H E M A T I C A L I N T R O D U C T I O N 51

1

*2

0 *2X1 *0

Figure 1: Logist ic m ap

Plot of x n + 1 against x n for k=l

1 0 X, Xo x, 1

Figure 2: Logist ic map

Plot of x n + j against x n for k=4

cated first on the vertical axis, and then on the horizontal axis, in the sameway. Figure 2 shows a s teeper parabola, representing the logis t ic map for k-4.A few i terat ions, beginning from jc 0=0.6, are illustrated there.

It is possible to ask when the iterated sequence converges, or exhibitssome other patterned behavior. I t turns out that , for some values of k, the se-

quence of numbers appears random, and highly sensit ive to the ini t ia l choice,x 0 ; this is the case for the sequence whose beginning is plotted in Figure 2. Forother values of the constant k there is a recognizable pattern in the sequence ofnumbers generated by iterating the logistic map, no matter what is chosen forx 0. For example, some iterated sequences steadily decline toward 0, like theone plotted in Figure 1. O thers con ver ge to som e non- zero limit. Still othersequences never converge but oscil la te s tably between two or more values . Inother cases, though the final pattern that emerges does not depend on the initialvalue chosen for x 0 , the way that pattern emerges does depend on x 0.

It is fascinating that a single equation such as this displays both stableand chaotic behavior, depending merely on the value of k, which is oftencalled the tuning constant. Imagine being able to increase the metabolic rate ofDr. Jekyll by turning a s ingle knob on some dastardly machine, eventuallyreaching a point at which Mr. Hyde emerges, with his characteristically un-predictable behavior. That is an apt analogy for what happens to the sequenceof numbers generated by the logis t ic map as k is increased. Such characteris-t ics are extremely common in mathematical dynamical systems. But manyphysical systems also seem to behave in the same way as this innocent lookingequation, with its Jekyll and Hyde personality.

2 .1 Modeling N ature: The Moth Colony Example

In jus t the past tw o decade s, scientis ts have m ade dram atic breakthro ughs byusing the logis t ic map and s imilar dynamical systems to s tudy a vast range ofpreviously intractable or unnoticed problems in the physical , biological , andsocial sciences. A sampling of the areas studied with some success include

financial markets , meteorology, ecology, turbulence in f luids , periodic behav-



5 2 W E S L E Y J. W I L D M A N A N D R O B E R T J O H N R U S S E L L

ior in chemical reactions, the spread of disease, the onset of war, and humanphysiology (see the bibl iography for references) .

For instance, the population of successive generations of moths in certain

habitats is a biological variable that displays both predictable and apparentlyrandom behavior. I t turns out that the humble logistic map is quite serviceable

as a model for moth colony populat ions when the var iat ions in moth popula-

tion are predictable. The fact that the logistic map displays chaotic behavior

under cer tain mathematical condi t ions (values of k) therefore may suggest the

beginnings of an explanat ion for the apparent randomness that character izes

successive moth populat ions under cer tain special environmental condi t ions,

though this is a problematic form of explanation, as we shall see later.

Thought of as such a model, the logistic map expresses the fact that the

moth population of one generation (scaled to a number between 0 and 1; call i t

*„+,), depends on the population of the previous generation (also scaled down;

call it x„) in three ways:

1. It de pe nd s directly on xn since, if there are lots of moths this generation,

there will be lots of baby moths to boost the next generation.

2. It a lso dep end s on ( l -x „ ) because, i f there are too many m oths, there

will be a shortage of food and extremely rapid spread of disease.

3. Final ly, the popu lat ion de pen ds upon the ' tun ing ' constant , k, which

corresponds to such effects as the general avai labi l i ty of resources, the

level of fecundity of the moth population, and other factors that remain

unchanged from generat ion to generat ion.

It may seem unlikely that such a simple model actually works, and thetruth is that i t does not always work that well; the complexities of moth l ife

can quickly muddy the logist ic map's clear waters . I t i s qui te useful , neverthe-less, especially when the ' tuning' of the system is low; that is, when the gen-erationally invariant factors lead to a constant, k, that is not too high.

2 .2 Regimes of Behavior

The unit interval, [0,1], is of great importance for understanding the logisticmap. To see this, notice that the graph ofxn+ ]=kxn(\-x„is an inverted parabolawhen k>0, intersecting the horizontal x„-axis at 0 and 1 (see Figure 1 fo r k=1).The value of k determines how steep the inverted parabola is , because themaximum value , which occurs a t jc =0.5, is 0 .25k. It follows that, when x0 is in[0,1] and the constant k l ies between 0 and 4, the numbers generated by i terat-ing the logistic map never l ie outside the bounds of 0 and 1, no matter what x0

might be. I teration in this range of x0 and k creates a kind of feedback process ,making possible such dynamics as convergence of the i terated sequence.

Of course, the logistic map can be i terated no matter what k and x0 mightbe. But when k>1, i terations tend rapidly toward infinity unless the first num-

ber in the sequence, xh lies in the unit interval, [0,1]. For 0<A<1, exponential



CHAOS: A MATHEMATICAL INTRODUCTION 5 3

I • k=0 5 , in i t ial x= 0.000 1 j

0 .8

0 6

0 4

0.2

0 0

I 10 20 30

Figure 3 : Regime I (0 < k < 1 )

Plot of x n against n showing that

iterations tend to zero

• k=1.5 , in i t ia l x=0.0001

10

0 8

0 .6

0 .4

0 .2

0 0

0 10 20

Figure 4 : Regime II (1 < k <, 3 )

Plot of xn against n showing that

iterations tend to a non-zero limit

explosion of the sequence occurs unless x 0 is in the interval [(k-\)/k9\ /k]. Onthat interval, which includes [0,1] as a subset, iterations converge to 0. Thus,the interesting dynamics of the logistic map for Q<k<4—that is, the variousbehaviors of the sequences obtained by i terat ion—are encountered when jc isconstrained to lie in the unit interval.

Interest ing dynamics also occur when Jo 4. Though the iterated sequenceexplodes to infinity for almost every starting value, x 0 , i t remains within [0,1]

if jc0 belongs to a special subset of [0,1] that depends on k. In this case too,therefore, the unit interval is crucial.

Once we limit the discussion to x 0 in the unit interval, the dynamics ofthe logistic map turn out to depend fundamentally on k. Just as a caterpillarpasses through a number of stages in its life cycle, or a civilization takes onnew forms as one era gives way to the next, so the behavior of the logistic mapundergoes beautiful changes as the tuning constant, k, is increased. Here wedescribe the logis t ic map with reference to f ive Regimes of the tuning con-stant, A, in which the logistic map has distinctive dynamics.

We will discuss these Regimes beginning with 0<A<1 and ending withk>4. Along the way we wil l make excurses to consider themes of more generals ignificance. We will sometimes describe the behavior of the logis t ic map us-ing the highly suggestive moth colony population example.

To help readers keep track of the movement of the discussion through thevarious Regimes of the logistic map, we list them here, with a summary of thedynamics they exhibit . The number k cr i t is roughly equal to 3.59, and its impor-tance will be described below.

R e g i m e Ac-values S u m m a r y o f D y n a m i c s

1 0<k<\ Ex t i nc t i on Reg ime: C o n v e r g e n c e t o 0

II \<k<3 Convergence Reg ime: Conv e r genc e t o non - z e r o l i m i t

II I 3 <k<k c r i t Bi fu rca t i on Reg ime: Spl i t ti ng o f s tab le l im i t s ta tes

IV k c r i t<k< 4 Chaot ic Regime: M i x t u r e o f s t ab l e pe r i od i c and c hao t i c behav i o r

V 4 <k Second Chaot i c Reg ime: Chao t i c dy nam i c s on a s ubs e t o f [ 0 , 1 ]



54 WESLEY J. WILDMAN AND ROBERT JOHN RUSSELL

2 .3 Regime I: Extinction (0 < k < 1)

Mon otonically decreasing sequ ences converging to 0; no significant depend-

ence on initial conditions.In this Regime sequences of iterated values fall monotonically (that is ,

always in one direction) to zero. (See Figure 3 for £=0.5).If £=1, or is very close to 1, the sequence descends to zero appreciably

more slowly than if k is close to 0. The initial value, x 0, plays no s ignificantrole, except to give some sequences a head start on the convergence process(of course, if x 0= 0 or 1, convergence of the sequence to 0 is immediate). Therate of convergence is determined solely by k. This means that all informationabout the initial state is lost more or less rapidly (i.e., in a matter of a few gen-

erations, or iterations, depending if we are thinking about moths or numbers).In moth language, the population inevitably declines to extinction.

2.4 Regime II: Convergence (1 < k < 3)

Increasing sequences converging to single limits>0 that depend on k; no sig-

nificant dependence on initial conditions.

When k is between 1 and 3, iterated sequences converge to non-zero lim-

its (see Figure 4 for £=1.5). Whereas in Regime I the limit is always 0, thevalue of the limit in Regime II depends on £; it can be calculated easily, sinceit occurs when x= x n+ x=kx n(\-x n). Graphically, this is the intersection of theline y=x with the parabola y=kx(\-x). The limit, therefore, is ( k - \ ) / k . Ofcourse, if x 0 =0 or (k-\)/k—or one of the points that are iterated by the logisticmap into 0 or (k-\) /k—then convergence occurs in a f ini te number of s teps.Beyond this trivial dependence on initial conditions, the value of x 0 only givesthe process of convergence more or less of a head start, as in Regime I.

The way convergence occurs , however, varies within this regime. For

1<£<2, after possible initial bumps, convergence is monotonic from below(Figure 4 for £=1.5), wh ereas for 2 <£<3, the sequ ence fluctuates above andbelow the eventual limit, moving gradually closer with each iteration (Figure 5for £=2.5). Figure 6 is a close up illustration of the fluctuating convergence ofthe iterated sequence.

[ . k= 2 5 . in i t ia l x=0 .0001)

1 0

0 8

0 6

0 4

0 2

0.0 i • • • •«« • • « f ? * T ,0 10 20

0 7 5

k=2 95 . in i t ia l x=0 .3

Figure 5: Regime II (1 < k < 3)

Plot of x„against n illustrating the

breakdown of monotonic convergence

Figure 6: Regime II (1 < k <, 3)

Plot of xn against n illustrating a

fluctuating population close up




2 .5 Excursus: Technical Definitions

The following technical terms wil l be helpful for understanding the detai ls of

the logistic map as the more complex aspects of its behavior are introduced.Some require abstract definitions, but all are quite intuitive. Each is a specifi-cation of a concept important for s tudying chaotic dynamical systems.

(i) A fixed point of the logistic map is one that remains unchanged by it-erat ion. For example, 0 and (k- \ ) fk are fixed points for k>0.

(ii) A periodic point of period n is one transformed into itself by the lo-gis t ic map after exactly and no fewer than n iterations. For example, fixedpoints are periodic of period 1, and we shall soon see that, in Regime III, thelogistic map has periodic points of period 2, 4, 8, and so on. When the logistic

map is chaotic, it has infinitely many periodic points.(iii) The forward orbit of the logistic map for a given k and x, denoted

0 +(k 9x) i is the set of num ber s gen erated by iterating the log istic m ap for A,beginning f rom x. So, for example, 0 +(k£k-\)/k)={(k-\)/k} fo r k>0. Thebackward orbit or preimage for a given k and x—the same thing in the reversedirection, denoted 0~(kjc)—is the set of numbers that the logistic map iteratesinto x. For example , O'(kfi) includes at least {0,1} for Jo0, because 0 and 1are iterated to 0. The orbit for a given k and x, denoted 0(kjc) y is just the union

of the forward and backward orbits . For convenience, forward orbits wil lsometimes be called orbits when the abbreviat ion is not misleading.

(iv) Orbits only rarely consist of a finite number of points, as in these ex-amples. In fact, orbits of the logistic map usually have infinitely many pointswith intriguing patterns . For example, suppose that 0<£<3, and further supposethat x 0 is in [0,1], but not in the preimages of 0 or (k-\)/k, so that convergenceis never interrupted by hitting a fixed point. Then O(kjc 0) is an infinite set ofpoints. The interesting feature of the orbit just described is that it has one andonly one limit point: 0 for k in Regime I, and ( k - \ ) / k fo r k in Regime II. Note

that a limit point does not have to be in the orbit itself (and usually is not).However , the closure of an orbit includes all of its limit points. The time series

plots in this paper are essentially diagrams of forward orbits organized in

such a way as to draw attention to their limit points, if they exist.

(v) A fixed point or a periodic point is attracting for a given k if it is al imit point of some orbit for k\ otherwise it is repelling. For example , (k-\)/k

is an attracting fixed point for \<k<3, and repelling otherwise. Orbits drawattention to attracting fixed and periodic points because they are limit points,

and the points of an orbit accumulate around its limit points. Repelling fixedand periodic points are less visible, especially in the sense that they are unde-tectable by computer calculat ions of orbits .

(vi) The set of limit points for a given orbit is called the attractor for thatorbit; for non-chaotic orbits, it is usually the set of attracting fixed and periodicpoints. For example, the attractor of orbits in Regimes I and II is a single point.In Regime III, as we shall shortly see, the attractor may contain 2, 4, 8, ormore points , depending on k. In Regimes IV and V, the attractor may haveinfinitely many points, none of them attracting fixed or periodic points. Attrac-

tors for chaotic orbits usually have extremely complex and s trange s tructures .



5 6 WE S L E Y J . WIL DMAN AND RO B E RT JO H N RUS S E L L

In dynamical systems that are described with ordinary different ial equat ions,

attractors are typically attracting, simple closed curves.(vii) The logistic map is said to be in equilibrium for a given k if the at-

t ractor for 0(kjc) consists of the same single point for almost all x in [0,1].

2 .6 Excursus: Convergence

The sequences in Figure 7, Figure 8, and Figure 9 il lustrate how the rate ofconvergence s lows dramat ical ly as k nears the value 3. Note that these se-quences are oscillating above and below their eventual l imit. For instance,

when £=2.95 (Figure 7) , variat ion betweensuccessive iterations is barely discernible

L ^ - ^ 9 5 ' L n , t , a l x = 0 ^ J o n t h e s c a j e 0 f t ^ a t d i a g r a m after 80 itera-t ions, whereas convergence is muchslower (maximally slow, str ict ly speaking)

. . for k=3 (Figure 9). This is a reminder of anV ^ ^ ^ / W W W ^ w w ' ^ i m po rta nt g en er al p oin t: w h en c on ve r-

gence is not cut short by iterations hitt ing afixed or periodic point, the occurrence of

convergence, as well its limit and rate,

0 .7 0

0

2040 60 so depend only on the value of k. By contrast,Fi gure 7: Regime II (l < k < 3) the initial value, x 0, does not have a consis-

Rapid convergence for k=2.95 t e n t in f luence on convergence.

From a technical point of view, we| k=2 98 , init ialx =o.64] m u s t always keep in mind the (by now)

0 7 4 t famil iar exceptional case that convergenceonly requires a finite number of i terations,which happens whenever x 0 lies in thepreimage of a f ixed or periodic point . For

a given w e shall call the set of values ofx 0 for which convergence occurs in a f ini tenumber of i terations the finite convergence

0 .7 0

0.66

0.62

0 .7 0

o 20 40 60 so set of k, and denote it FC k. The f ini te con-Figure 8: Regime II ( l < k < 3) verge nce set for a given k can be described

Slow convergence for )h=2.98 as fol lows: Denote by P k the set of fixed

and periodic points, both attracting andf n ^ T o o , initial x=o.64| repel l ing. Convergence wil l be achieved in

a f ini te number of i terat ions whenever x 0 isin one of the preimages of the points in P h

so FC k=0'(k,P k).

When 0<£<1, 0(k tP k)= {0,1}. When1<£<3, 0~(k 9P k) contains infini tely many

°62 4 points: the preimage of the repel l ing f ixedpoint 0, which consists only of 0 and 1;

o 2o 40 eo g^and the preimage of the attracting fixed

Figure 9: Regime II (1 < A < 3) ^ w hl

ii

c h » a n i n f ™ t e S e t . S C a t -

Maximal ly s low convergence for k= 3 t e r e d

symmetrically through the unit inter-



C H A O S : A M A T H E M A T I C A L I N T R O D U C T I O N 5 7

val. As k increases above 3, FC k becomes larger with an extremely complexstructure, but its overall size remains comparatively small in the sense that ithas Lebesgue measure zero .

We can define the infinite convergence set of k, denoted as ICh

to be thecomplement of the finite convergence set on the unit interval. That is to say,IC k=[Q,\]-FC k. If jc lies in the infinite convergence set, then convergence, if itoccurs, is never completed after a finite number of iterations, and the orbit of k

and x 0, O(kjc0), contains infini tely many numbers . The infini te convergence setis much larger than the fini te convergence set—though both sets contain infi-nitely many points , IC k contains almost all possible starting values—but itsprecise s ize (Lebesgue measure) in some cases is a tr icky problem (we shallhave more to say about this presently). We will need to refer to the infinite

convergence se t , IC h repeatedly in the succeeding pages, because the general ipattern of the logis t ic map's behavior is determined solely by k only when x 0

lies within IC k. For convenience we wil l sometimes s imply say "for almost al lstarting values, x 0" wh en we mean "fo r all x 0 i n / Q . "

We can summarize these technical observations as follows. I t is t rue thatw h e n x 0 is in the finite convergence set of A, convergence is affected by ini t ia lcondit ions. Apart from this interest ing way—trivial though i t may be fork<3—in which convergen ce d epends on jc, the value o f k determines all con-

vergence issues for almost all xQ

. In graphical terms, the steepness of the in-verted parabola is the key; the choice of starting point for iteration results onlyin more or less of a head start on the process, for almost all jc. This is typicalof dynamical systems: the tuning variable that determines the Regime of thesystem also settles all convergence questions.

2 .7 Regime III: Bifurcation (3.0 <k< k crU = 3 .57)

Bifurcation Regime consisting of fluctuating sequences with multiple attracting

periodic points that depend on k; minor, permanen t dependence on initialconditions in the form of phase shifts.

Immediately after the tuning constant is increased beyond k-3, some-thing truly s tr iking begins to occur: equil ibrium, or convergence to a s inglelimit, breaks down. In its place, the iterated sequences oscillate closer andcloser to multiple distinct values: first two, then four, then eight, and so on in

[ " -«- k =3 .0 2 . i n it i al x = 0 6 4 ] | k = 3 0 5 . i n i ti al x =0 .6 4 |

0 20 40 60 80 0 20 40 60 80

Figure 10: Regime III (3 < k <

Slow divergence for k= 3.02

Figure 11: Regime III (3 < k < k^,)

Rapid divergence for k= 3.05



58 WE S L E Y J. WIL DM AN AN D RO B E RT JO H N RUS S E L L

Figure 12: Regime III (3 < k < k a

Limit cycle, period 2

• k= 3 51, ini t ial x= 0 3

k=34. in i t ia l x=o.31 increasing powers of 2 as £ increases. Put

precisely, for a given £, and for all x 0 inIC h the orbits for k and jc0, 0(k,x 0), have

the same limit points, and they are all at-tracting periodic points of the same period,a power of 2. The value of k alone deter-

l ^ mines the limit points and their period, for

almost all x (h (The fixed points 0 and^ { k -X y k are both repell ing in Regime III ,

and so are not limit points of any orbits).

An apparently stable oscillation be-tween two population levels has been no-

ticed in moth colonies, and was unex-plained until the effectiveness of the logis-tic map as a model suggested a way. Inmoth language, moth colonies can be in astable state even when they do not have aunique population: after some initialbum ps, they can s imply fl ip -flop fromgeneration to generation between two dis-

tinct population levels. In number lan-guage, the oscillation of the sequence ofiterated values we noticed in Regime IIIeventually overpowers the tendency toconverge to a single limit. Put figuratively,alternate halves of the iterated sequenceconverge, even though the sequence as awhole is oscillating with each iteration,and displays no tendency toward overall

convergence whatsoever. (See Figure 10for £=3.02 and Figure 11 for £=3.05.)

The splitting of the equilibrium stateof the iterated sequence into stable oscilla-

6 0 tion between attracting periodic points ofperiod 2 is called a bifurcation. Whereasorbits have jus t one limit point be fore thebifurcation, after £=3 they have two limit

points. Of course, these are not limits of iterated sequences as a whole, butonly of intertwined sub-sequences of iterated sequences. The pair of periodicpoints defines a limit cycle of period 2. The entire series of graphs from Figure7 through Figure 11 illustrates a bifurcation as k is increased above 3: theequilibrium state of convergence to a single limit (for 0<£<3) is transformedinto stable oscillation between attracting periodic points (for 3<k<k c r i l).

Bifurcation of ' l imits ' does not stop with the split at £=3. As £ increases,more and more attracting periodic points appear. At £=3 the first bifurcationoccurs, producing stable oscillation of the iterated sequence between two at-

tracting periodic points of period 2, and the formerly attracting fixed point,

Figure 13: Regime III (3 < k < k cril)Limit cycle, period 4

• k=3 .561, in i t ial x= 0 3

Figure 14: Regime III (3 < k < k a




C H A O S : A M A T H E M A T I C A L I N T R O D U C T IO N 5 9

Q Limits: 1 2 0| Limits: 3 1 42 -j

Figure 16: Limit Cycle (period 4)

xn+1 against xn for k=3.51 corresponding

to the stable limit state of Figure 13

Figure 15: Limit Cycle (period 2)

xn+i against x„for £=3.4, corresponding

to the stable limit state of Figure 12

(£- l ) /£ , becomes a repel l ing f ixed point . At £=3.449, the second bi furca t ionoccurs, producing four attracting periodic points of period 4, with the periodicpoints of period 2 becoming repelling instead of attracting. Figure 12 (for£=3.4) illustrates stable oscillation between two clearly defined attracting peri-

odic points of period 2. Compare that to Figure 13 (for £=3.51) where each ofthese limit points of the orbit has, in turn, given rise to two new limit pointseach, all periodic points of period 4.

Successive bifurcations occur at £=3.544 (8 periodic points of period 8;see Figure 14 for £=3.561), £=3.564 (16 periodic points of period 16),£=3.569 (32 periodic points of period 32), and so on. Because the bifurcationsoccur for values of £ that are packed increasingly closely together, the useful-ness of the logistic map as a model for physical systems such as moth colony

populations breaks down; the real world is not well enough behaved to main-tain fecundity and food supplies (corresponding to a precise value of the tun-ing constant , £) perfectly invariant .

Each one of these limit cycle situations is stable, in the sense that the val-ues for £ and x 0 can be changed a little and, so long as x 0 is in IC k (i.e., for al-most al l jc0), the nu m be r of attracting periodic po ints in the perturb ed orbitremains the same as that of the unchanged orbit . Stabil i ty can be mathemati-cally quantif ied by measuring the effects of perturbations of this kind. Notsurprisingly, it turns out that stability is weakest in the vicinity of bifurcations,

and greatest between bifurcations.It is possible to illustrate geometrically the way iteration of the logistic

map produces sequences that oscil la te s tably among at tracting periodic points :Figure 15 (for £=3.4) shows 2 attracting periodic points of period 2, and Figure16 (for £=3.51) displays 4 attracting periodic points of period 4. The intersec-tion of the diagonal line and the parabola in these two figures locates the fixedpoint at (£-l)/£. No orbit will have this point as a limit point, however, becauseit is repelling for £>3, though all of the points in its preimage terminate itera-

tion there.



60 WE S L E Y J. W IL DM AN A ND RO B E RT JOH N RUS S E L L

1.00

0.75

0.50

0.25

0.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Figure 17: Bi furcat ion Diagram

Plot of the limit points of orbits of the logistic map against k

The change from being an at tracting to a repell ing fixed point can bepictured graphically as being caused by the s lope of the tangent to the parabola

at (k-l) /k becoming progressively s teeper. As i t passes 45 degrees to the hori-zontal axis at k=3, it changes from attracting to repelling. In a similar way,periodic points of period 2 are present in Figure 16, but they can never be thelimit points of any orbit because, as k moves through the bifurcation at k=3.5,they change permanently from attracting to repell ing.

2 .8 Excursus: The Bifurcation Diagram

The limits of orbits of the logistic map can be plotted against values of k in

what is called a bifurcation diagram (Figure 17). For a given k, the orbits0(kjc), hav e the same limit points, for alm ost all x0. The vertical slice of thebifurcation diagram at that value of k is effectively a plot of the limit points(the attractor) for those orbits.

The bifurcation diagram graphically illustrates how the limit points splitsuccessively and without ceasing in Regime III as k increases from 3 to thecritical value kcrit=3.51. Because it plots orbits as they approach their limitpoints, where they exist, i t does not draw attention to repelling fixed and peri-

odic points, but only their attracting counterparts. As we have seen, each bi-furcation spawns two new attracting periodic points of period twice that of theattracting fixed or periodic point from which they sprang. The parent at tract inglimit point ( thought of as changing continuously with k) does not disappear,but merely becomes repelling, and so ceases to be a limit point of orbits afterthat bifurcation. If repelling periodic and fixed points were plotted on the bi-furcation diagram, they would continue on the trajectory they were on beforeeach bifurcation splits the new periodic points off in opposite directions.

The structure of these successive splittings is an important geometrical

feature of the logistic map. All bifurcations in the bifurcation diagram look



CHAOS: A MATHEMATICAL INTRODUCTION 61

similar because they really are: they turn out to be approximately self-similarin the same way that fractals are, with smaller instances being very nearlyidentical to scaled down versions of larger ones. In fact, the diagram itself is a

fractal. For example, the bottom branch of the first bifurcation, when inverted,replicates almost exactly the structure of the entire diagram. (See Figure 24and Figure 25 for illustrations of the fractal geometry of Regime IV.)

2 .9 Excursus: The Feigenbaum Constant

The shape of bifurcations (disregarding their size) varies slightly, especially inthe early stages of a bifurcation cascade. However, the shape changes less andless as these bifurcation splittings become smaller and smaller, approaching alimit bifurcation shape. The scaling constant that gives the ratio of sizes ofadjacent bifurcations as they approach this limit shape was named afterMitchell Feigenbaum, a mathematician who has made many contributions tounderstanding the logis t ic map. He calculated i t to be 4.6692016091029. . . .This means that each bifurcation of the cascade in Regime III of the logisticmap is roughly 4.6692 times smaller than the previous one, and the approxi-mation gets better the further through the cascade we go.

The same constant applies to all cascades in the logistic map (there are

more of them in Regime IV), to the magnification ratios used to observe thefractal character of the bifurcation diagram as a whole, to the ratios of bandingdivisions (see below for more on this), and to other features of the bifurcationdiagram. Thus, the Feigenbaum constant is an extremely efficient indicator ofthe behavior of the logistic map. Unsurprisingly, in view of these observationsabout scaling, the bifurcation region of the logistic and related iterated mapshave important connections to the topic of renormalization in physics.

The following table indicates the way the ratios of adjacent bifurcationsizes approach the Feigenbaum constant .

bi furcat ion beg ins ends w id th ra tio to next

per iod 2 3.0 3 . 4 4 9 4 8 9 . . . . 4 4 9 4 8 9 . . . 4 . 7 5 1 4 . . .

pe r iod 4 3 .449 489 . . . 3 .544090 . . . .094601 . . . 4 . 6 5 6 2 . . .

pe r iod 8 3 . 5 4 4 0 9 0 . . . 3 . 5 6 4 4 0 7 . . . . 0 2 0 3 1 7 . . . 4 . 6 6 8 3 . . .

per iod 16 3 . 5 6 4 4 0 7 . . . 3 . 5 6 8 7 5 9 . . . . 0 0 4 3 5 2 1 . . . 4 . 6 6 8 7 . . .

pe r iod 32 3 . 5 6 8 7 5 9 . . . 3 . 5 6 9 6 9 2 . . . . 0 0 0 9 3 2 1 9 . . . 4 . 6 6 9 2 . . .

pe r iod 64 3 . 5 6 9 6 9 2 . . . 3 . 5 6 9 8 9 1 . . . . 0 0 0 1 9 9 6 4 . . .

It turns out that this same scaling constant applies to a whole family ofmaps on the unit interval: smooth maps with one hump graphs and non-zerosecond derivatives at the critical point (0.5, for the logistic map). Besides thelogistic map, this family includes the sine wave, and even maps with non-symmetrical graphs. That makes Feigenbaum's number an intriguing mathe-matical constant with profound geometric s ignificance, much l ike n and e.

The mystery was only to deepen, however, when i t was discovered that

the Feigenbaum constant also appears in nature. There have been numerous



6 2 WESLEY J . WILDMAN AND ROBERT JOHN RUSSELL

• k=3 .561, in i t ia l x=0 .3

4 k=3.561. in i t ial x =0 .8

0 9

0.5

0 10 20 30 40 50 60

Figure 18: Regime III (3 < k < k crit)Phase shifting

» k = 3 . 5 6 1 , in i ti al x = 0 . 3

»--k=3 .561. in i t ia l x=0 .8

40 45 50 55 60

Figure 19: Regime III (3 < k < k

Close up of Figure 18

experiments in the last two decades designed to calculate the same ratio forphysical dynamical systems exhibit ing period doubling cascades (see the bib-liography for examples), and the results agree rather closely with Feigen-baum's number. I t appears , therefore, that this number is more than an impor-tant mathematical constant. It also seems to be a kind of natural constant; thesense in which this is so is a pressing question for many scientists.

There are other scaling constants for the many classes of mathematicaldynamical systems. In fact , above one dimension, there are as many families

of maps with characteristic scaling constants as there are real numbers. Likethe Feigenb aum constant , some of these m ay also be detectable in nature.

2 .10 Excursus: Depend ence on Initial Cond itions

We have already seen one kind of dependence on ini t ia l condit ions—trivial for£<3— in that , for a given k, convergence is achieved in a finite number of stepswhen x 0 is in the finite convergence set of k, FC k. That means that the value ofk determines convergence of sequences not for all x 0, but only for almost all

xQ. Dependence on initial conditions would occur in a non-trivial form if itwere evident for almost al l jc, rather than the relatively few exceptional valuesin FC k. This happens for the first time in Regime III, where initial conditionsaffect the order in which sequences bounce close to the attracting periodicpoints of its stable limit state. This effect is called 'phase shifting. '

Figure 18 shows phase shift effect for a limit cycle of 8 periodic points ofper iod 8 . Since p lot t ing two orbi ts—0 + (3 .5 61,0.3) and <9+(3.561,0.8)—on thesame diagram can be a little confusing, we have provided Figure 19, which is a

blow-up of the data from Figure 18 beginning at the 40th iteration. In theblown up diagram , we can see that the sequence for x0 =0.3 cycles through 8periodic points one s tep ahead of the i terated sequence beginning from x0 = 0 . 8 .That is , the 43rd iteration for the x 0 =0.3 sequence regis ters a value of ap-proximately 0.9, whereas this value occurs for the 42nd i terat ion of the jc 0=0.8

sequence . This shift is preserved indefinitely by successive iterations.

The phase shift represents what can be called an historical element inthese systems; the initial conditions continue to affect the system indefinitely,and the effect (the size of the phase shift—here one iteration) is independent of

time. The size of the shift, however, differs for different starting values.




o

1 0

100 200 300 400

o k=3.569946, in i t ia l x=0 .3

» k=4 0, in it ia l x=0.3

0 100 200 300 400

Figure 20: Regime IV (k crit <k< 4)

Chaos over the entire unit interval (£=4)

Figure 21: Regime IV {k^, <k< 4)

Chaos in bands (k=3.57 and k=A)

2.11 Regime IV: Chaos (3.57 s k crit <k< 4)

Chaotic orbits separated by densely packed bifurcation regions; maxima l de-

pendence on initial conditions.

In Regime III, bifurcations occur closer together as k increases until acritical value of k, k crji=3.5699456..., is rea ch ed. At this poin t, the logistic m apis chaotic, in a sense that will be made precise after we have presented a sum-

mary of the s tructures of Regime IV and Regime V. For now, we wil l be con-tent with a rather limited but suggestive phenomenological definition: the it-erated sequences for k=k crit and almost all x 0 are chaotic in the sense that, shortof knowing that the logis t ic map produced them, no known mathematical tes tcould distinguish these sequences from one that is random, such as the se-quence of numbers obtained by listing, in order, the last digit of each tele-phone number in the New York telephone directory.

We want to i l lustrate the difference between dependence of Regime IVsequences on k, and their dependence on initial conditions, x 0. First we hold k

fixed, and vary the initial conditions slightly, as shown in Figure 20 for k-4.Though the two plotted orbits are generated from start ing values very closetog ethe r (they diffe r by only .0000 01), the iterated sequence s are evid entlyquite different from one another. This is suggestive of the exquisite sensitivityto initial conditions that characterizes chaos.

Next we hold the initial conditions fixed and vary k, as shown in Figure21 for jc 0=0.3, and k=k crit and k-4. No tice the wa y the orbit for k=k cri( confinesi tself to bands (between what are called 'constraints ' ) . These bands widen as k

increases above kcrjl

through Regime IV unti l orbits for k-4 (and almost all x0

)cover the entire unit interval. The bifurcation diagram (Figure 17) gives anoverview of banding in Regime IV, and we will pause presently to ask whatthese bands are. For most k in Regime IV, attractors for orbits of k are ex-traordinari ly complex. Banding discloses one aspect of these at tractors , how-ever: they are constrained as i l lustrated in the bifurcation diagram, and—as wehave seen for other convergence issues—the constraints depend only on k.

Regime IV, which begins when k=k crit, is cal led the 'chao tic ' Reg ime.The term 'chaotic ' may be misleading, since it suggests that orbits for all k in

Regime IV are chaotic. This is very far from being the case. In fact, while it-




| • k =3 84. in it ia l x=0 31 • k= 3.846. in it ia l x= 0.3

0 10 20 30 40 50 60 70 80

Figure 22: Regime IV (k crit <,k< 4)


0 10 20 30 40 50 60 70 80

Figure 23: Regime IV (k crU <k< 4)


erated sequences appear to fluctuate entirely at random for most values of £ inthis Regime, and the limit cycles of attracting periodic points so obvious in thebifurcation cascade of Regime III appear to be absent, there are actually sub-regions in which the bifurcation structure of multiple attracting periodic pointsfound in Regime III recurs .

For example, a t £=3.82843, s table oscil la t ion among at tracting periodicpoints of period 3 occurs for almost all x 0. A s k increases slightly, the 3-foldstructure bifurcates, with each periodic point giving birth to two attracting

periodic points , and producing a 6-fold l imit s tructure at £=3.8416. This inturn spli ts into twelve-fold, twenty-four-fold, and forty-eight-fold s tructureswith ftirther slight increases of k. Feigenbaum's constant again describes therat io of adjacent bifurcation s izes as they become smaller. The process contin-ues indefinitely through a cascade of bifurcations, culminating at £=3.84945with ch aotic orb its, much as the cascad e of Regim e III culminated at k crit.

Figure 22 and Figure 23 illustrate 3-fold and 6-fold limit cycles for values of £that l ie between these bifurcations.

Other bifurcation cascades are visible. In Figure 24 it is possible to dis-

cern indications of smaller cascades beginning from limit cycles of period 18,15, and 9. Each of these bifurcations is characterized by Feigenbaum's con-stant, and culminates in a value of k for which the logistic map is chaotic.

The main difference between the cascade of Regime III and those of Re-gime IV is that the logistic map has infinitely many repelling periodic pointsthroughout the cascades of the chaotic regime, while only finitely many inRe gim e III. W e can state the result in technical languag e using Sa rko vsk ii 'sfamous theorem.

Sup pose that the natural numb ers are ordered in the follow ing way (usingthe symbol > to mean 'precedes ' ) :

3 > 5 > 7 > 9 > . . . > 2 - 3 > 2 - 5 > . . . > 2 2 - 3 > 2 2 - 5 > . . . > 2 3 - 3 > 2 3 - 5 > . . . > 2 3 > 2 2 > 2 > l

Sarkovskii 's theorem states that a continuous map with periodic points of pe-riod m will also have periodic points of period n for all n such that m>n. Whenthe logistic map has periodic points of period 3, therefore—whether attractingor repell ing makes no difference—it has periodic points of every period. Theonly way to have finitely many periodic points is for all periods to be powers

of two, which is the situation in Regime III.




0.75 -

0.50 -

• * +

0 0 0

3.828 r 3.836 3.844 3.852 3.860

3.849 3.851 3.853 3.855 3.857Figure 24: Bi furcat ion Diagram: Cascades in the Fractal Chaot ic Regime

Plot of the limit points o f orbits of the logistic map for k between 3.828 and 3.860,

indicating the location of narrower 9-fold, 15-fold, and 18-fold bifurcation windows.

The rectangle in the top diagram is blown up in the lower diagram. When inverted, this diagram

is almost identical to the bifurcation diagram for Regime IV (see Figure 25).

The bifurcation cascades visible in Regime IV constitute only the tip ofthe structural iceberg. It is known that the set of k for which the logistic map

has stable orbits with periodic attractors—we shall call this the set of periodic

k—is open and dense in Regime IV. That is , this set is a (possibly infinite)union of open intervals, and its closure (the set plus its limit points) is thewhole of Regime IV. For these values of k, the logistic map does not producechaotic behavior even though i t may have infini tely many repell ing periodicpoints and its orbits may be so complex that there is no way visually to distin-guish them from chaotic orbits . Regime IV is mad e up of infinitely ma ny bifur-

cation cascades. Some bifurcation cascades develop in relat ively wide win-dows of k y such as the one beginning with 3 periodic points illustrated in



66 WESLEY J. WILDMA N A N D ROBERT JOHN RUSSELL

Figure 24, but most begin and are completed in much narrower windows of k.

In fact , for each n, there are approximately (and never more than) 272n win-

dows in which the logis t ic map has s table periodic orbits of period n.

There is an extraordinari ly diff icult and technical question about therela t ive space in Regime IV taken up by periodic values of k (for which the

logis t ic map has s table periodic orbits) , and aperiodic values of k (for which i t

has no periodic behavior) . I t is known that the s ize (Lebesgue measure) of the

set of aperiodic k is greater than zero—even though there can be no interval of

such points , because any interval would contain a t leas t part of a bifurcation

cascade in which the logis t ic map exhibits periodic behavior. An apt analogy

is with irra t ional num ber s , wh ich take up a ll the ' sp ac e ' (Le besg ue m easu re)

of an interval, even though there is no interval of them, since the rational

numbers are dense. Unlike the irra t ional numbers , however, the se t of aperi-

od ic k cannot take up all of the space in Regime IV, s ince bifurcation cascades

take up most of i t . The question as to how much space the se t of aperiodic k do

consume is therefore a complex one, and i t is the object of much sophis t icated

work in mathematics a t the present t ime. The diff iculty of this question is an

indication of the complexity and amazing intr icacy of chaotic dynamical sys-

tems—even the s imples t o f them, such as the log is t ic map.

2 .12 Excursus: Banding

To unders tand banding, consider that the darker regions of vert ical s l ices of

the bifurcation diagram correspond to the values a t which orbits have the

greates t density . Orbits tend to vis i t these regions re la t ively more often than

other regions because the logis t ic map or i ts i tera tes are contracting in these

regions . That is , they map re la t ively large intervals into re la t ively small ones

there , so that a wide range of points get concentra ted into a small region. I t is

possible to deduce the shape of these bands with some degree of precis ion.

To venture into technical terr i tory, we wil l do the small amount of calcu-lus required for this deduction not merely because the calcula t ions are s imple ,

but a lso to show how a beautiful and complex aspect of the behavior of the

quadratic map can be easy to describe .

The geometric indicator of a contracting region of a graph is a horizontal

tangent (a zero derivative), which the logis t ic map has a t i ts cri t ical point , 0 .5 .

Moreover, the f la t regions of the graph of any i tera te of the logis t ic map are

directly caused by the f la t region around the cri t ical point . To see this , denote

the logis t ic map by L and note that the flat regions of its « t h i tera te occur when

(L (w )) 'M =0. The chain rule implies that

(L{n)y(x)=L'(L in- l\x)) • L\L {n2\x)) .... L'(L i2\x)) • L\L(x)) • L\x)

so we can deduce that those f la t regions wil l occur when any of the factors inthis product are zero, which in turn is when x is such that

&'\x)=0.5, L (n'2\x)=0.5, .. . , L {2\X)=0.5, L(jc )=0.5, or x=0.5.

These va lues of x are the first n-1 s teps of the preimage of the logis t ic

map ' s c r i t ica l po in t , 0 .5 . The nth

iterate has a crest or a dip that flattens out at




3.6 3.7 3.8 3.9 4.0Figure 2S: Banding in the Bifurcat ion Diagram

Plot of the first 10 iterates of the logistic map for k between k crit and 4

above a plot of the bifurcation diagram for the same range of k.

each of these points, which may number as many as 2"-l. The broadest crest or ^dip, and so the most powerful contraction, occurs when jc=0.5, and at the value |jl } " \0.5). This will be the major constraint contributed to orbits by the n th iter- jate of the logistic m ap. The second m ost pow erfu l contra cting region of the n ft

iterate occurs when jc=L ('°(0.5), at the value L { n \ & 1 }(0.5))=l}"~1 (0.5 ), but this |is also the m ajo r constraint f or the (n- l ) t h iterate. f

From this it follow s that the constraints eviden t in Reg ime IV of the bi- |furca tion diagra m trace (closely, but not precisely ) the trajecto ries of iterates |of the critical point throu gh £ -spac e. Figure 25 illustrates the first ten iterates Jof the critical point, and offers a comparison with the constraints in the bifur-cation d iag ram . The flat region of the logistic map itself (the first iterate) is the | |s trongest contr actor, and will pro duc e the highest orbit density. The resulting 1

constraint (at the top) traces close to the graph of k->Lk

(0.5)=k/4. The flat re- jj




gions of the second iterate produce lower orbit densities than those of the firstiterate, though still higher than average. The resulting constraint is at the bot-tom of the bifurcation diagram, and traces close to the graph of

k->L k (2\0.5)=kik/4)i\-k/4). The constraint running from top left to bottomright traces close to the graph of the third iterate of the critical point:£ ^ ( 3 ) ( 0 . 5 ) = £ [£ (£ / 4 ) ( l - £ / 4 ) ] [ l - £ . ( £ / 4 ) . ( l - £ / 4 ) ] . Su cc es si ve i te ra te s w ill b eresponsible for smaller increases in the average orbit density, and lighter con-straints, all of which depend only on k.

2 .13 Excursus: Chao s in Regime IV

There are many types of chaotic dynamics in Regime IV, and much work isbeing devoted to classifying and understanding the dynamics of each type.Here, we wil l m ake som e inevitably rather technical com m ents on just a fewtypes.

First, at the culmination of a bifurcation cascade, the logistic map ischaotic on a Cantor set, which is an uncountable closed set of isolated pointsof measure zero. The construction of a different Cantor set is described in thediscussion of Regime V (see Figure 26). The dynamics of the logistic map atthe culmination of bifurcation cascades is described as follows. Denote the

Cantor set at kcrit

by C. Then C=PUQUR , where P, Q , and R are disjoint and:

/^ {r ep el l in g per iodic points of per iod 2" for some n}£>={preimage of periodic points of period 2" for some n)

/?={closure of the forward orbit of the critical point, 0.5}

The set P is infinite and dense in the Cantor set, C, and its orbits are periodic.P and Q together consti tute the fini te convergence set for k crit. The set Q iscountably infinite in size, and orbits of points within Q are eventually periodic,

for they are forced sooner or later into P, where they settle permanently intosome unstable l imit cycle. All other orbits—there are uncountably many ofthem—are pushed away from the dense repell ing periodic points in P, andtoward the attractor for the logistic map at k cril (the set R). This is an un-countably infinite set, dense in C, called the Feigenbaum attractor, which canbe constructed by closing (i.e. adding in the limit points of) the forward orbitof the critical point, 0.5. The logistic map is chaotic on C with this most pecu-liar attractor, the Feigenbaum attractor. This is a good example of the fact thatat tractors do not necessari ly—and in the case of chaotic orbits do not—consis tonly of f ini tely many at tracting fixed and periodic points . The dynamics of thelogistic map are more or less the same for the other values of k at which a bi-furcation cascade culminates—called Feigenbaum-like values .

The Feigenbaum-l ike va lues of k are countable, and so have measurezero in the set of aperiodic k, which has positive measure. Thus, there is a lotmore chaos in Regime IV besides that occurring at the culmination of bifurca-tion cascades, even though the set of periodic k is dense in Regime IV. A sec-ond type of chaotic dynamics occurs when k is in a countable set of so-called

Misiurewicz points, for which orbits of the critical point land on one of the




repelling periodic points. In this case, the logistic map is chaotic not on aCantor set, but on an interval. To be precise, it is chaotic for almost all x in theinterval or union of intervals that is the closure of the set of periodic points. A

Misiurewicz point occurs at k=4, for example, because the critical point is it-erated to the fixed point at 0. This confirms what we know otherwise, namely,that chaos occurs over the entire unit interval for k= 4.

The Misiurewicz points and the Feigenbaum-like points mark out ex-tremes in relation to which the many other kinds of chaotic dynamics of thelogis t ic map in Regime IV are something l ike middle cases . These middlecases make up all of the non-zero measure of the set of aperiodic k.

2.14 Regime V: More Chaos (k > 4)

Chaotic orbits on a Cantor subset of the unit interval.

Reg im e V is part icularly co m plex, and can only be described in so me -what technical terms. We have seen that sequences generated by iterating thelogistic map rapidly explode to infinity if x 0 is not within the unit interval. Ifthe tuning constant , k y is increased above 4, then the feedback situation thathas characterized the logistic map for 0<k<4 breaks down for at least some x 0.

For example, the logis t ic equation maps j t 0=0.5 into £/4, which is greater than

1 for £>4. When k is greater than 4, therefore, the logistic equation will map anopen interval around 0.5—and the preimage of this open interval—outside theunit interval, and the possibility of convergent, periodic, or chaotic orbits nolonger exists. The size of this interval, Ih will depend on k.

The first question about all this is, for a given A, whether the open inter-val I k and its preimage exhaust the unit interval. It turns out that a specialclosed set of isolated points—a Cantor set, denoted A k—remains a f t e r I k andits preimage is removed from [0,1]. The set A k changes shape as k increasesabove 4 , because Ik grows larger as k does, but A k is always a Cantor set.

To see the way A* is form ed from the pre im age of Ih suppose k is givenand denote I k as A1. Then denote by A2 the set of points mapped by the logis-tic equation into the open interval, A1. A2 is a pair of open intervals symmetricin that part of the unit interval left after AI has been rem ov ed. Th en den ote byA3 the points mapped into A2. This is a set of four open intervals in the fourparts of the unit interval left after the removal of A \ and A2. Continue thisprocess, so that A[n ] is a set of 2"~ ] open intervals lying within each of the 2"'

parts of the unit interval left after A\,A2,A3,...,A[n-\] have been removed. Inthis way, all of the space (Lebesgue measure) of the unit interval is eventuallyremoved, and A k, an uncountably large set of measure zero, remains. A k is aperfect set of isolated points, because it contains all of its limit points. It is alsoa fractal, since any part of it is approximately a scaled-down version of thewhole. Figure 26 illustrates its construction.

The second question is about the behavior of the logistic map on the setA k. The answer is that the logistic map is chaotic on A k for all k>4. There areno bifurcation cascades in this Regime, as in Regime III and Regime IV. Thisis because the flat part of the graph of the logistic equation is the geometric

feature necessary for any stable behavior, including stable limit cycles of peri-



7 0

Formation of the set A k for £=4.1, using the cobweb method.

odic points, but all points heading into the flat region of the logistic equationare eventually mapped outs ide of [0,1] when £>4.

Chaos in Regime V cannot be illustrated with a computer, because com-puting devices are not precise enough either for specification of an initial valuein A h or for avoiding rounding errors in calculation. Either limitation causesiterations to be pushed out of the unit interval, and sends the iterated sequence

accelerat ing toward infini ty.The re is an interesting com parison to be mad e between chaos on A* for

£>4, and chaos for Feigenbaum-like values of k y such as k crm both of whichoccur on a Cantor set. Orbits of the logistic map for £>4 have no attractorsmaller than all of A*; all orbits in K k range throughout A*. Orbits of the logis-t ic map for k=k crih by contrast, do have an attractor; at k cril it is the Feigenbaumattractor, a strict subset of the Cantor set. Moreover, the logistic map is neverchaotic (whether on an interval, a Cantor set, or something else) for an interval

of values of k in Regime IV, whereas in Regime V chaos occurs for all k>4,even though only on a Cantor set.

Early in the investigation of chaos, it was discovered that the constantbreaking up of chaotic dynamics by other sorts of dynamics is a quirk of theone-dimensional case. In higher dimensions (even in the complex plane, infact) chaos frequently occurs in entire regions and for intervals of ' tuning'constants. The virtue of chaos in higher dimensions is that it is more conduciveto research using mathematical modeling and computers , because perturba-tions of the chaotic map tend to have the same chaotic dynamics. Attractors

could never be found for chaos in natural systems modeled with one-




dimensional maps, because perturbations of these maps in computer s imula-tions or in the specification of initial conditions totally alter the dynamics ofthe model. In higher dimensional systems, however, chaotic dynamics fre-

quently vary continuously, and perturbations of these sorts do not upset dy-namics .

Chaotic orbits are no more predictable because of this, of course, butmodeling and the identification of attractors underlying chaotic orbits aremade possible . For example, an at tractor could not have been found for thedripping faucet if t ime-series data had been analyzed only one-dimensionally.The at tractor for a higher dimensional model, however, agreed tolerably wellwith that suggested by apparently chaotic orbits of the natural system. The

stability of chaos in higher dimensional systems is the key to this type ofanalysis .

2 .15 Excursus: Chaos

What, precisely, is chaos? We began with a phenomenological definit ion thatlikened chaos to randomness by means of the unpredictability of chaotic or-bits. This is problematic, however, for reasons that we shall discuss in the nextsection. It also fails to come to grips with some of the most important charac-

teristics of chaos. Geometrically speaking, the key to chaos in mathematics isthe s tretch-and-fold character of certain maps. They expand rather than con-tract most of their domain (stretch), and then map the stretched parts back intotheir domain (fold), ready for more stretching and folding. But this is very farfrom being a precise definition of chaos, so the question remains: how shouldchaos be characterized?

There are many definit ions of chaos, some stronger than others . The mostcommonly used characterization refers to the rate at which a typical set of

nearby orbits of a map diverge from one another: for maps with chaotic dy-namics, this divergence is exponential—that is , similar to e an as n—>co for somea>0. In the case of the logistic map, because the difference between chaoticorbits never ex cee ds 1, this exp onen tial condition m ust be interpreted in termsof the rate at which the difference between two orbits becomes statisticallyindistinguishable from the two orbits themselves (see the discussion of Figure27, be low).

Exponential deviation of orbits is not, however, a sufficient condition forchaos. The exponential map itself, for instance, amplifies orbit errors by a

factor of e, and so has this characteristic, even though it is not chaotic. Otherproperties must also be important, and are essential in designing a definition ofchaos that includes of all chaotic dynamical systems of interest. To appreciatewhat these properties might be, recall that the attractors of chaotic orbits haveconstraints and that they occur (roughly speaking) where repell ing periodicpoints do not . Thus, there is something organized about chaotic orbits. But theapparent randomness of chaotic orbits also suggests a kind of disorderly char-acter, too. And the way nearby orbits diverge suggests a kind of steady, sys-tematic breakdown of all topological features of a set under iteration of a



72 WESLEY J . WILDMAN AND ROBERT JOHN RUSSELL

chaotic map, in much the same way as increasing entropy in closed thermody-namic processes indicates their increasing disorder.

There is as yet no generally accepted definition covering all instances of

what mathematicians would l ike to call chaos. However, for the discrete caseof i terated m aps, the three characteris t ics just m entioned — orderl iness , disor-derl iness , and topological entropy—correspond to three propert ies that arejoin tly suff icien t to characterize chaos. These propert ies— m ixing, density ofperiod ic points , and sensit ivi ty— are defined as follows. A functio n, / is cha-otic on a set, 5, if it exhibits:

1. Mixing , a property characterizing the disorderliness of the dynamicalsystem . W e say that the fun ction /m i x e s S by analogy with the way apinch of spices will be spread throughout a lump of dough if thestretch-and-fold operation of kneading is executed properly.

Technically, i f U and V are open subsets of S, then / ev en tu a l l y it er -ates some points from U into V. For maps on compact intervals, such asthe logis t ic m ap on [0,1], this is equivalent to there being an orbit o f /that is dense in S.

2. Density of periodic points, a property characterizing the orderliness of

the dynamical system. Think of the way sour cream curdles in hot cof-fee: the cream moves in al l directions away from points throughout thecoffee cup, which are l ike densely dis tr ibuted repell ing periodic points ,in order to clump at certain other points, which are akin to points in achaotic at tractor.

Technically, each arbitrarily small open set in S contains periodicp o in ts f o r t he fu n c t i o n / o n S. Of course, all of these periodic points arerepelling, for otherwise the attractor of the orbits o f f on S would be alimit cycle of periodic points and not chaotic.

3. Sensitive dependence on initial conditions, a property characterizingthe topological entropy of the dynamical system. Think of the butterflyeffe ct , wh ich describe s the way an intricately connected system allowstiny in fluence s to have large effects .

Technically, given any point in 5, there is an arbitrarily close point inS such that/ i terates the two points arbitrari ly far apart . This is a weakercondit ion than exponential divergence of orbits , s ince i t only demands

separation by an arbitrary dis tance. The l inear map/jc)=ax for a> 1 sat-isfies this condit ion, for example, whereas this map does not meet theexponential divergence condit ion. In the case of i terated maps on com-pact sets , however, the exponential condit ion is s tronger than needed,and sensit ive dependence does the job.

This definition of chaos, with its three simple properties, captures the ex-amples of interest in the vast family of discrete (iterated) chaotic maps. How-ever, in the case of one dimensional, discrete maps on compact sets, such as

the logistic map on [0,1], these conditions are not independent. In this special




case, mixing implies density ofperiodic points, wh ich in turn implies sensitivity

to initial conditions. In higher dimensional discrete systems, however, theseimplications do not necessarily hold, and all three conditions are needed.

From all of this we learn that sensitivity, and even exponential diver-gence, do not by themselves indicate chaos. In the discrete case, it is onlywhen the properties of mixing and dense periodic points give rise to sensitivitythat the kind of unpredictability associated with chaos appears. More vaguelyand generally, chaos requires the simultaneous presence of a measure of or-ganization, disorganization, and topological entropy. This is achieved by manym aps that s tretch and fold their dom ains in a feedbac k mechan ism.

2.16 Excursus: Unpredictability

The behavior of chaotic systems is in some sense both predictable and unpre-dictable. With regard to predictability, for example, pick k-4, so that the lo-gistic map is chaotic. Then pick any number, x 0l so that the resulting iteratedsequence is chaotic—that is , x 0 is in the infinite convergence set for k-4 (IC 4).

What are the succeeding numbers in the sequence, the numbers to which thelogis t ic map bounces after jc 0? Well, that 's easy; just calculate: j c , = 4 x o ( 1 - x 0 ) .

Then calculate x 2 and x 3 and all the rest in the same way. In this sense, the be-

havior of chaotic sequences is completely predictable.But how should the unpredictability of chaotic dynamical systems be

characterized? Consider that neither k nor * 0 can be specified precisely in al-most all instances. Indeed, in general, a number can be expressed preciselyonly if it has a finite decimal representation, and such numbers take up no'space ' (Lebesgue measure). Even if jc and k could be specified precisely, sothat x n would have a finite decimal representation for every n, the number ofdecimal places in x n would increase exponentially with iteration. This infor-mation cannot be stored or calculated with in practice without some kind of

rounding errors being introduced.Such errors are not important in Regimes I-III of the logistic map, and in

most bifurcation windows of Regime IV. To see this, consider two iteratedsequences, beginning from * 0 and y 0. If y 0 is a close approximation to x 0, thesequence iterated from y 0 will eventually bounce between the same ' limits 'that the sequence beginning from jc does, albeit perhaps in a different order—and if y 0 is sufficiently close to jc, the iterated sequence will hit a limit cycle in

phase with the sequence generated from x 0.

At the chaotic values of k such as k=4, however, details are everything.Every last decimal place of information is important as the iterations continue.If>> 0 approximates x 0 to 6 decimal places, we might achieve tolerable accuracyfor a certain number of iterations, but the sequence generated from y 0 will bearno relat ion to the sequence generated from x 0 beyond that point. Figure 27illustrates this by plotting the first 50 values of the sequences generated fromjc 0=0.3 and j> 0=0.300001, together with the difference between the two se-quences. After 18 i terat ions, the sequence representing the difference betweenthe orbits is qualitatively indistinguishable from either of the sequences them-

selves, showing that all information about initial states has been lost.




0 .8

- k=4 . in i t ia l x=0 .300001

D i f fe re n c e b e tw e e n th e s e q u e n c e s ]

1 . 0

• k=4, mjtiai x=o_3] In sum , th ere is no w ay to predic t

the value of successive iterations for achaotic value of k except actually tocalculate them, and this depends on ourhaving complete knowledge of the ini-tial conditions. Thus, the chaotic behav-ior of the logistic map is unpredictablein the sense that the map's sensitivity atchaotic values of k, and the impossibilityof infinitely precise specification ofmost starting points, blocks indefinite

prediction of future iterations. We shallcall this eventual unpredictability.

It is vital to know that 'eventual 'unpredictabil i ty entai ls ' temporary 'predictability. In fact, because the cha-otic orbits of the logistic map (for k-4)

are generated by an equation, it is evenpossible to deduce the number of itera-tions before predictions will fail to

match the orbit, as a function of theprecision of initial conditions. To seethis, note that it can be shown that theamplification of small errors proceeds atthe rate of roughly a factor of two foreach iteration of the logistic map. Now,in Figure 27 the difference between thetwo orbits is 0.000001. If the error dou-bles with every iteration, a simple calcu-lation shows that it should surpass 0.5after 19 iterations. From our computersimulation, we can see that there is infact an error of about 0.4 after 19 itera-tions, and about 0.9 after 20 iterations,

confirming the error estimate. This error estimate implies that, if the predictionwere to be accurate (within a small positive number, e) after n iterations, thenthe error in specification of initial conditions would have to be less than s2"n—

and the computing machine would have to be capable of the correspondingorder of precis ion (roughly n+\log 2z\ bits) to avoid increasing the error.

It is the predictability in principle afforded by the equation for the logis-t ic map that makes possible temporary predictability, the conco mm itant ofeventual unpredictability. These correlated features of chaotic maps al low usto say that chaotic randomness, even with its eventual unpredictability, is nev-ertheless predictable in principle, and temporarily (though not indefinitely)predictable in practice. This form of predictability in practice is weak, to besure, but it is important to know that eventual unpredictability entails it .

0 .2

Figure 27: Eventual Unpredictabi l i ty

Two iterated sequences and the

difference between them (k=4)




3 Reflections on Random ness, Determinism, and Chao s in Nature

There are many questions affected by chaos theory, including those concern-

ing complex systems, evolutionary novelty, and reductionism in scientificmethod. We will refrain from extending our reflections into these areas, how-ever. Our aim in this section is the limited one of connecting the mathematicaldiscussion of chaos to both the phenomenological characteristics of chaos (theway chaos seems to us), and to philosophical questions surrounding meta-physical determinism. To that end we wil l make some more abstract remarkson the themes of randomness, determinism, and chaos in nature.

By way of indicating the direction of the argument, we shall first givechaotic randomness a precise definition in terms of eventual unpredictability,

drawing on the discussion in the previous section. We shall then show thatchaotic randomness so understood is a tertium quid; it is mathematically dis-t inguishable from both s tr ict randomness and the complete absence of ran-domness. Finally, by means of a discussion of chaos in nature, we shall arguethat chaotic randomness s trengthens the case for metaphysical determinismwhile s imultaneously introducing a fundamental l imitat ion on how completethis case can be made. The concluding section of this paper draws out thetheological implications of this result.

3.1 Randomness and Determinism

It is often said that chaotic orbits look random , but the meaning of randomnessis murky given chaos. In common usage, to declare that a sequence of num-bers is random means either that it has no discernible pattern, or that it is un-predictable. As we have seen, however, chaotic orbits are often quite struc-tured, with banding constraints and a close relationship to repelling periodicpoints. Calling chaotic orbits random in the sense of having no discernible

pattern thus seems inappropriate. If there is to be a connection with intuitiveideas of randomness, therefore, it will be through the idea of unpredictability.

At this level, we are jus tified in saying that ch aotic orbits are random inthe limited sense of eventual unpredictability. However, randomness usuallymeans not eventual unpredictabil i ty but total unpredictability—the absence ofany equation for a sequence that consistently permits, given one number, evenan approximate calculation of the next. We call this kind of randomness strict

rando mn ess. If chaotic rando m ness means 'eve ntual un predictabil i ty,' thenstrict randomness means ' total unpredictability. ' Chaotic orbits of the logisticmap are not random in the strict sense since, obviously, they are produced byan equation (namely, the logistic equation). On the other hand, the sequencerecording the count of each kind of item on the shelves of an indoor market ata part icular moment, arranged alphabetically, is random in the strict sense.

These examples of randomness would make sense mathematicallywhether or not Laplace was correct that the natural world was a mechanistic,unfree, unbroken web of causal connections, and so entirely predictable to thegreat divine mathematician whose calculations are not limited by practical

considerations. Some other uses of ' randomness, ' however, seem to presup-



76 WE S L E Y J . WIL DMAN AND RO B E RT JO H N RUS S E L L

pose that Laplacian determinism is false. For example, consider radioactivedecay. The average number of alpha part icles emitted by a uranium sample ispredictable; i t decreases exponential ly with t ime. The exact number of alpha

decays each second, however, is random. Randomness here always means atleast that no known equation determines this exact number, but i t sometimescarries addit ional suggestions of metaphysical indeterminism. The connectionto metaphysics is hazardous, however, because i t depends upon choosing be-tween confl ict ing interpretat ions of quantum physics—and both determinis t icinterpretations (such as non-local hidden variables) and indeterministic inter-pretat ions are presently defended.

Other examples of the word ' randomness ' being used so as to presupposemetaphysical indeterminism follow the same pattern: speaking of randomness

in mathem atics does not by itself presuppose metaphysical indeterminism; in-stead it must be linked to metaphysics by an additional layer of interpretation.Thus, we must f ind a definit ion of randomness in terms of unpredictabil i tyalone, considering i t neutral toward metaphysical questions about determin-ism.

W ith this , then, w e are just if ied in speaking of two m etaphysically neu-tral kinds of randomness (chaotic and strict) defined in terms of two varietiesof unpredictability (eventual and total), and correlated with several types of

predictabil i ty. Chaotic randomness is neither absence of randomness norsrict randomness but a tertium quid1 This is one way in which the phenome-non of chaos in mathematics is remarkable. Whereas it might on ce have been

supposed that predictability and unpredictability were directly opposed, chaos

theory opens u p a nether-world in which this supposedly sharp distinction is

blurred to the extent that a particular kind of unpredictability (eventual) oc-

curs in the context of predictability-in-principle and even what we have called

temporary predictability-in-practice. We are thus justified in speaking of a

more or less unforeseen albeit weak type of random ness, nam ely chaotic ran-

domness.These types of randomness exis t in mathematics and apparently also in

nature, and they have been defined in metaphysically neutral fashion with re-spect to the question of determinism, so we may consider this central meta-physical question separately. Thus, we are led to the following table, notingtha t 'de terminism' means Laplac ian de terminism, and many opposed viewsare col lec ted under ' indeterminism. '

t y p e s o f t y p e s o f t yp es o f p red ic tab i l i t y m e t a p h y s i c a lr a n d o m n e s s unpred ic tab i l i t y in-pr inc ip le in -p rac t i ce s c e n a r i o s

n o n e n o n e y es y es Is determin ism or

c h a o t i c e v e n t u a l y e s t e m p o r a r y indetermin ism

st r ic t to ta l no no the best hypo thes is?

Types of mathematical randomness can be defined precisely in terms of

type? of unpredictability and correlated with types of predictability.

However, there are no direct logical connections between the these

types of randomness and the thesis of metaphysical determinism.



CHAOS: A MATH EMATICAL INTRODUCTION 7 7

Now we may pose the basic metaphysical question: which metaphysicalscenar io— determinism or indeterminism — offers the bes t explanation of thefact that no n-ran dom ness and two kinds of random ness appear in m athem atics

and apparently also in nature? Even with the distinctions introduced up untilnow, this question is poorly framed, because it begs the question of the rela-t ion between chaos in mathematics and chaos in nature. This question must beanswered before it is possible to raise the deeper question of the relation be-tween chaos and an ult imate account of nature such as metaphysical determin-ism.

For example, i t is superficial ly possible to say—indeed, some writers ap-pear to have said—that, s ince the mathematical equations for chaotic systemsare determinis t ic , nature must be metaphysically determinis t ic if chaos actually

occurs in nature. This, however, is to mistake a metaphorical use of'dete rm inis t ic ' in mathem atics for a l iteral one; the precis ion of a m athem aticalequation does not imply that the use of an equation in a modeling physicalsystems only makes sense if nature is metaphysically determined. Thus, wemust consider questions surrounding chaos in nature in order to press themetaphysical question any further.

Idealizing natural systems when using mathematics to model them hasproved to be an extremely useful s trategy for centuries , sponsoring profound

understandings of nature. When the aim is to match natural and mathematicaldynamical systems in detai l , however, the complexity of nature and the ex-quis i te sensit ivi ty of chaos profoundly complicate modeling, and an entirelynew range of questions appears . One group of these questions concerns themeaning of such modeling: What is the s tatus of mathematical models as ex-planations of nature 's dynamics? Does chaos actually occur in nature at e i therthe macro- or quantum levels? Another group of questions surrounds the diffi-

culties of using mathematical dynamical systems to model natural dynamicalsystems, such as specifying initial conditions for natural systems with great

precis ion, and keeping exquisi tely sensit ive mathematical dynamical systemsin s tep with enormously complex natural systems over t ime. We will considerthese two groups of questions in what follows, and then reopen the issue ofchaos and metaphysics , hopefully better prepared to address i t .

3 .2 Chaos in Nature: The Meaning of Modeling

Model ing na ture wi th mathemat ics a lways involves making s impl i fy ing as -

sumptions. In a good model, these s implifying assumptions render the modelmathematically manageable, while s t i l l useful for predict ing the behavior ofthe natural system in question. When a model proves serviceable in this way,the hope is that it i llumines not just the future behavior of the system but alsothe reasons why the natural system works the way i t does. To understand thecomplexit ies surrounding the s tatus of chaotic models as explanations, a s im-pler example wil l be useful .

When we use Newtonian mechanics to model the causal relat ionshipbetween gravity and fal l ing objects the mathematics of the model is s implest

wh en w e ignore al l a tm osph eric effe cts and the gravitational effe cts of ev ery-



78 WE S L E Y J. WIL DM AN AN D RO B E RT JOH N RUS S E L L

thing except the earth. The model yields accurate predictions in spite of theseapproximations because we stay with billiard and cannon balls rather thanfeathers and polystyrene packaging, thus minimizing the impact of the atmos-

phere. The model also produces a powerful explanation. It supports an hy-pothesis about what is in nature (forces and massive objects), says somethingabout how these constituents operate (with an equation for gravitational force),and links the theory to observations with fair precision. When the problem ismodeling complex natural dynamical systems, however, the form of explana-tion is quite different.

Consider the moth colony population case, for example. No at tempt ismade to model this system with forces and objects; the model would be ab-surdly complex and utterly unenlightening. A description in the form of a sta-

tistical catalogue of moth biographies seems to be the only option: so manymoths were born this generation, a percentage of these died from disease, apercentage starved, a percentage reproduced with an average of such and suchoffspring, and so on.

While such a description is interesting, and enables computer simula-tions, it leaves the apparent patterns of population in successive generations(decline to extinction, growth to equilibrium, stable oscillation, apparentlyrandom fluctuation) something of a mystery. When it is recalled that such

patterns are characteristics of the system as a whole and not of individualmoths, however, i t makes sense to use as a model a mathematical dynamicalsystem that ignores details of moth life and only attends to system-wide prop-erties such as the total population, and generationally invariant environmentalconditions. We saw that the logistic map suggests itself as a serviceable modelat this overarching system level, and that the model exhibits patterns of popu-lation change (extinction, equilibrium, oscillation, random fluctuation) similarto those of the moth system. But in what sense does the mathematical dynami-cal system explain the natural dynamical system?

The form of explanation appears to be similar to that of statistical me-chanical models for well-behaved gases. System properties such as pressure,volume, and temperature follow statistically precise laws that can be deducedby averaging the behavior of the numerous components of the system. Pres-sure, for instance, is the same throughout the system: higher pressure in oneplace is quickly diffused on average, rather than being intensified, so it can bespoken of as a reliable system characteristic. Thus, statistical mechanics sup-ports the amazingly simple and eminently testable hypotheses that pressure isproport ional to temperature and inversely proport ional to volume (PocT/V).

The use of the logistic map to model moth colonies is more complex thanstatistical models of gases, both because the interaction of system componentsis far more complex in the moth case than in the gas case, and because system-wide features of moth colonies are more difficult to quantify than pressure,temperature and volume. Nevertheless , the same form of explanation seems tobe at work: the moths with their different biographies are assumed to havebeh avior that av erag es out in large collectives so as to ju stif y speak ing aboutreliable system variables—in this case, population. Then changes in population

can sensibly be thought to be modeled by the logistic equation, even as PccT/V



CHAOS: A MATHEMA TICAL INTRODUCTION 7 9

for most gases. The same form of explanation applies to other instances inwhich mathematical dynamical systems are used to model natural dynamicalsystems; the bibliography lists several examples.

There is another respect in which applying the logistic map to a mothcolony is more complex than applying s tat is t ical mechanics to a well-behavedgas, and this consideration affects the validity of explanations advanced on thebasis of the model. In the chaotic regime of the logistic map, the premise forthe s tat is t ical form of explanation—namely, that behavior of system compo-nents averages out to make rel iable system variables—breaks down because ofthe exquisi te sensit ivi ty of the mathematical model. Quite apart from the prac-t ical problems surrounding whether the natural system can be modeled, there-fore, there is a very serious reason to think that chaos in an otherwise useful

mathematical model does not explain very much about the natural system itmodels. It may well explain after the fashion of statistical mechanics when themodel accurately predicts fairly straightforward behavior, such as equilibriumand simple periodicity, but the logic of this kind of explanation does not ex-tend without further ado to chaotic or highly complicated periodic behavior.

We are driven by this argument directly into asking an important ques-tion: does chaos occur in nature, or only in mathematics? Scientists are led towonder if a mathematical model in the form of a chaotic dynamical system

might apply to a natural system at the macro level when they notice ' regimes 'with characteristic behavior in the natural system, and especially bifurcationcascades. On many occasions such clues have led to effective modeling andprediction using chaotic dynamical systems. In what sense is this kind of suc-cessful modeling evidence for chaos in nature?

On the one hand, testing such models in detail is impossible unless thesystem exhibits equilibriated or simple periodic behavior. Add to this thebreakdown of the logic of the statistical form of explanation when the model isdisplaying exquisi te sensit ivi ty, and we have s trong arguments that models

based on chaotic dynamical systems have l imited usefulness and questionableexplanatory power at precisely those times when we would most like to relyon them, namely, when we are trying to model apparent randomness in naturalprocesses using mathematical chaos.

On the other hand, the fact that a model tracks a natural system throughseveral regimes and types of behavior suggests that the model might also applyto the apparent randomness of the same natural system. Moreover, while pre-dictive testing is not feasible in any chaotic dynamical system, indirect evi-

dence of chaos in nature can still be secured. As mentioned earlier, chaos ap-pears s tably in some higher dimensional mathematical models , in the sensethat the attractor for one orbit is nearly identical to the attractor for any slightlyperturbed orbit. Eventual unpredictability still applies, so testing predictions ofthe model is not made possible by this form of stability. However, such amodel does sometimes make possible the identif icat ion of at tractors for appar-ently chaotic orbits of the natural system. Thus, geometric or statistical con-firmation of mathematical models for chaotic dynamical systems is s t i l l a pos-sibility when direct confirmation of orbit predictions is not. This kind of con-

firmation has been used in a number of experiments, including the chaotic



8 0 WESLEY J. WILDMAN AND ROBERT JOHN RUSSELL

regime of the dripping faucet, but it remains somewhat indirect because it hasno recourse to testing orbit predictions; the model could be quite wrong indetai l , therefore, and we might never know.

In spite of the problems with the status of explanation in models based onchaotic dynamical systems, and in spite of the impossibility of testing theirorbit predict ions in detai l , there is s trong evidence—not unequivocal , to besure—for chaos in nature. Of course, the most l ikely s tate of affairs is that theglobal features ( ' tuning') of natural dynamical systems are in continual subtlemigration, so that an ordinary chaotic orbit that could be sensibly comparedwith a model 's chaotic orbit would never be encountered. Furthermore, three

kinds of behavior— chaos, sufficiently complicated p eriodicity, and what we

have called strict random ness—ca n rarely be phenom enologically distin-

guished from each other, even though they are mathem atically quite distinct

alternatives. Consequently, a natural system could move among al l three withsubtle shifts of its tuning, or under the influence of other factors unknown tous, and there would be no way for us to tell in most cases which kind of behav-ior was occurring. Indeed, this constant subtle migration, and the washing outof chaotic orbits that it entails, may be one of the factors accounting for theomnipresence of equilibrium and other forms of stability in nature, despite theubiquity of chaos in mathematics .

The question of the occurrence of chaos in nature is more difficult at thequantum level . The Schrodinger equation, for example, is l inear, and so cannotbe a chaotic map, which is one of several reasons to think that quantum chaosis impossible . This is a superficial conclusion, however, because quantumsystems are only governed indirectly by this equation. The Schrodinger equa-t ion describes the t ime-development of a mathematical function, the wavefunction, whose absolute value indicates the relat ive probabil i ty of f inding thephysical system in a specific state. The extent, if any, to which the wave func-tion refers to the physical system as such is one of several contentious issues in

the interpretation of quantum physics. To date, no single such interpretation isuniversally agreed upon. Moreover, the experimental search for evidence ofquantum chaos is only in its infancy. The basis at the quantum level for chaosin nature at the macro level remains a research challenge.

3 .3 Chaos in Nature: The Difficulty of Testing Models

We now turn to the intriguing factors complicating the modeling of naturaldynamical systems with chaotic dynamical systems from mathematics . Sup-pose that there is a chaotic dynamical system in nature, and that this systemhas high-level features whose varying moves the system from one regime toanother, changing i ts characteris t ic behavior. Suppose further that we are try-ing to assess the virtues of a mathematical model that has already proved itselfserviceable for predict ing equil ibrium and s imple periodic behavior of thesystem, by virtue of one or more tuning variables that correspond to the tuningfactors in the natural system. There are several problems facing any attempt todetermine the predict ive adequacy of this mathematical model when i t is tuned

to produce complicated periodic or chaotic behavior.




Firstly, modeling the tuning of the system with the tuning constant is dif-ficult, even when the tuning of the system can be quantified with reasonableprecision, as it can in some well-controlled laboratory experiments. This is

important because testing predictions of the model only makes sense if we aresure that the tuning of system and model match. But the model's orbits varydramatically with even a miniscule variation of its tuning constant in chaoticregimes. Of course, outside of the discrete, one dimensional case, chaos canoccur stably, but this only applies to the fundamental dynamics of the system;the eventual unpredictability of chaotic orbits still interferes with the testing ofthe model's predictions, and the tuning of the model plays into this.

Secondly, supposing (contrary to fact) that it were possible to be sure thatthe model and the natural system were identically tuned, the matching of ini-

tial conditions in system and model is similarly complicated. Practical limita-tions include heat noise and the openness of all systems to minuscule, ineradi-cable effects, even influences as extraordinarily minute as the gravitationalattraction of an electron in a neighboring galaxy. The ultimate limitation isobviously quantum uncertainty.

Thirdly, supposing (again, contrary to fact) that it were possible to matchtuning and initial conditions in both natural system and model, we would stillbe faced with the problems surrounding calculation that apply in the mathe-

matics of chaos, and have already been discussed. Moreover, because expo-nentially greater precision is needed to express successive iterations, exponen-tially greater time would be required to perform the calculations. For example,in the logistic equation, with errors increasing by a factor of 2 each iteration,calculation will eventually be slower than the evolution of the system, sincetwice as much precision in initial conditions would be required for the sameprecision in each successive iteration.

The literature on chaos theory has tended to discuss these impediments totesting chaotic models against natural systems under different terms, speaking

of algorithmic complexity, computational complexity, the continuum problem,and the butterfly effect. Algorithmic complexity means that there is typicallyno analytic solution by which the development of a mathematical chaotic sys-tem can be expressed directly in terms of initial conditions, so that the onlyway to track its development is painstakingly to calculate each step; there areno shortcuts . Computational complexity refers to the exponential ly increasingtime needed to perform calculations of chaotic orbits, so that a natural systemeventually develops faster than the predictions of the model can be calculated.The continuum problem refers to the impossibil i ty of representing most num-bers (and so most initial conditions) with the finite decimal representationsneeded to express them precisely in computing machines. The butterfly effectrefers to the practical problems flowing from sensit ive dependence of chaoticorbits on initial conditions, including the openness of natural chaotic systemsto ineradicable, miniscule eff ects of many kinds.

We have presented these customary considerations s l ightly differently soas to reflect more adequately the fact that some factors interfering with testingof chaotic models are purely mathematical, while others derive from nature.

However they are classified, these reflections establish that there are insur-



8 2 WESLEY J. WILDMAN AND ROBERT JOHN RUSSELL

mountable problems facing any at tempt to evaluate specific predict ions de-rived from the behavior of orbits in a chaotic dynamical model. When theseproblems are added to those connected with the meaning of modeling dis-

cussed earlier, we can see that modeling apparent randomness in a naturalsystem with the aid of a chaotic dynamical system from mathematics is ex-traordinari ly difficult . The epistemic and explanatory limitations at the root of

this difficulty are important considerations in weighing evidence for and

against metaphysical determinism, because they place a fundamen tal, new

limit on the extent to which it can be known that a chaotic dynam ical system in

mathem atics, with its 'deterministic' equations, provides the right explanation

for 'randomness' in a natural system.

3.4 Chaos and Metaphysical Determinism

Now we are in a more appropriate position to pose the question suggested bythe table defining types of randomness in terms of types of predictabil i ty:W hich scenario — m etaphy sical determ inism or its opp osite— offers the bestexplanation of chaos? The intervening discussion has made clear the difficul-t ies at tending the movement from chaos in nature to a metaphysically deter-ministic explanation of apparent randomness in nature, and this has an intrigu-

ing influence on the question.We can say without hesitation that chaos in nature gives no evidence of

any metaphysical openness in nature. The fact that a natural dynamical systemis open to its environment, which is sometimes described in terms of awhole/part causal relationship, does not entail metaphysical openness, for theentire environment may be causally determined. Neither does the butterflyeffect imply metaphysical openness , to at tack a l inkage dear to the popularreception of chaos theory. In fact , sensit ive dependence—a feature of chaoticdynamical systems in mathematics—is at tr ibuted to natural systems on the

basis of the power of mathematical dynamical systems to model them. To theextent that this modeling works—and we have seen that it is problematic inchaotic regime s— the natural presuppo sit ion is that the (m etaphorical)'determinism' of mathematical chaotic dynamical systems corresponds to themetaphysical determinism of nature. Put bluntly, the butterfly effect testifies tothe high degree of causal connectedness in certain natural systems, and so ismost naturally exploited in support of the thesis of metaphysical determinism.

More generally, the hypothesis of metaphysical determinism is s trength-ened by chaos theory because i t enables the apparent randomness of evensimple natural dynamical systems potential ly to be brought under the umbrellaof determinism. Instead of the theoretical instability of planetary orbits being abone in the throat of apologists for determinism, for example, it is construed asan ordinary consequence of a s imple determinis t ic system. Laplace wouldhave been delighted with chaos theory.

While chaos theory offers not one shred of evidence against metaphysicaldeterminism, it does introduce an imposing limit on how well the deterministichypothesis can be supported. This is the significance of the epistemic and ex-

planatory problems surrounding the question of the occurrence of chaos in




nature that have just been discussed. To see this, consider two opposed scenar-ios from among the many conceivable metaphysical possibil i t ies . On the onehand, it is possible that what we have called chaotic randomness never occurs

in nature, that all randomness is of the strict variety, as we defined it earlier,and that nature is metaphysically open to acts by free causal agents.

On the other hand, it may be that nature is in fact metaphysically deter-mined, and chaos omnipresent within it . If so, then only the free agency ofGod—and not human free agency, which seems ruled out by assumption—could act to change the course of nature. God might do so and have s ignificantm acros cop ic effe cts by taking advantag e of the phen om enon of sensitive de-pendence, as only an unlimited super-calculator being could. But this still begs

the question of the presumed natural determinism governing the setting of ini-tial conditions by their prior natural conditions, ad infinitum. Ultimately, then,even a super-calculator being would have to intervene in nature so determined,either by breaking or suspending its natural causal sequences. The interventionof law-suspe nding miracles w ould di ffer only in that sensitive depen dencepermits these acts of interference or suspension to be at an extremely smallscale , rendering them undetectable. Why one form of interference would bepreferable to the other from God's point of view—assuming there is somedivine choice in the matter , an assumption process metaphysicians might be

likely to reject—would then be a question for theologians.Chaos theory insists with its introduction of an epistemological limitation

that neither of these metaphysically opposed scenarios can be ruled out. It

must be said, therefore, both that the hypothesis of metaphysical determinism

has never been as well attested as it is after chaos theory, and that it cannot be

made stronger than chaos theory makes it.

Of course, there are other domains in which one might venture to test thehypothesis of metaphysical determinism. I t comes off rather badly in those

regions of inquiry that must presuppose that humans are free causal agents ,such as ethics and the various s tudies of the phenomenology of human experi-ence. But there are competing determinis t ic vis ions of human consciousness asepiphenomenal and of human societies as inculcating a mistaken habit of in-terpret ing humans as free, responsible agents . Metaphysical determinism alsoseems to come off rather badly in the quantum world, where one widely heldinterpretat ion assumes that genuine metaphysical openness grounds bothquantum uncertainty and the probabil is t ic nature of the wave function. Buthere, too, there are al ternatives , for some interpretat ions of quantum mechan-

ics suppose that the uncertainty principle shields a deeper deterministic proc-ess.

Metaphysical determinism and its opposite, it seems, are locked in battle.There can be no question that chaos theory adds its considerable weight to the

side of determinism. How ever, just as there is the epistemic limitation of self-

reference in the study of huma n existence, and the epistemic limit of the Heis-

enberg u ncertainty principle in the quantum world, chaos theory highlights an

epistemic limit in the macro-w orld of dynam ical systems, tethering the deter-

ministic hypothesis even as it advances it.




4 Conclusion: The Relevance of Chaos Theory or Theology

The development of chaos theory has been welcomed by some theologians as

powerful evidence that the universe is metaphysically open (i.e. , not com-pletely deterministic) at the macro-level. Metaphysical indeterminacy at thequantum level does not even need to be assumed, on this view, for chaos the-ory makes room for human freedom and divine acts in history that workwholly within nature's metaphysical openness and do not violate natural laws.At a number of places in this essay, this interpretation of chaos theory isshown to be without justification. It makes little sense to appeal to chaos the-ory as posit ive evidence for metaphysical indeterminism when chaos theory isitself so useful for strengthening the hypothesis of metaphysical determinism:

it provides a powerful way for determinis ts to argue that many kinds of appar-ent randomness in nature should be subsumed under determinis t ic coveringlaws.

On the other hand, we have seen that chaos theory also imposes a funda-mental limit on how well the deterministic hypothesis can be supported, thuspreserving the relevance of chaos theory for forming a philosophy of nature,and assessing the possibility of free divine and human action in accordancewith natural laws. Setting aside the mistaken enthusiasm just mentioned, the

relevance of chaos theory for theology can be assessed rather differently de-pending on one 's s tart ing point . To appreciate this difference concretely, con-sider the reaction to chaos theory of two hypothetical (and, sexes aside,probably archetypal) thinkers, one a natural scientist and the other a theologianfrom a theistic tradition, such as Christianity, with a commitment to divineaction.

Laplace thought that metaphysical determinism was the best way to ex-plain the apparently well-founded Newtonian assumption that nature is an un-broken causal web. Laplace 's determinism has been one of the assumptions

guiding scientific inquiry into nature at least since Newton's time, and ourhypothetical scientist is inclined, notwithstanding quantum mechanics, to seethe world in deterministic terms as a first approximation to her actual experi-ence. O ur scient ist 's assum ption that determ inism is the mo st adeq uate ac coun tof things will be strengthened by chaos theory, since it allows her to give ex-plici t determinis t ic accounts of many seemingly random processes . Of course,she always assumed that some enormously complex determinis t ic account ofeach apparently random dynamic process would apply, but chaos theory al-lows her to describe the deterministic behavior of some of those systems withrelat ively s imple dynamic models , thus furnishing her with evidence that manyrandom processes can actually be given determinis t ic explanations. Though wehave seen that this form of explanation is far from straightforward, it strength-ens the case for metaphysical determinism by bringing apparent randomness(of some kinds at least) into its explanatory reach.

On the other hand, our theologian is accustomed to assuming that natureis metaphysically open, since he is committed to interpreting the free actionsof God and people within history, and must assume that metaphysical deter-

minism is a flawed hypothesis if his task is to make sense. Even though he



CHAO S: A MATHEMATICAL INTRODUCTION 8 5

does not know how to speak of any specific mechanism by which God influ-ences nature, his project calls for the assumption that God acts in 'natural, 'law-like ways. For our theologian, the strengthening of the deterministic hy-

pothesis by the development of chaos theory will be bad news, so long as hethinks that what we will call (purely for convenience) the see-saw principle istrue, namely, that a stronger case for the deterministic hypothesis necessarilyimplies a weaker case for the possibility of free divine and human acts in his-tory.

Not al l theologians accept the see-saw principle , of course. ImmanuelKant 's dual argument that we are forced by our mental apparatus to under-stand nature as a determined, closed causal web, and that things in themselveshave to be assumed to be undetermined to make sense of our moral life, has

long been the standby for many theologians, radical and traditional, liberal andconservative alike. If our theologian accepts this central tenet of Kant's sys-tem—and i t can be affirmed quite independently of some of the more prob-lematic aspects of Kant 's philosophy—then the see-saw principle wil l be re-jected and chaos theory will be irrelevant: even if the case for determinismwere completely conclusive, divine and human freedom would not be im-pugned, for we cannot help seeing things in terms of a closed causal system,no matter what they are like in themselves. Moreover, Kant's is not the only

way to avoid assuming the see-saw principle . Coarsely speaking, the philoso-phy of organism ( 'process ' metaphysics) and some forms of panentheism andpantheism (including some versions of ' the world is God's body') are al terna-tive philosophies of nature that, when appropriately tweaked, provide lessclear cut, but still reasoned, ways of avoiding it .

So far, then, we have the scientist who is inclined to see chaos theory assimply specific confirmation of what she believed al l a long, and so not helpfulfor theological purposes. And we have a theologian who sees chaos theoryeither as irrelevant because of a supervening solution to the problem of divine

action, or as bad news, for the same reason that it would have been good newsfor Laplace: it strengthens the case for the hypothesis of metaphysical deter-minism. This goes part of the way to account for the negative reactions to theattempt to bring chaos theory and the problem of divine action into conversa-tion: both scientists and theologians have legitimate reasons to think of it asirrelevant or as bad news for the theological attempt to justify the traditionalassertion that God acts freely in accordance with natural laws.

As we have seen, however, there is another level at which chaos theory is

good news for this theological project and perhaps bad news for polemicaldeterminis ts . We will conclude this essay by summarizing what has been saidabout how this can be so.

Consider a natural system that exhibits apparently random behavior un-der certain conditions. Could this system be described with relatively simpledynamics, so that i ts apparent randomness would be only the expected behav-ior of that simple dynamical system in its chaotic regimes? Trying to answerthis question is fraught with difficult ies , as we have shown, but suppose thatwe came up with a decent hypothesis, and set about testing it . If the model

were any good at all , (1) it would be fairly easy to show that it predicted sys-



86 WESLEY J. WILDM AN AN D ROBERT JOHN RUSSELL

tem behavior in non-chaotic regimes; and (2) if we were lucky, we could evenfind an attractor for some chaotic regimes of the natural system, as has beendone for the dripping faucet. But (1) it is impossible to show that the model's

predictions are accurate when the system is in a chaotic state; and (2) the basisof the statistical form of explanation needed to interpret the model breaksdown when the dynamics are chaotic . Though the model might predict systembehavior perfectly in s i tuations of equil ibrium or relat ively s imple periodici ty,therefore, it is impossible to be sure that another, unknown model of the dy-namical system (say, one that involves God as a causal factor) does not finallyprovide a better description of the system's behavior. Thus, there is a limit tohow well the hypothesis of metaphysical determinism can be supported.

Again, it is important not to misinterpret this result, as some enthusiasts

have done. We are not here speaking of chaos theory warranting the assert ionof any degree of metaphysical openness in nature. Nor is the obvious resultthat chaos theory s trengthens the case for determinism being called into ques-t ion. The point is just that chaos theory discloses a limitation in how compel-l ing the case for determinism can be made, a l imitat ion unnoticed before chaostheory drew attention to it . For some theologians (those who assume the see-saw principle), this is a kind of limited good news. Chaos theory might havemade the case for metaphysical determinism stronger than i t has ever been

before, but chaos theory also guarantees that the case cannot get any s tronger.The small degree of ambiguity in the analysis of dynamical systems is, there-fore, irreducible. Perhaps that is not much to get excited about, especiallysince so much theological work seems to rely on a usually anonymous Kantiancompatibilism (the strategic denial of what we have been calling the see-sawprinciple), making any result of chaos theory irrelevant to the problem of di-vine action. But it does open a window of hope for speaking intelligibly aboutspecial , natural-law-conforming divine acts , and i t is a window that seems tobe impossible in principle to close.

5 A Bibliographical Note

Most of the mathematics in this discussion of the logistic map appears in manyother places. Rather than arbitrarily citing sources, therefore, a list of selectedworks organized according to key themes seems more appropriate . We wouldlike to acknowledge the help we received in conversations with Bob Devaneyand Karl Young, who saved us from several errors . We, of course, and notthey, are responsible for any that remain.

4.1 Text Books

A number of books give detai led coverage to chaos and i terated maps on theunit interval . Major examples , from quite different perspectives , are:[1] Ralph H. A brah am ; Ch ris topher D. Shaw . Dynamics: The Geometry of

Behavior. 2nd ed. Redwood City, California: Addison-Wesley, 1992. A

unusual and fascinating visually oriented introduction to dynamical




systems and chaos.

[2] Pierre Co llet; Jean-P ierre Eckm ann. Iterated Maps on the Interval as

Dynamical Systems. Boston, Basel, Stuttgart: Birkhauser, 1980. A de-

tailed discussion of most of the interesting characteristics of iteratedmaps on the interval, focusing on kneading theory, renormalization, andthe classification of one dimensional maps. Includes a lengthy discus-sion in Part I of the motivation for and interpretation of the mathemati-cal details of the difficult remainder of the book.

[3] Robert L. Devan ey. An Introduction to Chaotic D ynamical Systems. 2nded. Redwood City, California: Addison-Wesley, 1989. A well organizedintroduction to the mathematics of chaos, accessible to college graduatesin mathematics. Includes proofs of all results, and an emphasis on the

logistic map in the examination of one-dimensional dynamics in Part I.[4] John Gu cken heim er; Phil ip Holmes. Non-linear Oscillations, Dynamic

Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag,1983. A standard reference for chaos in continuous systems.

[5] Steph en H. Kellert. In the Wake of Chao s: Unpredictable Order in Dy-

namical Systems. Science and Its Conceptual Problems Series, David L.Hull, Gen. Ed. Chicago: University of Chicago, 1993.

[6] F. C. M oon . Chaotic Vibrations: An Introduction for Applied Scientists

and Engineers. New York: John Wiley & Sons, 1987. A introductorytextbook for the audience named in the title.[7] Heinz -Otto Peitgen; Hartm ut Jurgens; Dietmar Saupe. Chaos and Frac-

tals: New Frontiers of Science. New York, Berl in, London: Springer-Verlag, 1992. A well presented textbook of almost 1,000 pages aimed atcollege level mathematics and science students. Includes clear explana-tions of key mathematical ideas, imaginative diagrams illustrating allaspects of chaos, several sections devoted to the logistic map, and a de-tai led bibliography.

4 .2 Key Technical Articles

A few of the key articles containing breakthrough work on the logistic mapand other iterated maps are:[8] J. Ba nk s; J. Bro oks; G. Cairn s; G . Dav is; P. Stacey. "O n D ev an ey 's

Definit ion of Chaos." American Mathematical Monthly 9 9 / 4 (1 9 9 2 ) ,pp. 33 2-3 34 . R epo rting the result that topolo gical transitivity and den-sity of periodic points implies sensitive dependence on initial conditions,as Devaney defines these terms in [3].

[9] M. J . Feige nbau m . "Qu anti tat ive Universali ty for a Class of No nlinearTrans forma t ions . " Journal of Statistical Physics 19(19 78) , pp . 25-52.Reporting Feigenbaum's discovery that the bifurcation cascades of avery large class of iterated maps are characterized by the same scaling(renormalization) constant, together with an estimate of that constant.

[10] M. J . Feig enba um . "Un iversal Behavior in N on-Lin ear System s."Physica 7D(1983), pp. 16-39. A useful s tatement of the major results

concerning universali ty.




[11] M. Jakob sen. Com mun ications in Mathem atical Physics 8 1 (1 9 8 1 ) ,pp. 39-88. Reporting the result that the set of k<4 for which the logisticmap has no periodic orbits has positive Lebesgue measure.

[12] Tien-Y ien Li; James A. Y orke. "Period Three Im plies Chaos." TheAmerican Mathematical Monthly (N ove m ber, 1975), pp. 985-9 92. Re-porting the vital result that, if a particular type of map has a periodicpoint of period three, then it has periodic points of all periods and cha-otic behavior on some set .

[13] E. N . Loren z. "Determ inis t ic Non-P eriodic F low." Journal of Atmos-

pheric Science 20(1963), pp. 130-41. A breakthrough paper later rec-ognized as initiating contemporary research in chaos theory.

[14] M . M etrop olis; M . L. Stein; P. R. Stein. Journal of Com binatorial The-

ory\ 15A (1973), pp. 25-44. Presenting some key results in the symbolicdynamics of maps on the unit interval .

[15] S. Sm ale. "D iffere ntiab le Dy nam ic System s." Bulletin o f the American

Mathematical Society 73 (1967), pp. 747-817. The first report of the vi-tal result that chaos appears stably (perturbations do not alter dynamics)on a whole space in some higher dimensional systems.

4 .3 Experimental Applications of terated Maps

There have been many experiments relat ing i terated maps to physical dynami-cal systems. Here is a selection covering a wide range of topics; the titles areusually self-explanatory.[16] F. T. A recc hi; R. M euc ci; G. Pucc ioni; J. Tredicce . "Experim ental Evi-

dence of Subharmonic Bifurcations, Mult is tabil i ty, and Turbulence in a0-swi tched Gas Lase r . " Physical Review Letters 4 9 / 1 7 (1 9 8 2 ) ,pp. 1217-1220.

[17] J. P. G ollu b; Ha rry L. Sw inne y. "O nset of Tu rbulen ce in a Rotating

Fluid ." Physical Review Letters 35/14 (1975), pp. 927-930.[18] M ichael R. Gu evara; Leon Glass; Alvin Shrier. "Phase Locking, Period-

Doubling Bifurcations, and Irregular Dynamics in Periodically Stimu-lated Cardiac Cells ." Science 214 (1981), pp. 1350-1353.

[19] A. Libch aber; C. Laroch e; S. Fauve. "Period D oubling Cascade in Mer-cury , a Quant i ta t ive Measurement . " Le Journal de Physique-Lettres

43 (1982) , pp . L211-L216.[20] Rob ert M . M ay; Geo rge F. Oster. "Bifu rcation s and Dyn amic Co mp lex-

i ty in Simple Ecological Models ." The Am erican Naturalist (July-August , 1976), pp. 573-599.

[21] Edg ar E. Peters . Chao s and Order in the Capital Ma rkets: A New View

of Cycles, P rices and Market Volatility. New York: Wiley & Sons,1991.

[22] Alvin M. Saperstein. "C hao s— A M odel for the Outbreak of W ar." Na-

ture 309, pp. 303-305.[23] Reu ben H. Simoy i; Alan W olf; Harry L. Swinney. "On e-Dim ensional

Dynamics in a Mul t icomponent Chemical React ion." Physical Review

Letters 49/4 (1982) , pp . 245-248.




[24] Jame s Testa; Jose Perez; Carson Jeffrie s . "Evide nce for UniversalChaotic Behavior of a Driven Nonlinear Oscil lator" Physical Review

Letters 48/11 (1982), pp. 714-717.

4 .4 Useful Introductions and Surveys

There are a large number of introductory and survey articles and even somebooks covering the topics of chaotic dynamical systems, chaos, and the logis-t ic map. Here are some of the most useful:

[25] Jam es P. Cru tchfield; J. Do yne Farmer; No rm an H. Packard; Robert S.Shaw. "Chaos . " Scientific American 255 (Decem ber, 1986), pp. 46-57.This article is included in the present volume. It furnishes a non-

technical account of the identification of a strange attractor for the drip-ping faucet .

[26] Josep h Ford. "W ha t is Ch aos, that W e shou ld be M ind ful of it?" PaulDavies, ed. , The New Physics, pp. 348-3 72. Ne w York and C amb ridge:Cambridge Universi ty Press , 1989.

[27] Joseph Ford. "H ow rando m is a coin toss?" Physics Today (April, 1983),pp. 40-47.

[28] Jam es Gleick. Chaos: Making a New Science. New York: Penguin

Books, 1987.[29] John Ho lte, ed. Chaos: The New Science. Nobel Conference XXVI.Lanham, Maryland: Universi ty Press of America, 1993.

[30] John Horg an. "In the B eg inn ing . . . . " Scientific American (February,1991), pp. 117-125.

[31 ] John T. Ho ughton . Does God Play Dice? Leice ster: I VP, 1988.

[32] Leo P. Ka dan off. "Ro ads to Ch aos." Physics Today (December, 1983),pp. 46-53.

[33] Robert M. M ay. "Sim ple Mathem atical M odels with Very Com plicated

Dynamics . " Nature 261 (Jun e 10, 1976), pp. 45 9-4 67. T his survey arti-cle focuses particularly on the logistic map.

[34] Ilya Prigo gine; Isabelle Steng ers. Order out of Chaos. New York, Ban-tam Books, 1984. An introduction to the theory of complex systems,which is intimately connected to chaos theory.

[35] Ian Stewart . "Re cipe for Ch aos." Does God Play Dice? pp. 348-372Cambridge: Blackwell , 1989.

4 .5 Key Works on Chaos Theory and TheologyDuring the 1980s, theologians and philosophers interested in such questions asprovidence and divine action began discussing the connections with chaostheory and, more often, the connected theory of complex systems. Some of theimportant art ic les and books including extended discussions of chaos theoryand theology are:

[36] Steven Dale Cra in. Divine Action and Indeterminism: On Mod els of

Divine Action that Exploit the New Physics. Universi ty of Notre Dame,

Dissertation, 1993.




[37] Niels Henrik Gregersen. "Providence in an Indeterminis t ic World."CTNS Bulletin 14/1 (Winter, 1994).

[38] Phil ip J . H efne r. "G od and Chaos: The Dem iurge Versus the Ung rund ."Zygon 19 (1984), pp. 469-485.

[39] J . T. Ho ugh ton. "New Ideas of Chao s in Physics ." Science and Christian

Belief 1/1 (1989), pp. 41-51.[40] Bern d-O laf KOppers. "O n a Fund am ental Paradigm S hift in the NaturalSciences." W. Krohn, et. al. , eds. , Selforganization: Portrait of a Scien-

tific Revolution, pp. 51-63. The Hague: Kluw er Aca dem ic Pu blishers ,1990.

[41] D. M . M ackay. Science, Chance and Providence. Oxford: Oxford Uni-versity Press, 1978.

[42] John Polk ingho rne. "Th e Na ture of Physical Reali ty." Reason and Real-

ity: The Relationship Between S cience and Theology, chapter 3, pp. 34-

48. London: SPCK, 1991.[43] John Polkin ghorn e. "A N ote on Chao tic Dy nam ics." Science and Chris-

tian Belief Ml (1989), pp. 126ff.[44] John Polk ingho rne. Science and Providence: God's Interaction with the

World. London: SPCK, 1991.[45] Keith W ard. "Th e Constraints of Creation ." Divine Action, chap ter 7,

pp. 119-133. London: Coll ins , 1990.[46] Walter J. Wilkins. "Chaos and the New Creation." A paper delivered in

the Religion and Science Section of the American Academy of ReligionAnnual Meet ing, November 21, 1988.



II

CHAOS, COMPLEXITY, AND

THE PHILOSOPHY OF LIFE



U N D E R S T A N D I N G C O M P L E X I T Y 10 3

Bernd-Olaf Kuppers

1 Introduction

One of the most impressive features of contemporary science is the enormousprogress that has been made in the understanding of complex phenomena. Anoutstanding example of this is the development of modern biology, which atpresent is as rapid as the deve lopm ent of physics at the beginning of our century.

Above all, the results of molecular biology have become the focal point ofinterest, because they have led to deep insights into the physical basis of livingorganisms, including the physical principles of inheritance. Furthermore, theresults of molecular biology have induced the development of a physical theory ofevolution and thus the development of a coherent concept of the physical origin oflife. Biologists are going to elucidate and understand the molecular principles ofdifferentiat ion and morphogenesis . Neurobiologis ts are learning more and moreabou t the physical structure and function of the central nervous system. Some day,

biologists will be able to simulate the intelligent achievements of the brain bymeans of artificial neural networks. Last but not least, the plan to determine thecomplete sequence of the human genome seems to promise an al l-embracingknowledge of the physical organization of the human being.

What has been paraphrased here is the present success and the future goalsof the so-called reductionistic research program. This program is based on thecentral working hypothesis that all biological phenomena can be explained totallywithin the framew ork of physics and c hem istry. In other w ords: the reductionisticresearch program starts from the epistemological premises that there is no principal

difference between non-living and living matter, and that the transition from thenon-living to the living must be considered as a qu asi-continu ous one, in w hich noother principles are involved than the general principles of physics and chemistry.If there are certain limitations with regard to our physical understanding of livingmatter, then these are supposed to have a temporary but not a fundamentalcharacter.

W ithin the fram ew ork of the reductionistic research p rog ram , such limitatio nsare attributed exclusively to the material complexity of the phenomena underconsideration, in the same way as certain restrictions of the physical fo und ation ofchemistry are attributed to the restricted computability of molecular structures. Togive just on e example of this kind of thinking: Although the Schrodinger equationcannot be solved fo r com plex m olecu les, a solid reductionist will hav e no seriousdoubts about his working hypothesis that chemistry can be reduced in principlecompletely to the laws of quantum physics.

According to its own conception of itself, the reductionistic research programclaims that it is purely and simply the increasing material complexity in thetransition from atoms to molecules and from molecules to living systems that gives



9 4 BERND-OLAF KOPPERS

chemistry and biolog y the status of sem i-autono m ous sciences, each with its ow nvocabulary and law-like statements. Nevertheless, the reductionistic researchprogram adheres to its central doctrine that all phenomena of chemistry andbiology can n principle be reduced to physics .

Despite the undeniable and overwhelming success of the reductionis t icresearch program in the past, a number of objections to its central doctrine havebeen put forward. An d it is m ore than o nly a historical note that those o bjection shave been made mainly with respect to the relat ionship between biology andphysics, although the relationship betw een chem istry and p hysics seems also to bea target of those objections. This already indicates that, to some extent, theobjections to the reductionistic research program have p sycho logical roots. Indeed ,

one can understand very well the discomfort that an anti-reductionist must feel.For, if the reductionistic view of the w orld is correc t and all biolo gical ph en om en acan be— at least in principle— explained by the laws of phy sics, o ne seem s to arriv eat the ontological conclusion that life is nothing but a complex interplay of a largenumber of atoms and m olecules . A ccording to this picture, even the p heno me nonof consciousness must be considered as a direct consequence of materialcomplexity that is thought to be governed exclusively by physical laws.

Now, in order to immunize themselves against the desperate picture of theworld drawn by reductionism, some biologis ts and associated philosophers of

science have invented the conc ept of " em erg en ce" and the closely related conc eptof "downward causation." The main idea behind these concepts can be summarizedby the general claim that, if a material system reaches a certain level of com plex ity,manifested in a high degree of relatedness of its components, then genuinely novelproperties and processes may emerge, which cannot be explained by the materialproperties of the components themselves. Consequently, the emergentists claimthat physics is not a sufficient tool for explaining complex phenomena, eventhough it is a necessary one.

In short, one can express the quin tessence of the concepts of eme rgen ce anddownward causation by two theses:(1) The whole is more than the sum of its parts.(2) The whole determines the behavior of its parts.From the first thesis follows the concept of emergence. From the second

thesis follows that of downward causation. Both concepts have been presentedmore precisely in the literature and have been discussed there at a sophisticatedlevel. For a philosopher of science wh o is interested in the mind-brain problem, theconcepts of emergence and downward causation are quite appealing. But from the

perspective of a scientist actually working at the bo rde rline of ph ysic s and biol ogy ,both concepts remain rather vague and mysterious.

It will be the main goal of this article to draw attention to a general problemof reduction in biology that has recently become apparent, and which may shednew light on the concepts of emergence and downward causation and theirrelevance for the understanding of complex phenomena. However, the referencepoint of the following discussion will not be the mind-brain problem, but the moregeneral problem of the transition from the non-living to the living. The last one isalmost paradigmatic for biology's challenge to physics, and its analysis during



U N D E R S T A N D I N G C O M P L E X I T Y 95

recent years ha s led to completely new insights into the possibilities and limitationsof understanding biological complexity. 1

In this article, the problem of understanding complexity will be approached

in the following way: first it is shown what kind of complexity one encounters innon-living systems. Then the nature of complexity encountered in living systemswill be describ ed. A nd fin ally the capacity of the reductionistic research progra min closing the explanatory gap between simple and complex systems will beinvestigated.

2 Emergence and Downward Causation in Non-living Systems

If w e ask the general question of ho w ph ysic s differs from biology, we usually getthe answer that physics deals with simple systems, whereas biology deals withcomplex system s. At first glance, this answ er seem s to be convincing , in that it isconsistent with our intuitive ideas about the subject matter. But, on closerinspection, this view is hardly tenable.

Let us consider a so-called "s im ple " system, typical of physics, for exam ple,one mole of an ideal gas. Under standard conditions, this amount of gas containsabou t 10 2 4 part icles—the exact number is given by the well-known Avogadro

number. If we wish to describe the system in its microphysical details, that is,starting from the fundamentals of classical mechanics, then we must specify at agiven time the position and velocity (or momentum) of each of the 102 4 particles.Or, expressed technically: we have to specify the so-called phase space. Thedynamical behavior of the system is then characterized by the mov em ent of a clou dof points in this phase space. However, the specification of all points in phasespace is a task that can only be solved in a "Gedankenexperiment" and cannot besolved in reality. So, even in this allegedly sim ple case, we are already dea ling withan extraordinari ly complex system.

However, there is a way out of this complexity. Instead of analyzing themicrostate of the system, which is given by the positions and velocities of allparticles in the phase space, we can restrict the analysis to certain macrostates ofth e system. The macrostates of the system are given by defined mean values of theparticle distribution. For example, instead of determining the velocity of eachindividual particle, one can consider the mean velocity of all particles of thedistribution. Such considerations lead to certain macroscopic parameters likepressure and temperature, that is, to parameters that can be observed and measureddirectly. Since each microstate has a uniquely defined macrostate, this form ofabstraction is a legitimate and useful procedure to reduce the complexity of thesystem b y reducing the complexity of its description.

This procedure, which is typical for equilibrium physics, allows us to speakin this case of a "simple" system. Of course, a price must be paid for such an

'Bernd-Olaf Klippers, Information and the Origin of Life (Cambridge, MA: MIT

Press, 1990).



9 6 B E R N D - O L A F K O P P E R S

abstraction. If we change the level of description, in that we now consider themacrostate of the system, we lose, as is unavoidable for any statistical consider-

ation, a certain amount of information. In the present case, we lose the information

about the microstates. And there is even a m eas ure for this loss of information: theen t ropy . 2

TTie relationship between macroscopic thermodynamics and statisticalmechanics, which I have sketched here, has been the subject of many investiga-tions concerning the problem of intratheoretical reduction in physics. If one adoptsthe reductionistic point of view, one is compelled to claim that the macroscopicobservables like pressure and temperature can be reduced by means of statisticalmechanics to the microscopic behavior of the system's particles. Ernst Nagel, inhis paradigmatic investigations of the problem , follow s essentially this reduction-istic argument, although he sees himself compelled to make use of so-called bridgelaws. 3 These are additional prem ises that link the vocab ularies of the two theoriesthat are to be reduced.

The emergentists, however, wou ld use this thermo dyn am ic e xam ple in orderto demonstrate the opposite, namely, the occurrence of emergent properties liketemperature and pressure in physical systems on the one hand and the inherentweakness of reductionism in explaining these properties on the other hand. Thebridge laws are the principal object of their attack. Most emergentists refuse to

accept the bridg e laws as a sufficient tool for carrying out th e redu ction. Em ergen t-ists would at least deny the availability of such bridge laws for the psychophysicalcase.

It is not useful to go into the details of the arguments. However, we mustconclude that fo r a true emergentist physics itself ca nno t be redu ced to ph ysi cs, thatis, physics itself must be considered as being irreducible. This may be the curiousmeaning of the notion that the concept of em erge nce is equivalent to non redu ctivematerialism, or, as Popper has expressed it , that "materialism transcends itself."4

The sam e line of argum ent holds for the concept of dow nw ard causa tion. O ne

can demo nstrate this very easily by means of the law of mass action. Consider tworeactants in chemical equilibrium. None of the molecules in such a system "knows"that it is in a chemical equilibrium and has to behave dynamically in a certain way,so that the equilibrium is preserved. Nevertheless, the equilibrium state is the stable

2 This can easily be seen. It is true that each microstate has a uniquely defined

macrostate. But, on the other hand, it is also true that a given macrostate can be realized by

more than one microstate. The entropy of a system is just the measure of the number of

microstates conta ined in its macrostate. This me ans that the entropy, and thus our ignorance

about the system, is the larger the more microstates are contained in their corresponding

macrostates. For the singular case in which a macrostate contains one and only one

microstate, the entropy is zero and our knowledge about the system is at a maximum.

3Ernest Nagel , The Structure of Science: Problems in the Logic of ScientificExplanation (Now York: Harcourt, Brace, and World, 1961).

4Karl R. Popper and John C. Eccles, The Sef and ts Drain (Berlin: Springer, 1977),

c h a p . 1 .




state of the system. In fact, it is some kind of downward causation or macro-determination that causes the regular behavior of the molecules. The law of massaction ensures that any fluctuation that disturbs the equilibrium becomes

dampened. The larger the deviations from the equilibrium, the larger is the forcerestoring the original state. In other words: with respect to its fluctuations, anychemical equilibrium is self-regulating. But the self-regulating power of anequilibrium system is a property of the system as a whole, and it cannot be deducedfrom the material properties of its components.

Thus, it seems to be a banal truth that emergence and dow nw ard cau satio n areintrinsic phenomena of our material world, and that these phenomena by no meansare restricted to the sphere of biological com plex ity. If this view is correct, o ne candraw some more interesting conclusions concerning the phenomena of emergence

and downward causation. In order to do so, let us forget for a moment the mind-brain problem and consider only the problem of life itself. Th e present theory ofthe origin of life yields no indication that there is a non -ph ysica l p rincip le involv edin the transition from the non -living to the living. No w aday s, the origin of life canbe completely understood on physical grounds as a quasi-continuous process ofmolecular self-organization in the course of which its material complexity steadilyincreases . 5 Consequently one has to give up the idea that the phenomena ofemergence and downward causation at once em erge when matter reaches a certain

level of complexity. Instead, both phenomena must be thought of as epiphenomcnaof self-organizing matter that continuously emerge when matter unfolds itscomplexity by organizing itse lf.6 It will be the task of the last part of this article toexpress this idea in precise physical term s. First, how eve r, s om e light m ust b e shedon the nature of the complexity that one encounters in biology.

3 Complexity in Living Systems

For this purpose, let us consider a system which is of intrinsic complexity andwhich cann ot be simplified by changing the level of description or abstraction. Theexample to be discussed here is taken from molecular biology and is known bymolecular biologists as sequence space. 7 In order to present this concept we mustmake a short digression into the mechanism of genetic information storage. As iswell known, the information required for the construction of a living organismresides univ ersally in a particular class of the cel l 's molecu les: the nucleic acids,usually DNA. DNA molecules are macromolecules: that is , they are made by

^Uppers, Molecular Theory of Evolution: Outline of a Physico-Chemical Theory ofthe Origin of Life, 2d., ed., trans. Paul Woolley (New York: Springer-Verlag, 1985).

'Thus, the extended version o f em ergen tism, according to wh ich the history of nature

is a process of emergent evolution, has to be brought into agreement with the modern

concepts o f physical evolution as a quasi-continuous process of molecular self-organization.

7 M . Eigen, "M acromolecular Evolution: Dynam ical Ordering in Seque nce S pace/*

Deratungen der Bunsengeselschaft fur physikalische Chemie 89 (1985): 658-6 7 .



9 8 B E R N D - O L A F K O P P E R S

joining smaller m olecu les, the so-called nuc leotides, into a long chain. In such aninformational macrom olecule, the m on om ers ha ve the sam e functio n as the lettersin a language. In particular, the detailed sequence of the monomers of a DNA

mo lecule determines com pletely i ts genetic inform ation.If, by spontaneous or site-directed mutagenesis, a letter in such a genetic

blueprint becomes altered, this may lead—as a typographical error in a book—toa distorted text and thus to the death and decay of the organism. One can speakhere of a distorting mistake, insofar as, in gen eral, th e disturb ed sub structu re of theorganism can no longer fulfill its specific function for the w hole system. From thisit becomes clear that the genetic information possesses a certain semantic aspectthat encodes the structural and functional properties of the organism and thatrepresents a measure of its material complexity.

Many insights into the problem of biological complexity arise from theconcept of sequen ce space. Sequen ce space is a high-dimensional hy percube forthe representation of all possible variants of a DNA sequence. By analogy withphase space, we can assign to the seq uenc e space a certain nu m ber of m icrostates,namely the number of sequences that can be built up form a finite class ofmonomers in a macromolecule of f ini te length. Even for extremely shortmacromolecules, the sequence space has a considerable complexity. However, assoon as we reach biologically significant orders of magnitude, we venture into

inconceivable dimensions of complexity. Even the informational sequence of thebacterial genome has about io 2 , 4 0 0 , 0 0 0 microstates in its sequence space, wherebyonly a vanishingly small fraction of all these microstates can b e assumed to en cod ebiologically meaningful information.

Thus, in contrast to physical systems of the type discussed before, inbiological systems the detailed k no wle dge of the microstate of their info rm ationalmacromolecules is of essential importance for the understanding of those systems.It is th e specific sequence of its DNA that gives a biological system the propertiesof living matter. Obviously, there is no possibility here of referring to any mean

values in order to reduce the complexity of the sequence space.8

There is nopossibility of finding a macrostate that yields sufficient information about thesystem. Moreover, if one wishes to understand how a living system could havearisen when there existed only non-living matter, one has to analyze the wholesequence space for the system and to investigate its evolutionary pathw ay throughall its possible m icrostates.

Thanks to the tremendous complexity of sequence space, biology forcesphysicists to a new intellectual approach. Certain kinds of abstraction andidealization, as are usual within the framework of equilibrium physics, are nolonger meaningful for biology. This s tatement is the more important as thephenomenon of intrinsic complexity is found in the living world on all levels of

"This can be illustrated by the following example. A sonnet by Shakespeare is

represented by a defined sequence of letters. All possible sequence alternatives of this poem

build up a ceitain sequence space. But the mean value of all those sequences will hardly

represent a Shakespeare sonnet as well .



U N D E R S T A N D I N G C O M P L E X I T Y 9 9

organization, whether we consider the sequ ence space of in form ational m acro m ol-ecules or the state space of the neu rons in a neural netw ork .

Can one explain and understand physically the immense complexity of living

matter or d o there exist definite limits of the physical method? Does the reduction-istic research program in this case fail, or is physics undergoing a new paradigmshift, thereby transforming the explanatory capacity of the whole program? Andfinally, how can one correlate the phenomenon of complexity with those ofemergence and downward causation? T hese qu estions now lead to the central partof this article.

4 Boundary Conditions and Downward Causation

For a long t ime, the investigation of complex phenomena by physicis ts wascharacterized by the expectation that new, fundamental laws of physics might befound in this area. However, these expectations have not been realized, and theprospect of the discovery of such laws is dwindling from day to day. If onetherefore concludes the converse, that is , that even complex phenomena must beexplicable on the sole basis of the known laws of physics, then one has to look fornew aspects revealing the physical roots of complexity.

Such an ew aspect beco m es clear in outline when on e directs one 's attentionto the logical structure of physical explanatory models. As is well known, physicaltheories possess a dual structure: they contain both general statements in the formof laws, which possess at least a local validity, and so-called initial or boundaryconditions. The latter conditions are not fixed by the theory itself but are specifiedby the given facts within the scope of application of the theory. Mathematicallyspeaking, the initial or boundary conditions are certain selection conditions ofpossible solutions to the differential equations by which the physical laws aredescribed.

We shall now attempt to justify the central assertion of this article, which isthat the complexity of a system or a phenomenon lies in the complexity of itsconditional complex, that is , in the complexity of its boundary condit ions.

The firs t to emphasize the s ignificance of boundary condit ions for anunderstanding of complex phenomena was the dis t inguished physicis t MichaelPolanyi. 9 Although his final conclusions with regard to biology ultimately provedto be erroneous, it will serve our purpose well to follow his analysis for some ofthe way.

First, let us consider a complex system made by human hands, such as asophisticated machine. We can use various criteria to characterize such a system.Above all, we can state the purpose of the machine and explain how it functions.The purpose that the machine is intended to fulfill is dictated by human goals. Itsmechanism, however, is dictated by the obedience of matter to natural laws. Wecannot construct a machine that functions in a manner contrary to natural laws.

9

M . P olanyi, "L ife's Irreducible Structure," Science 160 (1968): 1308-12 .



100 BERND-OLAF KOPPERS

There exis ts , for example, no "perpetuummobile" that can suspend the law ofconservation of energy or the second law of thermodynamics.

The function of a machine is la id down by the manner of i ts construction.

This includes both the driving force, that is , the source from which the machinedraws its energy, and the detailed arrangement of the components of the machine.Let us ignore the energy source for a m om ent. Th e structure of a m achin e is thengiven unambiguously by the internal relatedness of its components, which in turnis determined by the special shape of the com pone nts and by the wa y in which theyare put together. The relationship between the material components of the machinethus represents a boundary condit ion under which the natural laws becomeoperational in the machine. It is the joint action of all processes induced andconstrained by these boundary conditions that finally realizes the functional

purpose that the machine is to serve.

Every machine works under such a principle of dual control: the highercontrol principle is that of the machine's design, and this harnesses the lower one,which consists in the physical proce sses on which the mach ine relies. The designof the machine finds its expression in the internal boundary conditions. Theboundary conditions, which give the machine its special properties, are designedby the constructor of the machine. It is obvious that these cannot be deduced fromthe general laws of physics and chemistry.

Thus, the structure of a mach ine and the wo rking of its structu re show all th efeatures of an emergent system: the system represents a whole, which is neitheradditive nor subtractive. M oreov er, the properties of the system are not redu cibleto the material properties of its components. And, last but not least, all processesgoing on in the system are induced and constrained by the system's boundaryconditions, indicating the presence of some kind of downward causation.

Thus, the example of the machine focuses at tention upon the fundamentalimportance of the boundary conditions for an understanding of complex systemsand their emergent properties. This is of particular value here because the example

of the machine can immediately be transferred to the archetype of complexsystems, the living organism. In fact, the living organism is comparable in manyways to a complex machine. And it is not a matter of pure chance that an entirefield of research, namely cybernetics, has its origin in the machine theory of theorganism. As in the case of the machine, the organism is subservient to the mannerin which it is constructed, whereby the functional order of all its parts is preor-dained. Its principle of constru ction represents a boun dary cond ition un der wh ichthe laws of physics and chemistry become operational in such a way that theorganism is reproductively self-sustaining. Again, as in the case of the m ach ine, the

phenom enon of emergence as well as that of dow nw ard causation can b e observ edin the living organism and can be coupled to the existence of specific boundaryconditions posed in the living matter.

Clearly, it is the special structure of the boundary conditions that determinesthe overall construction of the system, both for the machine and for the livingorganism. We must therefore ask by what means the boundary condit ions areexactly determined. In the case of the machine the answer to this question isobvious. The boundary conditions are defined in the blueprints drawn up by the

constructor of the machine. But even for the living organism such a blueprint does



UNDERSTANDING COMPLEXITY 101

exist. It resides in the genome of the organism and is—in contrast to themach ine— an inherent part of the material organ ization of the system . If the gen eticmaterial of an organism is placed in a suitable physico -chem ical enviro nm ent, such

as an egg cell, then expression on the phenotypic level results; that is, theconstruction plan of the organism encoded in its genome is realized in matter, stepby step. Thus, the structures of all the boundary conditions that appear in thecomplete, differentiated organism are implicitly laid down in the genome of theorganism. The genome therefore represents a primary boundary condition, whichdetermines all other boundary conditions appearing in the living organism.

5 Boundary Conditions in Physical Systems

The above arguments underl ine the importance of the concept of boundaryconditions for the understanding of complex phenom ena. Ho wev er, u p to n ow theyhave been based exclusively upon plausibility considerations. We must nowcrystallize the term 'boundary condition* so as to bring it into line with itscorresponding concept in physics .

For this purpose, let us enlarge a little on the boundary conditions that liebehind the order of living matter. As already noted, all boundary conditions of a

living organism reside in particular physical structures, the DNA molecules. It isthe microstate, that is , the detailed sequence of the monomers in the DNA, thatencodes all structural and functional properties of the living organism. Themonomer sequence of a DNA molecule is a genuine boundary condit ion in thephysical sense. It can be specified by stating the coordinates in space of all theatoms in the structure of the molecule, along with other physico-chemicalenvironmental conditions such as the temperature, the ionic strength and so on . T hestructure represents a precise set of physical para m eters, w hich— accord ing to thedoctrine of genetic determ inism— govern s all the physical and chem ical processes

that take place in the system .It should be mentioned, however, that there is an important difference

between the boundary condit ions of complex and s imple systems. Complexsystems can be defined as systems that depend very sensitively upon theirboundary conditions. Thus, in living systems, even the exchange of a singlenucleotide in a genome can lead to instability and collapse of the system. Simplephysical systems beh ave differenUy in this respect. Simple systems may be definedas systems in which the natu re of the physical pro cesses induced by the bo und aryconditions will not change fundamentally if the boundary conditions are altered.

For example, a body in fr ee fall will alw ays show a qualitatively similar beha vior,irrespective of the initial cond itions fro m w hich the process starts. The bou ndaryconditions of simple physical systems, such as the position and momentum of aparticle at a particular time, are contingent quantities. 'Contingent' means in thiscontext that the bou ndary cond itions can b e chosen a rbitrarily. They are m arginalquantities that may be chosen freely in an experiment and whose values arerestricted only b y the range of validity of the natural law s in question.

The boundary condit ions of complex systems, on the other hand, are non-

contingent quantities, since any significant alteration in these boundary conditions



102 B E R N D - O L A F K O P P E R S

would also change significantly the dynamics of the system and thereby itsproperties. In addition, the boundary conditions are usually unique, in that theyrepresent a defined selection from a gigantic number of physically equivalent

alternatives. The reader will recall that the number of alternative sequences ormicrostates available to the genom e of a bacterial cell is no less than l O 2 , 4 0 0 , 0 0 0 .

So far, we have classified simple and complex systems according to thenature of their boundary condit ions. We have associated complex systems withnon-contingent boundary conditions and simple system s with contingen t bou nda ryconditions. However, it is important to notice that the transition from one of theseclasses to the other is a continuous one, in that the concept of contingency itselfallows this. The concept of contingency is the logical antithesis of that of law, andtherefore leaves open the question to what degree a phenomenon is restrained orunrestrained by natural law. Incidently, this view fits very well into the moderntheory of molecular self-organization, accord ing to w hich th e transition fr om no n-living to living systems must be regarded as a quasi-continuous one.

6 Boundary Conditions and the Reductionistic Program

After discussing the concept of boundary conditions, we shall now use it to obtain

deeper insight into the explanatory capacity of the reductionistic researchprogram.10 It will turn out ihat the concept of boundary conditions yields a key tothe comprehension of the paradigm shift that is induced in physics in connectionwith the investigation of complex pheno men a.

Let us start with some remarks concerning paradigm shifts in general. Theconquest of new phenomena by a branch of science very often results in changesin its theoretical frame. This is because a novel class of phenomena will usuallyrequire a new set of terms and concepts for its description. However, terms andconcepts only gain a precise m eanin g w ithin the fram ew ork of a theory. T hus, the

decisive step in a paradigm shift is always the expansion or the rebuilding of itstheoretical frame.

The rearrangement of the theoretical frame of a paradigm can take place attwo differen t levels. It can, for example, be a change consisting in the modificationand/or expansion of the theoretical fr am e. It can alternatively be the case that thetheoretical frame requires no modification or expansion, but merely an internalshift of emphasis. The former will alw ays b e the case w hen recurrent a nom alies ofexplanation bring a paradigm into an internal crisis, one that can be resolved onlyby a radical rebuilding of the theoretical frame of the paradigm. It was suchinstances that Ku hn had in mind when he spoke of scientific revolutions occurring

I0 Kiippers, "On a Fundamental Paradigm Shift in the Natural Sciences/' in Sef-Organisation- -Portrait of a Scientific Revolution, W olfgan g Krohn, Gunter Kuppes, and

Hclga Nowotn y, eds., vol. 14, Sociology of he Sciences (Dordrecht: Kluwer, 1990), 51-63.




f rom t ime to t im e. 1 1 The other case, that of internal shifts of emphasis, appears atfirst sight to be of less philosophical interest. However, we shall see that preciselythis seemingly uninteresting case forms the basis for the paradigm shift under

discussion here, and that its conse quen ces will be in no way less revolutionary thanthose of Kuhnian scientific revolutions.

In order to see this, we must first express more precisely the idea of aninternal shift of emphasis. This shift of emphasis need not necessarily refer to achange in the fundamental laws of physics. But it clearly means more than the mereextension of interest from simple to complex phenomena. We must rather regardthe internal shift of emp hasis as a chan ge in the inherent explana tory structure ofthe paradigm itself.

But what is a scientific explanation? In physics it is customary to say that

there is a scientific explanation for a class of natural events if a general law can beformulated that allows the appearance of such an event to be deduced from itsboundary conditions. For exam ple, in a physical experim ent na ture is subjected tocertain restrictions in order to observe its behavior under these restrictions. Byvariation or by narrowing or widening the experimental boundary conditions, thelaw-like behavior of matter can be detailed.

This explanatory schem e has been formalized by Hem pel and O pp en he im .1 2

Their model of scientific explanation is based fundamentally upon two classes of

statements: (1) a class of statements that describe the so-called antecedentconditions that precede the explanandum that is, the event to be explained and (2)a class of statements that desc ribe the gene ral laws lying b ehin d the explanandum.

According to the Hempel-Oppenheim scheme, the actual process ofexplanation consists in the logical deduction of the explanandum from theantecedent conditions and th e general laws, which together m ake up the so-calledexplanans. The antecedent conditions are nothing other than the boundaryconditions constituting the conditional complex for a natural phenomenon. In thetraditional models of physical explanation, the boundary conditions are irreducible

premisses for formulated natural laws. They represent the physical quantities thatexpress the contingency of the natural event. Now, within the framework of thereductionistic research program, the boundary conditions of complex phenomenaare no longer regarded as contingen t qu antities but rather as non -conting ent ones,which must themselves be explained so that they move into the center of theexplanation.

This has brought us to the decisive characteristic feature of the shift ofemphasis within the reductionistic research program, a shift that has led to theformulation of the so-called paradigm of self-organization and thereby to afundamental shift in the explanatory capacity of the reductionistic research

1'Thomas S. Kuhn, The Structure of Scientific Revolutions 2d cd., enlarged (Chicago:

University of Chicago Press, 1970).12 C.G. Hempel and P. Oppenheim, "Studies in the Logic of Explanation," Philosophy

of Science 15 (1948): 135-75; reprinted in C.G. Hempel, Aspects of Scientific Explanation:

and Other Essays in he Philosophy of Science (New York: Free Press, 1965), 245-90.



104 B E RND-O L AF K O PPE RS

program itself. The contingency of natural processes, previously firmly anchoredin the contingency of the boundary conditions of a natural phenomenon, now itselfbecomes the object of scientific exp lana t ion .1 3

However, this does not mean that the contingent quantities can in this way beeliminated completely from our model of scientific explanation. For, when theboundary conditions of a system or pro cess b eco m e the explan andu m, this in turnpresupposes the existence of other boundary conditions on a higher level ofexplanation. The resulting iteration either continues in an indefinite recursion, orelse breaks down when a level is reached on which the boundary conditions are nolonger explicable and thus adopt the status of classical contingent initial conditions.In either case, this recursive explanatory procedure will reduce considerably thenumber of contingent phenomena. This is exemplified well by the theory of the

self-organization of living systems, which represents an attempts to explain theorigin of non-contingent boundary conditions, namely information-carrying DNAmolecules, by appeal to contingent initial conditions, namely random molecularstructures.

The decisive step leading to the new paradigm of self-organization consistsin the recursive shift of the explanandum to the boundary conditions. Theparadigm of self-organization, which has become a central part of the reduc-tionistic research program, is still based upon the basic explanatory model as

formalized by Hempel and Oppenheim, but now a whole series of explanatorysteps are linked consecutively, so that one now can speak of the nested orhierarchically-organized structures and processes of living matter as directlyreflected in the hierarchical explanatory structure of the overall model of self-organization. The paradigm shift, discussed here, puts physics into a position torealize in a novel way its inner goal of demarcating the region of contingentphenomena and of tracing it back, by local inference, to the law-like behavior ofnature.

7 Explanation of Boundary Conditions

Let us finally ask to what extent the existence of the specific boundary conditionscharacteristic of living matter can actually be explained within the framework ofphysics. To answer this question we have to refer once more to the concept ofsequence space. This is because the boundary conditions of living organisms arematerialized at the molecular level in the DNA sequence of its genome and thusrepresent defined microstates in sequence space.

As w e have seen, even for the simplest organisms the number of dimensionsof the sequence space is tremendously large. We must therefore ask whether theexistence of a specific microstate can be explained by the laws of physics. Up tonow we have found no support for the hypothesis that the molecular boundary

"Similar conclusions have been reached by P. Hoyningen-Huene, "Zu Problemen des

Reducktionismus der Biologie,"

Philosophia Naturalis 22(1985): 271-86 .




conditions of a living organism are a direct consequence of physical laws. Instead,we ha ve a lot of experim ental evidence fo r the assump tion that all m icrostates insequence space have the same probability of becoming realized under prevailing

physical laws. Thus, since the total number of all possible microstates is extremelylarge, the probability of the realization of a certain predefined microstate b ecom esvanishingly small. This in turn means that the selection and stabilization of apredefined microstate, for example a microstate that carries biological info rm ation,cannot be explained within the framework of equilibrium physics.

Thus, a selective self-organization of the m icrostates in sequ ence space seem sonly to be possible under the conditions of nonequilibrium processes, in the courseof which an a priori indeterminable number of microstates is narrowed down to afew biologically relevant ones. 1 4 The present results of the new paradigm of self-

organization show unambiguously that the process of molecular self-organizationis essentially subject to certain principles of selection and optimization, and thesecan be reduced completely to the know n laws of phys ics. Ho wev er, the results alsoindicated an inherent limitation of the reductionistic research program. Thus,although the existence of specific boundary conditions can be completelyexplained as a general phenomenon within the framework of physics, it is notpossible to deduce their detailed physical structure. This has been revealed by athorough analysis of evolutionary dyn am ics in sequen ce space. The fine structure

of biological boundary conditions reflects the historical uniqueness of theunderlying evolutionary processes, which, by definition, cannot be described bynatural laws.

W e conclude that the concept of boundary conditions is indispensa ble for theunderstanding of complex phenom ena. M any qu estions of philosophical relevan cestill waiting for an answer fit closely to this concept. These concern above all therelationship between the concept of boundary conditions and that of information,as well as the possible connection between the notions of contingency andemergence. Furthermore the question of the relevance of boundary conditions for

the understanding of neural networks has yet to be analyzed—a question whichmay yield a novel approach to the old problem of the relationship between mindand b ra in . 1 5

14 Kuppers, "On the Prior Probability of the Existence of Life," in The ProbabilisticRevolution, vol. 2, ed. L. Kriiger, G. Gigerenzer, and M.S. Morgan (Cambridge, MA: MIT

Press, 1987), 355-69.1 5

I wish to thank Paul Woolley for stimulating discussions on the subject of this article.



C H A O S, PR O B A B IL IT Y , A N D T H E C O M PR E H E N SIB IL IT YO F T H E W O R L D

Michael Heller

1 ntroduction: Compressibility and Comprehensibility

There are quotations which mark imp ortant steps in the history of hum an thou ght.One of them is certainly the passage from Einstein:

The very fact that the totality of our sense experiences is such that by

means of thinking (operations with concepts, and the creation and use ofdefinite functional relations between them, and the coordination of senseexperiences to these concepts) it can be put in order, this fact is one which. . . we shall never understand. One may say "theeternal mystery of heworld s ts comprehensibility" (italics m ine ). 1

This mystery is seminally present in our p resc ient ific cogn ition, b ut it reveals itselfin full light only when one contemplates, as it has been expressed by E. Wigner," the unreasonable effectiveness of m athem atics in the natural scien ces." 2

What is meant here by the effectivenessof ma them atics in the natural sciencesis rather obvious (at least for those of us who are accustomed to the methods ofmodern physics): we model the world in terms of mathematical structures, andthere exists an admirable resonance between these structures and the structure ofthe world; by means of experimental results the world responds to questionsformulated in the language of mathematics. But wh y is this strategy unreasonable?In constructing mathematical theories of the wo rld w e invest into them info rm atio nwe have gained with the help of the joint effort of fo rm er ex perim ents and theories.However, our theoretical structures give us back more information than has been

put into them. It looks as if our mathematical theories were not only informationprocessing machines, but also information creating devices.

Let us consider an outstanding example. In 1915, after a long period ofstruggle and defeat, Einstein finally wrote down his gravitational field equations.He succeeded in deducing from them three, seemingly insignificant, effects bywhich his general theory of relativity differed from the commonly acceptedNewtonian theory of gravity. These effects were so small that the majority ofphysicists at that time could see no reason to accept a theory that required such ahuge mathematical structure and yet explained so little. However, "the equations

'Albert Einstein, "Physics and Reality," chap, in deas and Opinions (New York: Dell ,

1 9 7 8 ) , 2 8 3 - 3 1 5 .

2E. Wigner, t rThe Unreasonable Effectiveness of Mathematics in the Natural Sciences,"

Communications in Pure and Applied Mathematics 13 (1960) : 1 -4 .



108 MICHAEL HELLER

are wiser than those wh o invented th em ."3 This is certainly true as far as E inst ein 'sequations are concerned. In about half a century physicists and mathematiciansfound a host of new solutions to these equations. Some represent neutron stars,

gravitational waves, cosmic strings, stationary and rotating black holes, and so on.Fifty years ago nobody would even have suspected the existence of such objects.Now som e of them hav e been discovered in the Unive rse,4 and our confidence inEinstein's equations has grown so much that we are sure that the existence of atleast som e others will soon b e experimen tally verified. New information seems notonly to be created by the mathematical equations, but surprisingly often itcorresponds well to what we observe if we focus our instruments on domainssuggested by the equations themselves. It looks as if the structure of Einstein'sequations somehow reflects the structure of the world: information about various

strata of the world's structure seems to be encoded in the equations. By findingtheir correct solution, and correlating it , through suitable initial or boundaryconditions, with the given stratum of the structure of the world we are able todecipher this information, and i t often happens that this information wasunavailable befor e we solved the equations.

We often read in philosophy of science textbooks that the mathematicaldescription of the world is possible owing to idealizations made in the process ofconstructing our theories (we neglect the air resistance, the medium viscosity, or

we invent non-existing motions along straight lines under the influence of noforces, and so on). This is a typical half-truth. At least in many instances, it seemsthat the idealization strategy d oes n ot con sist in putting some information aside, butinstead it is one of the most pow erful mecha nisms for the creation of inform ation.For instance, the law of inertia ( unifo rm m otion under the inf luen ce of no forc es!)has led us into the heart of classical mechanics. We should also notice that therewere no experimental results that suggested which " influences" should beneglected, but it was the form of the equations of motion that selected those aspectsof the world upon w hich the experiments should foc us. Th e quantum world wo uld

remain closed to us forever if not for our mathematical models and idealizationson which they are based. Here we had no possibility at all to choose what shouldbe taken into account and what should be left aside. We are totally at the mercy ofmathematical structures. Almost all of the more important concepts of our every-day experience—such as localization, motion, causality, trajectory in space andtime, individuali ty—drastical ly change their meanings when we move from themacroscopic world to the quantum world of elementary interactions. Th e only wayto visualize what happens in this world is to force our imagination to followmathematical structures and surrender to their explicative power.

Mathematics, as em ploye d to recon struct physical situations, en joys another"unreasonable" property—it has enormous unifying power: in an almostmiraculous way i t unifies facts , concepts , models , and theories far dis tant from

3This saying is ascribed to Heinrich Hertz.4 <(/niversf' will be used to refer to the Universe in the maximal possible sense. Later

we shall see that the Universe may contain many universes.



CH AO S , PRO B AB IL IT Y, A ND CO M PRE H E NS IB IL IT Y 109

each other. The huge field of phenomena investigated by contemporary physicshas been divided into a few subdomains, with each subdomain governed by asingle equation (or system of equations). The e quations of Einstein, S chrod inger,

and Dirac are the best known representatives of this aristocratic family ofequations. One printed page w ould be enough to write down the entirety of physicsin a compressed form. We prefer fat volumes because we want to explore thearchitecture of these mathematical structures: we gain understanding by analyzing,step by step, the system of inferences, and by interpreting the formal symbols,triggering this subtle resonance between the logical structure and the results ofm easure m ent W e feel entitled to believe that these subdom ains of phy sics, whichuntil now were separated from each other, are but different aspects of the samemathematical structure. Although still remaining to be discovered, it is often

credited with the name "Theory of Everything."To express a law of physics in the form of a differential equation means to

collect a potentially infinite set of events into a single schem e, in the fram ew ork ofwhich every event, by being related to all other events, acquires a significance andis explained. This is an example of what is called algorithmic compressibility.

However, what is really important is that it is always possible to disentangle whathas been compressed: if needed, each e vent can be extracted fro m the entirety (butalready in its reprocessed, significant form) by finding a suitable solution and

choosing the corresponding boundary conditions. Tod ay Ein stein's question "W hyis the world so comprehensible?" is often formulated: "Why is the worldalgori thmically compressible?" 5 Indeed:

[W ]ithoutthe development of algorithm ic com pressions of data all sciencewould be replaced by mindless s tamp collecting—the indiscriminateaccumulation of every available fact. Science is predicated upon the beliefthat the U niverse is algorithmically compressible and the modern search fora Theory of Everything is the ultimate expression of that belief, a belief thatthere is an abbreviated representation of the logic behind the Universe's

properties that can be written down in finite form by human beings .6

All these properties of mathem atics, wh en applied to physical the ories, oftenev ok e in scientists the feeling of encountering som ething extremely beautiful. O necould ask: Is mathematics beautiful because it is effective? This would be autilitarian theory of beauty. Or more in the Platonic vein, do only beautiful"mathematical structures prove to be effective in physics? Probably these questionshave no straightforward answer, but the fact that they are so often asked points

5 I shall not discuss here the question of whether the statements: "The world is

comprehensible," and "The world is algorithmically compressible" are equivalent, or

whether the latter is but a part of the former.

6 John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation(Oxford: Clarendon Press, 1991), 11. Se e also Joseph F ord's essa y, "W hat is chao s, that w e

should be mindful of it?" in The New Physics ed. Paul Davies (New York: Cambridge

University Press, 1989 ), 34 8-7 2, for clarification regarding sc ien ce 's belie f that the Universe

is algorithmically com pressible.



110 MICHAEL HELLER

toward the significant (albeit not yet sufficiently acknowledged) role of estheticsin the philosophy of science.

Was Einstein right when he expressed his belief that the comprehensibility

of the world will remain its "eternal mystery"? There is an attempt to neutralizeEinstein's puzzlement over the question of why the world is so comprehensible byreducing all regularities present in the Universe to the blind game of chance andprobabil i ty.

[I]t is just possible that complete anarchy may be the only real law ofnature. People have even debated that the presence of symmetry in Natureis an illusion, that the rules, governing which symmetries nature displays,m ay have a purely random origin. Some preliminary investigations suggestthat even if the cho ice is random among all the allowable ways nature couldbehave, orderly physics can still result with all the appearances ofs y mme t ry .7

Tw o essentially different implementations of this philosophy have been envisaged.The first and less radical attempt seeks to explain all regularities observed in thepresent Universe by reducing them to the chaotic (i .e. , "most probable") initialconditions. The second, maximalistic one, claims that the only fundamental law isthe "game of probabilities," and all the so-called natural laws are but averageswhich won in this game. Although only partial results have been obtained so far

in both of these approach es, the philosophical ideas lying behind them seem to bean interesting counterproposal with respect to Einstein's philosophy, and certainlyare worth wh ile to discuss. This is the goal of the present p aper.

The problem is of key importance for the topic of this public ation . In its m ostfundamental sense, God's action in the world consists in giving to the world itsexistence, and giving it in such a way that everything that participates in existencealso participates in its rationality, that is, is subject to mathematically expressiblelaws of nature. If Ein stein 's "m ystery of com preh ensib ility" is indeed neutralizedby the 4 <pure game of chance and probability," then the central meaning of God's

action in the world seems to be in jeopardy: anarchy takes over, the world at itsfoundations is not rational. Since rationality and existence are very close to eachother, the existence of the wo rld, in turn, no longer seems to be the mo st pro foun dlocus of G od 's act ion but a random outcom e of a degraded my stery.

Hence, I shall show that such an attempt to neutralize Ein stein 's fascinationwith the comprehensibility of the world leads us even deeper into the mystery.Probability calculus is as good as any other mathematical theory, and even ifchance and probability lie at the core of everything, the important philosophicaland theological problem rem ains of why the w orld is probabilistically comprehen-

sible. Why has God chosen probability as God's main strategy? In fact, the theoryof probability perm eates all aspects of our present un derstanding of the world. Inparticular, deterministic chaos theory and the theories of complexity and self-

7Joh n Barrow and Joseph Silk, The Left Hand of Creation: The Origin and Evolution

of he Expanding Universe (London: Unwin, 1983), 213.



CH AO S , PRO B A B IL IT Y, A N D CO M PRE H E NS IB IL IT Y 111

organization—the main subject of this volum e on divine action— wo rk bec ause theworld enjoys certain probabilistic properties.

We begin by presenting in more detail those approaches which attempt to

explain the present world's regularities probabilistically. Hence, in section 2, weturn to the question of whether the chaotic initial conditions for the Universe areable to explain its actual structure. In section 3, w e discu ss the p rog ram of red ucin gall physical laws and symmetries to pure chance and randomness. To dealresponsibly with the problems posed in the two preceding sections we mustundertake a thorough discussion of the foundations of probability calculus. Thisis the aim of section 4. The conclusions are drawn and their theological implica-tions are discussed in section 5.

2 The Sharpest Needle Standing Upright on ts Point

Although the need to justify certain large-scale properties of the observed Universe(such as its spatial homogeneity and isotropy) was noticed rather early by manyauthors, the paradigm of the "anthrop ic princ iple" stressed the fact that the initialcondit ions fo r the Universe had to be extremely "fine-tu ned " to produ ce a w orldwhich could be the subject of exploration by a living observer. There is no need to

repeat here all arguments which have been quoted on behalf of this thesis.8

Allthese argum ents point to the fact that the prese nt state of the U niv erse is as hard toproduce from random initial conditions as it is hard to mak e "the sharpest N eedlestand Upright on i ts Point upon a Looking-Glass" ( this is Newton's expressionintroduced in, essentially, the same context).9

The additional difficulty is that each mechanism proposed to explain thelarge-scale properties of the Universe must first be able to overcome the barrierscreated by the limiting velocity of the propagation of physical interactions (the so-called "horizon problem"). Within the s tandard world model, to answer the

question why a certain property of the Universe (for instance, the temperature ofthe microw ave background radiation) is the same in regions which were never ableto comm unicate with each other, o ne essentially n eeds to postulate the fine-tu ningof the initial cond itions resp onsib le for this fact.

An early proposal to overco m e th ese difficulties goes back to C.W. Misner 'sclassical works 1 0 on the so-called Mixmaster program in cosmology, nowadaysmore often known under the name of the chaotic cosmology. The idea is that it wasthe "mixing" character of physical processes in the very young Universe that led

8 S e e Barrow and Frank J. Tipler, The Anthropic Cosmological Principle (Oxford:

Clarendon Press, 1968); and John Leslie, Universes (Ne w York: Routledge, 1989).

9 Sir Isaac Newton, "Letter 2," in Isaac Newton's Papers and Letters on NaturalPhilosophy and Reated Documents, ed. I.B. Cohen and R.E. Schofield, (Cambridge, MA:

Harvard University Press, 1958), 292.

1 0 C.W. Misner, 4 The Isotropy of the Universe," Astrophysical Journal 151 (1968):

431-57; and dem, "Mixmaster U niverse," Physical Review Letters 22 (1969): 1071-74 .



112 MICHAEL HELLER

to its large-scale properties in their present shape, independently of any specialinitial conditions. To put it briefly, the "mixing" processes end up alwaysproducing identical universes regardless of their initial state. Various processes

were tried as mixing candidates: hadron collisions, particle creation, neutrinoviscosity, but all these mechanisms are strongly constrained by the "horizonproblem." This means that they can work efficiently only in those cosmologicalmodels which enjoy a very special geometric property: The expansion rate of theUniverse mu st be related to the velocity of prop agation of the m ixing proc ess suchthat the mixing should be able to re ach distant region s of the U nive rse before theyare too distant to be affected (the goalpost cannot recede faster than the runner canrun). This means that there must exist a large-sc ale prop erty of the U nivers e wh ichcontrols the mixing process by synchronizing it with the global expansion rate and

does this without exchanging physical signals between distant parts of theUniverse. But this is exactly what we wanted to avoid. 1 1 Let us note that thisproblem is strictly connected with the phenomenon of deterministic chaos, whichis one of the main topics in this volume. In fact , the Misner program does not w orksince—as deterministic chaos theory predicts—the relaxation time in theMixmaster model is reached after an infinite lapse of time (the so-called Omegatime appearing in Misner's equations).

A n ew er at tempt to solve these difficult ies , proposed by A . G u th 1 2 and A.

L i n d e ,1 3

is known as the "inflationary scenario." In its standard version, at theepoch when the Universe was 10"35 seconds old, the splitting of the strong nuclearforc e from the electroweak force m ade the factor driving the world 's ev olu tion 1 4

negative and caused a rapid (exponential) expansion of the Universe to besuperimposed on its ordinary expansion. In a fraction of a second the radius of theUniverse increased from about 10" 23 cm to 10 cm (22 orders of magnitude!), thatis, from something which was 10 billion times smaller than the size of a proton tosomething about the size of an orange. After this dramatic inflation phase theUniverse came back to its standard, much slower expansion. Such a rapid inflation

erased from the Universe all vestiges of its pre-inflationary state; in this way, theinitial conditions are unim portant. On the othe r h and , regio ns of the U niv erse , now

n S e e , Z .A. Go Ida, M. Szyd low ski, and M. Heller, "Generic and Nongen eric W orld

Models," General Reativity and Gravitation 19 (1987): 707-18; and A. Woszczyna and M.

Heller, "Is a Horizon-free Cosmology Possible?," General Reativity and Gravitation 2 2

(1990): 1367-86 .

1 2 A. Guth, "Inflationary Universe: A Possible Solution to the Horizon and Flatness

Problems," Physical Review D23 (1981): 347-56 .

1 3 A.D. Linde, "A New Inflationary Scenario: A Possible Solution of the Horizon,

Flatness, Homogeneity, Isotropy and Primordial Monopole Problems," Physical Letters108B (1982): 389-93 .

"Strictly speaking, the factor is p+3p, where p is the energy density and p the pressure

of the fluid filling the Universe.



CH A O S , PRO B AB IL IT Y, AN D CO M PRE H E NS IB IL IT Y 113

very dis tant from each other, remember information from the epoch when theywere in mutual contact. In this way the horizon problem can be overcome.1 5

However, one should notice that the inflationary strategy is able to explain

probabilistically the present large-scale properties of the Universe only if the setof initial conditions leading to the inflationary pha se is "large en ou gh " in the spaceof all initial conditions. There are strong suspicions that this is not the case.1 6 If thisis true we again face the problem of fine-tuning to explain the inflation itself. Andso, difficult questions return through the back door.

3 Laws rom No-Laws

The standard view today, underlying all efforts to achiev e the final unifica tion ofphysics, is that at extremely high energies, somewhere beyond the Planckthreshold, everything had been maximally symmetric, and that the subsequentbreaking of this primordial symmetry led the Universe to its present diversifiedrichness of forms. There is, however, another possibility: there could be nosymmetry at high energies at all or, equivalently, all possible symmetries couldcoexist on an equal footing, with order and law emerging only later from theprimordial chaos. Barrow and Tipler, considering this po ssibility, ask th e fol low ing

questions: "'Are there any laws of Nature at all?' Perhaps complete microscopicanarchy is the only law of Nature?" 1 7 What we now call the laws of nature wouldbe the result of purely statistical effects, a sort of asymptotic state after a longperiod of averagin g and selecting processes. "It is possible that the rules w e nowperceive governing the behavior of matter and radiation have a purely randomorigin, and even gauge invariance may be an i l lusion' : a selection effect of thelow-energy world we necessari ly inhabit ." 1 8

There are several attempts to implement this philosophy in working physicalmodels. I shall mention two of them.

(1) W ithin the so-called chaotic gauge program only preliminary results havebeen obtained so far. The idea is to show that physical laws and symmetries shouldarise, by some averaging processes, from a fundamental, essentially lawless andnon-symmetric, level. In this approach, at low energies (i .e. , on our macroscopicscale) on e sees maximum symmetry, but this gradually disappears if we penetrateinto more fundamental levels of high energies.1 9 In particular, this approach shouldrefer to gauge symmetries, which seem to play an ever increasing role in

1 5SeeL.F. Abbot and So-Young Pi , eds. nflationary Cosmology (Singapore: W orld

Scientific, 1986).

, 6 S e e G eor ge F.R. Ellis and W illiam Stoeger, "H orizons in Inflationary Unive rses,"

Classical and Quantum Gravity 5 (1988): 207-20.1 7Barrow and Tipler,Anthropic Cosmological Principle 256.1 8Ib id .1 9 S e e J. Diopoulos, D.V. Nanopoulos, and T.N. Tomaras, "Infrared Stability or Anti-

Grandunification," Physics Letters 94B (1980): 141-44.



114 MICHAEL HELLER

contemporary physics. The prop onen ts of this program write: "It would be nice toshow that gauge invariance has a high chance of arising spontaneously even ifnature is not gauge invariant at the fundamental scale ." 2 0 Or more technically, it

would be nice to show that if the Lagrangian, from which physical laws are to bederived, is chosen at random, then at low energies local gauge invariance willemerge, and it will be a stable property in the space of all possible Lagrangian-based theories. However, the same authors were only able to show that a gaugetheory arises at low energies fro m a the ory wh ich at high ene rgies differs f rom theexact gauge invariant theory b y no m ore than a specified am oun t of non-in variantinteractions, that is, that it is necessary to assume an approximately gauge-invarianttheory at high energies in order to obtain the usual gauge theory on our scale.Advo cates of this program express their hop e that, by using this strategy, it will b e

possible to estimate the order of mag nitude of at least som e fund am ental constantsand to dem onstrate their quasi-statistical origin.

(2) Another possibility is Linde's chaotic inflationary cosmology.21 T hedynamics of the Linde universe is dominated by a non-equilibrium initialdistribution of a non-interacting scalar field ({> with the mass m, m«Mp, whereM p~ 1 0 1 9 GeV is the Planck mass. If the Universe contains at least one domain ofth e size b H ' 1 ^ ) w i th (J )^M P(M P /m ) ' , w here H =R '/R, R being the scale factor ofthe locally Friedman universe, it endlessly reproduces itself in the form of

inflationary mini-universes. In fact, this reproduction process leads to anexponentially growing number of causally non-interacting universes. Since thebirth of each new mini-universe is independent of the history of the motherUniverse, "the whole process can be considered as an infinite chain reaction ofcreation and self-reproduction which has no end and which may have nob e g i n n i n g . " 2 2 When, during such a birth process, the Universe splits into manycausally disconnected mini-universes of exponentially growing sizes, "all possibletypes of compactification and all possible vacuum states are realized."2 3 This leadsto various kinds of physics in various daughter-universes. Linde writes:

Whereas several years ago the dimensionality of spacetime, the vacuumenergy density, the value of electric charge, the Yukawa couplings, etc. ,were regarded as true constants, it now becom es clear that these "co nst an ts"actually depend on the type of compactification and on the mechanism of

2 0 D . Foerster, H.B . N ielsen , and M . Nino mi ya, "Dynam ical Stability of L ocal G aug e

Symmetry," Physics Letters 94B (1980): 135-40.2 1 See, A.D. Linde, Fizika Elementarnykh Chastits I Infliatsionnaia Kosmologiia

[Physics of Elementary Particles and Inflationary Cosmology] (Moscow: Nauka, 1990); and

idem, "Inflation and Quantum C osm ology," in 300 Years of Gravitation, S.W . Haw king and

W . Israel, eds. (Cambridge: Cam bridge University Press, 1987), 6 04- 30.

2 2 Linde, "Inflation and Quantum Cosmology," 618.

^ i d . , 627. Roughly speaking, by compactification L inde understands the process by

which the number of space-time dimensions is established inside the newly-born mini-

universe; this number may be different from that of the mother Universe.



CH AO S , PRO B A B IL IT Y, AN D CO M PRE H E NS IB IL IT Y 115

symmetry breaking, which may be different in different domains of ouru n i v e r s e . 2 4

In this way, a "chaos" 25 is realized not within the one Universe but within the

ensemble of many universes, and som e sort of the anth ropic princip le is ne cessaryif our "local universe" is to have the physical laws we now discover and thes truc ture we now obse rve . 2 6

4 Probabilistic Com pressibility of the Wo rld

The strategy presented in the two preceding sections was aimed at understandingthe Universe by reducing its laws and structure to a pure game of probabilities. Our

first reaction to such strategies is that if one of them succeeds (especially one oftheir stronger versions presented in section 4), then the "eternal mystery of theworld's comprehensibility" that Einstein stressed would disappear: comprehensi-bility would give place to probability and mystery would change into an averagingmechanism. However, to go beyond "first reactions" and to critically assess suchan approach to the "rationality of the world," we must turn to the foundations ofthe probability c alculus. This is the aim of the present section.

Many branches of modern mathematics have their origin in an interplay of

theory and application. This is also true as far as the probability calculus isconcerned. Moreover, one would be inclined to say that in this case m ore depe ndson application than on theory. This is not only because the probability calculusoriginated from experience but mostly because it is very difficult to separate thevery notion of probability from its empirical connotations. This fact gave rise tomany philosophical discussions concerning the foundations of probability. In whatfollows I shall try to avoid entering into these discussions; instead I shall trace themeaning of some fundamental concepts by placing them within the mathematicalstructure of the probability theory in its standard (Kolmogorov) formulation. 2 7

In the contemporary standard approach, probability theory is a specialinstance of measurem ent theory. Measure, in the mathem atical sense, is a func tiondefined on subsets of a certain space called the measure space. These subsets ,called measurable subsets y can be thought of as objects to be measured. Thefunction defined on these objects ascribes to each of them the result of ameasurement (i .e. , i ts measure, a number). For instance, the objects in questioncould be subsets of the Euclidean space and the measure a function ascribing to

2 4 Ib i d .

^ this case, as in the case of the chaotic gauge program, the term 'chaos* is not used

in the technical sense of deterministic chaos, although one could expect that in both cases

deterministically chaotic phenomena (in the technical sense) are involved.

^See Barrow, The World within the World (Oxford: Clarendon Press, 1988), 281-89.

R eg ar din g different views and philosophies of probability, see D. Home and M.A.B.

Whitaker, "Ensemble Interpretations of Quantum Mechanics: A Modern Perspective,"

Physics Reports 210 (1992): 223- 317.



116 MICHAEL HELLER

each subset its volume. From the mathematical point of view, the essentialcircumstance is that outside the measure space the concept of measuring ismeaningless .

Some cases are known in which not every subset of a given space ismeasurable. In such a space there are "thing s" (subsets) wh ich can not be m easu red ,that is , no measurable result can be meaningfully ascribed to them. This runscounter to the com mo n view that "wh at cann ot be measu red d oes not exist." S uchsubsets might indeed seem rather unu sual, but on e can find them even in the openinterval (0,1) of real n um be rs . 2 8

Probability is just a mea sure satisfying one additional condition: the measureof the entire space should be equal to o ne. C onseq uently, the m easu re of an y of itssubsets is either zero or a fractio n betw een zero and one . If this axiom is satisfied

the measure space with its measurable subsets is called probability space, and themeasure defined on it the probability distribution.

Let us no tice that so far there is nothin g in our theory wh ich w ould suggestthe uncertainty or indeterm inacy w e intuitively con nect w ith the idea of p roba bil-ity. All consequences follow from the axioms in a strictly apodictic manner,exactly the same as in other m athem atical theo ries. Intuitions w e connect w ith th econcept of probabil i ty enter our theory via its reference to reality, that is, via itsinterpretation. The standard method of referring mathematics to reality is by the

intermediary of physics: some mathematical structures are used as building blocksof a physical theory, and the task of this theory is to investigate the world. Themathematical theory of probability, however, seems to relax this rule. It oftenmakes referen ces to reality with no direct help of a physical theo ry. For instance,when making probabilistic predictions of the outcome of throwing dice or of aprice increase in an approa ching fiscal year, a certain ph ysical-like interpretationof a mathematical structure must intervene, but it is so natural and so closely linkedto the mathematical structure itself that we prefer not to call it a physical theory butrather a probabilistic model of a given situation (with no reference to physics).

To be more precise, physical intuition enters the probabilistic model throughthe definition of the probability distribution. For instance, if we want to modelplaying with ideal dice math em atically, w e defin e the probability d istribution as afunction which ascribes to each elementary event, that is, to each of six possibleoutcomes, the value of the probability m easu re equal to 1/6. This particular v alueis taken from experience, namely from a long series of throw ing dice, but onc e putinto the definition of the probability distribu tion, it bec om es a structural par t of themathematical theory itself.

The feeling of a "probabilistic unc ertainty" is connectcd with the frequency

interpretation of the distribution fun ction de fined in the abov e w ay. The v alue 1/6

^For examp le, let aand bbe real numbers in the open interval (0,1). If a-b is a rational

number we write a#b. This is clearly an equivalence relation. We define A to be a subset of

real numbers consisting of exac tly one number of each equiva lence class. It can be show n

that A is not measurable. See Robert Geroch, Mathematical Physics (Chicago: University

of Chicago Press, 1985), 254-55.



CHA OS, PROBA BILITY, A ND COM PREHENSIBILITY 117

of the distribution function at a given (elementary) event, for instance at the event"outcome three," is interpreted as giving the relative frequency of the "outcomethree" (i.e. , the ratio of the number of fortuitous events, in our case "outcome

three," to all possible events) in a long series of thro w ing dice. In deed, exp erim entsshow that, in this circumstance, relative frequencies are approximately equal to 1/6.The longer the series of throws, the closer the relative frequency approximates thisvalue. This property of the world is known as its frequency stability. It is a propertyof the world, and not of the mathematical theory, since it is taken from experienceand has no justificatio n in the theory itself.

The frequency stability of the world is of fundamental importance for ouranalysis. In both everyday life and in physics we often meet random events orrandom experimental results. The result of an experiment is said to be random if

it is not uniquely determined by the conditions under which the experiment iscarried out and which remain under the control of the experimenter. Subsequentresults of such an experiment are unpredictable. If in a series of n such experi-me n t s , n A experiments give the result A, and n-% give some other results, thenumber f(A) = njn is called the frequency of A. It turns out that as n is larger andlarger, f(A) approaches a certain number more and more closely. This tendency tocertain numerical results reflects the world's frequency stability.

This is indeed an astonishing property. One cannot see any a priori reason

why the world should be stable in this respect. But the world is frequency stable,and it is clear that without this property the probability calculus could not beapplied to analyze the occurrence of events in the world. We can say that owing toits frequency stability the world is probabilistically compressible. A priori w ecould expect that truly chaotic or random phen om ena would evade any m athem ati-cal description, bu t in fact the description of pheno m ena we call random or chaoticis not only possible but can be compressed into the formulae of the probabilitytheory. The probabilistic compressibility of the world turns out to be a specialinstance of its algorithmic compressibility, and one would dare to say that it is the

most astonishing (or the most unreasonable) instance of it .This is even mo re the case if we remember that the applicab ility of pro bab ilis-

tic ideas to the real world u nderlies m uch of the foun datio ns of statistical physics,and also the derivation of the classical limit of quantum theory, as well as theanalysis of observations. All these aspects of probability applications are closelyrelated to the problem of the arrow of time. Since the law s of fund am ental physicsare time reversible they mu st be involve d in a subtle ga m e of pro bab ilities in orde rto produce irreversible phenomena on a macroscopic scale. There are strongreasons to suspect that the answer to the question of why the cosmic process

evolves in time, rather than being reduced to an insta nt, is but another aspec t of theprobabilistic compressibility of the world.

And we should not forget that probability theory is as good as any othermathematical theory. The distribution function is defined by idealizing someexperimental results, but the probabilistic model, once constructed, producesuniquely determined results. The frequency interpretation of the probabilisticaxioms does not influence formal inferences or the manipulat ion of formulae; itonly allows us to look at the Universe in a special way—in a way in which events

are not just g iven but seem to have a certain potentiality to happen, and the cosmic



118 MICHAEL HELLER

process does not just unf old but se em s to have th e possibility of choo sing variou sbranches in its unfo lding.

The above considerations have shown that even if we were able to reduce the

comprehensibility of the world to its probabilistic compressibility (as it waspresupposed by the strategies and ph ilosoph ies presented in sections 2 and 3), thequestions would remain: Why does probabil i ty theory apply to our world? Whyhas our world the property of being frequen cy s table?

W hen w e ask the question "W hy is the world ma them atical?" we should alsowonder why it is subject to the "game of probabilities." Clearly the riddle ofprobability does not eliminate the mystery of comprehensibility.

5 God of Probabilities

The ideas presented in sections 2 and 3 have their origin in an interesting propertyof the human mind, for which the high probability of an event is a kind ofsufficie nt reason f or its occu rrence, b ut low probab ilities alway s call fo r so m especial justification. One could guess that this property of our mind has evolvedthrough an intricate agglomeration of selection effects in the world, the structureof which is predom inantly shaped by frequency-stab le processes .

In classical natural theology, the justification of low probability events wasoften sought in the direct action of God. The low probability itself was consideredto be a gap in the natural course of events, a gap that had to be filled in by the"hypothesis of God." In this way, high probabil i ty becomes a r ival of God. Wehear the echo of such views in metapho rs contemp orary scientists so m etim es ev ok eto impress the reader with how finely the initial conditions should be tuned toproduce the Universe in which the reader-like be ing could be b orn and evolv e. Forinstance, in a famous book by Roger Penrose, the caption under the picture of Godpointing with the pin to the initial conditions (or equivalently to the point in phase

space) from which God intends to create the world, reads:In order to produce a universe resembling the one in which we live, theCreator would have to aim for an absurdly tiny volume of the phase spaceof poss ib le universes—about 1 / 10 1 0 1 2 3 of the entire volume. 2 9

On the contrary, the at tempt to reduce phenomena to the random eventshiding behind them (e.g. , to random initial conditions) is often thought of assupporting an atheistic explanation. For instance, the main argument of Leslie 'sbook on the anthropic principles 3 0 is that the principal competitor of the Godhypothesis is the idea of multiple worlds in which all possibilities are realized,along with some observational se lection effects which w ould just ify our ex is tenceas observers of our world. The God hypothesis relies on the argum ent f rom design,

2 9R oge r Penrose, The Emperor's New Mind: Concerning Computers, Minds, and theLaws of Physics (New York: Oxford University Press, 1989), 343.

3 0

L es l i e , Universes. See also Barrow and Tipler, Anthropic Cosmological Principle.



CH AO S , PRO B AB IL IT Y, AN D CO M PRE H E NS IB IL IT Y 119

which is "based on the fact that our universe looks much as if it were designed."However, there might be immensely many universes .

And their properties are thought of as very varied. Sooner or later,

somewhere, one or more of them will have life-permitting properties. Ouruniverse can indeed look as if designed. In reality, tho ugh , it ma y be m erelythe sort of thing to be expected sooner or later. Given sufficiently manyyears with a typewriter even a mo nkey w ould produce a s on net .3 1

A different view of probability ca m e with the adven t of quantum m ech anics .The Hilbert space, an arena (in fac t, the phase spa ce) in w hich quan tum proce ssesoccur, is a very beautiful and very solid mathematical structure, but wheninterpreted in a standard prob abilistic way it reveals the unexpected ima ge of themicro-world: Wave functions, containing all information about a quantum object,are essentially non-local en tities. They are define d eve ryw here; for instance, fr omthe wave function you can compute the probability of finding an electron at anyplace in the Universe. Wave functions evolve in time in a strictly deterministicway, but when a measurement is performed deterministic evolution breaks down,all available information reduces to the unique measurement result, an infinitenumber of possibilities collapses to the single eigenvalue of the measurementoperator.32 Less informed philosophers speak about th e free will of electrons; betterinformed ones see that the time-honored antinomy between lawfulness and

probability should be reconsidered ab initio.Recent developments in deterministic chaos theory have shown that this is

also true as far as the macroscopic world is concerned. An instability of the initialconditions leads to unpredictable behavior at later times, and there are strongreasons to believe that a certain am oun t of such a rando m ness is indispen sable forthe emergence and evolution of organized structures.

The shift we have sketched in our views on the signific ance of p rob ability hashad its impact on modern natural theology. Randomness is no longer perceived asa competitor of God, but rather as a powerful tool in God's strategy of creating the

world. For instance:G od is responsible for ordering the world, not through direct action, but byproviding various potentialities which the physical universe is then free toactualize. In this way, God does not com prom ise the essential ope nne ss andindeterminism of the unive rse, but is nevertheless in a position to enc our-age a trend toward good. Traces of this subtle and indirect influence maybe discerned in the progressive nature of biological evolution, for example,

31 Lcslie, Universes 1. However, Leslie clearly expresses his own opinion: "While the

M ultiple Worlds (or World Ensem ble) hypothesis is impressively strong, the God hypothesis

is a viable alternative" (p. J).

3 2 In quantum theory, any measurement is represented by an operator acting on the

corresponding w av e function. E igenva lues of this operator represent poss ible results of the

measurement.



120 MICHAEL HELLER

and the tendency for the universe to self-organize into a richer variety ofever more complex forms. 3 3

O r:

On this view Go d acts to create the world through what we call "chanc e"operating within the created order, each stage of which constitutes thelaunching pad for the ne xt Ho we ver, the actual cou rse of this unfold ing ofthe hidden potentialities of the world is not a once-for-all pre-determinedpath, for there are unpredictabilities in the actual systems and processes ofthe world (micro-events at the "Heis enb erg " level and possibly no n-lineardynamical complex system s). There is an open -ended ness in the course ofthe world's ' 'natural" history. We now have to conceive of God as involvedin ex plor ation s of the m any k inds of unfulf illed potentialities of theuniverse(s) he has created. 3 4

Still, either a God with a sharply pointed pin in hand choosing the improbableinitial conditions for the Universe, or a God exploring the field of possibilities byplaying with chance and randomness, seem to be but a Demiurge constrained byboth a chaotic primordial stuff and the mathematical laws of probability (just asPlato's Demiurge was bound by the preexisting matter and the unchanging worldof ideas). Of course, we could simply identify the laws of probability with God (orwith the ideas present in God's mind), but this would bring us back to all

traditional disputes surrounding the Platonic interpretation of God and mathemat-ics.

Instead of immersing ourselves in risky disputes, I believe we should oncemo re ask Ein stein 's question: W hy is the world so comp rehensible? As w e haveseen, there is no escape from this question via the "gam e of probabilities," since ifwe reduce comprehensibility to probability, new questions will emerge: Whyshould the theory of probability be privileged among all other mathematicaltheories? 35 Why is the world probabilistically compressible? And if the answer tothe last question is: The world is probabilistically compressible since it enjoys the

property of being frequency stable, we will then ask: Why is it frequency stable?Any natural theology is sentenced to the "God of the gaps" strategy. But if

there are no gaps in the natural order of things, if the world is a self-enclosedentity, then there is no way from the world to its maker. The essential point is todistinguish between spurious gaps and g enu ine o nes. Sp urious gaps are tem pora ryholes in our knowledge usually referring to an incomplete scientific theory orhypothesis and to a restricted domain of phenomena. Genuine gaps are trulydisastrous; they overwh elm everything. I think that all gaps are spurious except forthe follow ing two or three:

"Pau l Dav i es , The Mind of God: The Scientific Basis for a Rational World (New

York: Simon & Schuster, 1992), 183. Davies refers here to Whitehead's philosophy of God.

^Arthur R. Peacock, "God as the Creator of the World of Scienc e," in nterpreting theUniverse as Creation: A Dialogue of Science and Reigion, ed. Vincent BrUmmer (Kam pen,

The Netherlan ds: Kok Pharos, 1991), 110-11.

3 5

To see that this question is not trivial, see section 4.



CH A O S , PRO B AB IL IT Y, AN D CO MPRE H E NS IB IL IT Y 121

First is the ontological gap. Its meaning is encapsuled in the question: Whyis there something rather than nothing? The problem at stake is sheer existence.Even if we had a unique theory of ev erything (and so m e physicists prom ise us we

shall have it in the not too distant future), the question would remain who or what"has breathed fire into the equations" to change what is merely a formallyconsistent theory into one modeling the real universe.

Second is th e epistemological gap: Why is the world comprehen sible? I havedealt with this question in the present paper . It is truly a gap . Science presup posesthe intelligibility of the world, but does not explain it. Philosophy of science canat most demonstrate the non-trivial character of this question, but remains helplessif one further asks "Why?"

From the theological perspective both gaps, the ontological gap and the

epistemological one, coincide: everything that exists is rational, and only therational is open to existence. The source of existence is the same as the source ofrationality.

I strongly suspect that there is the third genuine gap; I would call it theaxiological gap—it is connected with the meaning and value of everything thatexists. If the Universe is somehow permeated with meaning and value, they areinvisible to the scientific method, and in this sense they constitute the real gap asfar as science and its philosophy are concerned. Here again, by adopting the

theological perspective, I would guess that the axiological gap does not differ f romthe remaining two: the sources of existence, rationality, and value are the same.

Modern developments in science have discovered two kinds of elements (inthe Greek sense of this word) shaping the structure of the Universe—the cosmic

elements (integrability, analycity, calculab ility, and predicta bility), an d the chaotic

elements (probability, randomness, unpredictability, and various stochasticproperties). I think I have convincingly argued in the present paper for the thesisthat the chaotic elem ents are in fact as "math em atical" as the cosm ic ones, and ifthe cosmic elements provoke the question of why the world is mathematical, the

same is true as far as the chaotic elements are concerned. On this view, cosmos andchaos are not antagonistic forces but rather two components of the same Logos

imm anent in the structure of the Univ erse .36 Einstein's question: "Why is the worldso comprehensible?" is a deeply, and still not fully understood, theologicalquestion.

^For examples of such a cooperation between "cosmic" and "chaotic" elements see

my paper 'Th e Non-Linear Universe: Creative Processes in the Universe" (espe cially section

5), to be published in the Proceedings of he Plenary Session of he Pontifical Academy of

Sciences (1992) .



C H A N C E A N D L A WIN I R R E V E R S IB L E T H E R M O D Y N A M I C S ,

T H E O R E T I C A L B I O L O G Y , A N D T H E O L O G Y 1

Arthur R. Peacocke

There is an element of "necessity" in the universe, the giveness, from ourpoint of view , of certain of its bas ic features: the fundam ental constants , the natu reof the fundamental particles (and so of atoms, and so of molecules, and so ofcomplex organizations of molecules), the physical laws of the interrelation of

matter, energy, space, and time. We are in the position, as it were, of the audiencebefore the pianist begins his extem porizations— there is the instrum ent, the re is therange of available notes, but what tune is to be played and on what principle andin what forms is it to be developed?

1 Chance

Given the limiting features wh ich con stitute our necessity, ho w are the potentiali-ties of the universe going to be mad e m anifest? Jacques M on od's answer was thatit is by "chance": indeed humankind's emergence in the "unfeeling immensity ofthe un iver se" is said to be "only by chance ." 2 So the question to which we turn isthat of the roles of chan ce and necessity , or "law ," in the evolutionary proces s, inparticular in the origin and development of living forms, and of the implicationsof this balance-and-interplay fo r discourse about belief in God as crea tor. (By 'law*here is meant the law-like framework constituted by the constraints of the laws ofphysics, chemistry, etc. , and of the fixed values of the fundamental constants.) It

will transpire that, by and large, I agree that chance, appropriately defined, is themeans whereby the potentialities of the universe are actualized but that from thisI shall draw conclusions d ifferent fro m those of M onod .

Ch ance has often been apotheosized into a metaphysical principle threateningthe very possibility of finding meaning in human life, as recognized in the bitter

*Paper given at the conference on "Our Knowledge of God and Nature: Physics,

Philosophy, and Theology," organized by the Vatican Observatory and held at Castel

Gandolfo, September 21-26, 1987. The proceedings of that workshop, which were

published as Physics, Philosophy and Theology: A Common Quest or Understanding, ed.

Robert John Russell, W illiam R. Stoeger, and George V. C oy ne (Vatican City State: Vatican

Observatory, 1988), did not contain this paper, which was published separately in

Philosophy in Science 4 (1990) : 145-80.

2Jacques Monod , Chance and Necessity: An Essay on the Natural Philosophy ofModern Biology, trans. Austryn W ainh ouse (London : Co llins, 1972), 267 .



124 ART H UR R. PE ACO CK E

comment of the author of Ecclesiastes: "Time and Chance govern all."3 In theancient Greek m yths Chanc e reigned in Ch aos , that state of affairs which precededthe Cosmos we now inhabit . Chaos was the mythical s tate of affairs which

preceded the emergence of the world order, of Cosmos, which was thought tom anife st itself in the totality of natural p hen om ena.

Even before Darwin, many w ere disturbed by this ancient fea r of chaos ruledby chance, and the publication of his ideas gave an impetus to the anguish of thosealready despairing of find ing me anin g or purp ose in the unive rse. To attribute theprocesses of the universe to "chance" can trigger off in the sensitive a profoundsense of despair at the m eanin glessne ss of all life, and of hu m an life in p articular.Such an emotive word warrants closer analysis , for there are more precisemeanings which may be given to it in the context of the sciences.

1.1 Two Meanings of'Chance9

For our present purp oses w e can dis t inguish usefu lly two m eanings of Chance.*(1) W hen w e toss a coin w e say that the ch ances of it coming dow n h eads or

tails are even . W e mean that in any long run of coin tossings 50% will come down"heads" and 50% "tails" to a proportional accuracy which increases with thenumber of throws w e mak e. But w e also know that, had we sufficient knowledge

of the exact values of the relevant parameters, the laws of mechanics would enableus in fac t to say in any particular toss which way th e coin wo uld fall. In practice wecannot have all the information needed to analy ze these m ultiple causes, and all w ecan know is that their net effect is equally likely to produce "heads" as "tails" afterany individual tossing. S o to apply 'ch an ce ' in this context is simply to reco gniz eour ignorance of the multiple parameters involved. It is a confession of our partialignorance, partial because we do know enough from the symmetry of the problemto say that in any long run of such tossing s there w ill be an equal nu m ber of he adsand tails uppermo st at the end of the process. Th e use of the word 'ch an ce ' in this

context does not imply a denial of causality in the sequence of events.(2) A second use of the word 'chance' is that of the intersection of two

otherwise unrelated causal chains. Suppose that when you leave the building inwhich you are reading these pages, as you step onto the pavement you are struckon the head by a hammer dropped by a man repairing the roof. From thisaccidental collision many con sequ ence s m ight follow f or your me ntal life and forthe welfare of your families. In ordinary parlance we w ould say it was due to "pu rechance." The two trains of events—your leaving the building at the time you didand the dropping of the ham m er— are eac h within themselve s exp licable as causalchains. Yet there is no connection between these two causal chains except theirpoint of intersection, and when the hammer hits you on the head could not havebeen predicted from within the terms of reference of either chain taken by itself.In this case causality is again not denied, but because there is no cross-connectionbetween the two causal chains we could not, unlike the previous case of the tossing

3

Eccl . 9 :11 .



C H A N C E A N D L A W 125

of a coin, m ake any accurate prediction of th e cha nce of it hap pen ing. (The second

instance is sometimes more properly called 'accident , ' and some authorsdistinguish between chance and accident in this sense.)

Much more needs to be said (and indeed is said in the vast literature on themathematical theory of probability); at least this initial simple analysis serves toshow that when, in ordinary parlance, some event is said to be 'due to chance' thisphrase is really not giving an explanation of the event in question or saying whatits cause is but is simply acting as a stop card. It is saying in effect "the event inquestion has many mult iple causes or seems to have been the result of the

intersection of unrelated causal chains, so that we cannot attribute any particularcause to it ." It is therefore a phrase to be avoided in our discussion. No doubt thephrase 'due to chance' has acquired currency because many of the laws in naturalscience are statistical in character. They do not take the form of statements to theeffect that event or situation A will be followed by event or situation B but ratherof the form tha t A will be followed by BB or B with different respectiveprobabil it ies . Whether this incom plete know ledge of the consequen ce of A arisesfrom a fundamental absence of causality in the old sense or is the consequence ofthe incompleteness of our knowledge of the operative multiple causes (as in the

coin-tossing example) will depend on the particular situatio n. Th e firs t of thes e tw oalternatives, a fundamental absence of causality, is sometim es called 'pu re ch an ce. 'An y event wh ose cause has not yet been discovered m ay b e view ed either a s a pu rechance event, which possesses no cause, or as a complex event of cause as yetunknown. However, the very notion of pure chance, of uncaused events in thesense of absolutely unqualified disorder, is self-contradictory as well as runningcounter to a basic assumption of scientists in their, not unsuccessful, work . As iswell known, the Heisenberg uncertainty principle raises important questionsconcerning causality at the sub-atomic level, but even such micro-events followstatistical probabilistic laws.

2 The Life Gam e

Until the recent past, cha nce and law ha ve of ten been regarded as alternatives forinterpreting the natural world. But the interplay between these principles is moresubde and complex than the simple dichotomies of the past would allow. For any

particular state of a system w e hav e to weigh c arefu lly what the eviden ce is abouttheir respective roles in determining its present behavior and for interpreting itspast. Th e origin and development of living orga nism s is no ex ception , and we nowmust consider some interpretat ions of the l ife game which have emerged fromscientific work of the last three decades—I refer to the ideas of Monod, inmolecular biology, and Ilya Prigogine in irreversible thermodynamics andtheoretical biology.




2.1 Mutations and Evolution

The contemporary debate was sparked off in the early 1970s by Monod, the French

molecular biologist and Nobel Lau reate, in his boo k Chance and Necessity, whichenjoyed a succis de scandale. He contrasted the "chance" processes which bringabout m utations in the genetic material of an organism and the "ne cessity " of theirconsequences in the well-ordered, replicative, interlocking mechanisms whichconstitute that organism's continuity as a living form. He pointed out thatmutations in the genetic material, DNA, are the results of chemical or physicalevents, and their locations in the molecular apparatus carrying the genetic informa-tion are entirely random with respect to the biological nee ds of the org anis m . T hu s,one causal chain is a chain of events, wh ich m ay be the chemical m odificatio n ofone of the nucleotide bases in DNA or its disintegration through absorption of aquantum of ultraviolet or cosm ic radiation. T hese c hanges in the nucleotide bases,and so in the information which the DNA is carrying, are incorporated into thegenetic apparatus of the organisms only if they are not lethal and if, on interactingwith its environment, they produce an organism which has a higher rate ofreproduction than before. This sequence represents a second causal chain—theinterplay between the genetic constitution (and behavior) of a living organism andthe pressures to w hich it is subjected by the environment. These two causal chains

are entirely independent, and it is in the second sense of chance that Monod iscorrect in saying that evolution depends on chance. It also qualifies for thisdescription, in the other sense of chance, since in most cases we are not now in aposition to specify all th e factors which led to the mutated organisms being selectedand, even less, the mechanism by which mutation was induced in the first place.(Indeed this latter is at a level at which quantum considerations begin to operateand is fundam entally precluded from any exact predict ion.)

The molecular biology of recent years has thus been able to give a muchmore detailed picture of the process of the interplay between mutation and

environment. This is the basis on which Monod stressed the role of chance:Pure chance, absolutely free but blind, at the very root of the stupendousedifice of evolution: this central concept of modern biology is no longerone among other possible or even conceivable hypotheses. It is today thesole conceivable hypothesis, the only one compatible with observation andtested fact. And nothing warrants the supposition (or the hope) that concep-tions about this should, or ever could, be revised.4

Monod went on to draw the conclusion that Homo sapiens, and so all theworks of human mind and culture, are the products of pure chance and thereforewithout any cosmic significan ce. The u niverse m ust be seen not as a directionallyordered w hole (a cosmos) bu t as a giant Monte Carlo saloon in which th e dice ha vehappened to fall out in a way which produced humanity. There is no generalpurpose in the universe and in the existence of life and so none in the universe asa whole. It need not, it might not, have existed—nor might we!

4

M o n o d , Chance and Necessity, 110.



C H A N C E A N D L A W 1 27

However , pace M ono d, I see no reason why this random ness of m olecularevent in relation to biological consequence, which Monod rightly emphasized, hasto be raised to the level of a metaphysical principle interpreting the universe, for,as we have already seen, in the behavior of matter on a larger scale manyregularities, which have been raised to the level of being describable as "laws,"arise from the combined effect of random microscopic events which constitute themacroscopic. So the involvement of chance at the level of mutations does not, of

itself, preclude these events manifesting a lawlike behavior at the level ofpopulations of organisms and indeed of population of biosystems that may bepresumed to exist on the many planets throu gho ut the unive rse w hich m ay suppo rtlife. Instead of being daunted by the role of chance in genetic mutations as beingthe manifestation of irrationality in the universe, it wo uld be m ore consistent withthe ob servation s to assert that the full gamu t of the potentialities of living ma ttercould be explored only through the agency of the rapid and freq ue nt rand om izationwhich is possible at the molecular level of the DNA. In other words, the designa-

tion 'chance* in this context refers to the multiple effects whereby the (very large)number of mutations is elicited that constitute th e "no ise," wh ich, via an indep end-ent causal cha in, the environm ent then selects for viability. This role of chanc e iswhat one would expect if the unive rse w ere so con stituted as to be ab le to explo reall the potential forms of organizations of matter (both living and non-living)which it contains. M oreover, even if the present biolog ical wo rld w ere on ly o ne outof an already large number of possibilities, it must be the case that the potentialityof forming such a world is present in the fundamental constitution of matter as itexists in our universe. The original primeval cloud of fundamental particles must

have had the potentiality of being able to develop into the complex molecularforms we call modern biological life. It is this that I find significant about theemergence of life in the universe, and the role of chance, in both its forms, seemsto m e neither repu lsive nor attractive but simply wha t is required if all the poten -tialities of the universe, especially for life, were going to be elicited effectively.

Since Mo nod w rote Chance and Necessity there have been developm ents intheoretical biology wh ich cast new light on the interrelation of chanc e and law inthe origin and evolution of life. In these developments it is possible to see moreclearly than M onod was able to analyze, in his consideration of the mutation of thegenetic material and their consequences for natural selection, the way in whichchance processes can operate in a law-regulated system to produce new forms oforgan ized and in form ation -carry ing systems of the kind which life requires. Tothese m ore recent ideas we must now turn.



128 A R T H U R R . P E A C O C K E

3 Irreversible Therm odynam ics and Theoretical Biology

"All kinds of private metaphysics and theology have grown l ike weeds in the

garden of therm odyn am ics . "5

This pung ent judg m ent of a dis t inguished his torianof science serves to remind us that, although thermodynamics has an austere andlofty intellectual and architectonic framework, it has nevertheless frequentlygenerated a plethora of gloomy emotions in those who have attempted to apply iton a cosmic scale .

What, in fact, is this aspect of modern physics and physical chemistry towhich is attributed such dire consequences? R.A. Butler wrote a book on politicsa few years ago which he called The Art of the Possible.6 Thermodynamics is thescience of the possible—it stands in relation to science as a whole very much aslogic does to ph iloso ph y. It does not in vent; it proscribe s. Parad oxically, classicalthermodynamics has been mo st successful in deriving the relationships that c harac-ter ize ph ysical sy stem s at equilibrium , that is , just those system s in which allprocesses are reversible, unlike m ost actual system s w hich u sually involve naturalirreversible pro cesse s. Th e state of equilibrium is that to which all processes tendto lead any actual system. So classical thermodynamics deals accurately andpow erfully with a kind of lim iting w orld— that to which the actual tends. It is not,on that account, to be underest imated. The therm odynam ic account of equil ibrium

and its interpretation of natural processes may be regarded as one of the bestestablished pillars of modern science.

It was one of the great achievements of nineteenth-century science which ledto the formulation of a property, the en tropy (5), that not only m easured the e xtentof irreversibility in a natura l proc ess in a par ticula r sy stem but wa s also a pro per tyof the state of that sam e system . The secon d law could then be stated in the form :"In any real process, there is always an increase in entropy." The greater the valueof the increase in entropy (AS) in a natural process occurring in a particularsystem, the greater the extent of its irreversibility—that is , the more "degraded"

and less available for perfo rm ing mechanical work had the energy beco m e in theprocess , and the more i t had become chaotic , thermal energy. Thus, changes inentropy measured something to do with the "character," and not simply thequantity, of energy in a system.

W hat this "character" was, that was related to availability to perform directedmechanical work, only became clear with the later development of statistical

thermo dynam ics, part icularly at the hands of L. Boltzmann. This developm ent ismo st easily u nderstood in the context of the realization that the e nerg y states of anysystem are all discrete and not continuous (even for translational energy). The"character" of the energy that is related to the entropy was proposed by Boltzmannto be the "spread" or distribution of matter over the possible available energy

^rwin H. Hicbert, 'The Uses and Abuses of Thermod ynamics in Religion," Daedalus95 (1966): 1075.

6Richard Austen Butler, The Art of the Possible: The Memiors of Lord Duller

(London: Hamilton, 1971).




states—the degree of randomness or "disorderliness," as it were, of the matter-energy distribution. To be more precise, the entropy (S) is related to a quantity,denoted as W t which is the "number of complexions" of the system, that is , the

number of possible dispositions of matter over the (equiprobable) available energystates (or, more precisely, the number of micro-states corresponding to a givenm ac ros tate identified through its macroscopic properties). The Boltzmann relationwas s imply:

S = k B In W

where k B , the Boltzmann constant, is equal to the gas constant (R) divide byAvogadro's number (NJ; and In W is the natural logari thm of W (i .e . , base e).

Note that W=l represents a maximum state of "order" with minimum entropy,nam ely zero, since In 1=0.

"Disorderliness" is, in this context, the zero v alue of a variable, "ord erline ss,"which is the extent to which "any actual specim en of an entity appro xim ates to the' ideal ' or pattern against which i t is compared."7 Such "orderliness" reaches itsmaximum extent in the "state of order," which is "an ideal reference state, laiddown and specified, according to certain rules or conventions, which is taken ashaving 100% order l iness . " 8 This "state of order" might well be that of the

geometrical order of a crystal lattice at absolute zero. Orderliness would decrease(i.e., disorderliness would increase) according to the extent to which the atoms ormolecules of the crystal were displaced from the lattice points and/or the extent ofthe spread of its quantized energy states relative to the ground state. For popula-tions rather than single entities, 100% order with respect to any parameter orproperty would be characterized by all the members of the population exhibitingthe same value of that param eter, or the sam e proper ty. So w hen, loo sely, en tropyis said to be a measure of "disor der " or "rand om nes s" it is this kind of orderlinessthat is being referred to. It is , to use an example of Denbigh,9 the kind of order

exemp lified by a perfect wall-paper pattern ra ther than that of an original pain ting .Suc h "o rd er " is therefore scarcely adequate as a measure of the com plexity andorganization of biological systems. Nevertheless it could be affirmed that the kindof b o r d e r measured by entropy is incomp atible with biological com plexity andorganization and, indeed, the state of maximum entropy, of maximum disorder inthe sense de fined , is equivalent to biological d eath. Thus, w e may say that a stateof low entropy is a necessary but not sufficient condition for biological complexityand organization to occur.

7K. Denbigh, "A Non-Conserved Function for Organized Systems," in Entropy andInformation nScience and Philosophy, ed. Libor Kubat and Jiri Zeman (Oxford: Elsevier,

1975).8Ibid.

I b i d .




3.1 Evolution and Thermodynamics—The Problem?

One of the implications of the classical thermodynamic account of natural

processes, just outlined, is that time has, in relation to natural events, a uni-directional character so that entropy has often been called "time's arrow," for theincrease in entropy displayed by natural proc esses appare ntly specifies (or, better,is closely linked co nceptually with) the direction of the flow of time. All of this hasa curious and apparently problematic relation with that other great scientificdevelopment of the nineteenth century—namely the "discovery of t ime" inbiology, more precisely, the idea of biological evolution. Time had already been"discovered" in the eighteenth century in the sense that the development ofgeology as a science had vastly extended the time-scale of the history of the earthas a planet and of the l iving organisms, including human beings, upon i t . Then,with Darwin and Wallace, and the activity their proposal engendered, anunderstanding of both the inter-connectedness of al l l iving forms and of theirprogressive development from single cells (them selves no t so simple) to m ore andmo re complex forms was surprisingly rapidly established, in sp ite of th e op pos itionwe all kno w ab out. Yet, accordin g to one version of the laws of the rm ody nam ics(Clausius): "T he en ergy of the universe is constant; the entropy of the universe isincreasing to a maximum." As we saw, entropy, and so "disorder" in the sense we

have defined, increases in all natural processes. So how is it that living orga nism scan come into existence and survive, swimming, as it were, against the entropicstream carrying all to thermal equilibrium and "heat-death"?

In living organisms, we see natural objects in which, while they are alive,complex organization is being maintained, and even enhanced, against theuniversal tendency of all processes to occur with an overall increase in "disorder."Are living organisms actually, in some way, breaking the second law of thermody-namics by maintaining systems in a high state of organization and so a low stateof disorder, of low entropy? The brief answer to this question is "No," when one

recalls that, for a natural process or change, one must take into account everythingthat changes. Now, l iving organisms are open systems exchanging energy andmatter with their surroundings, and the changes in entropy in both the organismand the surroundings have to be assessed. So it is perfectly possible for there to bea decrease in entropy associated with the processes of metabolism, etc. , occurringin a living organism while at the sam e tim e this decrease is m ore than offset by anincrease in the entropy of the surroun dings of the organism on acc ount of the heatthat passes to these surroundings fro m the orga nis m .1 0 So living organisms, oncein existence, do not in any sense "b rea k" the second law of therm ody nam ics— anymo re than these laws are broken in certain pu rely ph ysical proc esses wh en a m or eordered form of a system is generated with the evolution of heat, for exam ple, thefreezing of super-cooled w ater to form ice, or the generation of a density gradientin the molecular concentration along a tube of gas which is in co ntac t w ith a sou rce

10Recall the basic classical definition of entropy increase as heat absorbed divided by

temperature, foi a reversible process.




of heat at on e end of the tub e and a sink fo r heat at the othe r en d. In such system s,a steady state is eventually reached with respect to the through-put of heat and thedistribution of the molecules and in this state there is both energy flow and a steady

rate of production of entropy in the flow processes. In these physical samples it is,of course, an "ordering" that is occurring, at the expense of a "disordering" (=increase in entropy) of the surrou ndin gs— and not strictly an increase in org aniza-tion of the kind required to maintain living systems. But at least, an increase inorder, thus physically defined h. la Boltzman n, is a necessary pre-requ isite, if nota sufficie nt one, for the maintena nce of biological organization.

But it also has to be recognized that there are some natural processes, inwhich there is an overall increase in entropy, which nevertheless manifest anincrease in molecular "complexity" of a kind not entirely captured by the simple

concept of "order" already defined, thoug h related to it . Molecular com plexity can

increase in chemical reactions that involve association to more complex molecularforms, in full accordance with the second law. For any decrease in entropy thatresults fro m the decrease in the number of complexions (W 9 above) when atoms ormolecules combine, that is consequent upon the loss of translat ional modes ofmolecular motion, with their closely packed energy levels, to (by and large) vibra-tional modes, with their more widely spaced levels, is offset: (i) by an increase inthe entropy of the surroundings resulting upon the heat generated by a decrease

during the chemical combination in the potential (electronic) energy of chemicalbonds; and (ii) by an increase in entropy due to the increase in configurationalpossibilities that occur, in spite of reduction in the number of molecules, whenthere is an increase in molecular heterogeneity with the formation of new chemicalspecies (and this contribution is greater the greater the number of possible newchemical structures).

Wicken denotes ( i) and (i i) , respectively, as "energy-randomization" and"matter-randomization" to emphasize that it is the randomizing tendencies whichthe second law of thermodynamics formalizes that drive forward the formation of

m ore complex structures.11

The earth's biosphere is in a steady-state of free energyflux, from the sun to the earth (with its biosphere) to outer space, with the rhythmof the earth's diurnal rotation. Within the biosphere itself there is a continuoussteady flow of energy through the various trophic levels of the ecology, withconcomitant transfer of heat to the non-living environment and so to outer space.The formation of chemical bonds by process (i) then, entirely in accord with thesecond law and in conjunction with (ii), provides opportunity for the increase inmolecular, and so organizational , complexity upon which natural selection thenoperates. So the second law of therm ody nam ics, far from pro hibiting any increasein complexity, necessitates its increase at the molecular level. But does therecognit ion of this provide any thermodynamic basis for the actual coming into

n J. Wicken, "Information Transformations in Molecular Evolution," Journal ofTheoretical Biology 72 (1978): 191-204; "The Generation of Complexity in Evolution: A

Thermodynamic and Information-Theoretical Discussion," 77 (1979): 349-365; and "A

Thermodynamic Theory of Evolution," 87 (1980): 9-23.




existence, in the first place, of living , organ ized system s of m atter, as d istinct fr omproviding an interpretation of their continued existence, growth and death?

In the first half of the twen tieth century, classical the rm ody nam ics had been

extended to natural irreversible processes at the hands of L. Onsag er, J . M eixner,A. Katchalsky, S.R. de Groot, T. de Donder, and I. Prigogine and his colleaguesof the Brussels school. Although this extension reaped many rewards in otherfields, it did not assist much in the interpretation of biological processes. For thethermodynamics of irreversible processes was developed for the situation in whichthe flows and rates of the processes were linear functions of the "forces"(temperature, concentration, chemical potential gra dients) that im pelled them . Suchline ar, non- equilibriu m processes can, as we just saw, lead to the form ation ofconfigurations of lower entropy and higher order—so that non-equilibrium can bea source of order. But the "order" so created is not really structural and far from theorganized intricacies of biology. Moreover, and more pertinently, biologicalprocesses depend ultimately on biochemical ones and these, like all chemicalreactions not at equilibrium, are intrinsically non-linear (in the relation betweenreaction rates and driving forces, the "affinity," or free-energy difference) and falloutside the scope of irreversible thermodynamics at this stage of its development .

To show that the Boltzmann equilibrium ordering principle—coupled withexp ( -E /k B T) being proportional to the probability of occupation of a state of

energy E at temperature T—is inadequate to explain the origin of biologicalstructures, it suffices to take an example of E ige n. 1 2 Consider a protein chain of onehundred amino acids, of which there are twenty kinds—and biological systems areorders of magnitude more complex than this. The number of permutations of thepossible order of amino acids in such a protein , and on wh ich its biological activityand function depend, is 2 0 1 0 0 ( - 1 0 1 3 0 ), assuming all sequences are equally p roba ble.This is the number of permutations necessary to obtain a given arrangementstarting from an arbitrary initial distribution. If a change of structure occurred atthe (impossibly) high rate of one every 10"8 seconds, then 100 1 2 2 seconds would be

needed altogether to produce a given sequence—yet the age of the earth is 101 7

seconds. So the chance of "spontaneo us" for m ation of the protein, h la Bo ltzma nn,through processes at equilibrium, is indeed negligible. Equ ilibrium can not giv e riseto biological order. There is no chance of an increase in "order" of the Boltzmannkind by equilibrium consideration.

However, account now has to be taken of the earth not being a system inequilibrium but being, and always to have been, an open system through whichthere is a major flux of energy inwards from the sun and outwards into space (andperhaps some minor flux of matter, too, though this seems in practice to benegligible). Thus, at present, the earth receives energy from the sun during the dayand absorbs this heat both physically and chemically throu gh the gree n chlo rop hyllof plants; at night-time much of this energy is radiated out again but some is storedin the carbohydrates of plants and so finds its way into other living organisms

, 2 Manfrcd Eigen, "Sclforganization of Matter and the Evolution of Biological

Macro moleculcs," Naturwissenschaften, 58 (1971): 465-523 .




( including ourselves) as the intermediate source of their energy—before againbeing given up as heat to the atmo sphere , and so to space again. H ence biologicalevolution has to be considered thermodynamically in relation to the openness of

this whole system, and in particular, of the biosphere located near to and on theearth's surface. So it will be a thermodynamics of natural, irreversible processesin open systems that will be relevant to biological evolution and the coming intoexis tence of l iving systems. There have been a number of other approaches forquantifying the evolutionary process and these have often been intricatelyinterwoven in discussion of the relation of thermodynamics to the evolutionaryprocess. But it is , in the end, in my view, the concepts of complexity andorganization that are the most pertinent, and their relation to the thermodynamicinterpretations of evolution are considered in the following section.

32 Thermodyn amics and the Evolution of Biological Com plexity and Organ iza-

tion

The biological complexity we actually observe now in the natural world is theproduct of a long evolutionary history, and different levels in the hierarchy ofbiological complexity hav e appeared at successive stages in the histo ry of th e earth .Today's biological structures are the result of a long process of development from

earlier forms, a fact which is disregarded in the kind of calculations that try toestimate, say, the chanc e of a molec ule of a typical protein b eing fo rm ed de novo

from its constituent atoms, or even amino acids. Such calculations (a fortiori ifcomplete organisms are considered) usually result, as we saw, in the conclusionthat this probability is so low that the planet earth has not existed long enough forsuch a complex assembly to appear by the random motion of atoms andmolecules—whether this period be that of the total 4-5 x 10 9 years of the earth'slife, or the 1.1 x 10 9 years between the formation of the earth (4.6 x 10 9 years ago)and the oldest know n r ock s (3.5 x 10 9 years ago) containing the remains of living

cells (blue-green algae) found in rocks at Warrawoona, Australia. The fallacy ofsuch calculations lies in their ignoring the actual processes whereby complex self-reproducing (initially molecular and m acrom olecu lar) system s m ight self-org anizethemselves entirely consis tently with currently known thermodynamics andchemical k ine t ics ; 1 3 in ignoring the role of selection of organizations of macro-molecules that have favor ed repro ductio n rates and, on ce established, irreversiblychannel the evolutionary process in one particular direction; 1 4 and in ignoring thefundamental analyses of the architecture and evolution of complexity made bym any authors, in particular by H .A. Sim on .1 5 He showed that complex systems will

1 3Arthur R. Peacocke, An Introduction to the Physical Chemistry of BiologicalOrganization (Oxford: Clarendon Press, 1983).

1 4 Eigen, "Selforganization of Matter"; and dem "Molecular Organization and the

Early Stages of Evolution," Quarterly Reviews of Biophysics 4 (1971): 149-21 2.

1 5 H.A. Simon, 'The Architecture of Complexity," Proceedings of the American

Philosophical Society 106 (1962): 467 -82.




evolve from simple systems much more rapidly if there are stable intermediateforms than if there are not, and that the resulting complex forms will then behierarchic in organization. The requirement for stability of an atomic or molecular

structure reduc es to the requirem ent tha t the free energy of the structure be less byvirtue of its structure than that of its component atoms or molecules. The complexstructures that emerge in the evolution of the first living fo rm s, and of subseq uentforms, may be presumed to have a stability of this kind, though, since livingsystems are open, the stability attributed to them must not be identified directlywith the net free energy of formation of their structures. The point that is essentialto make here, in relation to the possibility of formation of complex forms, is thatnatural selection speeds up the establishment of each n ew stratum of stability in th esuccession of forms of life. Each stratification of stability is only a temporary

rest ing place before random mutation and natural selection open up further newpossibilities and so new levels of (tempo rary) stability — rathe r as if the free energyprofi le were a switchback with any given form stable only to the immediateenvironment of the controlling parameters and always with a finite chance ofmounting the next barrier to settle (again temporarily) into a new minimum.

Bronowski has also pointed out that this "stratified stability," which is sofundamental in living systems, gives evolution a consistent direction in timetowards increased complexity. 1 6 He used the metaphor of evolutionary time as a

"barbed arrow," because random change will tend in the direction of increasingcomplexity, this being the only degree of freedom for change—and Saunders andHo have also produced a neo-Darwinian argument along s imilar l ines for theinevitability of increases in complexity in evolution. 1 7

3 .3 The Origin of Living Systems from the Non-Living and Dissipative

Structures

One of the particular achievements of thermodynamic theory in the last few

decades has been its provision of a basis for understanding the spontaneous cominginto existence, as distinct from the maintenance, of organized structures (whichmay be as much kinetically as topologically organized) in open (and closed)systems far from equil ibrium when flux-force relat ionships are non-l inear. Thisanalysis by the Brussels school, under the leadership of Prigogine, has significanceespecially for understanding the emergence of functionally and structurallyorganized living matter from non-living, that is , non-self-copying, matter.1 8 Theyhave been able to show how, on a strictly thermodynamic basis, new organizedforms of systems can (but not necessarily will) come into existence and be stable,

if matter and energy are flowing through to maintain them. These new ordered

1 6J. Bronowski, "New Concepts in the Evolution of Complexity: Stratified Stability

and Unbounded Plans," Zygon 5 (March, 1970): 18-35.

17 P.T. Saunders and M.W . Ho, "On the Increase in Complexity in Evolution," Journalof Theoretical Biology 63 (1976): 375-84.

1 8

For references, see Peacocke, Biological Organization, 17-72.




forms are called dissipative structures and are radically different from the"equilibrium structures" studied in classical thermodynamics, the "order" of whichis attained only at low enough temperatures in accordance with Boltzmann's

ordering principle (as described above, and coupled with exp(-E/kBT) beingproportional to the probability of occupation of a state energy E at temperature T).In this non-linear range, non-equilibrium can indeed be the source of an order thatwould n ot be predictable by the application of Boltzmann*s p rincip le. In su ch statesthere can occur, under the right con ditions, flu ctuation s that are no longer dam pedand that are amplified so that the system changes its whole structure to a new

ordered state in which it can again become steady and imbibe energy and matterfrom the outside and maintain its new structured form. This instability ofdissipative structures has been studied by these workers who have set out more

precisely the thermodynam ic conditions for a dissipative system to m ov e fro m on estate to a new state which is more ordered than previously, that is , for "orderthrough fluctuations" to occur.

It turns out that these conditions (described below) are not so restrictive thatno system can even possibly obey them. Indeed a very large number of systems,such as those of the first living forms of matter, which must have involvedcomplex networks of chemical reactions, are very likely to do so, since they arenon-linear in their relationship between the forces and fluxes involved. The

ordered configurations that emerge beyond such an instability of the thermody-nam ic branch of non-linear systems were callcd dissipa tive structures, bec au se theyare created and maintained by the entropy-producing "dissipative" processesoccurring inside systems through which, being open, there is a continuo us flux ofmatter and energy.

Model physical systems undergoing such transitions are now well-known, forexample, the famous Bdnard phenomenon wherein a hexagonal organization atright angles to the vertical heat flow is observed, at a certain critical point, in acolumn of liquid heated from below—and others ci ted by H. Haken who, because

the awareness of them has now become so widespread, and because they shareco m m on features in the "bifur cation " of the solutions of non-l inear differentialequations controlling these ph enom ena, has invented a new na m e for the study ofsuch systems, nam ely "S yn erge tics ." 1 9 Even more pertinent to biological systemsis the observation of ordcr-through-fluctuations in chcmical systems. Chemicalnetworks can be of a very high degree of com plexity through incorpo rating one ormore autocatalytic steps and they are often non-linear (in the sense above) whennot close to equilibrium. Then various kinds of oscillating reactions and otherfeatures can occur. One of the most striking of these is the so-called Belousov-Zhabotinsky reaction, the oxidation of malonic acid by bromate in the presence of

19Hcrmann Hakcn, Synergetics—An ntroduction: Non-equilibrium Phase Transitionsand Sef-organization nPhysics, Chemistry and Biology, 2d cd., enlarged (Berlin: Springer-

Verlag, 1978).




cerium ions in solution. 2 0 With the right combination of solution conditions, andat constant temperature, the original hom ogene ous reaction m ixture changes intoa series of pulsing waves of concentration of cerium ions, moving up and down the

tube, until eventually a steady state is reached in which there are static, bandedlayers of alternating high and low concentrations of eerie ions. From an originallyhom ogeneous system, a highly ordered structure has ap peared throu gh the flu ctu a-tions that are possible in a non -linear system far remo ved fro m equilibrium . W hathas happened is that fluctuations in such a system have been amplified and,consistently with the laws of chemical kinetics, a new structure has appeared thatis ordered, at first in time and then finally in space—representative of an allianceof chance and law. Under the conditions of this reaction the structural formationhas a probability of unity, provided that the initial fluctuation arises from within

the system. The causal chain leading to this fluctuation, although it cannot bediscerned by ourselves, must itself be the result of law-like processes occurring atthe micro-level , some of which may be subject to "Heisenberg uncertainty."Because of the discovery of these dissipative systems, and the po ssibility of "or de r-throug h-fluctu ations," it is no w possible , on the basis of these physico-chem icalconsiderations, to regard not merely as highly probable, but as inevitable theemergence from non-l iving matter of those ordered and art iculated molecularstructures that are living. Instead of them having only an inconceivably small

chance of emerging in the "primeval soup" on the surface of the earth before lifeappeared, we now see that ordered dissipative structures of so m e kind w ill appearin due course.

As Eigen puts it , the emergence of self-copying patterns of matter, that is ,living systems is, through this new physico-chemical analysis, seen as "inevitable,"but the actual course it will take is "indeterminate."2 1

On e has to presume that before life had evolved there existed in this preb ioticstage a system containing replicating macro-molecules that could both maintainitself by means of some simple copying mechanism and have a potentiality of

change incorporated into its very structure and function so as to facilitate itsmult is tage evolution to more complex forms more efficient in survival andreproduction. Some of the kinetic and stochastic problems associated with suchprebiotic systems have been very fully investigated by Eigen and his colleagues atGot t ingen . 2 2

In the treatment of the B russe ls scho ol it is not o nly the instability bu t also asuccession of instabilities of dissipative systems, now appearing under the aegis ofthermodynamic laws, that bridges the gap between the non-living and the living.This succession of instabilities can be a process of self-organization, and of

2 0Jo hn J. Tyson , "What Everyone S hould Know about the Belousov-Zhabotinsky

Reaction," in S.A. Levin, ed. , Frontiers in Mathematical Biology, Lecture No tes in

Biomathematics, 100 (Berlin: Springer-Verlag, 1994), 569-87.

2 1 Ei ge n, "Selforganization of Matter," 519, n. 9.2 2 Ibid., nn. 9 and 11; and Eigen and P. Schuster, The Hypercycle: A Principle of

Natural Sef Organization (Berlin: Springer-Verlag, 1979).




evo lutio n, pro vide d the re are fulf illed the sam e conditions as fo r the initialemergence of dissipative structures. They are that a process of self-organizationcan oc cur in a system if: (i) the system is open to the flux of m atter and energ y; (ii)

the system is not at equilibrium and preferably far from equilibrium ; an d (iii) th esys tem must be non-linear in its flux-force relationships, that is , there must bestrong coupling between i ts processes .

Th e evolution to order through an instability induced by fluctu ation s, is onlya possible, not a certain, development and in fact requires, along with thesubsequent stabilization to a dissipative structure, that some other very stringentcondit ions be fulfilled.

3 .4 Thermodynamics and Kinetic Mechanisms

The existence of these other conditions rem inds us that, like patriotism , therm ody -namics "is not enou gh." For thermo dynam ics is alway s the scien ce of the po ssible:it can allow, it can forbid, but it cannot prescribe. What actually occurs in anysystem obeying the condit ions described above for i t to become (more) self-organizing depends on the ability of the actual molecules and higher structurespresent, on their spatial and temporal arrangements and on the numericalparameters specific to these features. In a m olecular system, this m ean s the patterns

generated will depend principally on chemical reaction rate constants and ondiffusion constants, controlling movement across space. Similar parameters charac-teristic of higher order structures will also operate at other levels (e.g., in thepatterning in predator-prey, herbivore-plant , and host-parasi te systems 2 3) . Eversince the seminal paper of A.M. Turing (1952) on "The Chemical Basis of Mor-phogenesis," it has become increasingly clear that suitable combinations of ratesof chemical reactions and diffusion processes can spontaneously generate patternsin space and t ime, both perman ent and oscil la t ing according to con dit io ns.2 4 Thisseparate development of dynamical theory, of kinetics and of fluctuation theory

opens up new vistas of interpretation of pattern formation at many levels ofbiology. These interpretations cannot be described here, 2 5 but the po int is that it isnow possible to understand the detailed mechanisms in actual dissipative systemsthat lead to new ordered ("self organized") forms appearing.

Particularly striking biological examples of such forms are provided by theoscillations in time and the patterning in space of the con cen tration of interm edia tesin glycolysis that have been observed by Benno Hess and his colleagues, and thequite extraordinary ability of individual unicellular slime mold organisms (inpart icular Dictyostelium discoideum) to come together, under conditions of

"Alfred J. Lotka, Elements of Physical Biology (New York: Dover, 1924; reprinted

as Elements of Mathematical Biology, N ew Y ork: Do ver, 195 6), reference is to reprint

edition.

2 4 A .M . Turing, "The Chemical Basis of M orphogenesis," Philosophical Transactionsof he Royal Society of London B237 (1952): 37-72 .

2 5

See Peacocke, Biological Organization, 111-213.




starvation, in organized spiral and annular patterns in a colony that then behaves,temporari ly, as an organized w hole unti l new fo od sources are fo un d.2 6

So, one may well ask, what is gained from the application of irreversible

thermodynamic concepts and criteria to biological systems? The primary andoverriding gain is undoubtedly in the ability of thermodynamics to provide, as itwere, an architectonic fram ewo rk w hich limits but does not in detail prescribe. Onecan then build on this framework by using other resources of dynamical theory, ofkinetics, of fluctu ation theory— and of precise experimen tal inform ation and newknowledge of modes of control and regulation at all levels in biology. Structuralorder com es from the exis tence of constraints and the macroscopic and phen om -enological approach of thermodynamics is uniquely fitted to handle such factors.

Therm odyn am ics can never work in isolation from other approaches basedon the theory of fluctuations, of stability, of stochastic processes, and of non-lineardifferential equations. However, it has its own unique insights which serve to linkreflection on biological systems with the whole corpus of physico-chemical theory.For the new concepts in irreversible thermodynamics of non-equilibrium as thesource of order, of "order through fluctuations," of the decisive role of non-equilibrium constraints and of dissipative structures (spatial, temporal, or both) inopen systems, broaden and deepen immeasurably our perspective on biologicalsystems and whole organisms and, indeed, have already proved to be a stimulus

for the kind of detailed work that is required to give them a "local habitation anda name."

4 Theological Reflections

4 .1 God and the World

The postulate of God as creator of all-that-is is not, in its most profound form, a

statement about what happened at a particular point in time. To speak of God ascreator is a postulate about a perennial or "eternal"—that is to say, timeless—relation of God to the world, a relation which involves both differentiation andinteraction. God is differentiated from the world in that he is totally other than it(indeed this dualism— of God and the world— is the only one that is foundationalto Christian thought). God is postulated in answer to the question: Why is thereanything at all? He is the "Ground of Being" of the world; or for theists, thatwithout which w e could neither make sense of the world hav ing existen ce at all norof its having that kind of intellectually coherent and explorable existence whichscience continuously unveils. But this affirmation of what is termed "transcen-dence" has to be held in tension with the sense of God's immanence in the world.

For the process of evolution is continuous with that of inorganic and cosmicevolution—life has emerged as a form of living matter and develops by its owninherent laws, both physico-chemical and biological, to produce new forms with

2 6

See ibid. , 203-12.




new em ergent qualities requiring new m odes of study (the various scienc es) a s w ellas new concepts and languages to describe and explicate them. So the stuff of theworld has a continuous, inbuilt creativity—such that, whatever "creation" is, it is

not confined to a restricted period of time bu t is going on all the time (an d indeedmodern physics would support seeing time itself as an aspect of the created order).So, if we identify the creativity of the world with that of its creator, we mustemp hasize that Go d is semper creator, all the time creating—God's relation to theworld is perennially and eternally that of creator. But to speak thus is to recognizealso that Go d is creating now and continuously in and through the inherent, inbuiltcreativity of the natural order, both physical and biological—a creativity that isitself Go d in the process of creating. So we hav e to se e G o d 's action as bein g in theprocesses themselves, as they are revealed by the physical and biological sciences,

and this means we must s tress more than ever before God's immanence in theworld. If the world is in any sense what God has created and that through whichhe acts and expresses his own inner being, then there is a sense in which God isnever absent from his world and he is as much in his world as, say, Beethoven isin his Seventh Symphony during a performance of i t .

The processes of evolution, initially the physical and cosmological, and thenmore strikingly the biological, are characterized by the emergence of new formswithin and by means of continuous developments subject to their own inherent ,

regular, law-like behavior that is studied by the sciences. What emerges is usuallym ore complex and, along certain branches of the evo lutionary tree, mo re and m oreconscious, culminating in the self-consciousness and the sense of being a personthat characterizes hum anity. In theological terms, G od 's imm anent creative actionin the world generates within the created order a being, the human being, whobecomes self-aware, morally responsible, and capable of himself being creativeand of responding to God's presence. Thus, the inorganic, biological, and humanwo rlds are not just the stage of G od 's act ion— they are in themselves a mode ofGod in action, a mode that has traditionally been associated with the designation

"Holy Spirit," the creator Spirit. I think that to give due weight to the evolutionarycharacter of God's creative action requires a much s tronger emphasis on God'simmanent presence in, with, and under the very processes of the natural worldfrom the "hot big bang" to humanity.

If I had to represent on a blackboard the relation of God and the world,including hum ankind, I wo uld not sim ply draw three spheres labeled respectively"Nature," "Humanity," and "God" and draw arrows between them to representtheir inter-relation. Rather, I would denote an area representing nature and placethat entirely within another area representing God, which would have to extend tothe edges of the blackboard and, indeed, poin t bey ond it (to infin ity). W hen I ca m eto depict human beings, I would have to place them with their feet placed firmlyin nature but with their self-consciousness (perhaps represented by their brains?)protruding beyond the boundary of nature and into the area that attempts to"depict" God , or at least refer to him . The basic aff irm ation here is that all-that-is,both nature and hum anity, is in some sense in God, but that God is, profoundly andult imately, "more" than nature and humanity—there is more to God, who is ,profoundly and ult imately, "more" than nature and humanity. God in his being

transcends, goes beyond, both humanity and nature, for God is either in everything



1 4 0 A R T H U R R . P E A C O C K E

created from the beginning to the end, at all times and in all places, or he is notthere at all. What we see in the world is the mode of God's creativity in the world.The analogy with Beethoven's Seventh Symphony as an expression of Beetho-

ven 's own inner creative bein g is, I think, a fair one. In the actual proc esses of theworld, and supremely in human self-consciousness, God is involving himself andexpressing himself as creator. However, s ince human beings have free wil l wehave also to recognize that God put himself "at risk," as it were, in creativelyevoking in the natural world, beings who have free wil l and who can transcendtheir perceived world and shape it in their own way.

4 .2 God and Chance

How may this understanding of God creating " in, with and under" the ongoingprocesses of the natural world be held in consonance with the recognition that new,and increasingly complex, forms of both inorganic and eventually l iving matteremerge by a com bination of what we recognize as "cha nce" and " law"— and thatthis combination is inherently creative in itself and involves, for sound thermo-dynamical and chemical reasons, an increase in complexity? 2 7 How can theassertion of God as creator be interpreted in the light of this new and profoundunderstanding of the natural processes by which new organized forms of matter

appear, both non-living and living? In evolution there is an interplay betweenrandom chance at the m icro- level and the necessity wh ich arises fr om the stuff ofthe world having i ts part icular "given" propert ies and law-like behavior. Thesepotentialities a theist must regard as written into creation by the creator's intentionand purpose, and they are gradually actualized by chance exploring their gamut.

I have e lsewhe re 2 8 tried to express this situation by seeing God as creator asl ike a composer who, beginning with an arrangement of notes in an apparentlysimple tune, elaborates and expands it into a fugue by a variety of devices. Thus,I suggested, does a J.S. Bach create a com plex and interlocking harm onio us fus ion

of his original material. The listener to such a fu gu e expe riences, with the luxurian tand pro fus e grow th that emanates f rom the original s imple s tructure, who le newworlds of emotional experience that are the result of the interplay between anexpectat ion based on past experience (" law") and an openness to the new("ch anc e" in the sense that the listener cannot predict or control it).

Thu s mig ht the creator be imagined to unfold the pote ntialities of the un ive rsewhich he himself has given it , selecting and shaping by his redemptive andprovidential action those that are to come to fruition—an improvisor of unsur-passed ingenuity? He appears to do so by a process in which the creativepossibilities, inherent (by his own intention) within the fundamental entities of that

^ P e a c o c k e , ' T h e r m o d y n a m i c s a n d L i f e ," Zygon 1 9 ( D e c e m b e r , 1 9 8 4 ) : 4 0 8 - 1 2 ; a n d

idem, Biological Organization, chap s . 2 and 4 - 6 .

M P e a c o c k e , Creation and the World of Science (Oxford: C l arend on Press , 1979) , chap .

3 , e sp . pp . 105-6 .




universe and their inter-relation, becom e actualized within a temp oral dev elop m entshaped and determined by those selfsame inherent potentialities.

The image of creation as an act of composing and of the created order as a

musical composition is surprisingly rich and fecund and, since propounding it inmy 1978 Bampton Lectures ,2 9 I have come across a number of other authorsresorting to the image of music, as flexible form moving within time, to expresswhat they wish to say about both the created order and the act of creation—authorsas diverse as Popper, Capek and Eigen. 3 0 One recalls in this connection that themusic of creation has also been a constant theme of the religions of India, forexample the South Indian representations, in bronze, of the dancing Shiva, thecreator-destroyer, as lord of the dance of creation.3 1

Both images, of the writing of a fugue and of the execution of a dance, serve

to express the idea of God enjoying, of playing in, creation. This is not an idea newto Christian thoug ht Th e Greek fathers, so Harvey Cox argues, con tended that th ecreation of the world was a form of play. "God did it they insisted out of freedom,not because he had to, spontaneously and not in obedience to some inexorable lawof necess i ty . " 3 2

H. Montefiore has criticized this wholehearted acceptance of the creativeinterplay of chance and law as a sufficient account of the observed growth ofcomplexity as leading to the "God of the deists"—that is , to a distant "absentee-

landlord" God who, as it were, sets the universe going and leaves it to get on withit—"a remote, unmoved, unloving" God. He asserts this because he believes"chance and necessity may produce creativity, but they canno t pro duc e pu rp os e."3 3

But what these new developm ents actually show is that the in terplay of cha nce andlaw bring about that increase in com plexity which is both inbuilt accord ing to thelaws of thermodynamics and chemical kinetics 3 4 and is also the basis of thatincrease of sentience and freedom of the individual organism which is thecondition for the appcarance of all those qualities in and values of humankind, theeliciting of which in the created order M onte fiore q uite pro perly wish es to attribu te

to the purpose of the creator God of Christian theism. D.J. Bartholomew, aprofessor of statistical and mathematical scicnce, has made a thoroughgoing studyof the role of chance in the natural order in relation to the concept of God.3 5 H e

2 9 I b i d .

3 0 S e e , K a r l P o p p e r , The Unended Quest: An Intelectual Autobiography, rev. ed.

(Lond on: Fontana, 1976); Mi l ic Capek, The Philosophical Impact of Contemporary Physics(Pr i nce ton , NJ: Van Nos trand, 1961) ; and E i gen and Ruthi l d Wi nkl er , The Laws of theGame: How the Principles of Nature Govern Chance trans . Robert and Ri ta Kimber

( L o n d o n : A l l e n L a n e , 1 9 8 2 ) .

3 1 Ananda Kent i sh Coomaraswamy, The Dance of Shiva ( L o n d o n : P et er O w e n , 1 9 5 8 ) .

3 2 H a r v e y C o x , The Feast of Fools: A Theological Essay on Festivity and Fantasy(Cambri dge , MA: Harvard Uni vers i ty Press , 1969) , 151 .

3 3 H u g h M o n t e f i o r e , The Probability of God ( L o n d o n : S C M P r e s s , 1 9 8 5 ) , 9 8 .

^ S e e n . 2 6 a b o v e .

3 5

D a v i d J . B a r t h o l o m e w , God of Chance ( L o n d o n : S C M P r e s s , 1 9 8 4 ) .




contends that chance is actually conducive to the kind of world which we wouldexpect a God, such as Ch ristians believ e in, to create, and that Go d uses c han ce toensure the variety, resilience, and free do m necessary to achiev e his pu rpos es. His

basic hypothesis is that God uses chance, w hich "offers the potential Creator m anyadv antag es w hich i t is difficult to envisage being obtained in any other w ay ."3 6

Even more s trongly, he believes "God chose to make a world of chance becauseit would have the properties necessary fo r pro duc ing being s fit fo r fellow ship withh i m s e l f . " 3 7 His whole posit ion merits careful s tudy al though, in my opinion 3 8 ittakes too externalist a view of God's mode of action in the world and does notemphasize sufficientiy, or develop any understanding of, God's immanence in thenatural creative processes . Like M ontefiore, who se views are otherwise co ntraryto his, Bartholomew fails to recognize 3 9 that the joint e m phasis both on the role of

chance in natural creativity and on the immanence of God in these same naturalprocesses which I , for one, have been making, leads not to deism but to thatintegration of immanence and transcendence to which I have already referred,namely that< 4the Being of God includes and penetrates the whole universe, so thatev ery pa rt o f it exists in Him, but . . . that his Being is m ore than, and is no texhausted by the universe." 4 0

4 .3 Living with Chance

This theoretical acceptance of the role of chance in creation and in the createdworld also has implication for our attitudes to the role of chance in human life.Rustum Roy, Director of the M aterials Research Lab oratory at Penn sylvania StateUniversity, entitled his first 1979 Hibbert Centenary Lecture, in London, "Livingwith the Dice-playing God." 4 1 He urged us to accept that the world displayspatterned chance. It is not a chaos, for there is only a "loose coupling" throughstatistical laws and pa tterns, w hich still allows talk of "cau ses." In hum an lif e wemust accept, for the stability of our own mental health and of our faith, that reality

has a dimen sion of chan ce interwoven with a dimension of causali ty4 2

—and tha tthrough such interweaving we came to be here and new forms of existence canarise. So we have to accept the interplay of chance and law as the mode of God'screativity. It seems to me to be more consistent with the fundamental creativity ofreality than the belief—stem ming from a Newtonian, mech anistic, determ inist viewof the universe with a wholly transcendent God as the great lawgiver—that God

^Ibi d . , 97 .

3 7 I b i d . , 1 3 8 .

P e a c o c k e , r ev ie w o f God of Chance, by DJ . Bartho lomew, In Modern Theology 2

( J a n u a r y 1 9 8 6 ) : 1 5 7 - 6 1 .

3 9 B a r t h o l o m e w , God of Chance, 9 7 .

™TheOxford Dictionary of he Christian Church, 2d ed., s.v. "Panentheism."4 1 See Rustum Roy, Experimenting with Truth: The Fusion of Reigion with

Technology Needed for Humanity's Survival (Oxford : Pergam on, 1981) , 188 .

4 2

C f . P a u l B u r r o u g h , God and Human Chance ( L e w e s : B o o k G u i l d , 1 9 8 5 ) .




intervenes in the natural nexus for the good or ill of individuals and societies. Wehave to learn to accept these conditions of creation and of creativity in theworld—"the changes and chances of this f leet ing world." Such an at t i tude can

rightly be urged not simply as a psychological necessity but also as the outcomeof the recognition that we have just been developing, that the creation of life itself,and the creativity of the living, inevitably involves an interplay of chance and law.

5 Conclusion

Norbert Wiener suggested that a thermodynamic perspective provoked the feelingthat the universe was somehow against the experim ent of life and that in nu rturing

our little enclave of organized existence, as biological and as social systems, wewere swimming against the entropic stream that was in fact sweeping all tor a n d o mn e s s a n d " d a rk n i g h t / * 3 But the picture that is emerging in more recentthermodynamic analyses of diss ipative systems and of l iving organisms has adifferent tenor. Certainly the stream as a whole m ov es in a certain genera l, overalldirection which is that of increasing entropy and increasing disorder, in the specificsense I have defined. However, the movement of the s tream itself inevitablygenerates, as it were, very large eddies within itself in which, far fro m there b eing

a decrease in order, there is an increase first in comp lexity and then in som ethingmore subtle— functiona l organization. No w there could be no eddies w ithout thestream in which they are located and so may it not be legitimate to regard thisinbuilt potentiality for living organization that the entropic stream manifests asbeing its actual point— namely, why it is at all? There could be no self-consciousness and hum an creativity without living o rganizatio n, and there could be no suchliving dissipative systems unless the entropic stream followed its general,irreversible course in time. Thus does the apparently decaying, randomizingtendency of the universe prov ide the necessary an d essential m atrix (m ot justel) fo r

the birth of new forms—new life through death and decay of the old.

4 3 N o r b e r t W ie n e r , I am a Mathematician: The Later Life of a Prodigy (Cambridge ,

M A : M I T P r e s s , 1 9 6 4 ) , 3 2 5 .



Ill

CHAOS, COMPLEXITY, AND

DIVINE ACTION



T H E M E T A P H Y S I C S O F D I V I N E A C T I O N 15 7

John Polkinghorne

1 Introduction

'M etap hys ics ' is not a popular w ord in contem porary culture but , in fact , no o necan live a reflective life without adopting some broad view of the nature of reality,however tentative and subject to possible revision it might need to be. Evenmilitant scientific reductionists, for whom "physics is all ," are metaphysicians.

They claim to be able to extend the insights and laws of physics into regimes, suchas human behavior, in which their total adequacy is an untested hypothesis. Theyare certainly going beyo nd (meta ) physics .

Anyone who wishes to speak of agency, whether human or divine, will haveto adopt a metaphysical point of view within which to conduct the discourse. Theconceptual edifice thus constructed must be consonant with its physical base, butit will no more be determined by it than the foundations of a house completelydetermine the character of the building. In each case, there is constraint but not

entailment. Metaphysical endeavor in general, and talk of agency in particular, willinevitably require a certain boldness of conjecture as part of the heuristicexploration of possibility. In our present state of ignorance, no one has access toa final and definitive proposal. The test of the enterprise will be the degree towhich it can attain comprehensiveness of explanation and overall coherence,including an adequate degree of consonance w ith hu ma n experien ce. T he principalstrategy of nearly all writers on divine agency has been to appeal in some way toan analogy with human agency, though our ignorance about the latter makes thisa precarious undertaking.

2 Epistemology and Ontology

Metaphysical theories are ontologically serious. They seek to describe what is thecase. It is a central philosophical question how what is the case is related to ourknowledge of the world. There is clearly no certain and simple way in which tom ake the connection. There has been a strong tradition since Immanuel Kant whichemphasizes the unknowability of "things in themselves." The spectacles we wearbehind the eyes (the presuppositions we bring to our interpretation of the world)and the epistemic blinkers imposed by our having to view reality from thelimitations of a human perspective are held so to refract and limit our perceptionsof the way things are that reality is inaccessible to us.

It is not necessary to give way to such metaphysical despair. Of course thereis no deductive way of going from epistemology to ontology. In fact, an importantaspect of the connection is precisely the problem of induction: what degree ofknowledge could lead to an ontological conclusion? Yet almost all scientists



148 JO H N PO L K ING H O RNE

believe that they are learning about the actual na ture of th e phy sical wo rld that theyinvestigate. Consciously or unconsciously, they are critical realists. One coulddefine the program of critical realism as the strategy of seeking the maximum

correlat ion between epis temology and ontology, subject to careful acknowledg-ment that we view reality fro m a perspectiv e an d su bject to push ing the search forknow ledge to any natural limits it m ay po ssess. Its m otto is "episte m olog y m ode lsontology"; the totality of what we can know is a reliable guide to what is the case.It has to be a critical realism because in som e regim es (such as the quan tum wo rld)what is the case is so counterintuitive in terms of common sense expectation thatit cannot be reduced to a simple-minded objectivity. We have to respect itsidiosyncrasy, but that does not prejudice its reality. One can see how natural thisstrategy is for a scientist by considering the interpretation of the uncertainty

principle in quantum theory. Heisenb erg's original d iscovery wa s epistem ologica l;he showed there were intrinsic limitations on what could be measured . Veryshortly, he and almost all other physicists were giving the principle an ontologicalinterpretation. It was treated as a principle of actual indeterminacy, not mereignorance.

There was no logical necessity to make this transition. It could not bededuced. This is clearly established by the existence of alternative interpretationsin which there is complete determinacy, but in ways that are hidden from human

knowledge. One such interpretation is Bohm's version of quantum theory,1

wherea hidden wave guides the perfectly determined motion of purely classical particles.Another is man y-worlds quantum the ory , 2 in which the perfectly deterministicSchrodinger equation controls all that is, but its consequences are spread betweenparallel universes , not s imultaneously open to hum an observation.

Neither of these interpretations has commended itself to the majority ofphysicis ts . They have freely (and in my view rightly) made the metaphysicaldecision to interpret quantum theory as indicating an intrinsic indeterminacy inphysical real i ty. I have been arguing 3 that it is a rational and attractive option to

pursue the same strategy in relation to other intrinsic unpredictabilities which we

'David Bohm, Wholeness and the Implicate Order (London: Routlcdge & Kegan

Paul, 1980); Bohm and B J. Hiley , The Undivided Universe: An Ontological Interpretationof Quantum Theory (London: Routlcdge, 1993).

2 H . Everett, Reviews of Modern Physics 29 (1957): 454. See also, Alastair Rae,

Quantum Physics: Illusion or Reality? (Cambridge: Cambridge University Press, 1986),

chap. 6.

3John Polkinghome, Science and Creation: The Search or Understanding (London:

SPCK Press, 1988) chaps. 3 and 5; dem, Science and Providence: God's Interaction withthe World (London: SPCK Press, 1989), chap. 2; idem. Reason and Reality: TheReationship Between Science and Theology (London: SPCK Press, 1991), chap. 3; and

idem, ' T h e Laws of Nature and the Laws of Physics" in Quantum Cosmology and the Lawsof Nature: Scientific Perspectives on Divine Action, ed. Robert John Russell, Nancey

Murphy, and CJ. Isham (Vatican City State: Vatican Observatory, 1993; Berkeley, CA:

Center for Th eo log y and the Natural Scien ces, 199 3), 43 7-4 48 .



T H E ME T APH YS ICS O F DIVINE ACT IO N 149

discover in nature. We should treat these epistemic limitations as being ontologicalopportunities for fruitful metaphysical conjecture.

3 Some Questionable Metaphysical Strategies

3.1 Primarily Science-Based: Physicalism

Our growing recognition of the remarkable powers of self-organization displayedby complex physical systems far from equilibrium has encouraged some to adopta refined form of physicalism. They suppose that this will enable the completionof an adequate descriptive program of human experience on the basis of natural

science alone. 4 I have already stressed that such a claim is metaphysical incharacter, however much it may seek to hide that fact behind the language ofphys ics .

Such a strategy may be defended on the grounds that science has alreadyexplained much which was not understood by previous generations and whyshould we set limits to its eventual successes? Indeed it can be argued that thelessons of history encourage this point of view. The boundaries between organicand inorganic matter, between living entities and inanimate objects, are no longer

perceived as total barriers to the advance of scientific explanation. Why shouldconsciousness or hum an ag ency be thought to be differen t?

I would respond by pointing out that the lessons of history are moreambiguous than this argument acknowledges. Even within physical science itselfthere arc many phenomena (the stability of atoms, superconductivity, the energysources of stars) which only proved intelligible in terms of an extremely radicalrevision of then currently accepted physical principles, represented by the adventof quantum theory and relativity. When one considers the big ugly ditch whichseems to intervene between physical talk (however complex and sophisticated in

terms of neural networking or whatever) and mental talk (even at the mostelementary level of perceiving a patch of pink), there seems no reason to supposethat its bridging will not require the most drastic revision, in unforeseeable ways,of our understanding of the nature of reality. In the words of the sharp-tonguedtheoretical physicist, Wolfgang Pauli, it is no use simply claiming "credits for thefutu re," waving on e 's hands and hoping that one day present understanding willturn out this way.

Physical science seems light-years distant from the unaided understanding ofthe mental or the intentional, an indispensable requirement for an adequatemetaphysical strategy. Moreover, the reductionist program that underlies physical-ism is threatened by developments in physical science itself. The non-localityfound in quantum theory shows that the subatomic world is one which cannot betreated atomistically. 5 The vulnerability of chaotic systems to the smallest

4 Sce Bcrnd-Olaf KUppers, "Understanding Complexity" (in this volume).5

Se e, e.g., Polkinghorne, The Quantum World (London: Longman, 1984), chap. 7.




influences from their environment, consequent upon the exquisite sensitivity ofsuch systems to fine details of their circumstance,6 shows that they are never trulyisolable. Physics is taking a holistic turn. The p ossibility of the existe nce of h olistic

laws of nature is one which should not be discounted. Certainly such laws wouldbe m ore difficult to discover than the familiar laws g ov ern ing the b eha vio r of par ts,and their form would surely be different from that of the differential equationswhich are the staple of current localized mathematical physics. Yet it would be aProcrustean imposition on science to deny that it could have access to such laws.It is clearly worthwhile to pursue the program of reductionist explanation as far asit can legitimately be pursu ed, but that is a metho dological strategy for investiga-tion, not a metaphysical strategy determining the total nature of reality. Thedawning holism of physics points in a more hopeful direction if science is

eventually to find a satisfactory integration into a comprehensive and adequatemetaphysical scheme.

O ne final criticism of too great a reliance on the prin cip le of self-o rga niza tionneeds to be m ade. The insights of non-equil ibrium thermo dynam ics seem helpfulin relation to the generation of structure and long-range order. Agency, however,seems to correspond to an altogether more flexible and open kind of time-development than that corresponding to typical self-organizing patterns, such asconvection colum ns or chem ical clocks.

3.2 Primarily Theology-Based: Primary Causality

At least since Tho m as A quinas, there has been a tradition of theological thinkingwhich seeks to explain divine agency by appeal to the distinction betwee n prim aryand secondary causality. A notable modern exponent of this point of view has beenAustin Farrer with his idea of double agency.7 The secondary web of createdcausality is treated as being complete and unriven. Yet the primary causality ofGod is supposed nevertheless to be in effab ly at work in and throu gh the se created

causalities. Ho w this is so is not explained. Indeed Farrer would regard it as riskingmonstrosity and confusion if one were to attempt to discern the "causal joint" bywhich divine providence acts .

It is not clear to me what is gained by so apophatic an account of God'saction. In the end, the answer seems to be "God only knows." I agree with ArthurPeacocke 's judgment on the paradox of double agency that i t "comes peri louslyclose to that m ere assertion of its truth . . . since Farrer on his own adm ission cangive no account of the 'causal joint ' between the agency of the Creator and evenhuman action."8 This seems to me to be a strategy of absolutely last resort, only to

^ e e , e.g., James Gleick, Chaos: Making a New Science (London: Heinemann, 1988),

c h a p . 1 .

7Austin Farrer, Faith and Speculation: An Essay inPhilosophical Theology (London:

A&C Black, 1967).

8Arthur P-^cocke, Theology for a Scientific Age: Beng and Becoming—Natural and

Divine (Oxford: Blackwell , 1990), 149.




be undertaken if it proves impossible to ma ke any satisfactory con jectu re about thecausal joint of G o d' s ag enc y. I do not belie ve w e are in so despe rate a case, and Imake my own suggestion in the course of what fol lows.

3 .3 Top-Down Causality

The causali ty which physics most readily describes is a bottom-up causali ty,generated by the energetic interaction of the constituent parts of a system. Theexperience of human agency seems total ly different. It is the action of the wholeperson and so i t would seem most appropriately to be described as top-downcausality, the influ enc e of the w ho le bringing abou t coherent ac tivity of the parts.M ay not similar forms of top-down causality be found elsewhere, including G od 's

causal influence on the whole of creation?It is an attractive prop osal, bu t it is important to recognize that without further

explanation top-down causality is a far from unproblematic concept. Its uncriticaluse would am ount to no more than sloganizing. It seems to me that two importantdifficulties have to be faced and discussed.

The first is one I have already referred to in discussing the limitations on theinsights provided b y the principles of self-organ ization. If on e is to giv e an acco untof intentional agency, it will require something much more open and dynamic than

simply the generation of long-range order or the propagation of boundary effects.Striking as instances of this kind can be (involving the coherent motion of billionsof molecules), they are often fully explicable in terms of a bottom-up approach,generating long-range correlations between localized constituents (phasetransitions in physics are good examples of this kind of phenomenon). Truetop-down causality will have to be more open and more non-local than that. Ibelieve that chaotic dynamics, with its picture of the open exploration ofproliferating possibilities within the confines of a strange attractor, may offer animportant clue to how this might come about. Self-organization offers the prospect

of the generation of different patterns of spatial order; chaotic dynamics offers theprospect of the generation of different temp oral p atterns of dynam ical h istory. Th elatter seems much closer to notions of agency than the former.

The second point, closely related to the first, is that if there is to be room forthe operation of true top-d ow n causality, then there w ill have to be intrinsic gap s,a degree of underdetermination in the account of the bottom -up de scription alone,in order to ma ke this poss ible . 9 It is to the possible identification of the source ofthis intrinsic openness that I now turn.

4 Ontological Gap s

It seems to me that our experience of human age ncy is basic and by itself sufficientto indicate that a metaphysical scheme affording no scope for top-down causality

9

S ee Thom as Tracy, "Particular Providcnce and the God of the Gaps" (in this volume).




would be seriously dcfcctive. Yet metaphysics must be consonant with its physicalbasis and so it is necessary to consider w hether there arc appro priate intrinsic gap salready known to us in the bottom-up description of the physical world. There

seem to be two broad possibilities:

4 .1 Quantum Theory

May not agents, human or divine, act in the physical world by a power todetermine the outcomes of individual indeterminate quantum events, even if theoverall statistical pattern of many such events may still be expected to lie within thelimits of probabilistic quantum laws? 1 0

This form of causality would actually be effected in the basement ofsubatomic processes. The proposal requires, of course, the adoption of themetaphysical strategy of interpreting quantum theory as involving intrinsicindeterminacies, but that is a strategy consciously or unconsciously endorsed bythe great majority of physicists. For agency thus exercised, these microscopicdeterminations would have to have their conscqucnccs amplified up to themacroscopic level .

There are a number of difficulties about this proposal in relation to humanand di vin e agen cy. One relates to the am plification effec t. Exactly how the

quantum world interlocks with the everyday world is still a question of unresolveddispute. In essence, this is the measurement problem in quantum theory. 1 1 Until thisquestion is settled, the micro-macro boundary is a difficult barrier to cross withconfidence. One might hope that a way around this might result from thesensitivity of chaotic systems to small triggers. Very quickly, there seems to beestablished a dependence of the behavior of such systems on details of what isgoing on at the level of quantum indctcrminacy. Yet the grave and unresolveddifficulties of relating quantum theory to chaos theory, 1 2 or of what is often called"quantum chaos," makes this a perilous strategy to pursue.

There is a particular difficulty in using quantum indctcrminacy to describedivine action. Conventional quantum theory contains much continuity anddeterminism in addition to its well-known discontinuities and indeterminacies. Thelatter refer, not to all quantum behavior, but only to those particular events whichqualify, by the irreversible registration of their effects in the macro-world, to bedescribed as measurem ents. In between measurem ents, the continu ous deter m inismof the Schrodingcr equation applies. Occasions of measurement only occur fromtime to time and a God who acted through being their dctcrminator would also

1 0Williain Pollard, Chance and Providence: God's Action in a World Governed byScientific Law (London: Fabcr, 1958); see also Nanccy Murphy, "Divine Action in the

Natural Order: Buridan's Ass and Schrodinger's Cat" (in this volume); and Tracy,

"Particular Providence."

n See, e.g., Polkinghorne, Quantum World, chap. 6.

12Joscph Ford, "What is Chaos, that we should be mindful of it?" in The New Physics,

ed. Paul Davies (Cambridge: Cambridge University Press, 1989).




only b e acting from time to tim e. Such an episodic accoun t of providential agenc y

does not seem altogether satisfactory theologically.

4 .2 Chaos Theory

The exquisite sensitivity of chaotic systems certainly means that they areintrinsically unpredictable and unisolable in character. In accordance with therealist strategy already discussed, I propose 1 3 that this should lead us to themetaphysical conjecture that these epistemological properties signal thatontologically much of the physical world is open and integrated in character. By'open' is meant that the causal principles that determine the exchange of energyamong the constituent parts (bottom-up causality) are not by themselves

exhaustively determinative of future behavior. There is scope for the activity offurther causal principles. By ' integrated' is meant that these additional principleswill have a holistic character (top-down causality).

The deterministic equations from which classical chaos theory developed arethen to be interpreted as dow nwa rd em ergen t ap prox ima tions to a m ore subtle andsupple physical reality. They are valid only in the limiting and special cases wherebits and pieces are effectively insulated from the effccts of their environment. Inthe general case, the effect of total context on the behavior of parts cannot be

neglected.Of course, with present ignoranc e, it is no mo re possible fo r m e to spell outthe details of the subtle and supple physical reality I propose than it is for thephysical reductionist to spell out how n eural netw orks generate co nsciou sness, orfor those who rely on quantum indeterminacy to spell out how it generatesmacroscopic agency, or for those who rely on an unanalyzed notion of top-downcausality through "bou nd ary con dition s" to spell out how it actually operates. W eare all necessarily w histling in the dark. I pre fer the tune I have cho sen b ecause ithas a natural anchorage in what w e know about m acrosc opic physical proce ss and

because it exhibits certain promising features which I will now discuss.For a chaotic system, its strange attractor represents the envelope of

possibility w ithin w hich its future motion will be contained. The infinitely variablepaths of exploration of this strange attractor are not discriminated from each otherby differences of energy. They represent different patterns of behavior, differentunfoldings of temporal development. In a conventional interpretation of classicalchaos theory, these different patterns of possibility are brought about by sensitiveresponses to infinitesimal disturbances of the system. Our metaphysical proposalreplaces these physical nudges by a causal agency operating in the opennessrepresented by the range of possible behaviors contained within the monoenergetic

1 3 See n. 3 above. See also Polkinghorne, Science and Christian Beief: TheologicalReflections of a Bottom-up Thinker (London: SPCK Press, 1994; printed in the United States

as The Faith of a Physicist: Reflections of a Bottom-up Thinker [Princeton, NJ: Princeton

University Press, 1994]), chap. 1.




strange attractor. What was previously seen as the limit of predictability nowrepresents a "gap" within which other forms of causality can be at work.

Because of the unisolability of cha otic system s, this new agency will have a

holistic top-down character. It will be concerned with the formation of dynamicpattern, rather than with transactions of energy. In a vague but suggestive phraseI have proposed that it might best be thought of as "active information." Thereseems a hope that here we might discern a glimmer of how it comes about thatintentional agency is exercised, either by our minds upon our bodies or by Godupon creation.

It is important to recognize that, in this scheme, the significance of thesensitivity of chaotic systems to the effect of small triggers is diagnostic of theirrequiring to be treated in holistic terms and of their being open to top-down

causality through the input of active information. It is not proposed that this is thelocalized mechanism by w hich agency is exercised. I do not suppose that either weor God interact with the world by the carefully calculated adjustment of theinfinitesimal details of initial conditions so as to bring about a desired result. Thewho le thrust of the proposal is expressed in terms of the complete holistic situation,not in terms of clever ma nipulation of bits and p iec es. 1 4 It is , therefo re, a prop osalfor realizing a true kind of top-down causality. It may fittingly be called con-

textualism , fo r it supp oses the behavior of parts to be influence d by their overall

context. This implies a strong form of anti-rcductionism in which processes arecapable of being modified by the context in which they take place. This will be sofor "cloudy" chaotic systems, but there will also be some "clockwork" systems,insensitive to details of circumstance, in which the behavior of the parts will beunmodified. Thus, one can understand the successes of molecular genetics indescribing the (mechanical) behavior of DNA, without having to suppose that thisjustifies a claim that all aspects of living systems are adequately described in thisreductionist fashion .

5 A Metaph ysical Proposal

The classical metaphysical options were m aterialism, idealism, and dua lism . N on eseems satisfactory. Materialism implausibly devalues the mental. Idealismimplausibly devalues the physical. Dualism has never succeeded in satisfactorilyintegrating the disjoint realms of matter and mind and it faces the problem of howto account for the apparent continuity of evolutionary history, in which a worldwhich was once a hot quark soup (apparently purely material) has turned into thehome of human beings.

In consequence, in the twentieth century some have felt encouraged toexplore the possibility of a dual-asp ect m onism , in which the mental and material

1 4 The discussion of Pcacocke in Theology for a Scientific Age p. 154, do es not

correctly represent my view. I have never supposed agency to be exercised through

(calculated!) manipulations of individual atoms and molecules. See n. 3 above.




are conceived of as being opposite poles (or phases, as a physicist might say) of asingle (created) reality. A key idea may well be that of complementarity. Quantumtheory discovered that the apparendy qualitatively different characters of wave and

particle were present in the nature of a single entity, light. This proved possible tounderstand when quantum field theory identified the feasibility of recon ciling thesecom plem entary descriptions as due to the presence of an intrinsic indefiniteness .(A wavelike state is associated with the presence of an indefinite number ofphotons.) The essence of complementarity is its ability to hold together apparentlyirreconcilable characteristics (spread out wave and point-like particle) in a simplereconciling account. We experience the apparently qualitatively different realmsof the material and the m ental. M ay n ot the und erstand ing of this duality be fou ndin the intrinsic indefiniteness associated by our hypothesis with the behavior of

chaotic systems, influenced by both energetic transactions and by active informa-tion? Of course consciousness is a much more profound and mysterious propertythan history form ation by ac tive inform ation, but at least the latter seems to po intin a mildly hopeful direction.

In common with all the other metaphysical proposals here discussed, adual-aspect monism based on a comp lementary m ind/m atter m etaphy sic, is largelyconjectural and heuris t ic . We do not have the knowledge to produce definit iveproposals of a fully articulate kind. Nevertheless, I believe this is a sensible and

hopeful direction in which to look for an understanding consis tent with ourknow ledge of physical process and with our experience of hum an age ncy . It w ouldafford a picture of reality wh ich w ould also be hospitable to the theological conceptof divine providential interaction with creation. Motivation for belief in divineprovidence is found in the religious experiences of prayer and of trust in a Godwho guides .

6 Some Comments

There are well-known relationships, due to Leon Brillouin and L eo Szilard, w hichcon ne ct the transfer of units of information (in a com mu nications-theory sense)with minimal transfers of energy. This might seem to imply that for a physicalsystem there could not be a totally pure distinction between energetic action andactive information . Carefu l analysis would be required befor e such a conclusionwa s firm ly established. It is not clear that active inform ation is subject to exactlythe same constraints as communications theory imposes on the storage of elementsof passive informa tion.15 Even if that were so, it would simply reflect the embodiedcharacter of human beings. We are mind/matter amphibians and are never in thestate of being pure spirits .

God, in any case, is not emb odied in the univ erse and there doe s not seem tobe any reason why God's interaction with creation should not be purely in the formof active information. This would correspond to the divine nature being pure spirit

1 5

See the discussion in Bohm and Hiley, Undivided Universe 35-38 .




and it would give a unique character to divine agency in a way that theologianshave often asserted to be necessary. (God is not just an in visible cause am ong othercauses.)

A world open to both bottom-up and top-down causality is a world releasedfrom the dead hand of physical determinism. It is a world of true becoming, inwhich the future has novel aspects not predictable from the past. It is a world oftrue tempo rality. 16 God knows things as they really are and this surely implies thatGod knows the temporal in its temporality. Divine knowledge of temporal eventsmust be knowledge of them in their succession, not just that they are successive.This implies, I believe, that the God who is the creator of a world of becomingmust be a God wh o possesses a temp oral p ole as well as an eternal p o le .1 7 Becauseth e future of such a world is not yet formed, even God does not yet know it. This

is no imperfection in the divine nature. God knows all that can be known, but thefuture is still inherently unknowable.

1 6 C f . C J. Isham and J.C. Polkinghorne, 'T he Debate over the Block Universe" in

Quantum Cosmology, 135-144 .

17

Polk inghorne, Science and Providence chap. 7.



T H E D ISC O V E R Y O F C H A O SA N D T H E R E T R IE V A L O F T H E T R IN ITY

Denis Edwards

The triumph of Newtonian science led to a view of the world that wasmechanistic, deterministic, and predictable. Recent theories of chaos andcomplexity, coming on top of the insights of quantum mechanics , have led to aradically different view of the world, as unpredictable and open to the new. Chaoticsystems are understood as unpredictable in practice, while quantum systems are

seen as unpredictable in principle and therefore as indeterministic.Essays in this volume consider divine action in the light of this new

worldview. I argu e that it is a matter of great im portan ce that we consider the viewof God that we bring to this inquiry.

Classical science, with its methodological reductionism, tended to objectifyphysical reality and to lend support to an Enlightenment concept of the humanbeing as the individual subject, the detached observer of the objects of science.This individualistic concept of the subject has led to well-known problems in

understanding human social relations and human relationship with other creatures.It has also tended to support a view of God as the great Subject, an individualisticcreator set over against creation.

When we ask about divine action we need to bring to our task not just a newscientific paradigm, but also a new, or retrieved, theological paradigm. The oldscientific worldview is giving way to a new paradigm of an open and self-organizing universe. It is equally important for our purposes to note that insystematic theology the old concept of God as the individua l Su bje ct is giv ing wayto a relational, dynamic trinitarian theology. We need to attend not only to a

renewed understanding of the complexity and dynamism of physical processes, butalso to a renewed view of a relational God.

In this paper, I will begin by exploring the general concept of divine actionfrom the perspective of a retrieved trinitarian theology. Then, in the second part ofthe paper, I will bring this trinitarian theology of divine action into dialogue withthe work of both John Polkinghorne and Arthur Peacocke, including theirreflections on divine action in the light of chaos theory. In this part I will beparticularly concerned w ith the question of what can b e said abo ut p articula r div ineacts.

1 Tow ards a Theology of Trinitarian Divine Action

As the scientific community is coming to a new understanding of physical process ,so, it seems to me, the theological community is at the beginning of a newappropriation of its central doctrine of the Trinity. The trinitarian theology whichwe hav e inherited in the West, under the influence of Augustine and Aquinas, has



158 D E N I S E D W A R D S

much to recommend it, but it has also had negative effects. It has emphasized anindividual psychological model of the Trinity rather than a communitarian one, thedivine unity rather than the persons, and the divine being rather than divine love.

In what follows, I will outline a theology of trinitarian divine action in whichthe Trinity is understood (1) as Persons-in-Mutual-Communion and (2) asdyn am ic, ecstatic, and fecund. I will argue (3) that the universe is God's trinitarianself-expression, (4) that there are "proper" roles for the trinitarian persons increation, and (5) that divine interaction with creation is characterized by thevulnerability and liberating power of love.

1.1 Richard of St. Victor: The Trinity as Persons-in-Mutual-Com munion

Great theologians such as Karl Barth and Karl Rahncr not only built on theAugustinian tradition, which stressed the one divine nature of the trinitarian God;they transformed it in terms of the nineteenth-century emphasis on the individualsubjec t In the light of their wo rk, there has been a tenden cy fo r Go d's unity to b estressed even more—God is seen as the on e self-consciou s subject, in three m odesof being or subsistence. By contrast, I would suggest that the contemporaryrecovery of the Trinity is more focussed on a relational and communal model ofthe Trinity—as a dynamic comm union of persons in mutual love. I am thinkin g of

the work of Jiirgen Moltm ann, Elizabeth Johnson, and Te d Peters, as well the wo rkof a number of other scholars who come from diverse theological perspectives,inclu ding W alter Kasper, John Zizioulas , Leonardo B off, Joseph Bracken,W olfhart Pannenberg, and Catherine M owry LaC ugn a.1 In light of this contempo-rary recovery of the communal and relational notion of the Trinity, I have foundit helpful to explore the line of trinitarian theology represented by Richard of St.Victor and Bonaventure.

Richard of St. Victor (d. 1173) was perhaps the supreme Western advocateof a relational theology of the Trinity. He built his approach on the model of

mutual human friendship. Richard l ived in a century that was marked by thediscovery of romantic love and by an intense interest in friendship in the new

Jiirgen Moltmann, The Trinityand he Kingdom of God (London: SCM Press, 1981);

Elizabeth Johnson, SheWho s: he Mystery of God nFeminist Theological Discourse ( N e w

York: Crossroad, 1992); Ted Peters, God as Trinity: Reationality and Temporality in DivineLife (Louisville, KY: Westminster/John Knox, 1993); Walter Kasper, The God of JesusChrist (London: SCM Press, 1983); Leonardo Boff, Trinity and Society (Maryknoll , NY:

Orbis Books, 1988); Joseph Bracken, Society and Spirit: A Trinitarian Cosmology(Cranbury, NY: Associated University Presses, 1991); Wolfhart Pannenberg, SystematicTheology, vo l. 1 (Grand Rapids, MI: W illiam B. Eerdmans, 1991 ); John Zizio ulas, Bengas Communion (Crestwood, NY: St Vladimir's Seminary Press, 1985); Catherine Mowry

LaCugna, God For Us:The Trinityand Christian Life (San Francisco: HarperSanFrancisco,

1991).



D I S C O V E R Y O F C H A O S 159

monas t i c movements . 2 Richard 's unique contribution was in his application ofreflection on Christian friendship to the central mystery of the Trinity.

He begins with an understanding of God as supreme goodness . Such

goodn ess, he argues, must involve full and perfect love. But love which is centeredon th e self cannot be considered to be the fullness of love, or charity. If there is thefullness of love in God, then it cannot be self-love or private love (amor privatus),

but only love which involves more than one person (amor mutuus or caritas). 3

Richard's thought moves from the fullness of goodness in God, to self-transcend-ing love, to the plurality of persons.

Richard sees the limited and imperfect human experience of self-transcen-dence in love as pointing to the infinitely more p rofo un d expe rience of trinitariancom mu nion. The Trinity is the "ideal of interpersonal relations be cau se here there

is infinite self-giving and infinite reception of love." 4 In the fullness of divine lovethe trinitarian persons give of themselves infinitely without fear of losingthemselves or of being rejected by the other.

Having argued towards an understanding of the plurality of persons in God,Richard's second step is to insist that the love between them must be completelymutual and equal. Since "nothing is m ore g lorious, m ore m agn ificen t than to wishto have nothing that you do not wish to share," we can conceive of the persons inGod only as sharing equally from all eternity.5 Supreme chari ty demands complete

mutuality and equality of persons. For supreme charity, the beloved must be lovedsupremely, and return love in the same way.

The next step in Richard's argument is to establish the meaning of the thirdperson in the Trinity. He argues from a subtle psych ological reflection on Christianfriendship that mutual love deman ds a third. Love between two can exclude others ,but this would not be mature or Christian love. In his thought, "the very dynamismthat led to self-transcendence in uniting the two, now leads to a further transcen-dence from the sphere of the tw o alon e to the thi rd." 6 For perfect love we look forone who can share in love for the beloved. Richard speaks of this person as the

"condilectus."7

This word seems to be his own invention. It refers to one who is"loved with," and to one who shares in love for a third.

This model of the Trinity as mutual love reflects the centrality of loverevealed in the "good news" of Jesus of Nazareth—above al l in the divine"foolishness" of the cross. It can lead to a radically different worldview. It offersthe basis for moving from a worldview, and a metaphysics, centered on being orsubstance to one centered on dynamic relationships. In this kind of theology, as

*Ewert Cou sins, "A Theology of Interpersonal Relations," Thought 45 (1970): 59-60 .3 See Richard of St. Victor, De Trinitate (Book III has been translated by Grover A.

Zinn, Richard of St. Victor: The Tweve Patriarchs, the Mystical Ark, Book Three of theTrinity [New York: Paulist Press, 1979]), 3.2 (PL 196, 916-917) .

4Cousins, "A Theology of Interpersonal Relations," 69-70.

•sDe Trinitate 3.6 (Zinn, 379).6Ibid.7

Ibid., 3.15.




Kasper comments, < 4the ultimate and high est reality is not substan ce but relatio n."8

Or as LaCugna puts it , person, not substance, becomes the ultimate ontological

ca tegory. 9

Today we are increasingly aware that Big Bang cosmology reveals ourcommon history and our interconnectedness with all other creatures of theuniverse. In addition, quantum mechanics tells us that we live in a reality which ismore a network of relationships than a world of billiard-ball-like atoms. Finally,the ecological crisis forces us to begin to think relationally, and to begin to see ou rown interconnectedness in the delicate web of life. Ric har d 's t r initarian theologysuggests that relationships of mutual love a re th e fou nd ati on of all reality. It argu esthat all creation springs from this dynamism of mutual love. Relationality is thesource of creaturehood.

1.2 Bonaventure: The Trinity as Dyna mic, Ecstatic, and Fecund

Many of those who offer a critique of the God of classical theism have not takeninto account the fecundity tradition of the Middle Ages, which proposes atrinitarian theology which is dynamic and related to the world. 1 0 The key fig ure inthis t radit ion is Bonave nture (1221-127 4). Bo naventure joined the Franciscans atan early age, was accepted as a Doctor of the University of Paris, and became

Minister General of the Franciscan order in 1257. As Zachary Hayes notes,Bonaventure's work reflects the interest of the early Franciscan movement in thetheological implications of Francis* religious experience, above all in theexperience of the goodness of God, and the experience of creation as expressiveof this divine goodness . 1 1

A ltho ugh he s tands in the Western Latin tradition, Bona ven ture 's thoug htowes to the East the concept of the dynamic fruitfulness of divine goodness . Heinherits from Pseudo-Dionysius the axiom that goodness is self-diffusive (b o n u m

diffusivum sui)> and this becomes one of the basic metaphysical principles

underlying his theolo gy of the Trinity and creation. The first nam e of God is ' t heGood' (Luke 18:19), and this divine goodness is radically self-communicative.1 2

8Kasper, The God of esus Christ, 156.

'LaCugna, God or Us 248-49 .1 0 See Cousins, "St. Bonaventure, St. Thomas, and the Movement of Thought in the

13th Century," in Bonaventure and Aquinas: Enduring Philosophers ed. Robert W. Shahan

and Francis J. Kovach (Norman, OK: University of Oklahoma Press, 1976), 16.

n See Zachary Hayes, Saint Bonaventures Disputed Questions on he Mystery of heTrinity: An Introduction and a Translation (St. Bonaventure, NY: The Franciscan

University Press, 1979), 32-33.1 2 St Bonaventure, tinerarium Mentis nDeum 5.2. For the Latin text with translation,

see Saint Bonaventures Itinerarium Mentis nDeum: Wth an ntroduction, Translation andCommentary, ja ns . Philotheus Boehne r (St. Bonav enture, NY : Th e Franciscan Institute

Press, 1956).




For Bonaventure, the life of the Trinity originates eternally from the one whois Fountain Fullness (fontalis plenitudo).n This Fountain Fullness expresses itselfperfectly in the one w ho is Image and W ord. This process reaches i ts con sum m a-

tion in the love between them, which is the Spirit .The procession of the Word arises by way of nature from the fecund, ecstatic

divine goodness . Goodness needs to communicate i tself . The Word is the fullexpression of God's primal fruitfulness . The infini te variety of things is givenunified expression in the Word. The Word is the locus of the divine ideas, and isthus called the eternal Ex em pla r.14 These divine ideas give rise to the created world,in God's free choice to create. They are dynamic causes of creation. Individualthings in their distinctness, not just Platonic universals, really are in God, in thed iv ine Exem pla r . 1 5 Here, in the eternal W ord, is the "Eternal A rt" (ar s eterna) of

the tr ini tarian God. 1 6

Cousins observes: "[B]y placing absolute fecundity in the Trinity, Bon-aventure has saved both God and the world." 1 7 He has rescued the transcen denceof divine fecundity, which is such that it cannot be exhausted by creation. God isnot swallowed up in creation. On the other hand, creatures are free to be theirspecific and limited selves, not overwhelmed by the divine power and immensity.

Bonaventure may have been the first in the West to speak of the circumin-

cessio of the Trinity. It is an equivalent of the Greek word perichoresis, which

expresses the idea of persons in a profound and dynamic communion ofinterdependence and mutuali ty. Circumincessio comes f rom circum-incedere, to"move around one another." It can bring to mind the image of the divine dance, adance of unthinkable intimacy and m utual love, a dan ce w hich f reely ov erflow s increation and becomes expressed in the dance of the universe.

1 .3 The Universe as Divine Self-Expression

In Bonaventure 's thought, the dynamic goodness of the Fountain Fullness f inds

expression in the Trinity, and freely "explod es into a thousand fo rm s" in the worldof creation. 18 In the free divine action of creation, the trinitarian fulln ess of div inegoodness "explodes" into what is not God, into creatures which are not God, but

1 3 See St. Bonaventure, Sent. 1.31, p.2, dub.7.14 Ibid., 1.6, a.u., q.1-3.

1.35, a.u., q.4, conc; dem, Breviloquium 1.8.7. See Leonard Bowman, 'The

Cosmic Exemplarism of Bonaventure," The Journal of Reigion 55 (1975): 182-83.

l6Sent. 1.6, a.u., q.3, resp.; Breviloquium 1.8; dem, Hexaemeron 1. Augustine had

used this expression in his De Trinitate 6.10 .11 .1 7Cousins, "Movement of Thought," 18.1 8Bowm an uses this expression in "Exemplarism," 183. He borrows it from Alexander

Gerkin , La Theologie du verbe: La reation entre VIncarnation et a Creation seon S.

Bonaventure trans. Jacqueline Greal (Paris: Editions Franciscaines, 1970), 132.




are Go d's self-expression. Hayes comments that creation can be understood as the"free overflow of God's necessary, inner-divine fruitfulness." 1 9

Bonaventure 's view of creatures is that they exis t by way of exemplary

causality. An exemplary cause is the pattern, model, or exemplar according towhich something is made. The Word is the Exemplar for all things. Bonaventurewrites that creatures seem to be "nothing less than a kind of representation of thewisdom of God, and a kind of sculpture." 2 0 They are the work of art produced bydivine Wisdom. He tells us that "every creature is of its very nature a likeness andresemblance to eternal wisdom." 2 1 It is an intrinsic characteristic of creatures thatthey represent and give expression to the Wisdom of G od .2 2

For Bonaventure, then, the universe is a book which can be read, a bookwh ose words reveal the creator:

From this we may gather that the universe is like a book reflecting,

representing and describing its Maker, the Trinity, at three different levelsof expression: as a trace (vestigium), an image, and a likeness . The aspectof trace is found in every creature; the aspect of image, in the intellectualcreatures or rational spirits; the aspect of likeness, only in those who areG o d - c o n f o r m e d . 2 3

What is this vestige of the Trinity that we find in all creatures? It is thereflection in a creature of the Trin ity as efficient, exemplary, and final cause of the

creature's inner structure. The first person of the Trinity is reflected as the Powerthat holds the creature in being (efficient causality). The second person is reflectedas the W isdom, or the Exem plar, by w hich it is created (exem plary cau sality). T hethird person is reflected as the Goodness which will bring the creature to itsconsum mation (final causality).

The center of Bonaventure's thought about creation has to do with exemplarycausality, because here we see, in the very form of a creature, its reference to theExem plar. From exemplary causality comes the truth, for m , species (intelligibility),

19 Hayes, "Incarnation and Creation in the Theology of St. Bonaventure," in Romano

Stephen Almagn o and Conrad L. Hawkins, eds., Studies Honoring Ignatius Charles Brady,Friar Minor (St. Bonaventure, NY: The Franciscan Institute Press, 1976), 315.

2 0 " U n d e creatura non est nisi quoddam simulacrum sapientiae Dei, et quoddam

sculp tile" (Hexaemeron, 12).

2 1 " O m n is enim creatura ex natura est illius aeternae sapientiae quaedam e ffig ies et

simultudo" Itinerarium, 2.12).

^See Etienne Gilson, The Philosophy of St. Bonaventure (London: Sheed & Ward,

1938), 215. See Sent. 2.16, a.u., q.2, where Bonaventure says that it cannot be an accident

in a creature to be a v estig e.

23Breviloquium (trans. Jose de Vinck in The Works of Bonaventure II: The Brevilo-quium [Paterson, NJ: St. Anthony Guild, 1963], 104.), 2.12. My italics. Bonaventure can

also mention the shadow {umbra) of God, which is the most elementary and general

reflection of God in creation. It reflects God as one, whereas the trace or vestige reflects the

three person s.




num ber, and beauty of a cre atu re .2 4 Bon aventure has a special word, "contu it ion,"to describe a way of seeing creatures in their relationship to God. It implies asimultaneous awareness of the reality o f, for exam ple, a giant sequ oia tree, and of

its eternal Exemplar. In this life, the apprehension of the divine Exemplar is veiled,distorted by sin, and indirect, but it is real.

Bonaventure 's t r ini tarian theology has much to offer a contemporarytheology of creation. Every creature is understood as an aspect of God's self-expression in the world. Every creature in its fo rm , proportio n, an d beau ty, reflec tsthe W ord and Wisdom of God , the divine Ex em plar. Ev ery cre ature is a revelatoryword written in the great Book of Creation. Every species and every ecosystem,every grain of sand and every galax y, are the self-ex pression s of the eternal art ofdivine Wisdom. For Bonaventure there is no s imple identif icat ion between God

and the world, no hint of panthe ism . But his teachin g co uld be d escribed as a kindof panentheism. As Ewe rt Cousins writes, " in a m ost em phatic way fo r B onaven-ture, G od is in the world and the world is in God." 2 5 God is profoundly present toall things, and G od is expressed in all things, so that each creature is a symbol anda sacrament of God's presence and trinitarian life.

1 .4 Creation is the Action of the Wh ole Trinity, but Involves Distinct and

"Proper" Roles of the Trinitarian Persons

In the previous three sections, I have been outlining some of the insights ofRichard of St. Victor and Bonaventure which I think are important to recover fortoday. In what follows I will enter into areas whe re a conte m por ary theolo gy need sto m ove beyond medieval theology. The first of these is the argu m ent that the self-expression of God in creation is "undivided" but properly tr ini tarian. TheAugustinian teaching that ilopera trinitatis ad extra indivisa sunt" ( the Trinity 'sacts ad extra are one) has led to the conviction that since creation is an action of theessence of God, there is no proper role for each person. This means that when we

attribute a particular role in creation to Wisdom or to the Spirit, we do so only by"appropriation." We attribute to one person what really applies to all three.

Contemporary theology has recovered the understanding that we mustattribute a proper role to the trinitarian pers ons in the salv ific mi ssion s of the W ordand the Holy Spiri t . 2 6 This needs to be extended to include a properly trinitariannotion of creation. This does not deny the unity of the divine action in creation, butpoints to distinctions proper to the persons within this common action. It suggeststhat the univers e is the self-expression of the trinitarian God: the Fountain Fullnessis the Source of the existence of each creature; the Divine Wisdom is the Exemplar

2 4 See Bowman, "Exemplarism," 190-94.2 5 Cousins, "Movement of Thought," 19.

*t )n the proper role of the persons in the economy of salvation see Karl Rahner, TheTrinity(New York: Herder & Herder, 1970), 27. On the Holy Spirit, see David Coffey, "A

Proper Mission for the Holy Spirit," Theological Studies 47 (1986): 227-50; and dem, "The

'Incarnation' of the Holy Spirit in Christ," Theological Studies 45 (1984): 466-80 .




for the unique identity of each creature; the Spirit is the im m ane nt P rese nce of G od

in all creatures and the Bond of Love who brings all things into unity.Three reasons support attributing prope r roles to the trinitarian pers on s in the

act of creation. First, the inner logic of the system of Bonaventure, which I amfollowing, suggests that the one trinitarian work of creation be understood asproper to each person, since for Bonaventure what is distinctive of the persons(Absolute Source, Divine Exemplar, and the Presence and Bond of Love) is whatcomes into play in the one work of creation. 2 7 Second, this seems faithful to thebiblical texts, including the texts which identify Christ and cosmic Wisdom andstress creation "in" and "through" Christ, and the biblical teaching which suggestsa real and "pr ope r" engagemen t of the Spirit in cr ea tio n.2 8 Third, I would argue thatonce theology posits proper missions of the Word and Spirit in salvation history,the inner theological connection between creation and redemption requires thatcreation too be understood as properly tr ini tarian. 2 9

1.5 The Trinity's Interaction with Creatures is Characterized by the Vulnerability

and Liberating Pow er of Love which Respects Hum an Freedom and Natural

Processes

Christian theology, as it engaged with Greek philosophical thought, removed

change and feeling from the biblical God. Theologians sought to preserve divinefreedom, and the classical ideal of divine freedom meant self-sufficiency andfreedom from dependency on creation. Hence, it seemed, God must be understoodas imm utable. Even the cross of Jesus was no excep tion bec ause , it was a rgu ed, thesuffering of Jesus touched only the human nature and not the divine. Later, Godwas thought of as "pure act" (ac tus purus) t and if the divine being was pure act,there was no movement from potency to act in God, and hence no change in God.

This theology has proved radically inadequate in the century of the holocaustand of Hiroshima. Feminis t theologians have analyzed the tradit ions of God's

invulnerability and omnipotence, and shown their relation with patriarchal cultureand its horrific effects . 3 0 There is widespread agreement in contemporary theology

^Lateran IV (1215) affirmed the Augustinian view that the world was created by the

divine essence. This teaching can co-exist with a proper role of the trinitarian persons in

creation.

^ n the biblical view of the work of the Holy Spirit in creation se e Jiirgen M oltmann ,

The Spirit of Life: A Universal Affirmation (Minneapolis, MN: Fortress Press, 1992).

2 9 See Moltmann, God in Creation: An Ecological Doctrine of Creation (London:

SCM Press , 1985), 94-103.

^ o r a strong analysis and theological argument along the se lines se e particularly the

last chapter of J oh ns on 's She Who s "Suffering God: Compassion Poured Out" (246-72).

See also An na Cas Winters, God's Power: Traditional Understandings and Contemporary

Challenges (Louisville, KY: Westminster/John Knox, 1990).




space for o ther s . 3 4 As Kasper notes: "For the Bible, then, the revelation of God'somnipotence and the revelat ion of God's love are not contraries ." Rather God'somnipotence is the supreme capacity to love: "It requires omnipotence to be able

to surrender oneself and give oneself away; and it requires omnipotence to be ableto take oneself back in the giving and to preserve the independence and freedomof the recipient ." 3 5

Polk ingh orne points out that Go d's love and fai thfu lness apply not just tohuman beings, but also to the physical universe. God is the great respecter andallower of freedom not only of human creatures, and other living creatures, butalso of physical pro cesse s.36 This suggests that we need to think of D ivine W isdomas responding creatively to the universe, as "im pro visin g" on the the m e of creationin the light of the interplay of chance and necessity. God's ongoing creative action(icreatio co ntinua) is throu gh loving, faith ful, and fru itfu l interaction w ith bothchance and lawfulness. Peacocke has done much to show the place of chance andlaw in Chris t ian theology. 3 7 He speaks of God's action in creation under thebeautiful im age of God as the Great Improvisor.

2 Reflections from a Systematic Trinitarian Theology on Particular D ivine Acts

I have been arguing that these key insights of trinitarian theology can illuminatewhat is meant by the word 'divine' in the concept of divine action. They are thebasis for a general trinitarian theology of divine action through continuouscreation, as well as for an approach to the issue of particular divin e acts. It is to thisissue that I turn no w . W hat do es this theology hav e to say about p articular d ivineactions, like the incarnation, the experience of the Holy Spirit, and the experienceof divine providence? I will attempt to explore this question through dialogue withthe works of Polkinghorne and Peacocke on divine action.

Polkinghorne and Peacocke are both, in their own distinctive ways,

outstanding contributors to the dialogue between science and theology. Inparticular, both have articulated new approaches to an understanding of divineaction in the light of chaos theory. I will attempt a brief summary of theirapproaches, and in the light of their views, offer my own reflections on the

^See Moltmann, Trinity, 108-11; and William Hill , The Three-Personed God: TheTrinity as a Mystery of Salvation (Washington, D .C.: Catholic University of Am erica Press,

1982), 76, n.53.

35 Kasper, The God of Jesus Christ, 194-5.

^ e e John Polkinghorne, Science and Providence: God's Interaction with the World(London: SPCK Press, 1989); and dem, Reason and Reality: The Reationship betweenScience and Theology (London: SPCK Press, 1991).

^Arthur Peaco cke, God and he New Biology (London: J.M. Dent, 1986), 97-98; and

idem, Theology J?r a Scientific Age: Beng and Becoming—Natural and Divine (Oxford:

Basi l Blackwell , 1990), 175-77.




contribution of the retrieval of trinitarian theology to the discussion of particulardivine action.

2 .1 Polkinghorne and Peacocke on Divine Interaction with Creation

Polkinghorne points ou t that chaotic system s are so exquisitely sensitive to initialconditions and circumstance that we can never know enough to predict theirb e h a v i o r . 3 8 This is a statement about our limited knowledge, an epistemologicalstatement. But Polkinghorne argues that this unpredictability suggests a realopenness in nature. It can suggest that there is an openness which is not justepis temological but ontological . 3 9

Physical processes can b e understood as open fr om be low , and as able to be

influenced by holistic organizing principles which are still unknown, but open toscientif ic discovery. 4 0 Polkinghorne suggests that this openness makes room notonly for human free acts, but also for divine interaction with creation. Physicalreality will be open from below to a proliferating world of possibilities. The futureof the system can be determined by dow nw ard causation, through wh at P olking-horne describes as information input.

He argues that human beings can be thought of as a matter/mind unity, forwhich the complementarity of wave/particle in quantum theory is an analogy. What

we call the material and th e men tal are really o ne "stuff ' encountered in differentregimes. He sees causali ty through information input as offering a gl immer ofunderstanding of how a mental decision to lift an arm, say, brings about thephysical act of movement.

Polkinghorne suggests that divine agency in the world might be understoodby analogy with human agency. God can be thought of as acting through

3 8

See Polkinghorne, 'The Laws of Nature and the Laws of Physics," in QuantumCosmology and the Laws of Nature: Scientific Perspectives on Divine Action, ed. Robert

John Russell, Nancey Murphy, and C.J. Isham(Vatican City State: Vatican Observatory,

1993; and Berkeley, CA: Center for Th eolo gy and the Natural Scienc es, 199 3), 4 37 -4 8; and

idem, 'The Metaphysics of Divine Action" (in this volume). See also dem, Science andCreation: The Search or Understanding (London: SPCK Press, 1988); dem, Science andProvidence; and dem, Reason and Reality.

3 9 It seems to me that Nancey Murphy is right in her criticism of an argument from

episte m ologic al unpredictability to ontological indeterminacy. How ever, Polkingho rne

allows that there is no strict argument from chao s theory to onto logy, and admits that he is

making a "metaphysical guess" about the nature of reality. In m y vie w this "gu ess" is w orth

exploring from a theological perspective. Se e Murphy, " Div ine Ac tion in the Natural Order:

Buridan's As s and Schrodinger's Cat" (in this vo lum e).

4 0 Polkinghorne writes that ". . . chaos theory presents us with the possibility of a

metaphysically attractive option of openness, a causal grid from below which delineates an

envelope of possibility (it is not the case that anything can happen but many things can),

within which there remains room for manoeuvre." Polkinghorne, 'The Laws of Nature and

the Laws of Physics," 443.




information input into the flexible and open process of cosmic his tory. ButPolkinghorne also sees God as valuing and protecting the freedom of creation. Thisprovides the basis for a theodicy w hich he calls a "free-pro cess de fen se" in relation

to physical evil, patterned after and along with a "free-w ill de fen se" in relation tomoral evil.

He insists that this theory of divine action is not a return to the discredited"God of the gaps" because the openness of the physical universe is not a gap inscientific information, but an intrinsic openness of the universe to top-downcausality. He insists, too, that God is not to be understood as simply one causeamongst other causes, and that God's input is not one of energy, but one ofinformat ion.

Polkinghorne argues that a God who is involved with phy sical pro cesses willbe radically involved with time. Borrowing from process theology he sugg ests thatGod needs to be understood in a dipolar (time/etemity) fashion, and as intimatelyinvolved in the world of becoming. He makes the more radical suggestion that Goddoes not know the future, s ince the future is not there to be known. There is akenosis of divine omniscience in creation, and God allows the future to be trulyopen. God's purposes wil l be brought about by way of "contingent paths"—through interaction with the processes of the universe.

Peacocke, too, points to the fact that many systems which are governed by

non-linear dynamical equations become unpredictable and that this unpredictabilitycannot be eradicated. He makes it clear that he sees this as an unpredictability inpractice and not in principle—he is not claiming that it stems from ontologicalindeterminacy in nature. But he points out that in certain cases, systems can reacha point of bifurcation, an either/or transition, which is completely unpredictable inprac t i ce . 4 1 Open dissipative systems, far from equilibrium, may evolve into newlevels of order and organization. Through the amplification of small fluctuations,a system can have access to novelty. In such systems we recognize that alongsidethe normal description of "bottom-up" causation, there is need for a " top-down"

or, more precisely, a "whole-part" description where this whole influences itsparts . 42 An example of this is found in the jaws of worker termites, which dependfor their effectiveness on particular proteins, whose efficiency has been enhancedthrough natural selection.

Peacocke suggests, as does Polkinghorne, that this influence can be thoughtof as a flow of information rather than of energy. It is "information" from theenvironment which determines the selection of the DNA sequence in the termitejaw. Peacocke speculates that the human brain operates through " top-down"causation, as the brain state as a whole determines what happens at the level ofindividual neurons. He suggests that this relationship between the brain state and

4 1 See Peacocke, '"God's Interaction with the World: The Im plications of Deterministic

'Chaos* and of Interconnected and Interdependent Complexity" (in this volume). See also

idem, Theology jr a Scientific Age.4 2

See Peacocke, "God's Interaction with the World."




individual neurons is better conceived of as a transfer of information than ofenergy.

Can G od be thought of as interacting with the un ivers e in the unp redicta bility

of chaotic systems? Peacocke answers no. He would see this as a new kind ofimplicit interven tionism .43 God has given a certain autonomy to natural processes.He believes that God's omniscience is freely self-limited, such that God cannotknow the outcome of unpredictable events and so cannot manipulate them. Whileour new awareness of open-endedness does help us see the natural world as amatrix in which openness and human freedom emerge, i t does not help usunderstand what Austin Farrer called the "causal joint" of God's action in theworld .

Rather, Peacocke sees God interacting with the world as a wh ole, and throug h

this with individual components of the world. God is then understood asinteracting in a "top-down" way, without abrogating the laws, regularities, orunpredictabilities of natural systems. He invokes the analogy of the relation of thehuman mind/brain to the body. Just as there is top-down causation from the stateof the whole brain— in the bod y— to bodily action, so God might be regarded asexerting con tinuous t4 top -do w n" causative influences on the world as a whole. G odis thus the unifying and centering influence on the world's activity. The successionof the states of the world is also a succession in the experience of God. God's

interaction with the world as a who le is envisaged as an input of information, ratherthan as a flow of energy. Since God is personal this can be understood as a"communication" to the world of God's purposes and intentions. Such a mode ofinfluence belongs to God alone, to one who is both transcendent and immanent.

In Peacocke's view, God can influence not only the whole system but alsoparticular events through top-down causative influence, but this would never bescientifically observ able, and wou ld not appear as a divine interven tion. It wouldnot interf ere with the laws, regularities, or unpredictabilities of nature .

2 .2 Reflections on Issues Raised by Polkinghorne and Peacocke

There is a significant measure of agreement between Polkinghorne and Peacocke.Both believe that the epistemic openness of chaos theory and theories ofcomplexity suggests, and allows for, a concept of the universe as unpredictable inpractice. Both use the image of human action and the mind/body unity as a way ofunderstanding divine action. Both suggest that divine action is by way ofinformation input rather that throug h en ergy input. And b oth ag ree that the fu tur eis undetermined and that God does not know the future.

4 3Polkinghorne also makes it very clear in his article in this volume that he does not

propose that chaos is "the localized mechanism by which agency is exercised." Rather, he

writes, "the whole thrust of the proposal is expressed in terms of the complete holistic

situation, not in terms of the clever manipulation of bits and piece s." Se e 'T h e M etaphysics

of Divine Action" (in this volume).



DIS CO V E RY O F CH A O S 171

natural processes. In such a theology the fu tu re is und erstoo d as radica lly open andnot determined by the present. But I do not see that ade qua te jus tific atio n has b eenprovided by Polkinghorne or Peacocke fo r the assertion that G od cann ot kno w the

future. The argumen t app ears to be that since natural pro cesses are unp redictable,and since God respects natural processes, God cannot foresee their outcome. Butthis, it seems to me, involves an unwarran ted logical leap. In a trinitarian theolog ywhich stresses the mystery and incomprehensibility of God, divine knowledge offutu re contingent events is not based on God's capacity to predict from the presentto the future. It is based on the conviction that God's eternity embraces all of time,and on the assumption that future contingent events are present to God. 4 5 T h etrinitarian knowledge of these events does not deny their contingent character. Theconcept of God's eternal presence to the whole of time is not in conflict with the

idea that the future is radically unpredictable from within time. The God revealedin Jesus Christ and in the outpouring of the Spirit is not only eternal but also freelyand radically involved with t ime. 4 6 But the trinitarian perichoresis is eternal anddocs transcend time and all our concepts of eternal life. We cannot see spacetimefrom an eternal divine perspective.4 7 On the basis of trinitarian theology and itsrespect for negative theology, I would be cautious regarding s tatements aboutdivine knowledge of the future.

3) A trinitarian theology points not only to the divine action of continuous

creation, but also to particular or special d ivine acts. In m aking this affirm ation,I am simply agreeing with other essayists here, including Polkinghorne andPeacocke, that the existence of particular divine actions constitutes a datum ofChristian tradition, experience, and theology. For Christian believers, these wouldinclude, above all, God's trinitarian self-communication in Jesus of Nazareth, andin the mission and presen ce of the Holy S pirit . Particular divine acts also includegreat historical events like the Exodus and personal experiences of healing and ofgrace, as well as the experience of providence in day-to-day events.

4) If God is acting creatively and responsively at all times, and also in

particular ways, then this seems to dema nd action at the level of the whole system(Peacocke's emph asis) as well as at the everyday level of events (Polkinghorne ' semphas is ) , and also at the quantum level (the emphasis of George Ellis, NanceyMurphy, Thomas Tracy, and Robert Russell) . 4 8 1 see every reason to embrace the

4 5 SeeS77i , 1 .14 .13 .4 6 O n this, see the argument deve lope d by Peters in God as Trinity.A7li may be relevant to note that science treats time as irreversible in some contexts and

as reversible in others, and there is no general agreement about the epistemological weight

of the "block" universe as compared to the "emergent" universe. See C .J . Isham and

Polkinghorne, "The Debate over the Block Universe," in Quantum Cosmology, 135-44.

4 8 S e e the articles in this volu m e: G eorge F.R. E llis, "Ordinary and Extraordinary

Divine Action: The Nexus of Intervention"; Murphy, "Divine Action"; and Thomas F.

Tracy, "Particular Providence and the God of the Gaps." See also Russell, "Theistic

Evolution," in Genes, Reigion, and Society: Theological and Ethical Questions Raised by

the Human Genome Project, ed. Ted Peters (forthcom ing, 19 96).




argument that G od can be und erstood as interacting w ith the unive rse as a who le,but this has to find expression in particular events. I have advocated a thoroughlyrelational trinitarian theology of creation—every creature exists at every moment

from trinitarian relations. In this kind of theology every creature, from a proton toa galaxy, in its being and its becoming, is the expression and the presence of thedynamic overflowing mutual love at the heart of all things. Divine action at thelevels of both the whole and of the parts is necessary for a trinitarian theology. Itis theologically inconceivable to think of divine action at the level of particularevents which is not interconnected and part of the divine action of continuouscreation with regard to the whole universe.

5) Particular divine acts are always experienced as mediated through created

realities. I agree with William Stoeger, that our experience of particular divineaction, whether it be of the incarnation, the promptings of the Holy Spirit , or ofdivine providence, is a lways mediated and indirect . 4 9 We have no experience ofunmediated or direct divine action. I agree with Stephen Happel that God acts inevery event to sustain its existence, but this action is always mediated in andthrough the s tructures of the world. 5 0 Our experience of the trinitarian God is, inthe first instance, through the "eco nom y" of salva tion. O ur C hristolo gical theo logyaffirms that God's action in Jesus of Nazareth is mediated through the humanityof Jesus.51 This is taken in Christian theology to be an indication that God's other

actions with regard to us are "incarnational" in structure, mediated throughcreation.

As liberation theologians like Gustavo Gutierrez have shown, God's actionin an event like the Exod us is mediated through the political struggle of a group ofs laves . 5 2 Our experiences of the Spirit and of providence are always mediated byour day-to-day experiences of life in the world, though these experiences may wellopen out into mystery, wonder, and grace. A critical analysis of experience revealsthat even the most transcendent of human experiences must be mediated inconsciousness through images, concepts, words, and stories, all of which are

socially and historically conditioned.6) The unpredictability, openness, and flexibility discovered by contemporary

science is significant for talk of particular divine actions becau se it provides the

basis for a worldview in which divine action and scientific explanation are

understood as mutually compatible, but it is not possible or appropriate to attempt

to identify the "causal joint" between divine action and created causality. While

4 9 S e e William Stoeger, "Describing G od's A ction in the World in Light of Scien tific

Knowledge of Reality" (in this volume).

^ e e Stephen Happel, "D ivine Providence and Instrumentality: Metaphors for T i me

in Self-Organizing Systems and Divine Action" (in this volume).

5l Happel writes in "Divine Providence and Instrumentality" that "it must still be noted

that the humanity of Jesus is an instrument, not an unmediated intervention of divine

action!" (p. 196).

5 2Gustavo Gutierrez, A Theology of Liberation: History Politics and Salvation, rev.

ed. (Maryknoll , NY: Orbis Books, 1988), 86-91.




I believe with Polkinghorne thai we can con ceive of G od acting in the openn ess ofthe universe at least as suggested by chaotic systems, and with Ellis, Murphy,Tracy, and Russell that it makes sense to think of God acting in the openness

suggested at the quan tum level, I would differ from these thinkers because I wouldargue that we cannot identify any one specific or exclusive locus of particulardivine action or any real "causal joint" betwee n div ine action and created cau sality.A trinitarian theology suggests a dynamic relational presence of God in everyquantum event, chaotic system, and hum an fre e act, but it suggests a pre sence anda causality that finally escapes comprehension. However, I agree with the writersmentioned above that the unpredictability discovered by contemporary science ishighly significant for talk of particular divine actions because it provides the basisfor a worldview in which divine action and scientific explanation are compatible.

As Murphy points out, it is an important intellectual gain that contemporaryscience, unlike its mechanistic precursor, does not positively exclude human ordivine free acts. There is an openness or flexibility in the modern scientificworldview which leaves intellectual room for both the insights of contemporaryscience and a theology of human and divine free acts .5 3 As Russell notes, it issignificant that the limitation on predictability found in the theory of deterministicchaos shows that science can never fully specify whether or not God might beacting in a particular w ay in a chaotic system:

The real message of chaos theory is that because of "eventual unpredict-abil i ty," we know that we can never know the future in advance in fulldetail. No improvement in technology, and no change in scientific theories,will ever overcome the problem entirely. The future will always be, in part,unknown to us , not just because we don' t have a good enough physicaltheory but for a much more fundamental reason, because we really cannotspecify the totality of the present. Theologically this suggest that we cannever fully specify what nature "on its ow n" is capa ble of, or what God theTrinity is doing in nature, let alone which is doing which.5 4

Chaos and quantum theories both suggest a hum bler epistemolog ical stance on th epart of science than that of mechanism, a stance which can leave room for bothscientific explanation and for a theology of divine action.

I do believe that w e need to struggle to unde rstand wh ere natural process isopen to divine action. This is wh ere I see the value of Polking horn e 's w ork, not asproviding an understanding of a "causal joint" between divine and createdcausality, but as show ing a rationale for moving beyond a closed worldview whichexcludes hum an and divine action, to a worldv iew which has spa ce for hum an andd iv ine ac t ion . 5 5 It is a worldview where, as Stoeger says, the laws of nature and

3 3Muiphy, "Does Prayer Make a Difference?" in Cosmos as Creation: Theology andScience in Consonance ed. Ted Peters (Nashville: Abingdon Press, 1989), 235-45.

^Russell, 'Trinitarian Chaotic Creation" (unpublished manuscript).

5 5 A S I have shown above, Polkinghorne takes a step beyond the position I am

espousing.




nature itself constrain but do not fully determine what develops or occurs. Manypossibilities are left open in natu re, and it is this flexibi / w hich enables h um an sbeings and other animals to influence reali ty. 5 6 There is, then, great theologicalvalue in attempting to show wh ere there is flexibility in nature both at the q uantumlevel and the macro-level.

But as I have said above, I agree with Peacocke, and with Stoeger, that wecannot expect to see directly wh at Farrer called the "causal join t" betw een divin eaction and natural proc esse s. 57 1 am cautious about fu rther speculative specificationof the locus of divine interaction with creation, because it seems to me that it runsth e risk of compromising the transcendence of God on the o ne ha nd, an d creaturely

autonomy and the integrity of scientific explanation on the other.If we are to follow the creative theological lead of Polkinghorne and

Peacocke and speak of divine action in the language of "information input" and4< top-down causation," then the analogical nature of this use of language must benoted, so that God does not appear once again as a cause within the world ofnatural causes, as explaining, for example, what science would attribute tob o u n d a ry c o n d i t i o n s . 5 8 It seems to me that this kind of language can functiontheologically to express the conviction that through God's creative (and mediated)action, one of many possible states of the physical universe actually occurs. But

such language must be understood as fun ction ing as creative theological m etapho rand not as alternative scientific explanation.

In the relational ontology I have been suggesting here, creation is essentiallya relation of both the whole universe and individual beings to the divine perichor-esis of m utual love. In this kind of trinitarian theo logy d ivine action and creaturelyautonomy are not in opposition. Rath er creaturely auton om y would be und erstoodas flourishing vis-^-vis divine action. Again, I believe that the model to w hich w eshould appeal is the model of mutual love, whe re the in fluence of the be loved doesnot annihilate autonom y but allows it to flourish . I would sug gest that this m odelshould be applied not just to divine grace at work with human persons, but to thework of the Holy Spirit in all creatures. The trinitarian vision of creation is onewhich involves the kenosis of love, love which winningly allows itself to becomevulnerable to human freedom and to the natural processes of the universe.

All of this sugg ests that the trinitarian will to save, revealed in the death andresurrection of Jesus, will be achieved in an open and (for us) unpredictableuniverse. This love is infinitely creative and powerful, but with the kind of power

^Stoeger, "Describing God's Action" (in this volume).

"Ibid.3 8 T h i s is certainly part of the messa ge to theologian s of Bernd-O laf KUppers in his

article in this volume, "Understanding Complexity." It also brings to mind the important

cautions expressed by Willem B. Drees in his article "Gaps for God?" (in this volume).



DISCOVERY OF CHAOS 175

revealed in the death and resurrection of Jesus. M y im age is that of the da nc e of theuniverse, a dance led by the trinitarian pe rsons in ever new imp rovisatio ns, wh ichtouch each creature and embrace the whole, which respect freedom and thestructure of all that is , and which open out onto what is radically new.



D I V IN E P R O V I D E N C E A N D I N S T R U M E N T A L I T Y :Metaphors for Time in Self-Organizing Systems

and Divine Action

Stephen Happel

There is no such thing as a theologicalstatement about a beetle.

Karl Rahner, Theology and the Arts

1 Introduction

I find it not a litde curious that a premier Catholic theologian assumed thattheology could dismiss realities other than hum an b ein gs .1 Indeed, I believe that theepigraph indicates flaw s in Rah ne r's ontolog y; but in this context, I wish to pointto the continued split between an anthropocentrically focused theology and anequally one-sided, objectivist science.

So Steven Weinberg, in Dream s of a Final Theory, asserts that "w e" are notlikely to find an "interested God in the final laws of nature." These laws are morelikely to lead inexorably toward a "chilling impersonality." It is better to avoid thecheap consolations of religion by courageously embracing the stoic resistance ofsc ience . 2

^arl Rahner, 'Theology and the Arts ," Thought 57 (1982): 26. Rahner's theoretic

interpretation of the relationships b etw een the natural/social sc ien ces and th eol ogy not on lydeveloped, but remained more complex than the seeming dismissal in the article cited.

Nonetheless, Rahner focused theology as a discipline (with interdisciplinary concerns) upon

human self-transcendence toward God. See Karl Rahner, 'Theology as Engaged in an

Interdisciplinary Dialogue with the Sciences," in Theological Investigations vol. 13, trans.

D av id Bourke (London: Darton, Longman & Todd, 1975) , 80-93 ; idem, "On the

Relationship between Theology and the Contemporary Sciences ," in TheologicalInvestigations vol. 13, 94-102; and dem "On the Relationship between Natural Science

and Theology," in Theological Investigations, vol. 19, trans. Edward Quinn (New York:

Crossroad, 1983), 16-23. In a 1967 essay Rahner argues that "sub-human" levels of natural

necessity are mea ningful on ly b ecause they are an elem ent in the history of free spirit. S ee

"Theological Observations on the Concept of Tim e," in Theological Investigations, vol. 11,

trans . David Bourke (New York: Seabury, 1974) , 298-308.

2Steven Weinberg, Dreams of a Final Theory: The Search for the Fundamental Lawsof Nature (New York: Pantheon, 1992), 257-58. Note how this position is restated (andparallels Karl Rahner's) by Philip Hefner: "Religious cosmological myths, then, do notreally answer directly the question, 'What is the Universe like?' Rather, they speak to the



178 S T E P H E N H A P P E L

2 An Intellectual Ma p

My particular metho d fo r understand ing th e relat ionship of science and theology

studies the language that both of these disciplines use. Religious thinkers oftenobserv e that there is a first-level discourse (a poetics and rhetoric) enshrined in thesymbols , metaphors , s tories , and experiences of revelat ion, though theologiansoften shed that language rather quickly. There is a lso an intermediate level ofdoctrines, creeds, and dogmas (an ecclesial pragmatics) that has a complexrelationship to the first-level languages. But in addition, there is theology, areflective discourse (dialectics) that primarily (until the rise of science andhistorical consciousness) ma de use of philosophy as a dialo gu e partn er (fo r the firstone thousand years, primarily Plato or neo-Platonism; then AristoUe). I use thehermeneutics of language as my primary dialogue partner. Religion is faithexpressed in particular first-level languages (the scriptures, popular piety, ordevotion) and must be dis t inguished from, but not divided from, theology, areflection upon those expressions (a linguistic version of fides quaerens intel-

lectum).

Science and theology can be related as disciplines about their respectiveconceptual content or about their methods of data manipulation. They can also berelated through the linguistic perf orm an ce of theolog ians and scientists. Scientists

and theologians m ay sa y they are doing one thing them atically, and in fact performquite another language. What are theologians and scientists really doing when theyuse language within these disciplines?

Christian theologians maintain a dependence upon revelation and faith. B utneither faith nor revelation is a univocal concept.3 "Objectively," theologiansdepend upon community tradit ions of worship, oral preaching, and rel igiousexperiences; genres of written expression (gospels are not visions; nor are theyletters or apocalypses); and institutional mediations (such as office or authorities)among others . "Subjectively," fai th is a condit ion for apprehending the meaning

of these revelatory discourses. But faith itself has many levels—from a willingsuspension of disbelief to the highest levels of contemplative participation in thedivine life. 4 Theology, therefore, is never a totally independent discipline.5 T h o u g h

question, 'What must we believe about the Universe—as we know it to be from our

sc ie n ce — in order for us to live optimally?" (Hefner, "Christian Assu m ption s about the

Cosmos," in Cosmology, History, and Theology, ed. W. Yourgrau and A.D. Breck [New

York: Plenum Press , 1977] , 351.)

3 See Paul Ricoeur, 'Toward a Hermeneutic of the Idea of Revelation," in Essays inBiblical Interpretation, ed. Lewis S. Mudge (Philadelphia: Fortress Press, 1980), esp. 73-95.

4 For a nineteenth-century version of this multi-leveled understanding of faith, see

Samuel Taylor Coleridge, Confessions of an nquiring Spirit, ed. Henry Nelson Coleridge

(London: William Pickering, 1840; reprint, Menston: Scholar Press, 1971).

5It is a subalternated discipline, as Aquinas stated. STh. 1.1.2, corp. The "higher

science" or know ledge in this case is God 's o wn k now ledg e of the divine identity, wh ich is

disclosed to human beings out of love.



D I V I N E P R O V I D E N C E 179

theology has an inner logic and dialectic, it also operates from a rhetoric whichprecedes its inception and to which it returns.6 Theology depends for i ts languageupon prior discourse.

Contemporary scientis ts also have such a rhetoric .7

Their performance asscientists is not simply involved in mathematical concepts (i .e. , dialecticalthinking). It also involves a rhetoric, a public community of discourse (in thepoli t ics of common speech and grant-gett ing) and the communication to non-scientists of their results. Moreover, the metaphors of such rhetoric and pragmaticsp e r d u r e during scientific activity, guiding investigations and expressing results.No netheless, scientists often maintain that the definition of science is to be limitedto the experimental and/or m athem atical dim ension s of their languag e. I deny thatassertion as a gratuitous assumption about the language of science.8

This essay focuses upon time because the historical consciousness thatentered with modernity in its successive phases has affected both science andreligion. "Science is rediscovering tim e." 9 Temporality is no longer simply a given,but a question. Prigogine states that "time becomes an operator or agent within

6For my own argument that foundational theology is a rhetoric, see Stephen Happel,

"Religious Rhetoric and the Language of Theological Foundations," in Reigion andCulture: Essays nHonor of Bernard Loner an, SJ. ed. Timothy P. Fallon and Philip Boo

Riley (Albany, NY: SUNY Press , 1987) , 191-203.7Marcello Pera and William R. Shea, ed., Persuading Science: The Art of Scientific

Rhetoric (Canton, MA: Science History Publ., 19 91); H erbert W . Sim on, ed., The RhetoricalTurn: Conviction and Persuasion in the Conduct of Inquiry (Chicago: University of

Chicago Press , 1990) .8 The classic collection of essays on metalinguistic issues in philosophy is The

Linguistic Turn: Recent Essays in Philosophical Method, ed. Richard Rorty (Ch icago:

University of Chicago Press, 1967). My own positions on language are more indebted to

continental hermeneutical phenomenology (H.G. Gadamer, Paul Ricoeur, JUrgen Habermas)

than to linguistic ana lysis. Thou gh both have had their effe ct on the philo soph y of scienc e,

linguistic analysis, particularly in its English-language tradition (especially in England,

where the use of continental hermeneutics continues to be suspect), has more affected issues

in the "hard sciences." For a brief discussion of the ways in which linguistic analysis has

affected science-and-rcligion debates, see Ian G. Barbour, Reigion in an Age of Science, T he

Giffo rd Lectures, 19 89 -1 99 1, v ol. 1 (San Francisco: HarperCollins, 1 990 ), 13-1 6. For an

argument about the role of hermeneutics in science more closely related to my own, see

Marjorie Grene, "Perception, Interpretation, and the Sciences: Toward a New Philosophy

of Science," in Evolution at a Crossroads: The New Biology and the New Philosophy ofScience ed. David J. Depew and Bruce H. Weber (Cambridge, MA : MIT Press, 198 5), 1-20;

and in an application to neurobiology, see Gunther S. Stent, "Hermeneutics and Complex

Biological Systems," in Evolution at Crossroads 2 0 9 - 2 5 .

9

I lya Prigogine, "The Rediscovery of Tim e," Zygon 19, no. 4 (1984): 434.




these sys tems." 1 0 (See section 3 below.) Ultimately, the discussion about divineaction in the world must ask if and how divine temporality relates in a non-confl ictual way with non-human and human t ime-consciousness .

The large-scale meaning of the universe seems to be involved with thenotions of whether or not the unive rse h as a narrative structure. T he stories w e tellelicit meaning within or from time. Can we say that these narratives emerge fromthe structure of the un ivers e itself as w e know it through science? O r m ust w e saythat they are impositions by a feckless intelligence, busy consumerizing andcolonizing tim e as a function of our need to surv ive? 1 1 W hether there is some inner

dialectical or mutually imp licative relationship between the condit ions andpotential of the universe and the spiritual and ethical imperatives of particularreligious traditions is an im portan t que stion. If philosop hy and science are simp lyimposing order upon disorder, if religion is simply proposing comm ands by f ia t,creating historical order upon reversible phy sical pr ocesse s, then the Tran scend entcan only appear as an intrusion, an intolerable burden upon nature and h is to ry.1 2

Part of what Christianity (at least) asks is w hethe r th ere is a potential (indeed eve nmore, an actualized potential) for its stories and their consequences in the cosmos?What I will examine here is whether the languages of science and religion ortheology share com mo n c haracteristics w ith regard to the notion of temp orality inself-organizing systems. Can their uses of language mutually illuminate one

another?My goals are the following:

Section 3: to describe the way contemporary scientists of self-organizingsystems use time and tem poral sequen ce as a constitutive facto r in their an alyses;

Section 4: to argue that Christian theology has (at least in the instance ofAquinas) an important resource for thinking about the interaction of God andcreation, such that pre-human self-organizing systems can have a role in enactingprovidence; and

10Prigogine, From Beng to Becoming: Time and Complexity in he Physical Sciences(New York: W.H. Freeman, 1980) , 206-10; see also Gregoire Nicolis and I lya Prigogine,

Exploring Complexity: An ntroduction (N ew York: W .H. Freeman, 1989) , 1 71-78 .1 1 See Umberto Eco, 'Travels in Hyperreality," in Traves in Hyperreality, trans.

William Weaver (New York: Harcourt, Brace, Jovanovich, 1986), 9-10.1 note the remarks

of Prigogine: "What is irreversibility on the cosmic scale? Can we introduce an entropy

operator in the framework of a dynamical d escription in w hich gravitation plays an essential

role? . . . I prefer to con fess m y ignorance." Prigogine, From Beng to Becoming, 214.

1 2 See Frank Kermode, "What Precisely are the Facts?," in The Genesis of Secrecy: Onthe nterpretation ofNarrative (Cambridge, MA: Harvard University Press, 1979), 101-23.

Kermode's stoicism is evidenced in the following: "World and book, it may be, are

hopelessly plural, endlessly disappointing; we stand alone before them, aware of their

arbitrariness and impenetrability, knowing that they may be narratives only because of our

impudent intervention, and susceptible of interpretation only by our hermetic tricks" (p.

145) .




Section 5: to indicate how and why this language can be transposed into acontemporary understanding for divine-creation interaction.

The title of this article is a rhetorical chiasmus—A:B::B:A. Self-organizing

systems are the relatively auto nom ou s instrum ental tem porality with w hich divin etemporality (i .e. , action) cooperates in creation.

3 Self-Organization, Far-from-Equilibrium Systems, and Chao s

Physics itself has become interested in the kind of order present in dynamicalsy ste m s, that is , natural or artificial system s that cha nge ov er time.13 Tempora loscil la t ions occur, both periodic and non-periodic, in mechanical vibrat ions,

electronic circuits, chemical reactions, and ecological systems, among others. Whatcan begin as an ordered dynamic motion can, at certain points, reveal nounder ly ing pa t t e rn . 1 4 The system moves to chaos in which no simpler algorithmthan a repetition of the points "explains" the data. S ystem s th at dis sipa te en ergy areordered forms of behavior, far from thermodynamic equil ibrium, exchanging massand/or energy with their environments. They have a sensitivity to initial conditionssuch that the most minute change can drastically affect the later state of thes y s t e m . 1 5 Here time itself becomes an operator or agent within these system^.6

Prigogine argu es for temp orali ty as an internal function within certain sys tem s.1 7

In effect, time becomes a variable in the constitution of the systems themselves.

1 3 See Arthur R. Peacocke, An Introduction to the Physical Chemistry of BiologicalOrganization (Oxford: Clarendon Press, 1983), 148-49; Milos Marek and Igor Schreiber,

Chaotic Behaviour of Deterministic Dissipative Systems (Cambridge: Cambridge University

Press, 1991); Nicolis and Prigo gine, Complexity; and Prigogine, From Beng to Becoming.See also Barbour, Reigion nan Age of Science, 156-65; and James Gleick, Chaos: Makinga New Science (New York: Viking Books , 1987) .

1 4 S ee Nico l is and Prigogine, Complexity, 26-28 .

1 5 Se e James P. Crutchfield, et al., "Chaos" (in this volum e). In fact, Prigo gine wo uld

go s o far as to say th a t" .. . [ i]rreversibility is the man ifestation on a macroscopic scale of

"randomness" on he microscopic scale." See Prigogine, From Beng to Becoming, 176 and

204-6. For an emphasis upon the mathematical dimensions of chaos , see Denny Gulick,

Encounters with Chaos (New York: McGraw-Hill, 1992), esp. 84-94 on sensitivity to initial

condit ions .

1 6Pr igog ine , From Beng to Becoming, 20 6-1 0; Nicolis and Prigogine, Complexity,171-78 .

1 7 The phrase "time as operator" is Prigogine's. Though I cannot claim to be

thoroughly knowledgeab le con cerning the phy sics and m athematics of this assertion, I find

Prigogine*s position persua sive. H e argues for a "m icroscopic entropy operator M and the

tim e o pera tor V as an "internal time quite different from the time that in classical or

quantum mechanics simply labels trajectories or wave functions." (Prigogine, From Bengto Becoming, 209). In this text, "the physical meaning of entropy and time as operators" is

discussed in chap. 7, as well as appendices A and C.




An analogy might be drawn to musical forms. The s low progression of aSarabande or a waltz is quite distinct from the tempo of a Scherzo or a rhumba;part of what makes particular dance movements to be what they are is the timing

with its sequences and shifts. This sense of "inner tim ing" seems true for inanim atesystems as well as animate ones in far-from-equilibrium situations. In animatebecoming, if the "timing" changes, either the system disintegrates and dies or itevolves into something different. Within a certain range, each system has atemporality appropriate to itself.

As Prigogine maintains , "three aspects are always linked in dissipativestructures: the function, as expressed by the chemical equations; the space-time

structure , wh ich results from the instabilities; and the fluctuations, wh ich triggerthe instabilities." 18 On e can no longer always deduce or predict what the future ofa system will be due to its initial state and a few simple multipliers as thoughtemporal mo vemen t were insignificant. As Ford states, "[chaos] is visible proof ofexistence and uniqueness without predictability."1 9 Though it is possible to speakof a system being attracted to certain positions in phase space, this attributes to thesystem a certain internal teleonomy that is neither reversible nor alwaysp re d i c t a b l e . 2 0 At certain points in chaotic behavior, a system undergoes abifurcation sequen ce in which either/or possibilities are available. A system seem sto choose a certain course of action. "[T]he bifurcation introduces history into

physics and chemistry, an element that formerly seemed to be reserved to sciencesdealing with biological, social, and cultural p he no m en a." 2 1 Nicolis even speaks ofself-organizing systems searching for new attractors when driven from equilib-r i u m . 2 2 As Nicolis says:

Such ord inary systems as a layer of fluid or a mixture of chemical productscan generate, under appropriate conditions, a m ultitu de of self organization

I8

Pri gog i n e , From Beng to Becoming, 100; see Pea cock e's discussion of thethermodynamics of dissipative structures in Biological Organization, 17-72.

J o s e p h Ford, "What is Chaos, that we should be mindful of it?," in The New Physics,ed. Paul Davies (New York: Cambridge University Press, 1989), 351.

2 0 Teeomatic, inanimate processes are those whose end states are the simple

co nse qu en ce s of their internal, fixed laws— end-directed in a passive, automatic w ay.

Teeonomicprocesses are goal-directed behaviors of l iving organisms—migration, feeding,

reproducing, courtship. It owes its goal-directedness to an internal operator that regulates

behavior. Teeological processes reflexively intend a goal by virtue of some activity. See

Ernst Mayr, Toward a New Philosophy of Biology: Observations of an Evolutionist(Cambridge, MA: Belknap Press, 1988); on predictability, see Crutchfield, et al., "Chaos."

2'Ford, "What is Chaos," 106. See Marek and Schreiber, Chaotic Behaviour, 51-102;

Gulick, Encounters with Chaos, 52-62; and Nicolis and Prigogine, Complexity, 71-75 . This

is not to say, as Peacocke points out, that there are absolutely unqualified uncaused events.

Randomness is not non-causal. See Peacocke, Creation and the World of Science, 92 and

95 .

^rdgoire Nicolis, "Physics of Far-from Equilibrium Systems and Self-organization,"

in The New Physics, ed. Paul Davies (New York: Cambridge University Press, 1989), 331.




phenomena on a macroscopic scale—a scale orders of magnitude largerthan the range of fun da m en tal interactions— in the form of spatial p atternsor tempora l rhythms. 2 3

The temporal order of the whole as a te leonomy has a governing role in thedetermination of the integration of the parts. 2 4

As a result, causation can operate in a different way than the usual axiom aticunidirectionali ty. Complex systems respond to the future emerging whole inbiological evolution. "W hen matter is appropriately organized, it becomes sensitiveto ca us es arising from the future instead of just the pa st ."2 5 Such hierarchical ortop-down causali ty, a whole "guiding" the parts te leonomically, needs to beexplored in this context . 2 6

Self-organization is first of all a factor in physical and chemical processes,

not s imply an element in l iving systems. 2 7 Som e systems provide the regulari t iesof a chemical clock. This is not just the rhythm of the pendulum, but a temporal

2 3 Ibid . , 316.

^"Chemical instabilities involve ong-range order through which the system acts as

aw/k?/£"(Prigogine, From Beng to Becoming, 104). Note that here we have the beginningof an argument that the whole is not otally given in the present. If it only exists as a system

in transition, in history, that means that its future state is part of the teleon om y of the present

situation, despite the fact that the system in operation do es n ot "know" wh at its future state

is or might be. These positions seem to assume that this is true of pre-human far-from-

equilibrium systems. One can argue that this indeterminacy is a condition for the possibility

of human freedom.

"John H. Campbell, "An Organizational Interpretation of Evolution," in Evolution ata Crossroads 154 . Th e arguments by scientists are both synchronic and diachronic. The part

and the whole are synchronically co-implicated, and the future states of the whole in

relationship to a present state are diachronically co-implicated.

2 6 Ibid., 154-61. Note that Kuppers maintains that "holistic phenomena are a part of

normal physica l and chem ical ex perien ce, and that they therefore do not cast doubt on the

validity of the reductionistic program" (KUppers, Information and the Origin of Life[Cambridge, MA: MIT Press, 1990], 121).

^̂ This is no longer an uncom mo n assertion. See H ans Meinhardt, Modes of BiologicalPattern Formation (London: Academic Press, 1982), 10, on autocatalysis and his attempt

to provide mathematical models for the process of self-organization; and Peacocke,

Biological Organization, 114 -24. David Bohm aims at self-organization and com plexity

with his notion of'"implicate order" opposed to "mechanistic" order; see Bohm, Wholenessand he mplicate Order (London: Routledge & Kegan Paul, 1981), 172-86. A more fruitful

application of self-organization c an be foun d in Eric Jantsch, The Sef organizing Universe:Scientific and Human Implications of the Emerging Paradigm of Evolution (Oxford:

Pergamon Press, 1984), though there is probably a not-so-crypto-vitalism in evidence. See

similar remarks about the "nesting" of temporalities in J.T. Fraser, The Genesis andEvolution of Time: A Critique of nterpretation in Physics (Amherst, MA: University of

Massachusetts Press, 1982), 144-75.



1 8 4 S T E P H E N H A P P E L

stability that realigns itself internally when disturbed. 2 8 The heartbeat, the circadianrhythms of nature, the cell division cycle—all belong to the same realm oftemporal structure and dissipative systems.

The appearance of t ime as a consti tut ive function (an "operator") in ourunderstanding of reali ty can be seen in emerging theories about complexdynamical systems, especially those that ar e self-o rgan izing, far- from -eq uilib rium ,and chaotic. This is as true in biology as in physics and chemistry.

3 .1 Molecular Biology

The role of time can be seen in recent theories of molecular biology. Utilizingcurrent inform ation theory, Bernd-O laf Kup pers argues persuasively that there isa continuity between l iving and non-l iving matter . Moreover, he argues that theroots of Darwinian natural selection can be explained by the physical properties ofmatter . Though this may sound "reductionis t" to those who hope for someineluctable, but measurable, principle of life, it is not. 2 9

Kuppers dis t inguishes (with others) three phases of evolution: a chemicaldevelopment in which prebiotic conditions establish nucleic acids and proteins; theself-organization of matter converging upon more complex coupling patterns; andbiological evolution with its development of primitive, unicellular elements toward

multicellular org an ism s.3 0

In the final phase, the genetic information is optimizedand diversif ied. The transit ion from the non-l iving to l iving matter takes placegradually during the second phase: self-organization.3 1

After arguing against a cha nce hy poth esis or a teleological appro ach f or thisevolution toward self-organization, Kupp ers m aintains what h e calls a "m olecu lar-Darwinis t ic" posit ion: that "biological proto-information arose by the selectiveself-organization and evolution of biological macromolecules ." 3 2 By pointing toselection as < 4that which produces information," he believes that he has a criterion

^Meinhardt, Modes 322. See also Peacocke, Biological Organization, 189-95 ; and

Gleick, Chaos 2 7 3 - 3 0 0 .

2 9 K u p p e r s , Information; cf. Kuppers, "On the Prior Proba bility of the Ex isten ce o f

Life," in

The Probablistic Revolution, 1806-1930: Dynamic of Scientific Deveopment, ed.

G. Gigerentzer, L. Kriiger, and M.S. Morgan (Cambridge, MA: MIT Press, 1987), 355-69.

Even Hans Driesch would argue for the methods of physicists in biology, but not their

results; see Driesch, The Science &. Philosophy of the Organism: The Gifford Lectures,1907-1908,2d. ed. (London: A & C Black , 192 9), 32. Cf. Pea cock e, Biological Organiza-tion, 268-72 and 255-63; and Barbour , Reigion in an Age of Science, 165-68. See also

Weinberg, Final Theory, 51 -64 .

^Kuppers , nformation, 26. See also Peacocke, Biological Organization, 2 1 4 - 4 1 .3 1 N o t e th?vt a narrative is being constructed about the origins of life.3 2

Kuppers , Information, 2 7 .




is compensated for by an infusion of energy; (2) self-reproduction; and (3)mutability, that is, a mutagenicity where self-copying is not error-free. 3 9

A fundamental underlying characteristic of dissipative systems is their

relationship to the environment with which they exchange matter, energy, andinformation. The temporality appropriate (of optimal efficiency?) to a particularself-organizing system (i.e., a t ime pattern that keeps the system operating)negotiates internal teleonomic activity and the constraints of the context withoutexhausting either the resources of the environment or of the internal program. 4 0

One must mark that there c ontinues to em erge a normative dimension to theexperience of time in scientific (here biological) language. A system has a "be t ter"or "worse" position for main taining or deve loping itself. Th e succ ess or failu re ofa system 's abi li ty to cooperate with the environment is im porta nt , 4 1 but the game

or military metaphors of competition or conflict are a more prominent part of therhetoric of biological explan ation.

C l i p p e r s , nformation, 131-32. Th e Darw inian and neo-D arw inian description of the

scale of value for success in this process ordinarily speaks of competition. Although i t i s

recognized that Darwin borrowed this image from Adam Smith's economics , who in turn

uses Hobbes, the fact that success in competition underlies the scale of value is rarely

attended to. In Kiippers himself, there is a correlative dimension of cooperation that is also

functional. See the mollifying remarks of G.G. Simpson:

Advantage in differential reproduction is usually a peaceful process in which the

concept of struggle is really irrelevant. It more often involves such things as better

integration into the ecological situation, maintenance of a balance of nature, moreefficient util ization of available food, better care of the young, elimination of

intragroup discords (struggles) that might hamper reproduction, exploitation of

environmental possibilities that are not the objects of competition or are less

effectively exploited by others. (S im pso n, The Meaning of Evolution [New Haven,

CT: Yale University Press, 1971], 201, quoted in Peacocke, Creation and the Worldof Science, 165-66 . )

4 0 K i i p p e r s , Information, 148. Se e also Prigog ine, Beng to Becoming, 123- 26; and

Meinhardt, Modes 189. On alternative paths for evolution, see John H. Campbell , "An

Organizational Interpretation of E vo lut ion ," in Evolution at a Crossroads esp. 141-46; and

Stuart A . Kauffman, "Self-Organization, Selective Adaptation, and Its Limits," in Evolutionat a Crossroads, 169-203.

4 ^ U p p e r s , Information: 'T h e selection value of every single species will as a rule

depend on the population variables of the other sp ecie s taking part in selec tion , so that ever y

evolutionary "step" changes the structure of the value profile. . . . This means that goal and

goal-directedness, even at the level of biological macromolecules, are interdependent" ( p.

150). N ote that this is not to say that some species are better or more important than others;

it is simply to explain

whysome systems continue and others do not.




3.2 Summary

The language that analysts use about far-from-equilibrium systems maintains that

such systems have an inner temporality that governs their organization andoperation. W ithout such a con stitutive temp oral d ime nsion (pattern and sequence )which affects their very identity as a system, they w ould either not con tinue to ex istor they would be differen t entities. Mo reove r, in such system s, the re is an optim alor normative temporality that involves internal and external cooperation withenvironm ents. In this sense, their temporality is chara cteristica lly op en — to a futurewhich is not the same as the past, to an environment that may affect them eitheradversely or posit ively. Self-organizing systems, therefore, are an importantdif fer en ce in the s tructure of our world. They display a self-directing autono m ywith an interior teleonomy that entails normative behavior for survival as a system.That there is a "before and after" is important in defin ing a narrative seque nce; how

that narrative sequence is described is also impo rtant. Bio logists like K upp ers use,without attention, m etaph ors th at are prim arily com petitive and c onf lictua l, ratherthan cooperative.

4 The Theorem of the Supernatural

Bernard Lonergan maintains that the development of the scientific theorem of thesupernatural in the writ ings of Albert the Great and Thomas Aq uinas provided anexplanatory perspective on the interaction between the divine and creation. Thesupernatural did not add further divine actions to the world. "[T]he idea of thesupernatural is a theorem, that [is,] it no more adds to the data of the problem thanthe Lorentz transformation puts a new constel lat ion in the heavens/ '4 2

To situate Aquinas's theory of divine transcendence, it will be useful tooutline the language about d ivine action in primo rdial societies. Such exp ression s

contextualize the theory; they also show something of what Aquinas wascriticizing. If w e are to understand what the Christian tradition has meant by God'saction in and upon the world, we must understand the rhetorical context in whichsuch a thinker was arguing.

4 .1 Divine Action in a Sacral Universe

In a primordial, often pre-literate, but not pre-sym bolic world, religion ap pears in

transformed people and actions. What changes things, people, and actions is notwithin sight or sound or touch, but the what exercises force or power and one

4 2 Bemard Lonergan , Grace and Freedom: Operative Grace in the Thought of St.Thomas Aquinas, ed. J. Patout Burns (Lond on: Darton, Longm an & Todd , 1 971 ; origina lly

pub l i s hed in Theological Studies 2 [1941], 3 [1942]), 16 (page reference is to the 1971

edition).




should respect it. 43 To know why or how , through what med iations and condit ionsthese unseen pow ers appear, is unnecessa ry . 4 4 According to Levy-Bruhl, the realmof these unseen forces is often vague, including, in an undifferentiated fashion, the

dead ancestors (both benign and threatening), the de ities, and the sp irits of n at u re .4 5

To negotiate the powe r of these realities, one needs the rituals of one 's ancestors,the traditions that protec t and hea l, the actions that will celebra te the jo ys with outawakening the envy of the gods . 4 6 It is the shaman or the priest who helps theindividual and the community across the thresholds and transitions.

The language used by anthropologis ts such as Levy-Bruhl providescategorical reification for the experiences (what he calls the "affectivecategories") 47 that underlie them. The experiential base, in effect, includes simplythe joys and misfortunes of day to day livin g.48 The difference, he notes, is that pre-literate cultures assu m e, b elieve , and trust that the pleasa nt and painful patterns ofexperience are produced by pow ers that are neither visible nor indifferent to humanand cosmic a f fa i r s . 4 9 Because there is a "blurring" of all non-visible causes,because they are not distinguished, one hopes to have all these powers on one's

4 3 See Lucien Levy-Bruhl, Primitives and he Supernatural, trans. Lilian A. Clare (New

York: Dutton, 1935) for a classic, if flawed description. I am here less concerned withwhether these analyses fit the self-understanding of primordial societies, than in how such

societies* religiou s data have b een perc eived by analysts.4 4 Ibid. , 20; and idem, Primitive Mentality, trans. Lilian A . Clare (N ew York :

Macmillan, 1923), 36-37. See also Bruno Snell, The Discovery of Mind: The Greek Originsof European Thought, trans. T.G. Rose nm eye r (Cam bridge, M A: Harvard Unive rsity P ress,

1953), 191-245; and G.E.R. Lloyd, Magic, Reason, and Experience: Studies in he Originand Deveopment of Greek Science (Cambridge: Cambridge University Press, 1979), esp.

1-8 and 10-58.

4 5

L6vy-Bruh l , Primitives and the Supernatural, 34.^ wo uld point out that more anthropologists vie w fear as the origin o f relig ious action

than to the celebration of joy. Th is m ay h ave as m uch to do with Enlightenment prejudices

about priestcraft and the normative espousal of human autonomy as with field data. See

Levy-Bruhl, Primitives and the Supernatural, 24-27, for an example of the conviction that

fear motivates prim itive religious activity.

4 7 Ibid. , 32 and passim; see also dem. How Natives Think, 22-32.

^Levy-Bruhl focuses upon the negative dimensions of experience (loss, misfortune,

disease, death) wh ere the follo w ing is representative. "How is [the primitive] to account for

these misfortunes wh ich at times seem to have com bined to overwh elm him?" He contrasts

the response of pre-literate cultures w ith the contemp orary search for answ ers (Lev y-B ruh l,

Primitives and the Supernatural, 153-54). See his remarks about the causes of success in

Primitive Mentality, 30 7- 51 . Le vy-B ruh l maintains that "not on ly the data, but ev en the

limits of experience fail to coincide with our own." But he means by this the fact that data

always involve interpretation and that the pre-literate mentality "is accustomed to a type of

causality which obscures, as it were, the network of such [secondary] causes." PrimitiveMentality, 96 and 92.

4 9

L£vy-Bruh l , Primitive Mentality, 65.




own side (so to speak). 50 The task of religion (if undifferentiated from medicine oragriculture) is to protect p eop le fro m wh at appears to be bad and to prolong whatis good.

The extended security of the ordinary, the diurnal order, is critical. That iswhy any intervention in the usual m ann er of thing s appears to be dange rous, evenmalign. "Nature" is not differentiated from the "supernatural" powers; hence, eventhe most improbable transformations are within the course of things. It is onlywhen their "conception of the inevitable order of nature is suddenly disturbed andups et" that they are "troubled " (my itali cs) .51 Unusual appearances are "transgres-sions" that require negotiation: avoidance, prayer-rituals (in effect, distancewithout flight), or submission (no distance and absorption). The recognition is thatth e powerful ancestors and the gods often intervene as unseen forces in experience.

"In these frequent occurrences, therefo re, the prim itive mind pays less attention tothe happenings themselves than to the suprasen suous realities w hose pr esen ce andinfluence they indicate ." 5 2

Historical religions, such as Judaism or Christianity, though they ha ve tendedto differentiate the realm of the divinity and the causes of n atur e (at least by placin gthe divine over natural causes—in theories and in some practices), nonetheless useimages, stories, and metaphoric symbols that describe the intervention ortransgression of God within and among the ordinary course of things and events.

So in Joshua's battle with the sheiks at Gibeon, God hurls hailstones killing theenemy soldiers or makes the sun stand still at his prayer (Joshua 10:11-13). Godpro vide s an earthquake, rocking P au l 's prison and releasing him fr om jai l (Acts17:25-28). The experiences are an unexpected transgression within the ordinaryexpectation of events, relayed in images and stories to indicate the activity of God.

These parallels between Judaic, Christian, and non-Christian stories are to betaken seriously, since it is this description of divine transcendence that is "taken forgranted" as a prime component in faith or in religious sensibility. It is also theanthropologists ' categorization of this experience as "primitive" that marks much

theological avoidance of language about divine action in the universe. Does Godwork in the world "alongside" other causes? Does God only operate in the"surprises," the extraordinary events that overturn or intrude in the ordinarynecessities of nature? If one discards these forms of divine interaction withcreation, then does one have only subjective, moral suasion on human subjects asthe mode of divine action? These questions can only be answered if one under-stands how metaphors, symbols, and stories (the rhetoric of religion) function inrelationship to reflective theology (the dialectics). The same pattern must bestudied in the methods of the natural sciences themselves.

"Ibid. 59-96. Bronislaw Malinowski disagrees with this position, asserting that pre-

literate cultures distinguish magical from primitive technological devices for agriculture or

hunting, though magic continues to be useful for unexpected situations. Cf. Malinowski,

Magic, Science, and Reigion and Other Essays (Boston: Beacon Press, 1948), 12-17.

5 1L e v y - B r u h l , Primitives and the Supernatural, 197-98.5 2

Ibid. , 57 and 64. See also dem, Primitive Mentality, 57-58.




4.2 A Methodological Critique: Aquinas

Thom as Aquinas, using Aristotle 's logic and m etaphy sics, a ttempted to und erstand

the relationship between primary and secondary languages in faith, as well asbetween the two poles of divine-creational interacdo n. T he nee d to distinguish the"what is divine" from "what is human" within human experience as the operativeand cooperative action of Go d encouraged theoretic disc ussio ns. T hro ug h A qu inas ,Christians have had a theory of the supernatural to account for the specificcharacter of divine action. It is im portan t that it is a theory, not an addition of data,"something like the discov ery of gra vitation an d not som ething like the discov eryo f A me r i c a . " 5 3 It is the difference between going faster as an experience andacceleration as a theory. The latter accords the differing moments of time, distance,

and velocity their relative relationship, providing analysis, generalization, andsystematic correlation of factors. They apprehend the same data, but accelerationexplains both going faster and going s lower.

The notion of the supernatural offers the same kind of precision in Aquinas'swritings. It tries to articulate the various factors at stake (human will, divine love,creation, redemption, evil, etc.) and correlates them much as one would do withdistance, time, velocity, and m ass. In effect, the Middle Ages always knew that thedata of their experience were from God; what the theorem of the supernatural

offered was a way of understanding God's relationship to nature. "Nature" itselfwas a conceptual abstraction; it was what was distinct from "supemature . " Naturewas not what was sensed or thought, our common experience; for our commonexperience included the dimensions of divine activity as well. 5 4 In this schema, itis not possible to say wh at is solely from human intention and execution. God wasthe ultimate intelligibility of what is, not an object with multiple attributes(omniscience, omnipotence, e tc . ) to be explained.5 5

Here I shall oudine Aquinas's position on the nature of divine transcendence,the universal instrumentality of creation, and divine action as they might apply to

self-organizing systems. Aquinas assumes that he has provided evidence andwarrants for God's exis tence and God's benign intention for creation. Questionsof human (as opposed to non-human) interaction with the divine are useful herein so far as they contribute to our understanding of his position on the questionswe are posing. To assist in mak ing a useful model of divine-creational interaction,

5 3 L o n e r g a n , Grace and Freedom 1 4 3 . Se e a l s o idem, Insight: A Study of HumanUnderstanding ( N e w Y o rk : L o n g m a n s , 1 9 6 1 ) , 6 3 4 - 8 6 .

* S e e K arl Ra hn er 's interpretat ion of "pure nature" as a Restbegriff, a t h e o l o g i c a l

abstract ion, that sorts out from our mixed, i .e . , graced and s inful , exper ience what is s inful

from what is d iv in e in i tia tive and hum an coop erat io n. R ahner , "C onc ern ing the R ela t io nsh ip

b e t w e e n N a t u r e a n d G r a c e , " Theological Investigations vol . 1 , trans . Corne l ius Ernst

( L o n d o n : D a r t o n , L o n g m a n & T o d d , 1 9 6 1 ) , 3 1 3 - 1 7 . S e e a l s o P i e t F r a n se n , Divine Graceand Man ( N e w Y o r k : D e s c l e e , 1 9 6 2 ) , 8 8 - 9 1 .

5 5

L o n e r g a n , Grace and Freedom 1 0 5 . Se e a l s o idem, Insight, 6 5 7 - 7 7 .




it will be necessary to transpo se these classical me taphysical categories into th ose

of an historical ontology (see section 5.3 below).

4 .3 The Nature of Supernature: Divine Transcendence

The meaning of supernature involves several terms: God's transcendence,creation's particular form of identity and self-organization, and their interaction.W hat links them all is the experience and affirmation of transcendence. "In a moregenera l sense , t ranscendence means 'going beyond ' . " 5 6 Insight and reflection donot simply reproduce images and sense data; they g o beyon d th em . Tra nsce nde nceis proportionate to the kind of reality about which it is predicated.

Aquinas's understanding of the supernatural was, therefore, a relational, not

a reified, term. It was emphatically not a term to cover the unusual transgressionsof nature in the scriptures! It was an abstraction understood in relationship tonature as a construct . The content of nature and supernature "s l ides ," depend ingupon the stages of meaning that hum ans inhabit. In a stage of hum an dev elopm entin which nature is the uncontrollable other, God is embodied in theophanies suchas the burning bush or Mt. Sinai . 5 7 In another age, divine transcendence mightappear as interpersonal suasion. But a theorem of divine transcendence permits thethinker to understand that God is always beyond.

To say that God is transcendent is to maintain that whatever creation does(whether human or non-human) is not to be identif ied with divinity. 5 8 Divinetranscendence cannot be a prop erty attributed to any c reature. Every created causefalls within the order of necessity or contingency; but God "produces not onlyreali ty," but also their modes of contingent or necessary emergence. 5 9 God bydefinit ion exceeds and determ ines the m odes of both contingency and n ecessi ty.The analogy Aquinas uses in De substantiis separatist is that of a geom eter wh onot only makes triangles, but makes them isosceles or equilateral at the same time.Were God to produce a contingent effect directly in our world with irresistible

^Lonergan, nsight, 635.5 7 See Lonergan, "Religious Experience," in A Third Collection: Papers by Bernard

J.F. Lonergan, SJ. ed. Frederick E. Crowe (New York: Paulist Press, 1985), 119-122.

^See Gordon D. Kaufman, "Two Models of Transcendence: An Inquiry into the

Problem of Theological M eaning," in The Heritage of Christian Thought: Essays in HonorofRobert Lowry Calhoun, ed. Robert E. Cushman and Egil Grislis (New York: Harper and

Row, 1965), 182-96. In this early essay, he distinguishes scientific and religious language

as cognitive, empirical language vs. intersubjective mystery. Images and stories are

necessary because of the interpersonal dimension of revelation (p. 193). Again, notice how

this is another version of scie nc e as "objective" fact and religion as "subjective" value.

5 9L o n e r g a n , Grace and Freedom 108.60Desubt. sep., 15 (Works of St. Thomas Aquinas: Marietti editions, para. 137), cited

in Lonergan, Grace and Freedom 108.




efficacy, it would hav e to be G od 's ow n se lf . 6 1 What the geometer cannot do is tomake equilateral triangles with only two sides equal.

What most people think of as divine intervention (the production of a

surpris ing continge nt effe ct with irresistible effectiv eness ), a direct manipulat ionof 4< nature" (as an inert object "out there"), a "miracle," is denied by Aquinas. ForAquinas, it is not that some astonishing moments might not appear in nature andhistory, but that they are not to be identified with divine activity in and of itself.6 2

An appropriate theoretic understanding of supernature will provide an explanationfor both the usual and unusual course of things. It will also "eliminate interven-t ion's implication of violence." 6 3

What occurs in our world (orderly, chaotic, and random) is in need ofexplanation. 'The supernatural t ranscendent ' is the name given to that realm ofultimate explanation. Nature is the relatively autonomous pole of creation thatoperates by virtue of its own internal structures and processes, utilizing their ownfor m s of transcendence and self-transcendenc e. Natural form s of transcendence,however, are dependent upon the supernatural for their relat ive independence.Nature does not operate on its own without divine initiative, supp ort, or direction;theoretically, however, it is possible to distinguish and relate the relative poles ofcooperation. Moreover, i t becomes clear that the two orders (nature and super-nature) constitute the definition of grace, God's love poured out in the world.6 4

4.4 Instrumental Causality: The Intermediary

The theoretical language that medieval and early modern Catholic theology usedto discuss this interaction of the divine and nature was instrumental causality. Thenotion of instrument was applied to a wide variety of experiences: Christ 'shumanity, prophecy, the sacraments, but also the peculiar, invisible operations ofnature, the influence of magical pictures, and (with Aristotle) the generation ofan ima ls . 6 5 Wherever it might appear that a more-than-finite agent was operative,

6 1 L o n e r g a n , Grace and Freedom 109.1 make a note of the language "direct" and

"indirect," since I will return to it section 5.4 .6 2 Cf. Thomas F. Tracy, "Particular Providence and the God of the Gaps" (in this

volume). Pure chance must be distinguished from causal chance and forms of deterministic

unpredictability. T hese latter two (due to a surprising convergence of local causal chains and

our cognitional limits) are often what are called "divine action." Indeed, the images they

conjure are the ordinary definition for the "supernatural." Aquinas would deny that they are

"solely" divine action.

6 3Lonerg a a, Grace and Freedom 4 3 .

"Lonergan, Method, 310, n. 13.65

L on ergan , Grace and Freedom 82.




the element itself could be construed as an instrumentum. 66 But in medieval life,that was true in all cases. God was neve r absent, even in death or sin.

Though I will focus upon the theoretical dimensions of the instrumentum,

particularly as these applied to the Christian sacram ents, I mu st note that the roleof magical images, moving statuary that healed, relics that cured diseases andprotected in childbirth, the blessing of saints w ho o vers aw a wh ole h ost of ord inarytasks from bread-baking and beer-brewing to journ eys and coronations cannot beignored in this context . 6 7 Anglo-Saxon rituals contained incantations in anamalgam of ancient and current languages to bring about fertile harvests, safehouse-rais ing, and protection from elf-shots . The Agnus Dei was a small disk(earlier in wax, eventually in precious metals) that protected against the devil,thunder, lightning, fires, and drowning. All of these were interpreted as

"instruments" of the divine power.Although theologians such as Thomas Aquinas argued s trenuously against

any magical interpretations of sacramental practice or of these items, still thefa ith fu l, including theo logians, com m only believed that eucharistic bread cou ldturn into Jesus' physical flesh and blood. Popular stories related the way in whichthe host was used "to put out fires, to cure sw ine fev er, to fertilize the fields, andto encourage bees to make honey." 6 8 The relation of the high culture of thetheologians and the knowledgeable churchmen and women to the low culture of

popular devotion and magic practices is the matrix for the sixteenth-centuryreformations of Christianity. Is it any wonder that the sciences of the sixteenththrough eighteenth centuries saw their control over common meanings as moreeffective than the prior theologies and philosophies?

The general law in the theory we are exploring is that everything is anins t rument . Instrumentum could be defined as a lesser reality accomplishing thework properly attributed to some proportionately higher reality.6 9 In the universe,all realities are m oved in relation to some cause higher than themselves. Only Godis not an instrument; nor can God be used as an instrum ent. H am m ers d o not m ov e

of their own accord, except in dreams and fantastic cartoons. To be able to operate

6 6 See Bernard Leeming, Principles of Sacramental Theology (London: Longmans,

1960 ed.), esp. 283-345, for an overview of the various uses of instrumental causality to

discuss sacramental efficacy.

^See Keith Vivian Tho ma s, Reigion and the Decline of Magic (New York: Charles

Scribner's Sons, 1971), esp. 25-50; and Valerie Flint, The Rise of Magic in the EarlyMedieval Europe (Princeton, NJ: Princeton University Press, 1991). For an art-historical

appreciation of the power of these images, see David Freedberg, The Power of Images:Studies in the History and Theory of Response (Chicago: University of Chicago Press,

1989) , esp . 82-135.

^Thomas, Decline of Magic, 35. See also Miri Rubin, Corpus Christi: The Eucharistin Late Medieval Culture (Cambridge: Cambridge University Press, 1991), 338-42, and

David N. Power , The Eucharistic Mystery: Revitalizing the Tradition (New York:

Crossroad, 1992) , 180-207.6 9

L o n e r g a n , Grace and Freedom, 8 1 .




beyond their own proportional ends, instruments must participate in a highersystem. For that to take place, som e participation is required in the higher ca us e's' 'productive capacity." 70 But because A quina s applies this participation in differen t

w ays to differing natural systems, i t becom es important to understand what hemeans in any given instance of instrumentality. It should not be assumed that theprimary analogue for instrument is an inert natural object, despite the fact thatsaws, ham mers, an d pipes are often his examp les .

4.4.1 Hum an History as Instrument

Divine providence (charity, infinite love for the other) in the mind of God is theprimary cause of all; but this providence exists in the created universe as

governance and fa te . 7 1 Providence is the art in the mind of the divine artisan andfate is the opera tive instrum entality in history. Prov idence is the intention of lovein divine life for all that is (including the divine self); governance is what takesplace in the universe as a result of the natural re alm 's coo peration or conflict w iththat intention. Fate is not a cause in addition to God, but the "order of second arycauses; it is their disposition, arrangement, seriation; it is not a quality and muchless is it a substance; it is in the category of rela tio n." 7 2 Fate is the de facto patternof what happens as the divine design unfolds in nature and history by virtue of

cooperation or conflict with divine love. Fate is the interaction of divine primarycause and human instrumental causes . 7 3 There is always a mediated execution ofdivine providence which in itself is strictly supernatural, an un-owed experienceand knowledge of the gift of love. "Ex tractin g" (so to speak) the divine dim ensionfrom the human ones is not so simple as pointing to the ordinary and theextraordinary, the usual or the unu sual. H ence th e langu age of the sup ernatural intheology functions as a critical upper blade on the stories, symbols, and metaphorswithin the primary languages of revelation.

4.4.2 The Sacraments as Instruments

Another example of Aquinas 's s trategy may be seen in his theology of thesacraments, the instruments of divine action par excellence. These signs of divinepresence and action are invitations and moments of cooperation. They have aninstrumental power of their own that lays a permanent existential claim upon

7 0Ib i d .7 1 Ib i d . , 82 -84 . S ee STh 1.116.2, ad 2um et 3am; and 1.116.3, in which fate is

precisely a "contingent necessity." God's providence orders the universe toward love

through both contingent and necessary secondary causes.

^Lonergan, Grace and Freedom 84.

89: " . . . [fate] is the dynam ic pattern of world events, the totality of relations

that constitute the combinations and interferences of created causes " Cf. Kaufman, "On

the Meaning o f 4 Act of Go d,'" in God the Problem (Cambridge, MA: Harvard University

Press, 1972), esp. 136-40. See also Tracy, "Particular Providence."




individuals and objects, but not without their participation. The res et sacramen-

turn (an intermediate, even symbolic, effect of God's grace) of sacramental life islike fa te in the de facto patterns of providence in the natural and historical world.

It can mean minimal personal cooperation (non ponitur obex) or it can be thepotential for holiness and communion with the divine. In any case, it is theinteraction of objects, persons, and common ritual that provides the instrumentum,

that is , the mediating reality for the transcendent act.7 4

For Aquinas, it was precisely through the internal organizing power of thenatural elements themselves that the divine presence and agency is disclosed.7 5 T hephysical signs of nature (sharing bread and drinking a cup) receive their historical(and divine) specification through the powe r of th e w ords of Jesus w ho se m em oryis activated within the present ritual instruments.7 6

In the Eucharist, the material and fo rm al ap pearan ces rem ain, so that "b rea d"is apprehended, but the "be ing " or "substa nce" is changed . This occurs by divinepow er, the pow er of the word of Christ, in which w hat is in com m on be twe en thebeing of the natural reality and Go d is transform ed into the being of the divine. Itis as though God simply "takes down" the barriers between the divine self andfinite creation, so that created reality can be the vehic le for divine lo ve .7 7 (Anotherway of viewing this, from the point of view of the "objects" is to say that, unlikehuman beings, they have no barriers [no obex] other than finitude, to divine

presence . )7 8

Aquinas compares the operation of words, gestures, and materialobjects to the mystery of the incarnation of the word in which flesh (a conjoint

instrument) perceived by the senses discloses th e di v in e. 7 9 But it must still be notedthat the humanity of Jesus is an instrument, not an unmediated intervention ofdivine action!

7 4 S e e Happel, 'T he 'Ben t World*: Sacrament as Orthopraxis," CTSA Proceedings 35

(1980) : 98 -99 .lsSTh. 3.60.6 , corp. and ad lum.16STh. 3 .60 .3 , corp.; and 3.60.5, corp. and ad lum. Divine institution by Christ's

words, specifying certain material objects for use, determines the meaning of the natural

signs. This is the way all natural signs are specified in history; but Christ's words are the

evidence of divine intentionality for the believer—precisely because the believer has faiththat in Jesus, God is speaking in human words. This Christological focus is important for

Aquinas .

^STh.5 .75 .4 ,

ad 3am:" . . . virtute agentis finiti non potest forma in formam mutari,

nec materia in materiam. Sed virtute agentis infiniti, quod habet actionem in totum ens,

potest talis conversio fieri: quia utrique formae et utrique ma teriae est co m m un is natura entis;

et id quod est entitatis in una, potest auctor entis convertere ad id quod est entitatis in altera,

sublato eo per quod ab ilia distinguebatur."

7 8 L e s t this appear as a "romanticism of creation," it is necessary to say that for

Aquinas, all created reality is in need of redemption. Everything participates in the decline

that is initiated by the sin of the first human parents. See Lonergan, Grace and Freedom 43-

53 .

19

STh. 3 .60 .6 , corp.




Not all interpreters agreed with Aquinas. 8 0 Some (l ike Henry of Ghent,Okham, Biel, Bonaventure and Scotus) viewed the instrument as an occasion, acond i t ion in which God operates externally. 8 1 Aquinas held out for the differe nce

of divine action, but not its extrinsic intervention. Others (Cano, Vasquez) arguedthat the instrument had a moral worth or value in itself that moved God to act.Aquinas denied this, since it seemed to make God dependent upon creationalconditions. Nonetheless, this position seemed to have great currency through theseventeenth and eighteenth centuries.

Later interpretations (S chm aus, C asel, Vonier) sim ply argued that there wasa "mysterious" power within the instrument that produced a more-than-humaneffect . Though Aquinas sometimes spoke of the power operative in a word thattransmitted divine transformation, he denied an independent sacral vitalismfunctioning within created reality. The divine and the human remained distinct; thewonder was (and is) that God has chosen to act through nature 's own self-mediating capacities. There were theological arguments throu gho ut the later m iddleages and early m ode rn period abou t whether it was the m aterial of the instrum entitself that was the ancillary cause to divine agency (looking for a causal n exus? ).Later thinkers, hoping to avoid a "physicalist" interpretation of the cooperativeaction in the sacraments, stressed that the instrument provided information toparticipants about God's intention to make them holy. Or they could be understood

as prac tical signs, like a juridica l ord er or a title-deed, saying so m ething , w hilesimultaneously accomplishing it .

4 .5 Instrumentality and Providence

Providence is God's characteristic way of being; it is love for the other in and forthe sake of the o ther (caritas or agape). For Aquinas, it is the prime analogue forknowing and loving. Everything outside of God is an instrument toward or awayfrom that love. So he can quote Augustine approvingly: "God cooperates with

good will to give it good performance; but alone [God] operates on bad will tomake it good, so that good will itself no less than good performance is to beattributed to the divine gift of grace." 8 2 But this deals specifically with the natureof human instrument. What about non-human instruments?

If I have interpreted Aquinas correctly on the sacraments, he is arguing thatcreated reality operates at different levels, permitting it to cooperate with divinelove each at its own level. Non-human created realities, whether animate orinanimate, interact at their own level of reality as well as between levels preciselythrough their own internal operation to cooperate with divine providence. So, for

exam ple, the ability of bread to bear the historical presence of divinity is due to the

^Nor do all interpreters of Aquinas ag ree with my reading of the relationship betw een

signs and causes in the theology of the sacraments. See, for exam ple, Pow er, The EucharisticMystery, e sp . 219-36 and 269-85.

8 1 See Leeming , Principles 2 8 7 - 9 4 .c

L o n e r g a n , Grace and Freedom, 3.




fac t that it is transparent to divine love. Insofar as each element operates at its ownlevel and cooperates with higher schemes of recur renc e, it will perm it the universa ltransformation of all things into divine love. To discover one's ow n proper

instrumentality is to encounter the divine agency in one's being. In other words,there is no other causal nexus than the self-organization of the entity itself.

4.6 The Language of Direct and Indirect Divine Action

To use language about "direct" and "indirect" action seems imprecise in thiscontext. It misrepresents the relationship between the language of the scripturesand it misunderstands the meaning of mediation. The assumption that Christianscriptural and doctrinal languages affirm that there are special acts of God or

special providence may be true, but intellectual smuggling occurs when the term"direct" is used to describe them.

First, the doctrinal (and Augustinian theological) language that is being usedis dependent upon metaphoric and narrat ive primordial language found in thescriptures. W hat is the relationship betw een these two or three forms of language?Is the derivation of no significance? Why privilege one over the other? Second,within the primary and creedal languages, divine action is often described inanthropomorphic fashion, as extraordinary (by human standards), and as more

powerful than nature itself could perform. "Special" seems to discriminate betweenunusual and usual. On what basis? Is the criterion smugg led into theolo gy fro m th eextraordinary, superpowerful agency described in scriptural texts?

The problem is in the images of direct and indirect and a misplacedconcreteness of their metaphoric intent. Aquinas would have said that God acts"direcdy" and "indirectly" at all times—namely, by originating, sustaining, andguidin g created realities through contingencies and necessities. The lack of clarityis caused by misunderstandings about what i t means to act through mediation.

God's transcendent act is providence, love for the other; it is always exercised

mediately, in cooperation with the other (first and p rim ord ially in triun e life; " then"in relationship to created realities). I have no doubt that God acts in and throughquantum events ; indeed, perhaps the science of quantum events may grant moreevidence for the underdetermination of micro- as well as macro-events . But theindeterminism of quantum events is no more opp ortunity for divine action than thenecessities of universal gravity.

For those who use the language of "direct" and "indirect," "indirect" seemsto mean "mediated," and "direc t" means "w ithout med iation." Sometimes there isthe assumption that interpersonal action is unmediated. Most philosophers(whether of language or no) would find this a difficult position to maintain. Thereoccurs "body language," the embodied self-presentat ion even at the surfaces ofone's skin. There is an assumption that God must act without mediation at somepoint (the "initial" stage) to begin the necessities and contingencies. The solecriterion for determining that it is God who is operating turns out to be asurprising, even uncann y effe ct from unexplainable causes. It is not simply that theaction is accounted an extraordinary event, but that what is extraordinary informsus about a special, particular, and personal action beyond our control. And this

becomes the meaning of divine transcendence.




How ever, for a thinker like Aquinas, d ivine transcen denc e is what is alway sabsolutely "bey ond ." Indeed, it is precisely the div ine distinction fr om creatio n thatpermits God to operate immanently and mediately in all created beings. The divine

freedo m to love involves triune life. God creates only "because" of the divine self-mediations of kno wled ge and love. This my stery envelo ps all the med iating con tactour world has with God. Any attempt to discover a causal nexus is a search for theGod of the gaps; it presumes that there is one or another particular negative orunambiguous condit ion under which one can expect God to act . This solutionseems to misunderstand the nature of divine action. G od is the nece ssary , b ut nev erthe sufficient condition for a created event. God's actions within creation arealways mediated by the self-organizing agency of the created reality. Moreover,since all God's actions are efficacious, God does indeed determine effects through

the disposition of created causes. That is part of Aquinas's explanation for theeffectiveness of petitionary prayer, not an "in principle" ability of God to intervenewithout intermediary in curing the sick or parting the seas.

What is curious is a continuing search for a causal joint. Th e me diations arewhat no n-h um an animate and inanimate realit ies are "abou t." I t is precisely theirself-organizing capabilities in relationship to the environment, with their law-governed structures and und erdeterm ination (wh ere that applies), that is the locus

of divine-created interaction. Rocks cooperate as rocks, plants as plants, and dogs

as dogs. One does not need to search for a further physical, vital, spiritual, ortranscendental "hook" into which God can insert divine operations. Thisimmanence of God to all reality is the place where divine-creational interactionoccurs. What the best science tells us abou t the way the world work s is what Godis telling us about the way divine action operates in our world. If one argues forany moderate realism in knowing, then one must say we do know something,however partial and mysterious, about the divine agent in the interaction. This istrue not only because God has chosen to speak, but because what we learn aboutthe created world is not deceptive or malicious.

The search for a causal joint or nexus in physics or biology seems to be aboutsomething else. (1) Positively, it is an attempt to make more inclusive the criteriaor cond itions und er w hich a jud gm ent can be m ade that "G od is acting " byextending the conditions from scriptural stories to the natural sciences. In thissense, the indeterminacies of both micro- and macro-level systems appear as partof the contingencies that allow an o pen-e nded universe, a cosm os in which hum anchoice might ma ke a difference. They articulate the conditions for a free universalstory. (2) The search for some intimate space in pre-human nature or in the humanmind or body where God is "more operative" than in others seeks to preserve a

theological and confessional tradition that protects the free sovereignty of God,such as in Biel, Okh am, Luther, and Calvin. God could have m ade another world,but chose to create this one. Nonetheless, according to Okham and the laterscholastics, divine power has made no intrinsic connections between reason andfaith. Divine power is absolute and could be arbitrary. It is this philosophicaldefense of the arbitrary that may appear useful as a description for divine action.If my arguments are correct, it is not. (3) The term 'direct ' often means not justimmediate, without mediation, but an action that seems to operate within nature,

even along side it , as a form of causation extrinsic to the orderly or random




processes of nature. As such, it reduces divine action to created prop ortions. W hatcausal nexus seeks to understand is the m om ent in which "natural coop eration"occurs. To all these the search for a "div ine vita lity" within nature m isund erstand s

divine transcendence and nature 's relat ive independence.

5 A Transposed Melody: Divine-Creational Interaction

If we are to go beyond the descriptive, but inexact, language of "direct" and"indirect," we must transpose the classical metaphysical categories of Aquinas. Wecan do so by using the language of self-organization and far-from-equil ibriumsystems. W e do so not simp ly by seizing upon the instabilities or indeterm inacies

of such systems, but by noting their fundamental inner temporality. Just as Aquinasused what he believed to be the best available scientific explanations concerninghow instruments work, we can integrate such scientific language into anoverarching scheme that art iculates divine transcendence and God's interactionwith animate and inanimate nature.

Much of our interest is with the kinds of interaction between divine andhuman agents . However, a theory of self-organizing systems provides a way ofspeaking about non-human agents (and humans) in their own right. Indeed,

theories of self-organization can specify the internal dynamics of non-human, self-directing realities and specify th e relative independ ence of non-human instruments .By developing a hierarchy of such relative ind epend ence, fro m chem ical reactionsto hum an teleonomies, it becom es po ssible to spe cify the characteristic instrum en-tality of each, its ability and level of cooperation with divine love. For Aquinas,God not only respects the proper temporality of creatures; God originates,supports , and encourages them to come to their appropriate completions. Forreasons known only to love, God ha s chosen to me diate divine temp orali ty throughthe structures of created self-organizing s yste m s. 8 3

5 .1 The Tem porality of Self-Organizing Systems

Self-organization theory provides an analysis of how certain kinds of systemswork, fro m inanimate through anima te to self-conscious l ife . Th e internal clocksof things operate as a self-constituting process by which a reality is what it is anddoes. In the particular kinds of systems d escribed abov e, there is the develo pm entof a future different from the past, often dependent upon a choice in a bifurcation

8 >Thoi igh the language sometim es used by theologians of the world as "God's bod y"

is descriptive, the explanatory value of such a metaphor requires an understanding of the

historical, self-organizing structures of the universe's systems to be helpful. See, for

example, Sall ie McFague, "Models of God for an Ecological , Evolutionary Era: God as

Mother of the Universe," in Physics, Philosophy and Theology: A Common Quest forUnderstanding, ed. Robert John R ussell, William R. Stoeger, and George V. Co yne (Vatican

City State: Vatican Observatory, 1988), 261-63.




process . Su ch unp redictabili ty o ffers (perhaps) a condit ion for the em ergenc e ofthe new—including the choices of human freedom (at a much higher level oforganization).

The "who le" in such a system is relative, a moving viewpoint; it is dependentupon its own evolution. One could speak about it synchronically as well asdiachronically. The reality emerges as its future attracts it toward that whole.History in an organism makes a difference to what it is.

The tempo rality of self-organizing systems articulates a rela tive ind epe nd en cethat is self-directing. This directionality is not totally separated from its environ-ment, but its ability to organize itself can be recognized as encoded within thesystem itself. Its success is dependent upon its ability to avoid stasis (i.e., to growand change) and to replicate itself. To be able to do that, there must be somemutability, that is, non-necessity in its replication. (These criteria for completenessare likely true of human actions as well as of lower self-organizing systems.)

5 .2 Providence as Divine Temp orality

God's time is the prime analogue for all temporality. It can be conceived as a"before" and "after" and a s imultaneity in which there is only cooperative love.Providence, as the fundamental divine intention, is for "all that is" to be itself in

love. For that to take place, there must be an other in whom and with whom asystem mediates itself. Reality is intrinsically relational, beca use G od is presen t asinner relationality. W ithin divin e life, there is the exp erience of lov e as identity anddifference, the same and other. In a prior article for this research project, I haveargued that in God there is an equiprimordiality of mystical simultaneity andnarra t ive sequence . 8 4

If we used our experience of s imultaneity as the prime analogue for God,then we would mix an intense attachm ent f or the other as well as boredom , an ger,fear, and rejection that consists of more of the same. If we use our "sequencing"

as the norm , we ha ve the exp erienc e of our history as a m ixture of evil and grace.However, for Aquinas, charity is the ultimate temporality of divine presence. InGod, there is only the mutual self-m ediation of know ledge and love. Divine loveis ever active. In effect, that is to say that God's time is "real" temporality; all othertemporalities are analogous and (fo r Ch ristians) participative . H um an b eings enter"real" time by more intensely cooperating in and with divine temporality, that is ,love and knowledge. As humans become more just, loving, and truth-telling, theyshare more deeply in divine inner life (temporality). In effect, it means that notonly does the finite created reali ty become more knowledgeable and more loving,but it mediates its own temporality through and with God's intentionality.

An allegory illustrates this theological position. How does paper catch onfire? It must draw closer to a flame already burning. As the paper grows closer tothe flame, it reaches combustibility, until finally it too is consumed. God is the

8 4 S e e Haopel , "Metaphors and Tim e Asymmetry: Cosm ologies in Physics and

Christian Meanings," in Quantum Cosmology, 103-34.



D I V I N E P R O V I D E N C E 2 0 1

eternal fire, burning but not consumed; as self-organizing realities draw closer tothis burning flame, they participate in the fire itself, eventually becoming thattoward which they are drawn. The human fear continues to be (not just s ince

Friedrich Nietzsche, but certainly philosophically thematized by him) that tomediate oneself in and through such an Other will destroy the very self-orga nizingtemporali ty that human beings s truggle to maintain in the context of harshenvironments. The Christian claim is that cooperation with an other, while it maybe the ultimate risk, is also the primary way to become one's truest self.

5 .3 Temporalities in Cooperation: Mutual Self-Mediation

The notion of mediation is a com m on on e in logic, of course, since it is the term

that intervenes between the first principle and the conclusion that follows. In anorganic example, one can see the heart as the "source" for the circulation of theblood, but the flow of blood is mediated through the arteries and the veins. Inmutual mediation, how ever, the systems operate as a function al who le. Theprinciple of m ov em ent fro m an origin and the principle of control in a system arecombined. There are differing centers of immediacy and their mediations overlap.In the same organic examp le, one can see that the res pirato ry system supp lies fre shoxygen to the whole body, not merely to the lungs; the digestive system provides

nutrition, and so forth. The result is a functional whole "that has fresh oxygen, isfed, is under control, and is moving, because there is a number of immediatecenters [sic] and from each center there f low s over the who le the consequences ofthat center." 8 5 It is not difficult to see an initial description of a self-organizingsystem.

If one adds to this notion self mediation, on e can see that the differen t centersof immediacy creating a functional w ho le are governed by an internal te le on om y8 6

that directs the identity of the system itself. Ch ang e is not simp ly a replication ofidentities, but a genuine integration that produces higher-level functions through

the operation of its parts. Lonergan sees a final notion of self-mediation inwardthrough which self-conscious mediation occurs. Self-consciousness implies a pre-reflex ive prese nce to self that is the condition f or all m ediations.

[F]or you to be present to me, I have to be present to my self . This presenceof the subject to [the self] is not the result of some act of introspection orreflection Co nscio usne ss is a prese nce of the subject to [the self] thatis distinct from, but concomitant with, the presence of objects to thesub jec t . 8 7

God is the perfect self-conscious, self-mediating subjectivity. God issimultaneously present to the divine self as well as p resen t in and throu gh that se lf-presencing to the other. So God knows and loves all created reality precisely

8 5Lonergan , 4 The Mediation of Christ in Prayer," Method 2, no. 1 (March 1984): 5.

"Lonergan calls it a finality, but clearly means an internal teleonomy rather than an

extrinsic te leology.

'"Lonergan, "Mediation of Christ in Prayer," 8-9.




through the divine relationality. For Aquinas, this self-presencing activity iscompletely knowing and loving, but inexhaustibly mysterious. The divine actcontinues to become "more and more" itself in and through the divine relational

identity. Here temporality as sequence can be understood as the deepening oflove's mystery and the continual exercise of wisdom; simultaneity can beinterpreted as the intense and constant exercise of encountering the other.Instrumentality means that the characteristic temporality of created realities isactivated, engaged, and brought to its highest form of complexity by mutual self-mediation with the divine. The gracious action of the divine within our world is notviolent confrontation, extrinsic intervention, but a synergistic cooperation. "Theintegrity of the dialectic of the subject is grounded in the gift of universalwi l l ingness or char i ty . " 8 8 Though this presentation is deliberately brief and

descriptive, it does show h ow A qu ina s's un derstand ing of Go d can be trans posedinto seeing the divine temporality as the ultimate "self-organizing system." 8 9

6 Final Remarks

This paper has argued that Christian theo logy , in the thoug ht of Tho m as Aq uinas,has had a coherent understanding of divine-created interaction. By developing a

clear theorem of transc ende nce or the supernatural and of universal instrum ental-ity, Aquinas was able to articulate the basic ways in which inanimate, animate, andhuman secondary causes cooperate or conflict with the divine act of love for theuniverse (providence). These terms can be transposed into an historical ontologyand a language of mutual mediation such that all levels of reality hav e their relativ eautonomy. Contemporary science, with i ts analysis of self-organizing systems,provides an understanding of the regularities and contingencies of inanimate andanimate created realities. Their language permits us to understand how an open,flexible universe can provide the conditions for cooperation among these systems

and with divine action without conflict or violence to the integrity of creation.There is an optimism inherent in this analysis; it is born of a religious

conviction that though the cosmos (whether human or non-human) is flawed andfinite, its internal logic is not vitiated, malicious, or deceptive. Images, the body,and the non-verbal a re no mor e (and no less) prone to sin than reason. W ithin thetemporal being of "nature," self-organizing, living, self-conscious beings canengage with their environm ent in a cooperative w ay. Ultimately, it argues that self-conscious creatures may learn that cooperating with the ultimate environment, anunfathomable Other, will not do violence to their own complex teleonomies.

M Robert M. Doran, Theology and the Dialectics of History (Toronto: University of

Toronto Press, 1990), 502.

8 9 I am indebted for my current reformulation of the argument to criticisms and

questions raised especially by Nancey Murphy, Robert John Russell , Thomas Tracy, Ian

Barbour, and to a former colleague at Catholic University, James R. Price HI, now at the

University of Maryland, Baltimore.



D I V I N E P R O V I D E N C E 2 0 3

Th e Christian claim, how eve r, goes fu rthe r. It m aintains that this m ysteriou senveloping environment is involved in a mutual self-mediation with crea t ion. 9 0

When one is in love, one mediates oneself in and through an other who is

discovering, planning, negotiat ing his or her personal identi ty in and throughon es elf . This is mu tual self-mediation. Chris t ians claim that they are not m erelyprojecting themselves abstractly into an alien environment to mediate themselves,but that the Other ha s cho sen out of lov e to m edia te the divine subjectivity in andthrough natural self-organization (because God is ul t imately a community ofmutual self-mediation!). The s tory of the Chris t could have been quite differentthan it was. Jesus could have mediated himself in some other fashion; but he didnot. He chose to off er his life fo r others in self-sac rificing g ene rosity . In this action ,he operated as though neither the natural nor human environment nor God were

an enemy. In loving creation, entrust ing his own l ife to others—even indeath—faith claims that there is here a divine love. This is what I have calledelsewhere the "double d ative of presence." W e ar e p resent to the divine who in thatsame mo vem ent is present to us. What we discover in this fragile and stumblingprocess of mediating ourselves and our world is an antecedent lover and friend .

^S ee Lonergan, "Mediation of Christ," 17 -19.



R E F L E C T I O N S O N C H A O S A N D G O D ' S I N T E R A C T I O N W I T H T H EW O R L D F R O M A T R I N I T A R IA N P E R S P E C T IV E

Jiirgen Moltmann

In this brief paper I want to describe five models about the God-worldrelat ion that are found frequently in tradit ional and contemporary systematictheology. Then I want to comment on how these models function in the currentdiscussions about the theological significance and implications of chaotic,complex, and evolutionary systems in nature. In doing so I will adopt an explicitly

trinitarian conception of God and suggest its importance to these discussions. I takethis paper to be something of a thought experiment, but that is , after all , entirelyfi t t ing to the theological program as a w hole.

1 Five Mo dels of the God-W orld Relation

Contemporary theologians often read the "book of nature" symbolically and

sacramentally as a s ign and m anifestat ion of a greater, m ore encom passing divinesystem. In doing so, they are asking not only "H ow does i t wo rk?" but also "W hatdoes i t mean?" and "What is i ts s ignificance?" The response to these questionsleads directly into a topic of fundamental importance in systematic theology,namely the relation of God and the world. A variety of models have beendeveloped to respond to this broad topic. Here I would like to comment briefly onfive of the most significant ones.

1 .1 The Thom istic Mo del of Dou ble Causality

The Thomistic model draws on a r ich tradit ion and flourishes in contemporarytheology. According to this model, God, as causa prima, acts through the causae

secundae which God has created. G od 's action in the world is ther efor e an indirect,mediated action. It allows for the relative independence of secondary causes, whichserve as the " instruments" through which God acts . Conversely, the secondarycauses point to God as primary cause and allow us to reason by inference from thefacts of nature back to the One who causes them. We can say here that theinstrumentalization of the world is at the sam e tim e its transce nde ntal transp aren cyin the fa ce of the brilliance of its beauty and order.

1 .2 The Interaction Mo del

Though found in a variety of theological contexts today, the interaction model ismo st frequently associated with process philos oph y. Co m pared with the Th om isticmo del, where God determines everything but is determined by nothing, the processmodel insists on a reciprocal influence between God and the world. Thus, God acts



2 06 J U R G E N M O L T M A N N

in the world according to the divine primordial nature bu t Go d also experien ces theworld according to the divine consequent nature. To use a human analogy, Godspeaks and God hears. This mod el is broad enough to contain the essential features

of the Thomistic model, but not vice versa: the interaction model cannot beintegrated as a whole into the Thomistic model.

1.3 The Whole-Part Model

A third model widely used today makes use of the concept of "whole-part"derived, most often, from biological systems theory. The essential idea is that ofthe "whole" as made up by i ts parts and yet as quali tat ively more than, anddifferent from, the mere sum of its parts. The idea is particularly relevant inconsidering complex and chaotic systems, such as those stud ied in the phy sical andbiological sciences, where we find a form of top-down causality in which thewhole determines the coordination of its parts. In this model, causal relationsprovid e only one possibility within a m ultitude of intercon nected relations, m aki ngthis model clearly superior to the previo us m odels we hav e consid ered. U sing thismod el w e can form impo rtant conclusions about G od 's indirect effect upon theworld. We do so on the basis of top-down causality by applying the analogy of"similarity in the face of ever greater dissimilarity." Thus, just as the whole is in

relation to its parts, so God acts in relation to the world as a whole.

1.4 The Mo del of Open Life Processes

I want to consider another important model derived from biological systemstheory. This on e specifically emphasizes the open character of biological processes.Every life system has a fixed past which corresponds to its present reality and apartially open future which corresponds to its possibilities. Drawing upon atheological insight first expressed by Augustine, we may say that its present is thus

constituted by the convergence of its remembered past and its anticipated future.In short, the present is both present past and present future. The process ofevolution and the progressive differen tiation of increasingly com plex life system sin nature corresponds to the hermeneutic circle of present past and anticipatedfuture in human history, or, in general, to tradition and innovation. According tothis model, the openness to God to the world process can be deduced from theopenness of life systems to their future. One can say that open life systems are readas real symbols of their own future even as that future is transcendentally beingmade possible .

1.5 Mo dels of Creation and Incarnation

Finally I shall discuss two specifically theologic al m ode ls: tho se of creation and ofincarnation, that is , of inhabitation by virtue of God's self-limitation (what theKabbala calls zimtzum). According to these models, God as eternal and omnipres-ent restrains Godself to allow creation to be, thereby giving it time and providingit with a habitat of its own. God's omniscience is limited by God to such an extent

that the future is open and experimental even to God. At the sam e time , the eternal



RE FL E CT IO NS O F CH AO S 2 0 7

and omnipresent God is self-limited such that God can inhabit the temporal, finitecreation and impel it from within without destroying it (schechina ), guiding it toits comp letion, that is , to its eternalization and divinization.

The challenge for this mod el is wh ether it can explain the previou s, simplermo dels and integrate them. That it should be ca pab le of doing so fo llow s fro m thefact, mentioned above, that complex systems can comprehend and explain simplerones, inasmuch as they contain the latter. On the other hand, a complex systemcannot explain an even more complex one because i t cannot know the whole ofwh ich it is a part.

2 Three Com ments on How These Models Function in the Discussion of Divine

Action and Chaos

First of all I would like to comm ent on the mo del of " G o d' s action/interaction with

the world" as it is understood in several of the essays in this volume.

2 .1 Theism, Deism, Pantheism, and the Theistic Mo del

"G od 's act ion/interaction with the wo rld" is perhaps best understood as a theistic

model of God, one derived from the paradigm of "reali ty as his tory." God isunderstood as an absolute subject , different from the world, and one who ei therintervenes at will or preserves the created order. In the same way as God savedIsrael with a "mighty arm" through the miracle at the Sea of Reeds, God calledcreation into being out of nothing and then brou ght forth order out of chaos. Go dcreates, maintains, saves, and perfects the world, for the world is "God'shand iwork . "

It is not necessary for me to describe this theistic model any further. Themodern reaction to it was essentially the emancipation of modern culture and

science from God. The more it was recognized that the laws in society and naturework independently, the mo re the theistic mode l declined and in its place a deistic

model was established. Here God's act ion is only needed to explain the world 'scontingent beginning. Today deism evokes the image of Go d going into retiremen t,but, ironically, in the Baroque period it was actually a "theology of glory" whichconceived of God as resting on th e Sabbath after creating the "best of all po ssibleworlds ." This is abundantly i l lustrated by the hymns of praise dating from thatt ime.

The contemporary reaction to the theistic model is not so much the atheismof the nineteenth or the agnosticism of the twentieth centuries. It is , instead, theelaboration of the pantheistic model. According to this model, self-organizingmatter and self-developing life are divine. For an interesting current example ofpantheism, see the writings of Erich Jantsch. 1

1Erich Jantsch, The Sef-Organizing Universe: Scientific and Human Implications of

the Emerging Paradigm of Evolution (New York: Pergamon, 1980).



2 0 8 J U R G E N M O L T M A N N

If one is to do just ice to the phen om ena embraced b y the pantheist ic m odelwithout relinquishing biblical-Christian theism, then what commends itself to meis the trinitarian model. It allows one to speak of "God and the world" in a

threefold fashion: God the father creates through the Logos/W isdom in the pow erof the Holy Spirit. All things exis t "out o f ' God, " thro ugh " G od, and " in " G od, andGod not only transcends the world but is a lso immanent in the world. ThroughGod's creative spiri t (ruah)> God is present and active in all creatures (Wisd. ofSol. 12:1), weaving the patterns of relationship w ithin the co m m unity of cre ation."In transfusing into all things his energy, and breathing in them essence, life andmovement, he is indeed plainly divine."2 'T h e H oly Spirit is l i fe-giving Life, theMover of the universe and th e Ro ot of all created b ein g" (Hildegard von Bin gen ).

By "cosmic Spirit" we mean that power and space in which fields of energyand material conglomerations form themselves, the symmetries of matter and therhythm s of l i fe , the open systems in their growing co mp lexity. Accord ing to thismodel we can say that Go d acts upon the w orld not so mu ch th roug h interven tionsor interactions, but rather through God's presence in all things and God's peri-

choresis with all things. What emerges is the image of the mutual indwelling ofGod in the world and the world in God through the Spirit . This mutual interpen-etrat ion fashions the community and the sympathy of al l things. From thisperspective, "God's actions in the world" and "God's interactions with the world"

are only a part of G od 's co m preh ensiv e perich oresis with all things and w ith theirrelationships. C ausality is also only one aspect of this netw ork of relationship s. Th eself-organization of matter and the self-transcendence of all that live s are th e div ineSpirit 's signs of life in the world and demand therefore neither an atheistic nor apantheistic interpretation.

2 .2 Creation a nd the Future of the Wo rld

My second comment touches upon the theological framework for dialogue with

science. I believe that Nancey Murphy and John Polkinghorne are correct toidentify God's continuing action in the created world in terms of sustenance,providence, guidance. Th is avoids the creationist iden tificatio n of creatio originalis

and creatio continua. On the other hand, the model of "God's continuing action inthe wo rld" ofte n takes on theistic overtone s w hich limit this action one-sided ly tothe conservation and preserv ation of the world that has already b een created (i.e. ,the original, temporal creation). W hen this happen s w e fail to give equal attentionto the future of creation, that is, tow ard th e new , eternal creation.

In her paper, Nancey M urphy poses the follow ing qu estion: "A re there statesin between this final state, when God will be all in all, and the present state ofGod's hiddenness in natural processes?" 3 My response is that creatio continua isGod's influence on what has already been created and should therefore be

2Calvin , nst. I, 13, 14.3 Nancey Murphy, "Divine Action in the Natural Order: Buridan's Ass and

Schrodinger's Cat" (in this vo lum e).



REFLECTIONS OF CHAOS 209

distinguished from the creation of the world. It is God's influence on time, for timewas established along with creation. This influe nce both preserv es and renew s theworld, as the Psalmist writes: "An d you renew the face of the ear th" (Ps. 103:30).

God's preserving activity in keeping creatures from self-destruction shows God'sfaithfulness, while G od 's renewing activity with creatures revea ls G o d' s ho pe. Th epreservation of the world occurs through G od 's patience, G od 's " lon g su fferin g."God 's "omnipotence" is God 's forbearance: God gives to the world t ime. Therenewal of the world takes place through anticipations of the new creation of allthings through rebirth to life. Thus, if we speak of "God's continuing action in theworld," we must also speak of God's intention and goal. The eschatologicalhorizon of the new creation of all things, the divinization of the cosmos and of theeternal creation, has been lacking in the discussion up to this point or, at least for

me, it has not been given adequate consideration.What is the futu re of creation and the goal of pro vid en ce? If on e ass um es that

the world is in the process of "becoming," then one implicitly expects the finalfutu re of the world to be a state of "being." In other words, if one supposes that theworld is "unfinished," then one expects that some day it will be finished andcompleted. If one understands the systems of nature with their openness to timemerely as "systems that are not yet closed," then one counts on their finalculmination and closure. In that case the world's future would consist of its

"being" taking the place of its "becoming," its time being replaced by its eternity,and its potentiality becoming actuality.

But biblical Jewish and Christian eschatology hopes that God will makecreation into God's dwelling place and temple, and that the glory of God, havingrenewed and completed creation, will "indwell" it . This implies the participationof finite creatures in the infinite existence of God as well as the participation of theeternal God in the creatures ' temporal existence. Therefore the indwelling of theliving G od 's unbound ed fullness does not mean th e end, but rather the op ennesspar excellence, of all life systems. They participate in God's creative abundance of

possibilities and so gain an eternal future and an eternal history.These theological insights seem increasingly consistent with the discoveries

of modern science. As we now know, chaotic, complex and evolutionary systemsof matter and life are built up in such a way as to display a growing openness totime and to an abundance of possibilities. These possibilities increase as theircomplexity increases, thus expanding the scope of their open, indeterministicbehavior. It would be difficult to imagine their future in a world system which hasbeen broug ht to com pletion, o ne in which all possibilities hav e been realized andthe future has become wholly a part of the past. Indeed, that would mean the"eternal death" of the world, which is only thinkable if the world comes to its endwithout God. If, however, our starting point is the expectation of God's"indwelling" of creation, then the future of the world can only be imagined as theopenness of all finite life system s to the abund ance of eternal life. In this way theycan participate in the inexhaustible sources of life and in the divine creative groundof being.

This means, however, that we can no longer think of God's being as thehighest reality (ens realissimum) for all realized potentialities, but rather as the

highest possibility and as the enabling of all potential realities: "All things are



210 JOR G E N M O L T M A N N

possible fo r God ." As that which enables potential ity, Go d' s futu re is in fact the

source of t im e.

2 .3 Open System vs. Closed System

M y last com m ent relates to systems theory. If the systems of matter and life k n o w nto us are best described as "open complex systems," then should the universe as awho le be conceived of as a "closed system" or as an "ope n system "? O pen system sare part icipatory and anticipatory, capable of communication and able to"experiment" with the differences betw een tenses or times. Their reality is fixed ina relatively stable fashion; their possibilities grow proportionately to their degreeof comp lexity. Their behavior is only partially determined by th eir reality; it is also,though only partially, undetermined. In "closed syste m s" the am ount of m atter andenergy is constant, whereas in "open systems" it is not, for they are by definition

matter and/or energy receiving systems.If we conceive of the universe as a system closed in itself, then the open

systems of matter and l ife are only subsystems and movements within a s tablewhole. If we conceive of the universe as an open system, then all individualsystems participate in this openness. In this case we do not need to posit a constantamount of energy, but rather we might expect to receive a constant inflow ofenergy. But how should w e conceive of the source of this energ y? Perh aps it w ouldbe possible to extend the idea of the self-tra nscen den ce of life, of w hich biolog istsspeak, to the self-transcendence of the universe, with God's transcendence as the"outer cause" and the "inner motive" for this self-transcendence. In this case theworld w ould be a "system op en to G od " and God a "Being open to the wo rld." W emight then look for " traces of God" (vestigia D ei) not so much in the realm ofregular or irregular realities, but rather in the realm of potentiality. By potentialityI mean first of all that which is really possible, but even more so I mean theFoun dation w ho enables all potential i ty.

I realize that this is an experiment in thought. But experimental theology alsobelongs to "systematic theology," because in the conception of God it deals with

an "open" system, not with a "closed" one. As with all theology, it is itself anexperiment with God.



T H E G O D O F N A T U R E 22 1

Langdon Gi lkey

In this paper I want to focus on two inter-related questions: first, whethernature's processes imply a god at all, and second, if they do, what sort of god theymight imply. These mo ves are, of course, a part of an old tradition: that of naturaltheology, in which an overview of nature, of history or of human existence itself,that is , a philosophical overview, is taken to be able to lead us to a rationallysecure, if rel igiously inco mp lete , "know ledg e" of God . They also presuppose the

claim that science gives us a picture of nature in which there are, arguably, signsof the sacred, "traces" of the divine presence and activity.1

Although what follows can fairly be called a modest and somewhat hesitantmem ber of the family of natural theologies— perhaps a distant cou sin— non ethele ssI wish to emphasize two points about it which diminish, if they do not extinguishentirely, the confident claims of most natural theology. The first is that naturaltheology represents philosophical reflection, or, better, logical reflection of aphilosophical sort . I t is generated by the urge to understand with as much

coherence, clarity, and accuracy as possible the entire welter of experience, toarticulate the structure and th e mean ing of th e wh ole as we ex perienc e it in all itsvariety and ambiguity. Religious existence is generated—usually and for most ofus—otherwise. It arises out of sharp awareness of the dilemmas of life, when lifeis experienced as estranged, at sea, and some disclosure of rescue, of reconciliation,of illumination is received.

Such experiences, of course, have for humans arisen continually in relationto nature. When they did—as throughout archaic l i fe—then nature was experi-enced as laced with the sacred. But such a religious relation to nature is vastly

different from the relation implied in a scientific inquiry into nat ure , an eng ineer inguse of nature—or even a vacation enjoyment of nature! With nature turned overlargely to science, technology, and leisure, our modern religious discourse, ourmyths, rites, and religious confidence, have mostly concerned the human self, itscommunity, and the wider history in which it lives—as the great modern "myths"of Progress, of the M aterial Dialectic, and of H um anism illustrate. Religio ns ariseout of disclosures to selves in community, in relation to the crucial realities inwhich those communities exist. If that latter reality be nature, then religion centers

! A s I ha ve w ritten elsew here , these were on ly, at best, hints; actually they w ere

questions raised by special inquiries that sprang up unexpectedly there, but received no

answer from these special inquiries. Nonetheless, they remained puzzles persistently there:

questions about power, about order, and especially puzzles about the strange "story" or

meaning, despite randomness, disorder, death, and negation that seemed implicit in the

process—and mocked us, like elusive ghosts, each time we looked carefully at nature.



2 1 2 L A N G D O N G IL K EY

on nature in relation to the comm unity. With us, how ever, our cru cial env ironm enthas been social and historical, and hence it has been there that fundamentalrel igious disclosures have arisen. The common thread, often remarked, between

modern historical and humanistic ideologies on the one hand and the religioustraditions of Judaism and Christianity on the other is that in all of these it is personsin comm unities and com mun ities in history that represen t the loci of disclo sure (thelatter are the so-called "historical religions"), whatever other differences they mayexhibit.

This effort of natural theology never represents, so it seems to me, theinitiating source of religious kno wled ge, and hen ce it canno t func tion as the finalcriterion of this knowledge. The center of religious apprehension lies elsewhere:first, i t does not appear out of inquiry itself, scientific or philosophical; and,second, it does not arise for us in relation to nature, but rather in relation to theexistential dilemmas of existence, of self, of com m un ity, of h istory . In o ur traditio nit is among the "People of God" that disclosure takes place, not in scientific orphilosophical reflect ion—though much in both may open one 's eyes and ears tothe disclosures within the rel igious community. Correspondingly, Buddhists '"knowledge" appears in the higher consciousness through meditat ion and inparticipation in the tradition, not in the sort of reflection even their philosophical"theology" represents. The reflections of the religious consciousness on the

structures of nature and history—natural theology in this modest sense—do not,therefore, either initiate and certainly they do not exhaust the knowledge of God.The important knowledge of God is not philosophical; it is "religious," that is , itis on the one han d existential, and on the other hand it is com m unicated throughsymbols to the com mu nity that acknowledg es the most fundam ental disclosure toits history and witnesses to that knowledge.

In fact reflective knowledge of God of a philosophical sort does not tell usvery much. Like the traces that point our minds beyond the processes of nature,such knowledge raises questions about that process—and, as we shall see, it begins

to suggest an apprehension of the divine presence there, the dim outlines of themystery of our origins. What it does do, and docs significantly, is to represent thefirst step in the articulated relation between what we know religiously orexistentially of God in relation to our community, our selves, and our history, andwha t we know elsewhere and by other sorts of inquiry into community, self,history, and nature. In each case, a "doctrine" is a correlation of what is known ofGod in revelation with what we know by other means of self, of community, ofhistory, and of nature. In this essay we are interested in what nature can tell us ofGod—and this represents the smallest enlightenment on the divine mystery, but itadds an important illumination to all the rest.

Second, and as an imp lication of the above, w hat is know n of God in natur erepresents by no means the center of the knowledge of the div ine f or m ost religio ustraditions, and certainly not of God for the Christian. The mystery of being and soof our being is at best only partially unveiled or clarified here; far more imp ortantfor o ur tradition, as for its biblical roots, is the presence and activity of God withinhistory, and especially within the communities of the covenant, the Hebrewco m m un ity and h e subsequent com mu nity established around the person and

work of Jesus the Christ. If in nature the divine power, life, and order (law) are



T H E G O D O F N A T U R E 2 1 3

disclosed through dim traces, and if the divin e redem ptive love is revealed only inambiguous hints in and through the tragedy of suffering and death, it is in the lifeof Israel, in the life and death of Jesus, in the promises to the people of God, and

in the pilgrimage of that people, that all of this is disclosed in much greatercertainty, clarity, and power. Moreover, when once God is known in this historicaldisclosure to the community, then these traces in nature themselves rel inquishm uch of their dimness and become genuine signs of the p ow er and the ord er of th ewill of the God of faith. As Calvin put it , "when one puts on the spectacles ofscripture, then the signs of God in creation are seen truly for what they are."

The consequence of these points is that what I am trying to do here, whileimportant, is not th e vital center of Christian th eolo gy. It is imp ortant b ecau se thedeeper understanding of nature 's mystery and value in and for i tself is very

important, and because the relation of Go d to natural p rocesses is an essential pa rtof our understanding, not only of nature, but of God and of ourselves. How elseare the immensity, the transcendence, the wonder, power, order, and glory of Godto be experienced, known, and articulated? How else are we to know ourselves astruly children of nature yet as ones called by our c om m on creator to respon sibilityfor nature 's integri ty, nature 's value for i tself , and nature 's preservation? Andfinally, it is , I suggest, only thro ugh a know ledg e of natu re inclusive of the signsin nature of transcendence, of ultimate power, order, and value that the mystery,

the depth, and the richness of nature can be ex pe rien ced , ar ticulate d, an d v alued byus. An important part of our know ledg e of na tu re 's reality is a religious app rehen -sion of natu re as well as a scientific, a technological, an aesthetic, and a responsible(a moral) knowing of nature. And basic for all of these is care in treasuring andencourag ing a bodily as well as a spiritual joy in nature, in nature's beauty, variety,and richness , experiences which we have almost lost . What we are doing,therefore, has its point as a theological/philosophical articulation of the presenceand activity of the divine in nature.

Let us turn to our picture of nature as seen through reflection on the

contemporary sciences and their apprehension of nature. This scientific knowledgeof nature represents an extraordinarily reliable (i.e. , valid) picture of the wayna tu re 's fo rces w ork; it is also a limited picture, an abstraction fro m the richnessand depth of nature, an abstraction that om its not on ly m uch of the m ystery withinnature 's processes but even more omits the subject , the scientis t—also part ofnature—who conducts the inquiry and paints our present picture. World and self,objective reality and interpreting subjects, arise together, constitute necessaryconditions for any knowing of "nature," and so alone each represents a relativeabstraction. Any full account, therefore, of the whole must include both of these.Interestingly enough, evolutionary science gives us new possibilities for thisinclusion; for nature also produc es the subjects that know nature.

What sort of world, then, appears from the perspective of science as a validyet partial understanding? (1) It is a dynamic proce ss, a stream of energy coalescin ginto events, into matter, and into the larg er societies of even ts w e call entities . Th isstream represents , therefore, the fundamental power to be of natural exis tence;power is the first characteristic of the universe science discloses to us. (2) Thisprocess is strangely defined and definite as it reaches actuality; here lie the

unavoidable, even the necessary, condit ions for each present . Nonetheless , as



2 1 4 L A N G D O N G I L K E Y

science, from contemporary physics ( including— perhaps— chaos theory), throughevolutionary biology, to psychology and social science reiterates, each present alsofaces indeterminate possibilities. It is apparently open to alternatives, to unpredict-able "jumps," "changes," "mutations"; what consistency it represents at this pointseems hardly necessitated or determ ined but only persistently predicta ble. De stinyand spontaneity represent the general categories of process as science describes it.

(3) Nonetheless, this passage from actuality to possibility is itself character-ized by order, an ord er, there fore, sp anning the entire stream of events. Th us, it isan order reaching into the defined past and yet perva ding the m ov em ent on in to theopen future—a movem ent characterized by indeterminate microcosm ic events , b yindeterminate mutations of organisms, and by the more radical indeterminateness

in the continuity of historical process. It is , moreover, an order running througheach dimension of this hierarchy, as does the stream of power. Causality and orderperva de natural existence as its constituent aspects , but they appear "analo gou sly,"in different dimensions, on different levels of nature. (4) There is continuingnovelty, a novelty that represents a "break" in the conditioned past but also aprocess in continuity with that past. The genuinely new appears in process; notonly change within given forms, but even more a change of forms. Thus, newpossibilities, still "not-yet" in the immediate past, become actuality in the present;open al ternatives become definite choices chosen; openness is t ransformed into

what appears (afterw ard) to be necessi ty— or to have been necessi ty, as we seemto see clearly in the field of dynam ic cha os. In a deeper way , evolutionary theoryhas underlined this coming to be of mutations, as does reflection on history;cosmology as a whole assumes it and describes its scope and importance. Time andits passage effect a "m odal" change fro m possibility to actuality, fro m the open nessof an infinity of option s to the definiten ess, even the necessity, of actual finitu de.

This sequence of novelties, of new not-yet possibilities becoming actual,seems itself to embo dy an ascen ding order, an order of in creasing v alue. V alue is,

as Alfred North Whitehead suggested, intensity of experiencing, of feeling, ofself-reality combined with creative interrelations beyond itself; value is at oncevalue for itself and for others, richness of experience united with richness ofrelatedness, relations in the present and for the future—these in combination andin contrast. There seems little question that if this be a useful description ofvalue—and another set of standards of value would also serve—then there has infact been an increase in value as there has in fact been a fund am enta l m orp holo gyof forms. As our discussion of hierarchy indicates, there are now beings who intheir self-awareness and their interrelating with others experience value for

themselves, value in others, and value for others to an extent almost infinitelyricher than was the case in the early organic world and certainly in the inorganicone. The biologists seem inescapably to reco gnize this "asc en t" of fo rm s and so ofvalue whenever they write abou t org anism s— and yet as soon as they do this, theydeny it officially. Of course, whether that increase of value is a result of "chance,"that is, of random mutations, or of some kind of inner teleology, or even of somefor m of divine "prov idence ," remains an issue which the mere increase of value,even if admitted, does not settle. Certainly, if it be admitted, it creates a reflectiveproblem for a purely naturalistic view of things.



THE GOD OF NATURE 215

These five principles seem to be aspects of nature and of nature's processesentai led directly by what science knows of nature—though they represententai lments and inferences not always drawn by scientif ic accounts . Many such

scientific accounts are intent on an analysis that reduces their explanatoryprinciples to the more universal and abstract terms of physics and chemistry. The"quest for certainty" can lead reflection in science, as it often did in religion, toignore many facts and their implications. Actually, these aspects of nature are onthe way to becoming principles of ontology or of metap hysics. Since the se a spectsare drawn from the inquiries of the physical sciences, they represent abstractionsfrom the whole of experience and so, by implication, from the whole of experi-enced actuality. As we noted, they omit the subject of inquiry and of reflection oninquiry—and thus the entire "inside" of being as we experience our own being as

knowers and doers . They also omit the experience of the other, and so theontological character of organic and human relations, of community, and so ofhistory. Finally, they om it the order and thus the p oss ible teleolo gy of pr oce ss bothoutside and inside.

There are, therefore, left over the fascinating problems of how a self-maintaining system of things comes to be and how it can be understood to embodyboth an order (there are no police), and an order moving into levels or dimensionsof increasing value. When all these omitted but crucial factors (ranges of data, one

might say) are taken into account, the resulting reflection about the structure ofac tua l i ty—now nature and history, scientific objects and scientific subjects(scientists), scientific theory and science—becomes ontology or metaphysics , theeffort to understand the s tructure of being qua being, of what it means for anyentity at all to be. Insofar as any theologian asks what the major symbols of his orher tradition mean or imply with regard to the structure of reality, and seeks toexplicate as far as he or she can that meaning (of creation, providence, humanbeing—and so of nature as well), that theology must borrow an ontology or forgeone for itself. Thus arises from theology's side the interesting problem of the

relation of theology to ontology or metaphysics, a problem the theologian cannotpossibly escape.

Reflection, we have said, must reach this philosophical level for two reasonsrelevant to our present enterprise (of natural theology): First, if the implications ofscience for our understanding of nature are to be a rticula ted— and not left to witherin a reductionist side street—our reflection mu st recog nize that scien ce im plies andeven n ecessitates a wider m etaphysical base or fram ew ork if it is to be rationallyand not irrationally grounded. Second, if the implications for theologicalconstruction—for our understanding of our tradit ional rel igious symbols in thelight of our contemporary world—are to be articulated, theological reflection mustinclude an ontological explication of its symbols if those are not to be conceivedliteralistically and "ontically" on the one hand or empty of content on the other.

There is, however, a further reason in religious reflection for this ph ilosoph i-cal level of discourse. If any a ttem pt at all is m ad e to show the reaso nab lene ss, thecredibility, and the persuasiveness of a religious symbol in relation to ordinaryexperience and its data, then such a reflective structuring of all of experience—ametaphysics or ontology—is essential. Proofs of all sorts, strict, "hard" proofs and

loose, "soft" ones, those that demonstrate, those that suggest, and those in



216 L A N G D O N G I L K E Y

between— all are " i f - then" proposi t ions, w hatever otherw ise they m ay claim to be.

Hia t is, they presup pose a n al ready ar t iculated (or assum ed) re f lect ive s t ructur ingof all of experience: be i t Platonic, Aristotelian, Ne w ton ian, He gelian , evo lution ary

-progressive, mechanist ic , or "process"; and then on the basis of that universe sounderstood , they con clud e that "G od " (or wh atever is here establ ished) isnecessary to that universe. If one accepts that metaphysical vision of things, then

the proof of God probably holds; i f one does not accept that vis ion—or i f one

concludes that metaphysics itself is im po ssib le— then the proof of G od a s es sentialto the universe so understood never gets started. Such pro ofs are p ersu asiv e as we ll

as viable when a com mo n st ructur ing of the w orld can be w idely ass um ed; p roo fs

accomplish l i t t le of what they intend (they may sti l l instruct us about what is herebelieved) if there is a wide plurali ty of competing visions abroad in the land. The

same ma y result if—as in our contemporary case—many intel lectuals suffer u n d e rthe i llusion that they share no such m etaphysical vision bu t that thro ugh the specialsciences they can "see things as they a re ." In any ca se, if we are to de velo p fur the r

an answer to our question of what nature, as understood in modern science, mightimply about God , then we mu st perfo rce mo ve fro m the ont ic (special sciences) to

the ontological; that is to say, we must re-present these aspects of nature just

rehearsed in more inclusive, universal form, namely, as pr inciples of al l experi -ence, categories applicable to all enti t ies whatsoever, symbols that represent "the

universal traits of being" —"what i t means for anything to be," as Aristotle put i t ,

or in Whitehead's words, " those pr inciples f rom which actual i ty never takes ahol iday, that are there and never not there."

With this in mind, let us re-present or re-phrase these aspects of nature as

suggestions for a possible m etap hy sics or o ntolo gy . W ere this the begin ning of anontology rather than a short t reat ise on rel igion and science, we would have

perforce to enlarge these suggested pr inciples into a coherent and adequate

ar t iculat ion of al l of experience. And, i f we were seeking to provide a ful lphi losophical theolog y, w e wou ld also have to just i fy such ontological pr inciples

not only in relation to the width of experience but even more in the l ight of theimplicat ions of relevant Chris t ian symbols about God and God's relat ions tonature, his tory, and human being.

There are, we suggest, f ive fun da m en tal ontologica l c haracterist ics of all thatthere is in our experience—all of finite actuali ty or, in theological language, all of

"created real i ty": (1) Tem poral i ty o r pass age — the ap peara nce of wh at is, the

vanishing of what is , and the fur ther appearance of what is new. (2) Thedefini teness or determinedness of actual i ty as the given; what is achieved in

process is def ini te , a new uni ty in and for i tsel f , and so effect ive beyond

i tself—and (as 1 makes clear) then i t vanishes. (3) The role of possibi l i ty, ofgenuine possibi l i t ies that have not been actual before, of novel ty—these are

somehow "there" as relevant possibi l i t ies , and then they become actual i t ies . One

cannot understand na ture as process , or hum an existence in his tory as co nt ingent ,open and " intent ional" without the category of possibi l i ty as paradoxical ly an

aspect of "rea li ty." (4) T he ro le of order as self-maintaining—that is , as an aspect

of the nature and behavior of actuali t ies in passage, a role that spans and sotranscends the dichotomies of past and present , of achieved actual i ty and

possibi l i ty, and of the vanishing present and the impinging future.



T H E G O D O F N A T U R E 21 7

(5) There is apparently self-determination in that actuality, a self-constitutionat each level of being fro m the spontane ity evident in inorg anic ex istence, throu ghself-direction in organic and social l i fe , to the self-choosing and autonomy of

human existence. On each level given conditions (destiny) inexorably set the termsand limits for spontaneity or, at higher levels, for freedom. W e never exper ienceany freedom greater than the capacity to choose those part icular possibil i t iesinherent in the given, m ore than the possibilities provid ed b y our "de stin ies" — w ecan, as S0ren Kierkegaard said, only "choose ourselves ." This ontologicalcharacteristic is known more vividly from the inside, in our "existential"experience and awareness of ourselves as subjects, in our experience of personalrelations, of choices, of inquiry and reflection, and of political and historicalactivities. There nature— for we are nature—is known from the inside, and on that

basis nature can be reinterpreted throughout its extent both in terms of self-awareness and in terms of the awareness of the other as person. For these samecategories of definiteness and spontaneity, of the given, and of open alternatives,of destiny and freedom , m ak e their appea rance an alogo usly and at different levelsall around us in nature. If "spirit" thus be the result of nature and hence anillustration of nature's creativity and mystery (as evolutionary science surelyimplies), then these analogical signs of spirit, in spontaneity and self-direction, maybe taken as "signs" of the ontological or metaphysical relevance of spirit as it is

known in personal awareness and in personal relations.These hints and traces of reality as characterized by spirit and meaning, aswell as by power and by causality, are universal throughout nature. They becomeclearer in personal and historical experience, w here th e level of m oral ultim acy — asreality and as demand— is ever presen t. Our pre sent q uestion , how eve r, is w hetherwhat we have said about nature has an y persu asive imp lications fo r the reality andthe nature of God : granted this is only the dim m est of glimp ses of the mys tery ofGod, what might that mystery begin to look like?

W hat, then, of God in our age? Are there groun ds in the preced ing for speech

about God or the search for God, for confirmed commitment to God? Be-yond—and also through—the abstractions of the scientif ic understanding ofnature, nature's reality has manifested itself as power, as spontaneity or life, asorder, and as implying a redemptive principle, a strange dialectic of sacrifice,purgation, redemption, and rebirth. In nature each of these appear in creaturelyguise, as vulnerable and ambiguous as well as creative, as non-being as well asbeing. Each, therefore, represents a trace of God, a limit question, to which, Ibelieve, God remains the sole reasonable answer. Each leads to an ontologicalprinciple or structure which appears to characterize all that is; let us look at themagain.

(1) The power of nature is the power of existence, the power to be. Yetexistence and its power are radically both contingent and temporal. Natureapparently has a beginning; i ts origin is , therefore, a puzzling and importantquestion. Even m ore imp ortant, existenc e com es, and then as quickly it goes; it isenergy-matter in process, through and through temporal. It is here in the present,and then it vanish es into the past and so into non-b eing . It is, and then as quicklyit is n o t Ho w then does the past, which imm ediately h as van ished, at th e sam e tim e

so thoroughly ground the existence and shape the character of the present, which



218 LANGDON GILKEY

i t surely does? How is i t that the conditioning, the causing, the effecting and

affect ing of the present by the vanishing past happen? How is i t that we canunderstand our common experiences of cont inui ty and cont inuing presence, of

causali ty and influence—of our being and ou r action f ro m the past into the fu tur e?Some deeper , more permanent power must be there , must cont inue f rom

moment to m om ent , if this " temporal p ow er," this power to be over t ime of f ini teexistence, know n to science, to all our co m m on exp erienc e, and in our inner sen se

of ourselves, is to be possible. For what is now present vanishes away, and yet i tseffects help to form the now on-coming present . What power is i t that does not

vanish but spans the gulf of past and present—if temporali ty be so real and sofundamental? 'God* is , therefore, f i rs t of al l the name for that omnipresent ,

ever -cont inuing and so eternal power, this necessary and hence non-cont ingentsource of cont ing ent , temp oral being . This uncondi t ional pow er has m any nam es

in different religions, different cultures, and different phi losophies; for example,

in "process thought" this is the function, not of God, but of Creativity. In all ofthem, reali ty as the temporal and radically passing, must also be Reality as

permanent if our experience is to be made intell igible; but the finite, vanishingreal i t ies around us (and in us) have no such capaci t ies . Therefore, as Thomas

Aquinas said, som e nec essary being is i tself necessary to explain this e xpe riencedcont ingency—"and this we cal l God." 'Cont inuing and necessary Power* is the

f i rs t name of God.(2) This power manifests itself originally as spontaneity and later as life. It is

determined, caused and "frozen" once i t appears and becomes def ini te; but i t i sundetermined, open, as i t now becomes what i t is to be. Certainly in chaotic

systems, nature exhibi ts " jumps" and unexpected turns; i t faces opt ions andalternatives that cannot be predicte d be fore ha nd . Wh ether this is a sign of ge nu ine

openness in the future is st i l l a debatable question, as the papers in this volume

suggest We, however, experience real openness from the inside as the inescapablepressure in our present on each of us to decide, to ch oo se am on g the optio ns fac ing

us in each impinging mo m ent coming to us from the future. In us this power, latentin nature's spontaneity and in i ts capacity for the new, becomes what we call

'freedom": reflection, deliberation, and decision among real alternatives. Processbecomes out of the past; but in the present it constitutes itself out of possibilities

before it in its futu re, bringin g togeth er in the presen t actuali ty alternatives wh ichonce were only possibili t ies. Ev ents around us, events as ob jects, al l app ear, wh en

we look at them, to be determined, caused—even i f , as in chaot ic systems, inunpredictable ways. They are now, of course, but when we look at them they are

already in the past . Events happening inside us on the other hand, events as

subjects and so in our present, are open; nature in us facing i ts future is open andnot determined. Even science as a creative human project requires in the subject

doing science deliberation and decision, reflection and assen t, as in ana log ou s w ay sdo all hum an and hence all cultural and historical ex perien ce. T hus , for science as

a hum an en terprise the future is open, even if i t seems "closed" for the inquiries ofscience. Henc e it is that in both nature and history genuine novelty is possible, the

new appears and becomes actual . Novel ty and openness l ie in the spontaneouspower of the present to determine i tself , to be self-creative, to be a relative,

dependent, yet creative source of what is original and unique.



T H E G O D O F N A T U R E 219

N ow neither the achieved past n or a set future can account for this spontane-ous power to become, the power of each present to c onstitute itself— lest we returnagain to determinism and lose novelty. Science is always tempted to speak only of

determinism—as it looks carefully at its objects of investigation (which, as wenoted, lie in the immediate past). But science as a human project, as the creativework of human subjects, is laced with openness, with deliberation and withcentered actions, with self-constituting freedom, directed at the future and itsprojects for the future .

'God' , therefore, is the name for this continuing ground of freedom, ofspontaneity in nature, and of self-constitution in humans and so in history. We donot create our freedom through our freedom, our power to choose ourselves andshape our future; such power of self-constitution is given to us as an essential

aspect of ourselves, of being selves at all—and we cannot, try as we may, avoid it.This human experience of dependence in our very freedom represents a deeplyreligious expe rience of the sacred gift of freedom. It is, incidentally, essential forall else theology says about our spiritual dependence on God (the grounding of ourfreedom in God) and our estrangement when our freedom seeks to ground itselfin itself alone. We are as dependent on God in our spirit as we are in our existenceor our life; hence God is the source of our freedom as an essential aspect of ourbeing. This divine grounding of freedom is analogously disclosed in all the

evidences of spontaneity and the origination of the new in nature's life. Thisfreedom or self-constitution is, therefore, given to us from beyond ourselves , froma source beyond ourselves, beyond our world and our past, as is our existenceitself. This sou rce lies beyond both the world which our choices affect and beyondour freedom which does not create itself. Again, this source must include bothworld and freedom, both determined past and open future, as the creative groundof each and the principle of unity of both. As Fried rich Sch leierm ache r argu ed, thisis another sign or pointer to God, now as the continuing ground of our freedom.

(3) This spontaneity or freedom—this openness leading to novelty—yet

remains mysteriously within an order, an order that pervades and unites theobjective cosmos, our inner deliberating consciousness, and external history. Thepresence of real novelty within a dependable and calculable order, and ofintelligible order characterizing the unexpected yet pervasive appearance ofnovelty, are genuine "w on ders ," even m iracles. Perhaps the most intriguing tracesof the divine l ie here. How random spontaneity and genuine freedom can unitewith continuing order is a puzzle baffling alike to scientific inquiry and philoso phi-cal reflection as it is to observ ers of history. 'G o d ' is , therefo re, the na m e for thatunlimited reality spanning the entire ordered past and the entire open future,

uniting into an ongoing order achieved actuality on the one hand with the openpossibilities of the novel future on the other, uniting destiny from the past withfreed om in and for the future.

God is thus the unconditioned power to be—yet present in each of the tiniestparticles of existence, the Infinite Power of Being in all that is . God is thetranscendent ground of freedom; the source of all that we know of freedom inourselves and others—and of the analogous levels of spirit in nature around us,creative in each quantum jump as in each human decision. God is the eternal

source of order amid novelty, uniting the determined past with the possibilities



220 L A N G D O N G I L K E Y

latent in the open future—and thus God is as essential for the unity and develop-ment of nature as for its being.

Without this transcendent yet imm anent principle active in all events we fac ethe very nest of contradictions we have outiined: a world outside of us bothdetermined at some levels and open at others, impossibly coupled with the creative

mind and shaping, self-constituting spirit of those who inquire into and manipulatethat determined/open wo rld. Ne ither one — the determ ined/op en w orld of materialcausality nor the ungrounded minds also implied by scientific inquiry—is true toour experience. Such an unreflected view, in which stark opposites are posed inuncoordinated juxtaposit ion, represents on both s ides the most extreme sort ofabstraction and thus an incoherent and perilous dualism. On the grounds, then, ofthe coherence of central ideas and adequacy to experience, theism seems morereasonable, philosophically, than its far more popular alternatives.

God is only dimly known here, barely perceived and s tumblingly

described—as is the wonder and mystery of nature through which God is thusdimly kno wn . As w e have seen , natu re is an im age of God, a creaturely reality ofimmense creative power, order, and value, an image of the sacred, and hence afinite reality or value for itself. Nature is also the instrument through which Godcreated us and now sustains us. Nature is for itself and for us the medium throughwhich God's power, l i fe , and order are communicated to us .

To the religious consciousness, however, there is more of nature, more of us,and especially more of God. God is more deeply, clearly, and truly known, as isappropriate, in our personal and communal existence, and there we also are more

deeply and clearly kno w n. Th ere G od is to be know n as the creative pow er of ourown exis tence in t ime, the ground of our being; the source of the freedom thatmakes us ourselves, the ground, therefore, of the responsibility that makes uspersons; and hence God is disclosed as the ordering or moral principle of ourtemporal and yet free existence. Finally, central to all we know of God isredemptive love bringing us back to unity again. Here lies the center of ourChristian message: in conscience, in law and promise, in prophetic judgment, inincarnation, teachings, atonement, and resurrection. But it is the same God who

can, by eyes that search there, be seen dimly but pervasively in the wonders ofnature. To know God truly is to also know God's presence in the power, the life,the order, and the redemptive unity of nature. Correspondingly, to know naturetruly is to know its m ystery , its depth, and its ultimate value— it is to know natu reas an ima ge of the sacred, a visible sign of an invisible grace .



IV

ALTERNATIVE APPROACHES

TO DIVINE ACTION



G A P S F O R G O D ? 23 3

Willem B. Drees

Chaotic and complex processes are as much a part of natural real i ty asl inear and s imple processes . Theories of chaotic and complex systems havemade c lear , even more than before , tha t a na tura l is t ic explanat ion may beavailable even in the absence of predictabil i ty. In this sense, they result in ashi f t in our unders tanding of 'unders tanding. ' Theories of complex sys temshave, by the explanations they offer and the shift in the concep t of ex planation,

c losed gaps in our unders tanding of na ture . Thereby they have enhanced thestrength of a natural is t ic view of reali ty.

The firs t section wil l develop this in a discussion of John Polkinghorne 'sunderstanding of the unpredictabil i ty of natural processes as a locus for divineaction in the world. The second section wil l give a more general discussion of'explanat ion ' as unders tood in contemporary phi losophy of sc ience . One mightdiscern two conceptions of explanation in contemporary philosophy of science.Ontic views of explanation consider an event explained if i t is understood as a

poss ib le consequence of a causa l mechanism. Epis temic v iews of explanat ioncons ider phenomena and laws expla ined i f they are seen as par t of a widerframework. Chaot ic processes can be cons idered expla ined, or expla inable ,wi th in each of these concept ions of explanat ion. Thus , th is more genera largument supports the conclus ion tha t a ques t for gaps in chaot ic or complexprocesses is misguided.

Denying such gaps within natural processes does not foreclose al l optionsfor a re l ig ious v iew of rea l i ty , as the f ramework does not expla in theframework i tself (upon an epis temic view of explanation) and the mechanisms

do not expla in the mechanisms (upon an ont ic v iew of explanat ion) . Thus ,ques t ions about th e who le and about th e most fu ndam enta l s t ruc tures of real ityare not excluded. One way of developing such an argument of a more generalna t u re , focus ing on the w or l d a s a wh ole , is A r th ur Peacocke 's m ode l fo rpar t icular d iv ine ac t ion via " top-down causa t ion." Some weaknesses in th ispos i t ion wi l l be pointed out in the th i rd sec t ion. Hence , ra ther than seek tounders tand God 's ac t ion in the world , we might a t tem pt to envisage the w or ldas God's act ion. Limit questions about reali ty are persis tent . Discussions about

re l ig ion in re la t ion to the whole of rea l i ty (cosmology) and to the mostfundamental structures of reality (e.g. , quantum physics), as well as discussionsabout the na ture of sc ient i f ic and re l ig ious knowledge (which, in d i f ferentways , seek to acquire a v iew of the world f rom a point wi th in the world) , a remuch more credible than a quest for gaps in the chaotic and complex. Even ifcomplex phenomena wi th in rea l i ty a re unders tood na tu ra l i s t i ca l ly , the wor ldas such is not thereby expla ined. Hence , there remains room for a sense ofw o n d er a nd gra t i tude . Th e w orl d ma y s ti ll be seen as depe nden t up on som esource which t ranscends the wor ld .



2 2 4 W I L L E M D R E E S

Before embarking on the cr i t ica l d iscuss ion of the proposa ls byPolkinghorne (section 1) and Peacocke (section 3), I wish to say that I focus onthese authors because I think their approaches are good examples of their kind

and deserve a s ignificant role in subs equ ent discussions. I wil l em phasize tho seaspects where I perceive problems rather than the many aspects which I admireand apprec ia te .

A second pre l iminary remark: I wi l l not d is t inguish in de ta i l be tweenchaotic processes and processes of self-organization, though in the firs t andsecond sections th e focus wil l be on l im ited predicta bil i ty (wh ich som e take asa s ign of openness), whereas in the third section the focus wil l be on theappearance of order (which some take as a s ign of a "self ," or even of" in tent ional i ty" ) .

A th i rd , more fundamenta l pre l iminary remark: Arguments a re shaped byassumptions and by the audience one has in mind. This essay is pr imari lywrit ten with an audience of people l ike myself in mind: those who take scienceser ious ly and who hold tha t there i s power ( for be t te r and for worse) inre l ig ious t radi t ions and symbols , but who are not eas i ly persuaded bytradit ional doctrine. On my view, intel lectual investigation in our t ime has totake the sciences very seriously, and thus has to favor them over other al legedsources o f knowledge , whe the r a s t ro logy , common sense fo lk wisdom, o r

re l ig ious t radi t ions , inc luding the Chris t ian t radi t ion . Otherwise , suchinvestigation runs the risk of demanding " less than i t could of theologians andmore than i t should of sc ient is ts . " 1 Th e burden i s on theo logy ra the r than onscience. As Peacocke has put i t , the retreat to conservative positrons is "a s ignnot so much of a recovery of faith as of a loss of nerve before the onslaught ofnew percept ions of the world ." 2 W ith G erd Theissen, I am convinced tha t on lyby deeply immers ing ourse lves in sc ience , ra ther than s topping shor t of theinne r m os t s anc tua rie s, the t rad i t ion m ay show up in a new l igh t .3

!L.B. Eaves , "Adequacy or Orthodoxy? Choosing Sides at the Frontier," Zygon 26

(1991): 496. Thus I deviate from Will iam Stoeger (see his art ic le , "Describing God's

Act ion in the World in the Light of Sc ient i f ic Knowledge of Real i ty" [ in th is volume,

p . 241] ) . At the conference he took the pos i t ion that we should s tart from

presuppos i t ions which favor ne i ther the sc iences nor re l ig ion . This seems to me toassume m or e equ al i ty and neutral i ty than is warranted. Un l ik e Stoeger , I do no t

consider as neutral presupposit ions th e existence of an act ive Go d and the reliabil ity of

knowledge provided by the sources of rel igious knowledge, such as scripture, tradit ion,

and experience. In giving primacy to the sciences in intel lectual matters , I also deviate

f rom contr ibut ions which employ h igh ly theo log ica l language .

2 Arthur R. Peacocke , Theology or a Scientific Age: Beng and Becoming—Naturaland Divine (Oxford: Basil Blackwell , 1990) , ix.

3 G e r d T h e i s s e n , Biblical Faith: An Evolutionary Approach (London: SCM Press ,

1984), xi.



G A P S F O R G O D ? 2 2 5

1 Polkinghorne's Defense of Divine Action in the Openn ess of Processes

Theories regarding chaotic behavior introduce an openness into our descriptionof the na tura l w orld w hich has been miss ing f r om c lass ical N ew to ni an phys icsso far . This openness would be a k ind of " loca l cont ingency" 4 w h i c h mi g h ta l low for human or d iv ine free will and human or divine agency. This view hasbeen e loquent ly defended by Angl ican pr ies t and theore t ica l phys ic is t JohnP o l k i n g h o r n e .

In a bot tom-up descr ip t ion of the phys ica l world , the onse t of f lexibleopenness i s s ignaled by the myriad poss ib i l i t ies of fu ture development whichpresent themselves to a complex dynamical sys tem. In a quas i -de terminis t icacc ou nt t he y ar ise f r o m the grea t ly d i f fer ing t ra jec tor ies wh ich w ou ld resultf r om init ia l condi t ions differing only infini tes imally from one another. Becauseof the i r undiff eren t iable pr ox im ity of c i rcumstance , there is no energet icdiscrimination between these possibil i t ies . The "choice" of the path actuallyfol lowed corresponds not to the resul t of some phys ica l ly causa l ac t ( in thesense of an energy input) but rather to a "selection" from options (in the senseof an in fo rma t ion inpu t ) .

I t i s by no means c lear tha t informat ion input of the k ind descr ibed

originates solely from animals , humankind, and whatever s imilar agentsthere might be. I do not believe that God is con ta ined wi th in the mind /m atte r confines of the wo rld, b ut i t is entirely conceivable that he m ightinteract with i t (both in relat ion to humanity and in relat ion to al l otheropen process) in the form of informat ion input . . . . God is not p ic turedas an in terfer ing agent among other agencies . (That would correspondto energy input . ) Ins tead, form is g iven to the poss ib i l i ty tha t heinf luences h is c rea t ion in a non-energ et ic w ay . 5

The laws of nature al low for gaps where one might envisage divine and/or

hu m an ac t ion. Centra l to th is a rgum ent is the poss ib il ity of info rm at ion inp utwi thou t ene rgy inpu t , thus wi thou t in te r fe r ing wi th phys ica l l aws rega rd ingenergy .

I question this l ine of argument for several reasons, especial ly insofar asit appeals to chaos theories and the like. Even if there is no difference in energybetween two states , energy might s t i l l be needed to change the system from onedef in i te s ta te to another . This energy is taken f rom the background (wi th i t s

4 See Ro bert Joh n Russe l l, "Cont ingency in Phys ics and Co sm olo gy : A Crit ique of

the Theo logy o f Wol fhar t Pannenberg ," Zygon 23, no. 1 (March 1988) 23-43, for a

def in i t ion of " local cont ingency."5 J o h n C . P o l k i n g h o r n e , Reason and Reality: TheReationship between Science and

Theology (London: SPCK Press , 1991) , 45. See also dem, "The Laws of Nature and the

Laws of Physics" in Quantum Cosmology and the Laws of Nature: Scientific Perspectiveson Divine Action, ed. Robert John Russe l l , Nancey Murphy, and C.J . I sham (Vat ican

City State: Vatican Observatory, 1993; and Berkeley, CA: Center for Theology and the

Natural Sciences , 1993) , 437-48.




non -zero temperature act ing as a source of energy f luctuat ions) , but i t i s not a

choice made by the sys tem i t se l f . Se l f -organiza t ion should perhaps be more

proper ly named "hetero-organiza t ion ," organiza t ion t r iggered by the immedia te

en v i ro nm en t . I n a sense Po lk in gh orn e g ran t s t h i s w he n he speaks abo u tin fo rma t ion inpu t , which sounds l i ke ex t e rna l de t e rmina t ion r a the r t han se l f -

o rgan iza t i on , t hough he a l so uses t he a rgument t o a rgue fo r human se l f -

d e t e r m i n a t i o n .

Po lk in gh or ne ' s a rg um ent i s based upo n the poss ib i l it y t ha t t he re is a

s ignif icant d i f ference in out pu t , even thou gh there is no energy difference in the

input . Take , for ins tance , two di f ferent menta l ac t s cor responding to a choice

be tween tw o o p t ions . W e exper ience t hem as d i f fe r en t i n i n fo rm a t ion con ten t ,

n o t {qua menta l ac t s ) as phys ica l ly d i f ferent in energy or l abor involved.

However , t ha t may we l l be an i l l us ion , due t o t he enormous ampl i f i ca to ry

powers of the cent ra l nervous sys tem. 6 The or ies on chaos and se l f -organiza t ion

show jus t th i s , tha t ampl i f ica tory powers of phys ica l sys tems wi th respect to

small init ial differences are much more impress ive than was previous ly thought .

One should avoid confusing zero and close to zero in this context ; i t i s essent ial

to Polk ing ho rne ' s po s i t ion tha t the energy inpu t is absolute ly zero ra th er th an

almost inf ini tesimal ly close to zero, as in the case of low energy events act ing

as swi tches modula t ing processes which expend la rger , observable amounts of

e n e r g y .In Science and Providence Po lkin gh orn e takes the example of a bead a t th e

top of an inver ted U-shaped wire . In th i s case , he argues , there would be no

energy ba r r i e r be tween the op t ions o f moving the bead to t he l e f t o r t o t he

r igh t ; God cou ld ac t w i thou t i npu t o f ene rgy . 7 An objec t ion to th i s c la im i s

tha t i f God were t o ac t w i thou t i npu t o f ene rgy , God ' s ac t i on would have t o

be inf in i te ly s low. Technica l ly speaking, a bas ic ru le of quantum mechanics i s

AE-At [ / 2 ( jus t l i ke t he be t t e r kn o w n un ce r t a in ty r e l a ti on fo r pos i t i on an d

m o m en tu m ) . H en ce , if t he ene rgy is t o becom e ze ro , t he t ime wi l l have t o

extend to in f in i ty . H ow ev er , inf in i te ly s low ac t ion i s ru led o ut , as th e dec is iveinpu t o f i n fo rma t ion shou ld t ake p l ace be fo re ene rge t i c d i s tu rbances have

changed the s i t ua t i on . 8

The re la t ion be tween providing informat ion and spending energy can a l so

be a rgued m ore pos i ti ve ly . In fo rm a t ion wh ich is embo died phys i ca l ly t h r ou gh

two (or more) dis t inct s tates , represent ing 0 and 1, requires a minimal energy-

6

D a n i e l C . D e n n e t t , Elbow Room: The Varieties of Free Wll Worth Wanting(Cambridge, MA: MIT Press , 1984) , 77-78.

7 P o l k i n g h o r n e , Science and Providence: God's nteraction with the World (Boston:

Shambhala, 1989) , 32.8 George F.R. Ell is suggests in his essay "Ordinary and Extraordinary Divine

Action: The Nexus of Intervention," ( in this volume, p. 377) that intervention without

energy can take place by controll ing the t iming of quantum events , say the decay of an

exc i ted atom. Th is seems to v io late the same Heisenberg uncertainty re lation b etw een

energy and t im e at the other end: control l ing the t iming prec ise ly would imply a major

indeterminacy in energy.



G A P S F O R G O D ? 2 2 7

difference to write or read. This is a consequence of the second law oft h e rmo d y n a mi c s . T h e r e l e v a n t i n e q u a l i t y 9 is Al A E /k B T ln2, which isequiva lent to AE [_ A l e k B T ln2.

There seems to be no basis in physics for the claim that there is t ransfero f in fo rma t ion wi thou t t rans fe r o f ene rgy . Invok ing quan tum phys ic s toprov ide th e miss ing premise is problematic . Working with a mixture of classicaland quantum phys ics , ec lec t ica l ly invoking the one which f i t s bes t a t anyspecific s tage of the argument, may be acceptable in a pragmatic context;however , i t i s methodologica l ly unsa t is fac tor i ly once one a ims a t morefun dam enta l , me taphys ica l c laims . O nce one unders tands the wo r ld a s aquan tum wor ld th roughout , one has to dea l wi th the ques t ion whe the r the reis a s imi lar d ivergence of t ra jec tor ies in the quantum world as there i s in the

classical world of chaos. I am not capable of judging that issue but, as far as Iam aware of the technical l i terature on "quantum chaos," the question has beenanswered in the negat ive .

Po lk inghorne i s cau t ious abou t quan tum chaos . He o f fe rs ano the ra rgu m ent fo r on to log ica l openness :

[ I ] f apparent ly open behavior i s associa ted wi th under ly ing apparent lydeterminis t ic equations, which is to be taken to have greater ontologicalser iousness—the behavior or the equat ions? 1 0

This p re fe rence fo r the phenomena (unpred ic tab i l i ty ) ra the r than thecur ren t exp lana t ion (determinis t ic chaos) is problematic, at least givenPolkinghorne 's defense of cri t ical real ism. Defenses of cri t ical real ism arguefrom explanatory power to ontology, tha t i s , to the rea l i ty of the theore t ica lent i t ies pos tula ted in the explanat ion. In th is sense , "epis temology modelson to lo gy , " a s Po lk in gh orn e a f f i rms and whic h h e in te rp re ts as " acqu iredknowledge is a guide to the way th ings are . " 1 1 The disagreement is as to whatcons t i tu tes the "epis temology," or the "acquired knowledge ," which theconvic t ions about the under ly ing ent i t ies and processes have to fo l low.

Polkinghorne seems to assume that the "epis temology" which is to be followedis the l imited predictabil i ty (which he sees as an indication of ontologicalopenness) . However , the epis temology is much r icher than the observat ion ofl imi ted predic tabi l i ty . The epis temology inc ludes the theory which expla instha t unpredic tabi l i ty and the processes by means of non-l inear , de terminis t icequat ions . In tha t sense , a comparison wi th the analys is of quantumuncer ta in ty is mis taken, as there the theory a l lows , a t leas t on some majorin te rp re ta t ions , the conc lus ion o f "genu ine inde te rminacy . " 1 2 P o l k i n g h o r n e

prefers to in terpre t un predic tabi l i ty as a sign of ontological openness, bypassing

9 L e o n B r i l l o u i n , Science and Information Theory, 2d . ed . (New York: Academy

Press , 1962) , 681; see also John D. Barrow and Frank J. Tipler, The AnthropicCosmological Principle (Oxford: Clarendon Press , 1986) , 661.

1 0 P o l k i n g h o r n e , Reason and Reality, 41.1 Po lk i ng ho rn e , "Laws o f Nature ," 440 .

1 2

P o l k i n g h o r n e , Reason and Reality, 42; and dem,"Laws of Nature," 440.




the (de terminis t ic ) explanatory theory avai lable . St icking to the phenomenaand discarding the available explanation is not a critical realist strategy, but anempir ic is t one .

The move from a de terminis t ic theory to ontologica l openness i s a lsoproblemat ic in re la t ion to the sc ience a t hand: there i s no new pr inc ipleinvolved in chaotic systems. There are, of course, new discoveries of order inand through chaos . And the i te ra t ion charac ter is t ic of se l f -organiz ingsystems—that the outcome of one s tage, say a l iving organism, is i tself thestart ing point of the next s tage—enriches our understanding of the his torici tyo f n a t u re . 1 3 Stil l , the scientif ic s tudy of self-organizing, complex, and chaoticsystems has no t revealed new gaps to be fi lled by som e external actor. A lth ou ghcomplex sys tems exhibi t behavior as i f they were guided by an externa lorganizing principle or an intentional self, the theories show that such behavioris expla inable wi thout invoking any such ac tor—whether a self, a life forc e, ora d iv ine In fo rm a to r . As such , chaos the ory is the ex tens ion o f the bo t tom -upprogram to complex systems rather than a suggestion of the exis tence of some"top" f rom which " in tent ional causa t ion" as " informat ion" proceedsd o w n w a r d s .

Polkinghorne acknowledges tha t the use of openness as the causa l jo in tbe tween God and the world seems l ike a "God-of- the-gaps" s t ra tegy, even

t h o u g h G o d is not competing as "an al ternative source of energetic causation."However , Polkinghorne argues tha t there i s a fundamenta l d i f ference be tweenthese gaps and earlier gaps, which "were epistemic, and thus extrinsic to nature,mere pa tches of current sc ient i f ic ignorance ." 1 4 I do agree that there is afu n d a me n t a l difference, but i t works in the other direction. Whereas in the caseof epis temic gaps ref lec t ing ignorance one might mainta in an agnos t ic s tancewith respect to the possibil i ty of a regular scientif ic explanation, with theadvent of chaos theor ies th ere i s no reason for such an open a t t i tude . Th ou ghthere is unpredic tabi l i ty , there i s a lso an under ly ing theory . To c la im gaps is

not mere ly to remain agnos t ic where we do not know, but to go agains t whatis current ly taken as knowledge—the unpredic tabi l i ty of sys tems which aredescribed by determinis t ic equations. At this level , we are not confronted withany indications of "gaps" in the processes , unl ike the s i tua t ion a t the quantumlevel and at the cosmological level.

Th e new ly wo n sc ient if ic insights regarding com plex i ty change o ur v iewof the world . Unpredic tabi l i ty i s , of course , very re levant beyond the s t r ic t lyscientif ic context , especial ly in the context of ethics . To what extent are we

responsible if we have only a l imited view of the consequences of our actions?For instance, l imited predictabil i ty and the instabil i ty of systems is very

1 3 Se e Bernd-Olaf Kuppers , "Unders tanding Co mp lexity" ( in th is volum e); and

idem "On a Fundamental Paradigm Shift in the Natural Sciences ," in Sef organization:Portrait of a Scientific Revolution, ed . W olfga ng Kroh n, Gu nter Kuppes , and He lga

N o w o tn y (Boston: Kluw er , 1990), 51 -63 .

1 4

Polkinghorne , "Laws of Nature ," 446.



G A P S F O R G O D ? 2 2 9

relevant in assessing the risks of a Jurassic Park. But i t does not offer orun de rg ird a specific view of divine action in individual eve nts or of a causaljo in t be tween God and the wor ld . Unpred ic tab i l i ty i s me taphys ica l ly

uninteres t ing, a t mos t a necessary but insuff ic ient condi t ion for metaphys ica lopenness . Peacocked a l te rna tive in tends to avoid the in terv ent ion is t^ approachof seeking gaps as specific causal joints . H e envisages G od 's interaction w ith thew o r l d as a whole. It is to such ideas that we will turn below. But before tu rn ingto al ternatives , I would l ike to consider briefly the concept of scientif icexplanation in relat ion to arguments about gaps, as i t a l lows for an addit ionalargument agains t the a t tempt cons idered here to f ind gaps for d iv ine ac t ionwithin unpredictable and "self-organizing" processes .

2 Explanations and Gap s

If there is in reali ty an openness which al lows for divine action (see Polking-horne ' s pos i t ion in the preceding sec t ion) , there should be e lements in theprocesses w hic h are not expla ined suff ic ient ly o therw ise . Th us , i t seems

re levant to spend some t ime on the not ion of explanation as i t fu nc t ion s in thecontext of the sciences.

Explanation is one of several notoriously difficult concep ts . 1 5 The "classic"view is the covering-law model of explanat ion, which expla ins an event on thebas is of on e or m ore genera l laws and one or m or e co nd i t io ns .1 6 On this v iew,an explanat ion is similar in s tructure to a predict ion from init ia l condit ions anda law. The covering-law model is of limited value, as the notion of laws is moreadequate to the physical sciences than to the other natural sciences. Besides, theconnect ion be tween explanat ion and causa t ion is absent in many cases . For

instance, the height of a flagpole is calculated o n th e basis of th e law s of op tics,the posit ion of the Sun and the length of the shadow—but i t is not caused bythese .

Given the p rob lems wi th the cover ing- law mode l , con tempora ryph i los op he rs have offere d oth er v iews of explanat ion. T he y seek to g iveaccounts of explanat ion which incorpora te not only predic t ive power but a lsosome other fea tures which make for successful explanat ions and jus t i fy themo v e f ro m e x p l a n a t o ry p o w e r t o a p p ro x i ma t e t r u t h . T h e re s e e m t o b e t w o

1 5 See Philip Gasper, "Causation and Explanation," in ThePhilosophy of Science ed.

Richard Boyd , Phil ip Gasper, and J.D . Tro ut (Cam bridge, M A : M IT Press , 1991) , 289-

98; and Phil ip Kitcher and Wesley C. Salmon, eds ., Scientific Explanation (Minneapol is ,

MN: Univers i ty of Minnesota Press , 1989) , of which one essay has been republ ished

indep ende nt ly as Sa lmon , Four Decades of Scientific Explanation (Minneapol i s , MN:

Univers i ty of Minnesota Press , 1989) .

1 6 C. Hempel and P. Oppenheim, "Studies in the Logic of Explanation," Philosophy

of Science 15 (1948): 135-75.




kinds of concept ions of explanat ion, an epis temic one and an ont ic one . Forins tance , Phi l ip Ki tcher s t resses unifying power 1 7 whi le R icha rd Boydemphasizes a realis t view of causes .1 8 Kitcher ' s epis temic approach se ts the

phenomena in a wide r theore t i ca l f ramework . Boyd seeks an on t ic approach ,a quest for the causes or mechanisms involved. Such ontic and epis temicapproaches "are not mutual ly exclus ive , but , ra ther , complementary ." 1 9

With the d is t inc t ion be tween epis temic and ont ic v iews of explanat ion,we can now re turn to our re f lec t ions on chaot ic processes . These processesexis ted , of course , before they were labe led as such. However , wi th thediscovery by E. Lorenz of a simple set of three equations which showed errat icbehavior in 1963, we enter the era of chaos theory . This theory dea ls wi thdeterminis t ic equat ions governing processes which are ext remely sens i t ive tom i n u t e differences in ini t ia l condit ions, and which therefore al low only l imitedpred ic tab i l i ty .

O n an epistem ic view of explan ation , chaotic processes are explained sincethey f i t in to a wider theore t ica l f ramework, par ts of which have been aroundfor centuries (e .g. , differential equations), other elements of which weredeveloped more or less a round the same t ime as chaot ic processes wererecognized (e .g . , f rac ta ls ) . Chaos theory has not d iminished the uni ty ofexplanatory accounts , but ra ther has increased i t as more phenomena are now

trea ted wi th in the f ramework o f ma themat ica l phys ic s .An ont ic v iew of explanat ion is not so much or iented to the s t ruc ture of

ou r know ledge as to the avai labil i ty of a m echanism w hich w ou ld expla in th ephenomena under cons idera t ion. With respect to chaot ic processes of l imi tedpredictability, such a causal account is readily available. Even though we couldnot have predicted a specific storm two weeks in advance, s ince we were unableto observe in sufficient detai l a l l the condit ions at that moment (e .g. , theb u t t e r f l y effect), w e have no p ro bl em envisaging a possible causal m echa nismwhich resul ted in tha t s torm. We cannot predic t the numbers tha t wi l l come

up when we throw a pair of dice. We are unable to predict which way the beadwill fall along an inverse U-shaped wire. But in either case, we can envisagehow i t may have come about the way i t ac tua l ly came about (e .g . , due tominute influences from the air , the surface, e tc . ) . Predictabil i ty is not anecessary condi t ion for expla inabi l i ty .

1 7

Kitcher , "Explanatory Unif icat ion ," Philosophy of Science 48 (1981): 507-31;reprinted in ThePhilosophy of Science ed. Boyd, et al.

1 8 Boyd, "Observat ions , Explanatory Power , and Simpl ic i ty: Toward a Non-

H u m e a n A c c o u n t , " i n Observation, Experiment, and Hypothesis in Modern PhysicalScience ed. Peter Achinstein and Owen Hannaway (Cambridge, MA.: MIT Press , 1985);

reprinted in Philosophy of Science ed. Boy d, et al . For other views of explan ation besides

the ep istem ic and o ntic v iew s considered h ere see Bas C. van Fraassen's "pragmatic view"

(The Scientific Image [Oxford: Clarendon Press , 1980] , 97-157); and Salmon's "modal"

concept ion o f exp lanat ion {Four Decades).1 9

S a l m o n , Four Decades x.



G A P S F O R G O D ? 2 3 1

We prefer deductive explanations, which tel l us that given the condit ionsand the laws (or the mechanism , or the f ram ew ork , or whatever unders tandingof explanation is involved), the event was certain to happen. However, we also

have s i tuations where we can say that given the condit ions and the laws, i t waslikely (say with 0.95 probabil i ty) or less l ikely (say with 0.3 probabil i ty) tohappen. If a theory predicts that an event might happen, say with a probab i l i tyof 0.3, and i t happens, would one say that the theory has explained the event?It certainly explains the possibil i ty of the event, even though i t does notexplain i ts occurrence on this occasion. This is the s i tuation which we face, fordiff ere nt reasons, in th e case of cha otic processes such as the weather, and in thecontext of quantum theor ies . For the moment , I wi l l res t r ic t the d iscuss ion tochaot ic processes . There the problem is not so much due to an in t r ins ic

openness in reali ty as described by the laws (as might be the case in quantumphys ics ) but to our l imi ted knowledge of the ac tua l s i tua t ion.

W it h respect to a proba bi l i s t ic explan at ion necessi ta ted by suchinsuf f ic ien t know ledge o f the cond i t ions I ag ree w i th the fo l low ing su m m aryof an a rgum ent by R icha rd Je f f rey :

[W]hen a s tochastic mechanism—e.g. , the tossing of coins or geneticde term ina t ion of inher i ted charac teris tics— produces a var ie ty ofoutcom es , some m ore prob able and others less probable , we unde rs tand

those with small probabil i t ies exactly as well as we do those that areh igh ly p robab le . Our unders tand ing re su l t s f rom an unders tand ing o ftha t mechanism and the fac t tha t i t i s s tochas t ic . 2 0

Jef fre y ' s po s i t ion is expressed w i th in th e context of an on t ic v iew ofexp lana t ion . On th i s v iew, we may we l l have unpred ic tab i l i ty wi thou tinexp l icab i l i ty , and wi thou t an oppor tun i ty to pos tu la te openness in theprocesses involved.

There is a wide range be tween the expla ined and an inexpl icable eventwhich would be l inked with a genuine "gap" in nature, or in our understanding

of na ture . In be tween are phenomena which could be expla inable but a recurrent ly inexpl icable as we do not have the correc t theory ye t—such was thes i tua t ion wi th the d iscovery of "high tempera ture" superconduct iv i ty ince ramic ma te r ia l s . Even wi thou t an exp lana t ion we as sume the phenomenonto be expla inable in te rms of phys ics , probably known phys ics , but o therwisewi th a m odi f i ca t ion o f k n ow n phys ics . Th ere ma y al so be ph eno m ena wh ichare explainable but wil l never be predictable—as is the case with chaoticprocesses . As the events wil l never be fully predictable, one can never exclude

part icular divine action hidden in the unpredictabil i ty. However, as I see i t , i fthere is no indication of or need for such an assumption of openness and divineac t ion, the assumption is not jus t i f ied . Quantum uncer ta in ty , such as in thedecay of a nucleus, may be of a different kind. Here we have good grounds to

2 0 S a l m o n , Four Decades 62, referring to R.C. Jeffrey, "Statistical Explanation vs.

Statistical Inference," in Essays in Honor of Carl G. Hempe, ed . N ich ola s Rescher

pordrecht : Re ide l , 1970) .




exclude an ordinary cause or "hidden variable," and thus an explanation of thelimited predictabil i ty as a consequences of an unobserved but real physicalp rocess . However , even wi th quan tum phys ic s we need to be cau t ious , a s

quantum phys ics wi l l be modif ied or replaced, and is open to var iousin te rp re ta t ions .

So far, we have not made an explici t dis t inction between explanations ofpart icular facts or events and the explanation of laws. However, this dis t inctionis re levant in th is context . Most accounts of explanat ion, inc luding thet radi t ional cover ing- law model , a re pr imari ly concerned wi th the explanat ionof fac ts , assuming a f ramework ( laws , mechanisms, or the l ike) . To someextent , the f ramework assumed can be cons idered as a fac t to be expla ined ina wider f ramework—as Ohm's law for e lec t r ica l currents can be expla ined inthe context of a m or e general the or y of e lect romagnet ism in com binat ion w i thsome solid s tate physics . There are sequences of explanations. Chemists referto as t rophys ic is ts for the explanat ion of the exis tence of e lements and toqu an tum phys ic ists fo r the explanation of the bonds be tween a toms. S om ehow ,these sequences converge: various questions about the s tructure of reali ty arepassed on unti l they end up on the desk of fundamental physicis ts (dealing withqu an tu m f ie ld th eo ry , supers t r ings , e tc .) and ques t ions abo ut the h is tor y ofreali ty end u p o n th e desk of the cosmo logis t . As an Am erican p resident is said

to have had writ ten on a s ign on his desk: "The buck s tops here." Thus, thephys ic i s t and the cosmolog is t may we l l s ay "Only God knows . " 2 1 T h i spart icular posit ion of physicis ts and cosmologis ts in the quest for explanationmay make i t c learer why they ge t drawn eas i ly in to phi losophica l andtheological disputes in a way foreign to geologists, biologists, or chemists. It isn o t th e claim th at i t is an effective, fr ui tfu l , or feasible heu ris t ic s trategy toexplain all ph en om en a f ro m "firs t principles"; calculat ions and deriva tions m aybe bey on d o ur capacit ies . T he arg um ent i s tha t ther e are l imi t q ues t ionsconc erning t he scientific enterprise. These limit questions sho w u p m ost clearly

in phys ics and cosmology, and—I would l ike to add to the example f romMisner and Weinberg—in phi losophy of sc ience , s ince on the desk of thephilosopher of science rest questions about the nature of the explanations anda rgum ents o f fe red , and the ro le o f hu m an sub jec ts the re in .2 2

2 1 T h e ima ge of hand ing ques t ions from one desk to another i s taken from C.W .

Misner , "Cosm ology and Theology," in Cosmology, History, and Theology, ed . Wolfgang

Yourgrau and Al len D. Breck (New York: Plenum, 1977) . See a lso Steven Weinberg,Dreams of a Final Theory (New York: Pantheon Books , 1992) , 242. I t may be that the

dis t inct ion between s tructural and his tor ical ques t ions breaks down in quantum

cosm ology , but that makes no d i f ference for the argument. O n qu antum cos m olo gy see

C.J. Isham, "Quantum Theories of the Creation of the Universe," in QuantumCosmology.

2 2 I onl y realized after com plet i ng this paper that this argument abou t co sm olo gy ,

physics , and philosophy of science is paralle l to the conclusion I reached in an earlier

contr ibut ion on t ime in cosmology, where I argued for two opt ions , a Platonic

cosm olo gica l on e and a cons truct iv is t one . See W il lem B. Drees , "A Case Agains t



G A P S F O R G O D ? 2 3 3

The pos i t ion tha t a l l phenomena can be expla ined in a f ramework whichwould be " incomplete" only with respect to questions about the basic s tructureand the whole , i s na tura l is t ic . I t i s wel l captured in a phrase f rom the

ph i loso phy o f Jo hn D ew ey: "Mou nta in peaks do no t f low uns upp or ted ; theydo not even res t upon the ear th . They are the ear th in one of i t s manifes to p e r a t i o n s . " 2 3 Such a na tura l is t ic v iew of rea l i ty f i ts wel l w i th co nte m po rar ysc ience and contemporary phi losophica l re f lec t ions on the concept ofexplanation. I t is a t odds with the quest for an openness for divine action incomplex or chaot ic processes . However , such a na tura l is t ic v iew does notexclude theological options at other levels . There s t i l l may be speculat ivetheologica l answers to ques t ions about the f ramework, the laws and in i t ia lcondi t ions , or whatever i s assumed.

Quantum phys ics i s one of the opt ions ; th is i s emphas ized by GeorgeEl l is , Nancey Murphy, and Thomas Tracy in th is volume. I do agree tha t th isis a more appropriate level for envisaging divine action than any process at ahigher leve l of rea l i ty . However , I am nonethe less skept ica l about the use ofq u an tu m phys ics to envisage divine ac t ion. O n e reason is tha t qu an tumindeterm inacy m ight be resolved e ither v ia a m odif ic a t ion of qua nt um phys icsor v ia a d i f ferent in terpre ta t ion. Another reason is tha t indeterminacy may bean opportuni ty for a metaphys ica l supplement to phys ica l causes , but , in my

opinion, i t does not require such a move. There is no need to adhere to ametaphys ica l pr inc iple of suff ic ient reason, even though the pr inc iple ofsuff ic ient reason is a good heur is t ic no t io n w i th in any na tura l is tic appr oach . Iwil l leave off with these brief remarks, as quantum physics wil l be the topic ofa fu ture conference . The next sec t ion wi l l cons ider an a t tempt to a r t icula te ano t io n of d iv ine ac t ion a t the leve l of the w or ld as a wh ole , draw ing on ou runders tanding of processes of se l f -organiza t ion in macroscopic sys tems.

3 Top-D own Causation as Divine Causation

An alternative to an interventionis t ic view of God's act ion within processes inthe w orld has been presented by A rth ur Peacocke in his Theology for a Scientific

Age. I t re l ies on the not ion of top-down causa t ion. I wi l l br ie f ly present theidea of top-down causa t ion and i t s appl ica t ion in the context of theology,be fore making some c r i t i ca l comments .

Tempora l C r i ti cal Rea l is m? Cons equences o f Qua ntum Co s m olog y for Theo logy ," in

Quantum Cosmology.2 3 J o h n D e w e y , Art as Experience (New York: Minton, Balch & Co. , 1934) ; a lso

quoted by H . F ink in Free Wll and Determinism: Papers rom an InterdisciplinaryResearch Conference, 1986, ed . Veg go M ortensen and Rob ert C. Sorensen (Aarhus,

Denmark: Aarhus Univers i ty Press , 1987) , 51 .




3.1 Some Examples of Top-Down Causation

Th ere are physical and chemical systems in w hich w e find coo rdinated behav ior

of billions of individual molecules. Chemical clocks and the Benard reaction areexamples of this . The system exhibits a global pattern as long as certaincondit ions at the spatial boundary are maintained. Individual molecules behaveaccording to th is g lobal pa t te rn , ra ther than in the manifold of poss ib le waysdescribed in the s tat is t ics of an ideal gas . As Peacocke formulates i t , afterdescr ib ing spa t ia l or tempora l ( rhythmic) pa t te rns :

In both these instances, the changes at the micro-level , that of thecons t i tuent u ni ts , a re wh at they are because of the i r in co rpo ra t io n in tothe system as a w ho le, w hic h is exert ing specific constraints on i ts units ,making them behave o the rwise than they would do in i so la t ion . 2 4

Bernd-Olaf Kuppers has on various occasions presented theories of self-organiz ing sys tems as theor ies regarding "boundary condi t ions ." 2 5 There a respatia l bo un da ry cond i t ions , such as the tw o plates w hic h se t the no n-equi l ibr ium which gives r i se to Benard convect ion. More re levant to ourunders tanding of rea li ty a re D N A molecules , wh ich shape the develop m ent ofeach organism and may be seen as a k ind of in i t ia l condi t ion . Boundarycondi t ions are , of course , a t radi t ional fea ture in phys ica l

desc r ip t ions—corresponding to the f reedom of the exper imente r to choose acertain experim ental set-up. H ow ev er, in the case of the D N A of organisms, w edo no t dea l wi th such a lmos t to ta l ly con t ingen t boundary cond i t ions . Theboundary condi t ions which are in i t ia l to one s tage are the outcome of thepreceding s tep, and so on. They are thus the product of a long iterated sequencetha t gave r ise to organisms wi th b iologica l complexi ty .

Th e re la t ion b e tween men ta l pheno m ena and bra ins is somet imes referredto as another example of top-down causa t ion. According to Peacocke , top-down causa t ion would p rov ide a midd le g round be tween an unaccep tab le

Cartes ian d ual ism of tw o ent i t ies and a phys ical is t reduct io nism of m enta ls tates to brain s tates . As far as I understand the discussion, the notion of top-do w n causa t ion is invok ed in an a t tem pt t o c lar i fy and i l lum inate the re la t ionbetween mind and bra in , ra ther than our unders tanding of the bra in and mindbeing invoked in order to explain top-down causation. That is the major reasonfor caut ion in appeal ing to th is example . Another reason may be tha t areduct ionis t ic approach, i f i t inc ludes the environment-organism interac t ionand the d i f ference be tween a f i rs t -person and a th i rd-person account , has a

s t ronger case than is granted by authors who see the need for top-down

2 4 P e a c o c k e Theology, 53-54.

2 5

See Kuppers , "Paradigm Shift ."



G A P S F O R G O D ? 2 3 5

causa l i ty to exp la in the mind /bra in p rob lem. 2 6 However , tha t would l ead usinto a discussion which far exceeds the scope of the present paper.

3 .2 Top-D own Causation as a Mod el for the God-W orld Interaction

Peacocke exercises welcome caution in pointing to the inadequacy of al l humanmo d e l s a n d me t a p h o r s r e g a rd i n g G o d . 2 7 That , however , does not keep himfrom an a t t empt to th ink th rough the mode l o f top-down causa t ion .

In the l ight of these fea tures of the na tura l world , might we notproperly regard the world-as-a-whole as a total system so that its generals tate can be a " top-d ow n" causat ive fac tor in , or co ns t ra in t up on , w hatgoes on at the myriad levels that comprise i t? 2 8

On this v iew, d ivine ac t ion could make a d i f ference wi thout v io la t ing inany way the regulari t ies and laws. Besides, th e m od el also envisages h o w natu ralevents , including human decis ions and actions such as prayer, could contributeto the s ta te of the whole . This t ru ly would be a model of d ia logue be tweenhumans and the d ivine . There is a fur ther ga in in th is model :

For these ideas of ' top-down' causa t ion by God cannot be expoundedwithout re la t ing them to the concept of God as, in som e sense, an agent,least misleadingly described as personal. . . .

M y sugges t ion is tha t a com bin at io n of the not i on of top -do w ncausa tion f ro m the in tegra ted uni tive min d/b ra i n s tate to hu m an bodi lyac tion . . . w i th the recogn i tion of the un i ty of the hum an m ind /br a in / -body even t . . . together provide a fruitful clue or model for i l luminatingh o w we migh t th i nk o f G od ' s in te rac tion wi th the wo r ld . . . . In th ismode l , God would be rega rded as exe r t ing con t inuous ly top-downcausative influences on the world-as-a-whole in a w ay analog ous t o tha tw he re by w e in ou r th in kin g can exer t e ffec ts on o ur bodies in a 'top -d o w n ' m a n n e r . 2 9

This i s be t te r conceived of in te rms of t ransfer of informat ion than ofenergy. The resul t i s more than a genera l inf luence on the world: " In i t ia t ingdivine ac t ion on the s ta te of the world-as-a-whole can on th is top-downcausative model thereby influence part icular events in the world," without everbeing observed as a d iv ine " in tervent ion." 3 0

Peaco cke acknowledges the p rob lem tha t a t rans fe r o f in fo rm a t ionrequires a transfer of energy at the levels w ith w hich we are familiar . H ow ev er,he locates i t a t a peculiar place, a t the interface between the world-as-a-whole

2 6 Accounts of the brain and mind without an appeal to "top-down" causation are

g iven by Denne t t , Consciousness Explained (Boston: Litt le , Brown & Co., 1991); and

John R. Searle, The Rediscovery of he Mind (Cambridge, MA: MIT Press, 1992). See also

Scientific American (September 1992), wh ich is dedicated to the min d/b rain ques t ion .

2 7 See Peacocke , Theology, 90, 167 and 188.2 8 Ibid. , 158 and 159.2 9 Ibid . , 161.

3 0

Ibid . , 163.




and God, ra ther than wi th in the na tura l order . "This seems to me to be theult imate level of the "causal joint" conundrum, for i t involves the very nature

of the divine being in relat ion to that of matter/energy and seems to me to be

the r ight p lace to loca te the problem."3 1

3 .3 God as the Top in Top-Down Causation?

The issue of energy and information has already been considered above. Here,I wi l l cons ider the appl ica t ion of the not ion of top-down causa t ion to theworld-as-a-whole.

T he examp le of the B enard cell is a clear instance wh er e th e co nd it ion s atthe boundary de termine the behavior of b i l l ions of individual molecules .Ho w ever , th is is a lso an example w here one could replace the te rm " top-d ow ncausa t ion" by "environment-sys tem interac t ion." That environment which se tsthe tempe ra ture a t the bou nd ary pla tes is a physical system , just as is the systemin which the Benard ce l ls occur . There is nothing pecul ia r ly g lobal about theexperiment; a l l influences can be traced to local phenomena within the space-t ime f ramework . For ins tance , s e t t ing the boundary cond i t ions has noimmedia te impact on the behavior of molecules a t some dis tance f rom theboundary; i t takes some t ime to set t le into the coordinated s tate . In the case of

D N A th e relat ions are also traceable as local relat ions w ith in the spacetim ef r a m e w o rk . T h e D N A s ha pe s t h e d e v el o p me n t of a n o rg a ni sm. T h eenvironment has an impact on the surviva l of the organism, the muta t ions ini t s D N A , t h e shuffle of D N A in sexual repro duc t io n , and so on .

In both instances, there is some sense in which a whole (such as the s tatea t th e boun dary -pla tes , o r the DN A ) serves as the bou nd ary f or the sys tem ,wh ile the nex t stage of the w ho le (for instance the D N A of the next generation)is shaped by the develop m ent of the system (the organism) in i ts en vi ro nm en t.However, there is no sense in which the system-as-a-whole has any mysterious

causal influence. All causal influences can be traced to local physical influenceswi th in the sys tem or be tween the sys tem and i t s immedia te env i ronment .Boundaries are local phenomena, rather than global s tates of the system-as-a-w h o l e .

In taking top -do w n causa tion as the poin t of dep ar ture fo r descr ib ing therelat ion between God and part icular events , there is a s ignificant extrapolat ionfrom par t icular environments to the encompass ing not ion of " the world-as-a-whole . " Go d is in t rodu ced as the one who se ts the boundary condi t ions for the

world-as-a-whole at the global level. This seems to me to be problematic, if notto say unwarranted, with respect to the sciences at hand. In the examples whichled to the not ion of top-down causa t ion, there i s a lways an important ro le forthe phys ica l environment . One could say tha t in the example of the Benardcells it is the e nv iro nm en t w hich acts as the " top," set ting the tem pera ture at theplates and the reb y the s tate of th e system . An d in the D N A exam ple, it is th e

3 1

Ibid . , 164.



G A P S F O R G O D ? 2 3 7

preceding his tory w hic h has resul ted in the D N A tha t serves as the bo un da rycondit ion for the organism that is to develop. When we s tart ta lking about " theworld-as-a-whole" the n the no t io n of a g lobal con text , of an e nv iro nm en t ,

becomes a metaphor. In science, we always deal with a context which is alsocaptured in terms of the same laws of physics . This is , i t seems to me, aninstance of the dis t inction between relat ive information, as i t arises in thescientif ic con text , an d absolute no tion s with roo ts in an idealis t ph ilos op hy andwhich keep cropping up in theologica l use of the sc ience a t hand. 3 2

The problem is not only the presence of absolute not ions , but the ideathat in the natural realm there can be activi ty proceeding from such absolutes .With Peacocke I agree tha t th is may be a more appropria te loca t ion for " thecausa l nexus" than any place wi th in the world of na tura l processes . However ,

as a ques t for an unders tanding of a causal nexus be tween the d ivine and theworld it still interferes with any (assumed) completeness of the natural account.A promis ing a l te rna t ive which avoids such in terference is the ref lec t ion uponthe natural account itself, and especially the themes of the existence, order, andin te l l ig ib i l i ty o f the wor ld . 3 3 Rather than seeking an unders tanding of d iv ineac t ion in the world , the world i t se l f is und ers tood as G od ' s ac t ion . W ha teve rstreng th scientific explanations have, there always remain l imit questions abo utrea l i ty and about unders tanding. These may evoke an a t t i tude of wonder and

gra t i tude . Even when phenomena wi th in the wor ld a re unders tandab le in ana tu ra l i s t i c way , the wor ld a s thus unders tood may be in te rp re ted f rom areligious perspective as dep ende nt up on , or created by, a t ranscendent source . 3 4

3 2 I o w e th is d is t inct ion to K uppers , dur ing a preparatory mee t ing in C astel

Ga ndolfo in Decem ber 1992. Th e same problemat ic mo ve from a relative to an absolute

lies behin d the dist inct ion betw een "the future as present ," as belo ngin g to the realm of

ph ysi cs , and "the future as future," as the dom ain of theo log y, a m ov e wh ic h is

important for some German and Swiss Protestant authors on theology and science. See

A.M. Klaus Miil ler , Die praparierte Zet (Stuttgart, Germany: Radius Verlag, 1972); and

C. L ink , Schopfung: Schopfungstheologie angesichts der Herausforderungen des 20.

Jahrhunderts Handbuch sys temat ischer Theologie , Bd. 7 /2 (Gi i ters loh: Gerd Mohn,1991), 444.

3 3 S ee M ichael Hel ler , "Chaos, Probab i l i ty , and the Com prehen s ib i l i ty of the

World" ( in th is volume) .3 4 This i s deve loped further in W.B. Drees , Reigion, Science and Naturalism

(Cambridge: Cam bridge Un ivers ity Press , 1996) . O ne of the elements in the art iculat ion

of a combinat ion o f a naturalist view of religion and a religious view of naturalism is the

need to differentiate betwe en scientif ic realism and theo logica l realism; neither doe s th e

one bui ld up on the other in the w ay mo dels in the sc iences bui ld up on each other , n or

is theo log ical realism defensible along th e same l ines as defenses of scientif ic realism.



D E SC R IB IN G G O D ' S A C T IO N IN T H E W O R L DIN L IG H T O F SC IE N T IFIC K N O W L E D G E O F R E A L IT Y

W ill iam R. S toeger, S J .

1 Introduction

I intend this brief essay as a "trial balloon." I shall sketch how we can describeG od 's action in the world, accepting with critical seriousness both our presen t and

projected knowledge of reality as we have it from the sciences, philosophy andother non-theological disciplines, and our present knowledge of God, his/herrelationship with us and our world, and his/her activity within it .

By saying that we shall accept the knowledge we have from both ranges ofexperience with "critical seriousness," I mean accepting it as indicating somethingabout the realities it claims to talk about, after carefully applying the criticalevaluations of such claims which are available within the disciplines themselves,and within philosophy and the other human sciences. This obviously involvesbeginning with a num ber of definite presupposit ions, som e of which favo r neither

the sciences nor religion and spirituality, and some of which do. But it alsoinvolves the presup position that the claims of each hav e been caref ully exa m inedin the light of the different ranges of experience and certain principles ofinterpretation and v alidation. I shall not spend tim e here go ing thro ugh that pro cessstep by step, but instead shall simply assert some general results in each area whichderive from such a distillation. It will be somewhat obvious to those in therespective fields what critiques I have applied to reach the results I shall assert.Then I shall attemp t to m arshall the se results into a rough ly- sketched , integratedtheory of God's act ion in the world.

The input into this integrated, coherent theory of God's action will not consistof highly technical assert ions—either from science or from philosophy andtheology—but rather assertions which more or less describe the general characterof the world as we know it from the contemporary sciences and the limits of ourknow ledge of it, and the general character of God's action in the world as we knowit from contemporary Christian belief and theology. The latter has alreadydeveloped a great deal in response to the input and challenges mediated to ourculture by the sciences. In other terms, we wish to attempt to describe more

adequately God's action in the world, given that we know that the world, itsstructures, and processes, are presently best described in such and such a way(from the sciences and philosophy) and that God and his/her relationships to theworld are presently best described in such and such a way (from theology andphilosophy). What we know from each set of disciplines must critically interactwith what we know from the other set according to certain principles (which weshall later outline). This interaction should modify each set of disciplines—particularly in our interpretation of the conclusions each one reaches at a



2 4 0 WIL L IAM S T O E G E R

philosophical level—and allow us to describe God's act ion in the world in anintegrated way.

Imp licit here , as Stephen H appel has pointed out to m e, 1 is the methodologi-

cal problem of how these two languag es are to be integrated. This is an issue whichis important, but one which is best treated after allow ing t he interac tion to occ ur viathe cri t ical apparatuses which are already available and functioning. The twolanguages of science and religion/theology, though different, are not isolated fromor out of contact with one another. They continue to be in dynamic interaction inour common cultural and academic fields .

In describing what we know about the world and about God, and his /herrelationship to us and to physical reality, I need to employ a language, a set ofcategories, and certain philosophical presuppositions. In particular, I assume a

weakly critical-realist stance and use some of the language, categories, andmetaphysical presupposit ions of Aris totel ianism and Thomism, most notably thenotions of primary and secondary causali ty. Other categories might have beenchosen and other assumptions might have been made instead. I have chosen thesebecause, in my opinion, they are more adequate to both the scientif ic and thetheological data, and lead to fewer difficulties in explicating the essentialdifferences between God and his/her creation, the relationships b etwe en them , andthe ideas of divine immanence and transcendence. It is important to note also that

I use the term 'law' in the context of both physical processes involving inanimateenti t ies—"the laws of nature"—and free human actions. 4 Law' is any pattern,regularity, process, or relationship, and by extension that which describes orexplains a pattern, regularity, process, or relationship. Thus it applies, in the rangeof the ways I use the word, not only to the inanimate and non-human, but also tothe human and the divine. 'Law' is a word used to specify, describe, or explainorder. It does not necessarily im ply de term inism . As I use it throu gho ut th e pap er,mod ified by v arious adjectives and adjectival phrases, its meaning should be clear.

1 .1 Presuppositions

An obvious presupposition w e ma ke in pursuing this discussion is that the sciencesgive us some knowledge of reality. W e are not a ble to specify that corr espo nd enc eprecisely, because we do not have an independent handle on reality as it is in itself.Furthermore, our knowledge of it is always only provisional and corrigible, and itscertainty is only relative, not absolute.2 But we are still reasonably persuaded to

Personal com munication. Here and elsewhere in this paper I am indebted to Happel's

very helpful comments.

2 See Frederick Suppe, The Semantic Conception of Theories and Scientific Realism(Chicago: University of Il l inois Press, 1989), 475; and William Stoeger, "Contemporary

Physics and the Ontological Status of the Laws of Nature," in Quantum Cosmology and theLaws ofNature: Scientific Perspectives on Divine Action, ed. Robert John Russel l , Nancey

Murphy, and C..\ Isham (Vatican City State: Vatican Observatory, 1993; Berkeley, CA:

Center for Theology and the Natural Sciences, 1993), 209-34.



DE S CRIB ING G O D' S ACT IO N 241

maintain that there is correspondence, however precarious and uncertain it may be.The care w e exercise in validating and confirm ing scientif ic kno wled ge indicatesthat this is what we as scientists are intending to do. And unless reality is

extraordinarily malevolent and contrary, the intersubjectively applied criteria usedin scientific observation, theory, and experiment assure us that the sciences give ussome purchase on the structures and the dynamics of the physical, chemical, andbiological world of which we are a part. We presuppose in doing this that in itsinteraction w ith us, reality reveals something of w hat it is. It could b e ve ry dev ious ,it is true, but we presume it is not so devious as to reveal nothing of itself in thephenomena we observe .

The other key presupposit ions we make here may not be so obvious orcommon. They relate to God and to divine action, and to our knowledge of i t

through Christian belief and theology, according to the critical principles ofdiscernment, validation, confirmation, and interpretation which are applied in theseareas. First of all , we presuppose that God exists and is and has been activelypresent and involved in our lives and in our wo rld. H ow this action, prese nce, andinvolvement are to be described and understood wil l be modified—evensignificantly modified—in the conversation with the natural sciences. We are notattempting to prove Christian doctrines by appealing to scientific evidence, butrather attempting to re-articulate and understand theological truths in a more

satisfactory way by looking at the relevant knowledge available to us in thesciences and other disciplines. As H appel has said, "religion and theolo gy are putin conversation with the data, concepts and langu age of scientific pe rfo rm an ce andtheory . " 3

Secondly, we presuppose that the sources of revelat ion, the scriptures ,tradition, and our living experience as believers who are individually andcommunal ly open—more or less—to God and to God 's ac t ion, do give us somereliable knowledge about God and about his /her act ion in our world. As in thesciences, this is very limited and corrigible knowledge, subject to error and

modification, particularly with regard to interpretation and understanding of thatrevelation, and of our overall response to it . And, as in the sciences, it too isdependent on the careful application of critical principles of interpretation,discernment, and confirmation suitable to the experiences being examined. Wemight also mention that the limits and uncertain ties of this know ledg e derive bothfrom the extraordinary but limited character of the revelation we have available,and perhaps most of all from our own limitations and lack of openness toreceiving, interpreting, and living out that revelation.

1 .2 The Aim of Our Discussion

Th e aim of our discussion is simply to describe God's action in the world in termswhich are faithful to Christian sources of revelation and consistent with what weknow from the sciences about reality, its structure, evolution, and processes,

'Private communication.



2 4 2 WILLIAM STOEGER

especially in view of the self-organizing capabilities of matte r, fr om t he cha otic and

dissipative structures evident even in inanimate systems to the complex systems of

living organisms them selves. O ne of the key issues her e is causality. How can w e

speak of divine causality within the world as we know it, without compromisingscientific and philosophical principles—without using an interventionist model, for

instance?But how can this aim be pursued? Where is the common mode of inquiry to

be found? How do we distill relevant information concerning God's action in theworld from the sciences and from the sources of revelation? Those questions arevery difficult foundational ones. But I do not think they can be answered from ana priori perspective. As I have mentioned already, I am assu m ing that w e ha ve usedand are using the relevant tools of philosophy, philosophy of science, the criticalmethods proper to scripture studies, historical and systematic theology, andhermeneutics to do this. I am also assuming that we can begin to integrate theseresults through the common ground of understanding and language which ourvarious specialized languages share with one another. They are not, as I havestressed above, completely isolated from one another, nor are the experiences towhich they appeal.

2 Wha t the Sciences Tell Us about Ou rselves and Our Universe

If we generalize from th e vast kn ow ledg e of the univ erse and all that ma kes it up,including living and conscious beings like our selves , w e can say that at eve ry levelthere are self-ordering and self-organizing principles and processes within natureitself, which can adequately describe and account for (at the level of science) itsdetailed evolution and behavior, the emergence of novelty, possibly even ofconsciousness, the inter-relationships between systems and levels, and even thevarious laws of nature themselves—and the unfolding of all this, its diversification

and complexification, from an epoch very close to the "initial singularity" or BigBang. Some of these principles and processes are well kn ow n and und erstoo d, andothers are at present only conjectured or suspected. No outside intervention isnecessary to interrupt or complement these regularities and principles at this level.Nor is an ilan vital called for to explain living things—nor an elan spirituel at thenext level of developm ent. At the level of the sciences there a re no "ga ps, " e xceptthe ontological gap between absolutely nothing and som ething .4

4 S o m e— fo r instance Ellis, Murphy, and Tracy— consider the indeterminacy at the

quantum leve l to be an essential gap which requires filling (see their papers in this volume).

Though this view needs much more careful discussion than is possible here, my assessm ent

is that indeterminacy is not a gap in this sens e, but rather an expression of the fundam entally

different physical character of reality at the quantum level. It does not need to be filled! T o

do so, particularly with divine intervention, would lead in my view to unresolvable scientific

and theological p-oblem s. The dem and for a cause to determine the exact position and time

of an event misconstrues the nature of the reality being revealed. Quantum events need a



D E S C R I B I N G G O D ' S A C T I O N 2 4 3

This general conclu sion is s trongly supported by detai led con clusions fro mphysics, chemistry, biology, molecular biology— particularly fro m tho se em anatin gfrom the s tudies of complex systems, information theory, molecular biophysics ,

and by the prom ised or envision ed adva nces in these fields. The g aps in scientif icknowledge have not al l been fi l led, but they are gradually being fi l led by newdiscoveries. And it has become clear that appealing to divine intervention is not anacceptable means for doing so. Nature itself is open and capable of realizing newpossibilities in a whole variety of ways. Even in the surprising transitions frominanimate beings to l iving ones, from living ones to conscious ones, fromconsciou s ones to hum an o nes, i t seems very unlikely that any intervention fromoutside natural processes was involved. Material, physical reality is much richer inits possibilities, particularly when it is in a highly organized form, than we usually

think. At the same time, an analysis of the sciences, the theories and the laws ofnature which derive from them, makes us very aware of their l imitat ions. Theknowledge given us by the sc iences—like a l l human knowledge—is imperfec t ,provisional, corrigible. In particular, it only very imperfectly describes theregularities and underlying inter-relationships, necessities and possibilities, andstructures which constitute reality. 5 Throug h the sciences we do not know reali tyas it is itself; w e do not know it directly, interiorly, com preh ensiv ely, exha ustively ,as we would like to know it—as God must know it. So, although we have throughtremen dous sustained effort and genius come to unravel a great deal about reality,we are far from com prehend ing i t a t its ul t imate d epths .

Iij particular, from the sciences we still are unable to answer the questions,why there is something rather than nothing, why there is order rather than disorder,and wh y there is openness to novelty—to new and more complex enti t ies—ratherthan just sterile uniformity. That is , why are there "laws of nature" in the firstplace? And why these " laws of nature" and not some others? In fact , not evenphilosophy can adequately answer these questions.

A third conclusion stemming from the sciences is one which is not usually

mentioned but one which I believe is quite important—but not for the first reasonthat will probably occur to us: The laws of nature and nature itself constrain butunder determine what develops or occurs. Great possibilities are left open innature. It is very pliable . This doe s not m ean that nothing hap pen s, obv iously , butit does mean that uncorrelated coincidences often end up "filling in" what isneeded to complete determination. It is this pervasive feature of reality—alongwith others, such as its knowability and its localizability—which enables humanbeings and other animals to manipulate and harness reality, and even to know it.W e can fly in airplanes, build bridges, and heal the sick, precisely because the lawsof nature as we know them, and perhaps even as they are in themselves, underdetermine events . In fact we are who we are as human beings because of thisimportant feature— we can decide to do things wh ich othe rwise wo uld no t ha ppen

cause and have a cause, but not a cause determining their exact time and position of

occurrence, beyond what is specified by quantum probability (the wave function).

5

See Stoeger, "Contemporary Physics."




within the constraints imposed by physics, chemistry, and biology. Some of thisunderdetermination is due to the indeterminism and unpredictability of physicalsystems at the quantum level and to the unpredictability of both simple and

complex systems on the macroscopic level . As we have seen in s tudying thebehavior of chaotic, nonlinear, or nonequilibrium systems, very slight changes inthe initial condidons or the boundary conditions can severely alter how they willbehave, and what sort of self-organizing behavior they will m anife st. Ho we ver, theunderdetermination of phen om ena by the law s of natu re is du e to m uch m ore thanthese important sources of indeterm inism and unp redictability. It is du e prim arilyto the freedom that exists in establishing initial condidons and boundary conditionsthroughout nature. An agent can, with som e expenditure of energ y, chang e initialcondit ions and/or boundary condit ions of a system or, even more importantly,

construct new systems, thus determining outcomes much different from thosewhich would otherwise occur.

"Aha! You have pointed this out in order to leave room for divine interven-tion!" someone might say. In fact I have not, because, as we shall see, thisunderdetermination of reality by the laws of nature does not easily allow for divineintervention—at least not direct divine intervention—because that would involvean immaterial agent acting on or within a material context as a cause or arelationship like other material causes and relationships. This is not possible; if it

were, either energy and information would be added to a system spo ntan eou sly andmysteriously, contravening the conservation of energy (and w e just do not hav esubstantiated cases of that happening) or God would somehow be actingdeterministically within quantum indeterminacy, which presents a number ofserious scientific and theological difficulties.6 No, I have pointed out this featureof reality in order to emphasize the potentiality, flexibility, and scope for newnessthat is within nature, as well as the m any d iffere nt levels of agenc y w hich ope ratewithin it , including the types of agency we exert as human beings.

Before going on to summarize what revelation tells us about God and divine

action, w e should point out that the scienc es the m selve s are limited in dealing withpersonal agency and personal relat ionships . In some ways psychology andsociology deal with the phenomena related to these, but I think we are all aware ofthe limitations under which they labor in their quest for knowledge in theseprofound and myster ious areas .7

3 Wha t We Know from Revelation and Our Reflection upon It

From revelation, and partially from reason, we know that God exists, created theuniverse and all that is in it, reveals him/herself to people, loves and cares for us,continually acts within material creation, particularly now through Jesus and the

6 S e e n. 1 above.

7Arthur Peacx ike, Theology for a Scientific Age: Beng and Becoming—Natural and

Divine (Oxford: Blackwell , 1990).



DE S CRIB ING G O D' S ACT IO N 24 5

presence of his spirit among us, and calls us to share his life and missionforever—a promise which wil l be fulfilled only after our deaths . 8

Here a couple of conclusions stand out in reference to the issue we are

pro bin g. T ho ug h it is not the primary revelation of Go d, the first is that he/s he issomehow the answer to the question, "Why is there something rather thannothing?"—and to the other similar fundamental questions we posed ab ove. He/shecreated what is not G od f ro m noth ing. B ut how tha t was d one is still very m uch amystery, as well as whether or not creation is eternal—does God create from alleternity? How that was done is understandable only to God, at the very depths ofthe divine being. We know in a very limited way how it was done by looking atnature as revealed to us by the sciences—or let us say, we know how it was notdone!

A second conclusion from revelation is G od 's motivation fo r creation and forhis /her interaction with the world—it is God's goodness , God's innate drive asGod to share that goodness, and God's love both for him/herself and for all thathe/she creates and holds in existence. So, interpersonal relationships are ofparamount importance to God—as are the values of goodness and truth. This istrue of God in him /he rsel f— G od as Trinity. But it is also true of G od 's relation-ships ad extra. This divine priority is mos t fully expressed in the Incarnation of theSon of God in Jesus, and in the sending of the Spirit . But it is m anife st thro ugh out

creation at every level.A third conclusion is that creation itself is good, and an expression of God'sgoodness and love. There fore, it m akes perfec t sense that it should reflect to s om eextent who God is and what his/her characteristics are. A lso, the m or e co m ple x andcapable beings are, the mo re they reflect who G od is— including hum anity, w hichis made in the image and likeness of God. This perspective—the priority of thevalues of goodness and truth, along with reverence and respect for all that is—isconsistent with the importance and value God gives to personal relationships.

A fourth conclusion is that, although God reveals him/herself through

everything in creation, G od 's mo st particular revelation is in term s of persons andpersonal relationships involving generous, self-sacrificing love and forgiveness.And our principal way of responding to God's revelation is in those same terms.So w e experience revelation as personal and social, God among us—as creator andsource of life, yes, but also as a personal presence and force who loves, inviteslove, gives and invites giving, forgives and reconciles, and invites forgiveness andreconciliation. The created, inanimate, and non-personal levels of reality, thoughthey exist in their own right and reveal G od and G od 's g ood ness, po w er, and lovein their own way, and give glory to God in their own way (they cannot dootherwise!), exist also to enable the development and maintenance of persons towhom God can reveal him/herself and with whom God can maintain a personal

8AS Happel points out (private communication), this creedal summary is deceptive.

The m eaning of the language used is neither static nor agreed on by all wh o ac cept it. It w ill

change, even radically so, as we live out of and reflect upon our individual and common

experience of God's presence and action among us.



2 4 6 WIL L IAM S T O E G E R

relat ionship leading to the ful l and harmonious union of the divine with created

reali ty. The degree to which this is desired by God is expressed in creation i tself ,

in the Incarnat ion a nd all that fol lo w s fro m i t, and in the sending of the Sp ir i t . 9

These are the pr incipal conc lusions f low ing from Chris t ian revelat ion wh ichI wish to highl ight . Our endeavor now wil l be to br ing these conclusions into

crit ical interaction with what we know about reali ty from the sciences, as outlined

in the preceding section. As I hav e already emphasized, th ese con clusio ns will h av e

to b e re-ar t iculated and m od if ied as a resul t of this interact ion. For instance, th e

strong anthropocentr ism of this par t icular ar t iculat ion would have to be s ignif i -

cant ly mit igated. And the radical non- object i f iabi l i ty of God would have to be

fac tored in , on o ther , m ore theologica l and re l ig ious gro un ds . 1 0

4 God's Creative Action and Science—P rimary Causality

I have already emphasized that the sciences—physics in particular—do not explain

or account for exis tence or for the general orde r of the unive rse. The y pre sup po se

it. They do not answer the quest ion, Why is there something rather than nothing?

They can deal very wel l wi th quest ions of or igin in which—as is usual ly the

case—the or igin of a s t ructure or an ent i ty der ives f rom something else which

already exists , for example, the or igin of chi ldren from their parents . But thesciences do not deal with ul t imate or igins. They cannot br idge the gap between

nothing (which includes no potent ial i t ies and no physical laws— absolu te ly

nothing) and something—or even be tween God and nothing e l se and God and

something else not God; and i t i s not clear that any branch of human knowledge

can adequately address this fundamental issue.

The God of Chris t ian revelat ion, bel ief , and spir i tual i ty, however , is an

adequate answer to this quest ion—though this answer, adequate as i t may be, is

somewhat impervious to adequate understanding on our par t . I t does not

adequately tell us how God bridged that gap. God is the one who in some way hasbroug ht something out of nothing; God is the agent of creatio ex nihilo . In one way

this is not accu rate , for , as I hav e al ready implied abov e, Go d has alway s existed

as a "necessary" being. He/she is , as the uncaused cause, or pr imary cause, as

Chris t ian theology has t radi t ional ly descr ibed him/her . So something ( i .e . , God)

has always existed. There was never "absolutely nothing," i f something exists .

What we real ly want to say is that the only explanat ion for something created to

emerge from the absence of anything created is God. This aff i rmat ion, as I have

just said, does not particularly deepen our understanding—

howthis happened, the

'My emphasis here on the priority of persons does not deny the wider role the Spirit

has throughout the created order, and the impact of the Incarnation on the cosm os. No r d oes

my formulation properly describe the relationship of non-conscious entities to the divine

presence and their essential mystery.

1 0 Jos6 Po firio Miranda, Marx and the Bible (Maryknoll , NY: Orbis Books, 1974),

40 f f .




details— but it is, strictly speaking, an adequate answ er to the fu nd am enta l questionwe are considering.

It should be clear, furtherm ore, that this is not basically a te m por ally we ighted

answer to the question of existence. It does not necessarily imply that there was astate or situation when there was nothing besides God, and then at some junctureGod created entities other than him/herself, and with them time, space, etc. AsThomas Aquinas 11 realized, it could be that G od h as created fro m all eternity— thatcreated reality is eternal in the sense that it has no tem poral beg innin g (there wasnever a state in which God existed and created reality did not), but it is stillradically contingent on G o d . 1 2 There m ay have been a beginning of t ime, but thatis by no means essential. Ultimate origin s are essen tially onto logica l, not tem po ral.In fact, I believe a good argument can be made for eternal creation on the basis of

who God must be as God. If God is of his/her very nature bonum diffusivum suiy

infinite love, and therefore creator, then he/she was always and eternally such.Therefore, in order to fully realize who he/she is, creation must in some sense, atleast in intention, b e an eternal process. This may at first seem to infringe o n G o d ' sfreedom to create. But it really does not do that at all. His/her creating is perfectlyfree , but is a lso a natural consequ ence of G od 's very nature. Nor does this m eanthat God or God's love is dependent on creation for self-origination. God andGod's love must be sovereign. But God's love must also be fruitful, and that one

pr in cip al m anife station of its fru itfu lne ss be an eternal created order is no tsurpris ing.

This primary divine, exis tence-endowing causali ty is a lways operative,holding things in existence, charging them with realization. It is essential toconceive primary causali ty very differently from the causes—secondarycauses—w e discuss and deal with each day. Th e prima ry cau se is not jus t a notherone of these—it completely transcends them and provides their ultimate basis inreality. There are no gaps is the secondary causal chain, but the whole chaindemands a primary cause to support and sustain it. Without the primary cause there

is no explanation for i ts exis tence or for i ts effi ca cy .1 3

But it is not just a question of existence. It is also a question of order. W hataccounts for the order which exists in nature— in the universe? W hy is there orderrather than complete disorder? Again this is not a question which can be answeredby the sciences. In the same bald and impoverished way as before,1 4 however , theexistence of God does provide an adequate answer: God is the ultimate source oforder in nature and in the universe, and of both necessity and contingency—andtherefore of any possibilities which might emerge from their interaction. A

n T h omas Aq u i n as , Summa Contra Gentiles 1.44.1 2 S e e Ernan McM ull in, "How Shou ld Cosm olog y Relate to Theo logy?" in The

Sciences and Theology in the Twentieth Century, ed. A.R. Peacocke (Notre Dame, IN:

University of Notre Dame Press, 1981), 39ff; and Stoeger, "Contemporary Physics."

1 3 Stoeger, 'The Origin of the Universe in Science and Rel igion," in Cosmos, Bios,Theos, ed. Henry Margenau and Roy A. Varghese (LaSalle, IL: Open Court, 1992), 254-69.

"Ibid.



2 4 8 WI LLI AM STOEGER

consequence of this, of course, is that God is ultimately the source of theunderlying regularities, constraints, and behavioral relationships and patternswhich are imperfectly described by the laws of nature we fo rm ul ate .1 5 The question

why the world behaves this way rather than som e other logically po ssible w ay canonly have an ultimate answ er in God as creator. He/she is the well-spring of b othnecessity and possibility in nature.

5 God's Creative Action—Creat io Cont inua and Secondary Causality

There is an important corollary to the foregoing discussion, which takes us into abrief consideration of God's continuing creative action in the universe, conceivednow more richly than s imply as just divine existential conservancy. It is that aprincipal mode of God's activity in the world at the level of inanimate and non-personal beings is precisely through the underlying regularities, constraints, andrelationships he/she has established in nature, and which we sometimes refer to as" the laws of na ture . " 1 6 This is a very rich way of looking at nature—as theexpression of God him/herself and as one of the fundamental ways in which Godacts within the world. The regularities, constraints, and relationships are as they areby God's allowance or choice—he/she works through the secondary causes of our

world. They g ive G od 's p resence and action concrete form . As new possibili t iesare realized God becomes present and active in new wa ys . 1 7 They express how Goddesires the world to be— the necessities that are imp osed along w ith the con tingen -cies, the possibilities and the openness to development and to novelty.

If we put this into an evolutionary context, then, and consider what we knowof the com plexific ation of structure and the diversification of physical, chem ical,

1 3

S e e ibid.; and dem,4,

Contemporary Cosmol ogy and I t s Impl i ca t i ons for the Sc i ence -

R e l i g i o n D i a l o g u e , " i n Physics, Philosophy, and Theology: A Common Quest forUnderstanding, ed . Rober t John Russe ll , Wi l l iam R . Stoege r , and Ge or ge V . C oy ne (Vat i ca n

Ci ty Sta te: Va t i can Obser vatory , 198 8) , 21 9- 44 .

1 6 I prefer to reserve this term for our imperfect formulat ion of the underlying

regul ar it i e s, cons tra int s , and re l a t i onshi ps w e d i scove r , or our m od e l s f or those . H ow ev er ,

we must d i s t i ngui sh be tween "the l aws o f nature" as God knows them, and the " l aws o f

nature" as w e have i mpe rfec t l y and pro v i s i on a l l y form ul ated them .

n T h o u g h t h e g e n e ra l p r i m a r y - c a u s e - s e c o n d a r y - c a u s e a p p r o a c h t o t h e p r o b l e m o f

G od 's act ion in the world i s very tradi t ional , I be l ie ve that i t i s the only on e that ho lds m uc h

p r o m is e . O w e n T h o m a s (" R e ce n t T h o u g h t s o n D i v i n e A g e n c y , " i n Divine Action, ed . Brian

Hebbl e thwai t e and E dward Henderson [E di nburgh: T & T Cl ark , 1991] , 35 -50 . ) arr i ves a t

a s imi lar conclu s ion, that in the current s tate of d i scu ss io n o nly the theorie s inv olv in g e i ther

primary and secondary causali ty or process th eo log y ev en app roach ad eq ua cy. I am than kful

to Ru ssel l ("In troduct ion," in Quantum Cosmology; and in this vo lu m e) for this refe ren ce .

In m y v i e w , the appro ach o f pro cess theo l ogy , thoug h a t trac ti ve i n so m e wa ys , has

unresolved phi losophical and theological problems, part icularly wi th regard to the doctr ines

of God, creat i on , and Chr i s to l ogy .



D E S C R I B I N G G O D ' S A C T I O N 2 4 9

and biological processes from a time shortly after the Big Bang, we see that we canconceive of G od 's continuing creative action as being realized thro ugh the naturalunfolding of nature 's potential i t ies and the continuing emergence of novelty, of

self-organization, of life, of mind, and spirit , as the universe expanded and cooled.Within this perspective, God's direct intervention—in the sense of operatingoutside of the regularities, constraints, an d relationships he/sh e has estab lished, orabrogating or mitigating them in any way, either ad hoc or regular, to fulfil s o mehigher purp ose— fails to ma ke m uch sense if God is real ly Go d, thoug h i t cannotbe ruled out. Even if intervention in the underlying principles, relationships, andregularities as they are in themselves som etimes occ urs, it is still clear, from criticalreflection upon both scientif ic kno wled ge and the know ledge we hav e fro m fai th,that the operation of the law s of nature, fro m the d ivine persp ective, is a p rincipal

channel of God's act ive presence in our world, and as such is an expression—inadequate and imperfect though i t may be—of who he/she is . Thus, ourinvestigation of these regularities, constraints, and relationships, and our imperfectformulation of them in scientific theories and in our "laws of nature," articulatesan important mode of divine activity in created reality.

I shall have more to say about this later w hen w e d iscuss G o d' s action withinpersonal and social contexts. Looking forward briefly to the issues which willemerge there, we see that it is crucial to distinguish carefully between the "laws of

nature," the regularities, constraints, and relationships realized in nature, as wehave conceptualized and formulated them, and the "laws of nature" as they in factfunction in created reali ty—from God's ful l and complete point of view, so tospeak—which somehow includes the internal or interior relat ionship he/she haswith nature, with us , and with other created enti t ies .1 8 We immediately see theimportance of this distinction—since our very limited account and formulation ofthese "laws" may leave out crucial relationships (even constitutive relationships)which organize the inanimate and unconscious world at a very profound level ,which function to subtlety l ink the personal and the non-personal , or which

subordinate the non-person al to the personal. We are not fully able to see how thismight happen, but we begin to see something of i t in the underdetermination ofphysical reality and its vulnerability to human agency, which can mold it within itsconstraints to our intended use, for better or for worse.1 9

From our point of view, manifestations of this may be interpreted by us ascontravening the " laws of nature" s imply because we have not ful ly understoodthem, whereas in fact they are in perfect accord with the "laws of nature" as theyare in reality. In other words, God may act in a purely "natural" way within therelationships and regularities he/she has established and maintained, but in a waywhich we see as supernatural intervention simply because we have not yet come

1 8Stoeger, "Contemporary Physics."1 9

Cf. Peacocke, Theology for a Scientific Age.




to comprehend fully the relationships and regularities (the "higher laws") whicho b t a i n . 2 0

In light of this, it is clear that the distinction we often make between the

natural and the supernatural really d erives fr om o ur limited perspe ctive on reality,and our imperfect knowledge of i t . We simply do not know enough to puteverything together. Where there are gaps in our knowledge we always seem toinsert God's direct intervention, with the implication that there is a concomitantabrogation, mitigation, or suspension of the "laws of n atu re. " Ag ain , the distinc tionbetween the two rather different m eaning s " the laws of natu re" may have is som ehelp to avoiding this confusion.

6 Problems of Conceiving Direct Divine Action and the Need for It

God's action in the world through the regularities, constraints, and relationshipshe/she enforces, as we have sketched it in the previous section—through the "lawsof nature" as they are in them selves— is in dire ct. 21 God establishes an order withinwhich processes occur and constraints are imposed. These processes andconstraints lead to the evolution of structures and even of other, higher-levelprocesses which govern their behavior, and to the emergence of new and more

com plex entit ies which are able to reproduce and evo lve further. The wh oleprocess culminates in entities which are con scious, able to kno w, free and capableof ma king d ecisions, and able to harn ess and control reality within certain limits.All this has been orchestrated by God—so to speak—through the divineestablishment and m aintenance of the " laws of nature."

W e can easily understand G od 's indirect action, bec ause we are fam iliar withanalogous instances of indirect act ion in our human experience—using aninstrument, making a machine, or constructing a prog ram wh ich will pe rfor m som efunction for us, setting an organization or a group into action to carry out some

series of com m and s directed toward fulfi l l ing som e desired end we hav econceived. God does something analogous in establishing and maintaining the"laws of nature."

But conceiving or modeling G od 's direct act ion is a very different kettle offish. We have the experience of what "direct act ion" means within humanexperience. It means active involv em ent w ithout an intermed iary— the agen t doe swhat he or she intends personally, without asking someone else or triggeringsomething else to do it . Any action will always have a direct component andindirect components . No action by an agent can be completely indirect . When I

2 0 Will all events be 4lawful* in his extended sense? Referring to how I characterized4law* in the introduction and in this section, that may very well be the case. However, it

needs more careful consideration than I can give it here. Certainly, relative to a more

restricted notion of law—as what is generalizable—some events will fall outside its

comprehension, e.g., what is important and significant in its radical pa rticularity.2 1

B y 'direct* I mean unm ediated; by 'indirect' I mean med iated.



DESCRIBING GOD'S ACTION 251

contract a firm to repair my roof, I indirectly repair the roof by doing so, and thesupervisor indirectly repairs the roof by directing his subordinates to do so andtelling them how to go about it , but I directly act to initiate the contract with the

roo fing firm (picking u p the ph one to call them , showing them w hat needs to bedone, making and communicating the decis ion to accept the est imate on theproposed wo rk, signing the contract, etc.) and th e s up ervis or directly acts to put hisroofers "into motion ." It will be the same in God's indirect action in the world. Wesee the results of the indirect components, and even have access to the agentsthrough whom God is acting indirectly. But we know or conclude that there mustbe a component of God's perceived indirect act ion which is direct . At somestage—some "init ia l" s tage—he/she acts without intermediary to ini t ia te theintended action or create a range of necessities and possibilities, for instance, by

directly establishing fund am enta l laws of nature and the funda m enta l constants ortheir primordial anteced ents. A t some level we know that Go d's direct action wasand is necessary to ground and maintain existence of everything that is not God,and to enforce the regularities, constraints, and interrelationships which we referto as the "laws of nature" and which endow reality with its interlocking levels oforder, necessity, and possibility.

But our ability to model God's direct action seems to encounter an insupera-ble barrier at this point. Our experiences of acting directly no longer provide a

helpful analogy or model for what divine direct action must be. Essentially, eventhough w e know that at som e fundam ental level God is and m ust b e acting directly,we never have direct experience of his/her doin g so! W e alwa ys exp erienc e divineaction as indirect—even though the action may sometimes seem to operate outsideof the "laws of nature" as we understand them. And we never have experience ofGod acting directly—even though we have assurances from revelation that he hasand does, in creation, in the Incarnation, within the realm of the personal. Wewould apparently not be able to determine if a particular consequence were theresult of God's direct action, instead of God's indirect action through a channel or

instrument we are not aware of or do not understand. Thus, an apparent divineintervention on our behalf—a miracle—in answer to our prayers, for instance, ahealing of a disease of paralysis which cannot be explained by contemporarymedical science, does not of itself m an ifes t the d irect action of G od , thou gh it doe smanifest God's personal loving and l ife-giving action towards us . We alwaysexperience i t through some intermediary datum or agent—through somesacrament. Even when there is no obvious cause—we just f ind ourselves wellwhereas before we were ill and dying— our experience of this is mediated by whathas occurred unexplainably in our bodies. Our experience is not of any direct

encounter with God, however mystical (in the extraordinary sense) that may havebeen. Furthermore, there is no assurance that the proximate cause of the healing,miraculous as it is, was not effected by God operating through a "regularity or lawof nature" which is beyond our present knowledge or understanding or through anintermediary agent, that is , a prophet or an angel.

My point is that, though the extraordinary character of the event, which isoutside what we normally expect in similar situations, leads us to believe that Godis perso nally respon ding to our need s and prayers, this does not of itself indicate

that the divine action is direct. It may indicate, how eve r, that it is special, partic ular,




and personal; I shall have more to say about this later. Even in terms of the

Incarnation, no one, not even Mary, had an unambiguous experience of directdivine action, however personal and gratuitous it was.

Another possibility for divine action, however, is what St. Ignatius of Loyolarefers to as "consolation without previous cause," as being an unequivocal sign ofGod's act ive graced presence in a rel igious experience.2 2 This may be, but it stillis not at all clear that it is an experience of direct divine action! It may be anunequivocal sign of God's presence and action, but it is very difficult to assesscritically as an ex perien ce of G od as a direct, unm ediated caus e. Perhap s the onlyplace where we shall experience that is in the beatific vision.2 3

The key point to this discussion is simply that we ha ve no experiential basisupon which to model God's direct act ion with regard to created reali ty.2 4 Thus ,although we know it occurs, it is apparently inaccessible to our experience andtherefore to our detailed understanding. The case of God's action in creating fromnothing and maintaining in existence is essentially direct divine action—perhapsthe clearest case of it. But here again, that extraordinary and pervasive relationshipof creatures with the divine, in which we ourselves p articipate, occurs at the verycore of our beings and is hidden from our eyes.

7 The Problems of the Primary-Secondary Causal Nexus, of Dou ble Causality,and of Top-Down Causality

There are a series of unsolv ed pro blem s related to divine action , which flow f ro mthis discussion of the impossibility of adequately articulating or modeling God'sdirect action towards a creature. From what I have said above, it is clear that God'sdirect creative action ex nihilo is not susceptible to experiential "detection" orprobin g. In a sense, in order to answer how it happens, we would have to be God!We have some access to the "why" because of revelat ion—in terms of God's

C S L Ignatius of Loyola, "Rule for the Discernment of Spirits," The Spiritual Exercises.See Karl Rahner, The Dynamic Element in the Church, trans. W J . O'Hara, vo l. 12,

Quaestiones Disputatae (New York: Herder & Herder, 1964), for a theological account of

this.

. Suppe, "The Scientific Vision and the Beatific Vision," paper presented at th e

"Notre Dame Symposium on Knowing God, Christ, and Nature in the Post-Positivisitic

Era," University of Notre Dam e, April 14 -17, 1993.

2 4 Russell (private communication) insists that we distinguish three different ideas

which I have tended to conflate here: (1) knowing where God acts directly (such as at the

quantum level or in the free moral agent); (2) having an immediate experience of such a

direct act; and (3) being able to model the act itself. My point here is that, though we may

know or suspect that God acts direcUy in a given place or situation, we are never in the

position to model it, simply b ecause w e do not have access to it in its im med iacy. W e have

mediated experience of it, but no experience of the direct action itself, which is precisely

what is in question.




goodness and love. When we turn to other categories of direct divine action, the

same obs truc t ion is fou nd . 2 5

7.1 The Primary-Secondary Causal NexusA key issue is the direct action of God with regard to secondary causes, throughwhich he/she acts indirectly. How does God operate on a secondary cause, otherthan by bringing it into existence and conserving it in existence, so that it is theinstr um ent f or carrying ou t his/her intentions? In som e cases this is just bymaintaining it in existence and continuing to endow it with the nature or propertiesit has, and we do not know how that is done. But in some other examples, there ismore going on—that is, in the sacraments, in the prophets, who are inspired to

speak for God, in individuals who are in personal relationship with him/her. Inother words, the causal nexus between God and any other cause or enti ty—incontrovert ible as i t is as a necessary condit ion for what we experience—isshielded from and inaccessible to our probing. Does God simply inject informationor intention into secondary causes, inducing them to act on his/her behalf? Doesthis happen within the framework of the physical and other laws of nature, as weimperfectly know them? Or does it instead at least sometimes involve anabrogation or a fulfillment of those laws in terms of higher laws operating in the

realm of the conscious and the personal and transcending those of physics,chemistry, and biology? We do not know for sure. I would strongly suspect thatthe last is often, though not exclusively, at work, simply on the basis of the prioritythe personal seems to have for God, as is c lear to us from reve lat ion. 2 6 But it seemsextraordinarily difficult to substantiate that suspicion independently and to modelsuch a causal nexus in concrete terms.

One of the difficulties here is simply that, in speaking of God's causalactivity, w e are trying to speak abou t a ca use wh ich is radically different from anyother cause we experience—God is the primary cause. And we have no direct

experience of this sort of causality. He/she is never one cause among many others,and cannot be conceived in his/her activity on the pattern of the created causeswhich we are and which we exper ience . 2 7 God's causal activity completelytranscends secondary causality, and at the same time is perfectly immanent insecondary causality, supporting it and giving it efficacy. To use metaphors , Godas primary cause is m uch m ore interior and present to creatu res tha n th ey are to on eanother as secondary causes. But at the same time, on the b asis of our lack of direct

experience of it, God's causality is extremely subtle and hidden, and does not

"Arthur Peacocke discusses this problem at length—the problem of the "how," or

what he refers to as the "causal joint" (Peacocke, Theology for a Scientific Age). He suggests

that the resolution of it can be approached by locating creation "in God" and applying

"top-down" causality, God acting on created reality.

*A t the same time, however, w e m ust find a way of avoiding an overly anthropocen-

tric theology.

"Stoeger, "Origin of the Universe."




interfere with necessities, regularities, and fre ed om s with wh ich secon dary causes

are endo wed , except in response to a higher or more personal law.

7 .2 Double Causality

Another problem with God's direct act ion in the world which is connected withthis issue of the causal nexu s is wh at w e mig ht call d ou ble ca usa lity. This is no t sodifficult in light of the conclusions we have already reached, but it bearsmentioning. I t is essential ly: How can we have two adequate agents causing thesame effect—God as primary ca use and the secondary causes throug h w hich Godis working?

There are several rather different issues which m ust b e distin guis hed he re: (1)God as primary cause acting to main tain seco ndary causes in existence, w ith theirow n particular capabilities, tendencies, and lim itations, w ithou t further determininghow they act to produce their effects (the und erdeter m ination we we re speak ing ofearlier); (2) God not only acting as prima ry cause to m aintain second ary c ause s inexis tence, but possibly working through secondary causes to produce an effectGod d esires, a special or particular effect, outside of the ordinary pattern of whatw e would expect; (3) Go d inviting secondary causes to act in a certain wa y, bu t no tdetermining o r forcing them to do so; and (4) God apparently being a sufficient

cause for an effect—directly or indirectly—and some created cause apparentlybeing a sufficient cause for the same effect.

Regarding this last issue, I believe that the only problem here may be ourconfu sion concerning what constitutes a sufficient cause—or reason—in a concretecase, along with whether the sufficient cause is acting directly or indirectly. Forexam ple, if on e cuts the stem of an ap ple h ang ing on th e tree and th e app le fa lls tothe ground, we might at first think that the person cutting th e stem is the suffic ientcause for the apple to fall, but that sufficiency presupposes a context in which othercauses are acting, namely gravity. Without the action of gravity the apple wouldnot fall. Nor is gravity a sufficient cause for the apple to fall; nor is God, who atsome level instantiated the "laws of nature,"—they are necessary conditions, butnot sufficient ones. The apple must be free to fall bef ore gravity can c ause it to fall.Applying this example to divine action, we see that God is never the sufficientcondition for an effect occurring—though he/she is always a necessary conditionfor what occurs and sometimes contributes ( in s i tuations involving free moralagents) to the fur the r con ditions nee ded to constitute sufficiency. Correlatively, asecondary cause is never an absolutely sufficient condition for an effect, only what

might be called a relat ively sufficient condit ion—given that other normalconditions are fulfilled, that is, that gravity is acting.

Again God as a necessary condit ion for the exis tence of something, or ofanything, is not in doubt, but God as sufficient condition is always in question.This is undoubtedly an aspect of divine keno sis (or self- em ptyin g) and hidd enn essin created reality—that God withholds his/her capability of being the sufficientcondition of particu lar effects. For instance, God is not the sufficient condition ofmy existence— by relying on secondary causes (my parents and the processes ofreproductive biology) divine causal sufficiency is surrendered. This is true even



DESCRIBING GOD'S ACTION 255

with respect to an event like the Incarnation. God invites it , but does not force it.T he iat of Mary was essential to the concrete realization of the Incarnation.

Now that they have been distinguished, the other issues, (1) through (3), lead

to fairly straightforward resolutions. I shall not discuss (1) and (3) further, as theonly one which may cause a problem is (2), that of God possibly determining aspecial or particular effect through secondary causes. The situations where thisoccurs are in G od 's personal action tow ards a person ope n to his/her presen ce andactivity, in God's activity through impersonal, animate, or inanimate beings orcausal chains, and more clearly in the cases where God apparently has directly orindirectly rigidly fixed general patterns of physical behavior, relationships, andstructures in the "laws of nature."

In the firs t s i tuation, God somehow communicates love and mercy—God's

life-giving presence—in a particular experience or concrete event to a person orgroup. This rarely involves even the appearance of abrogation of the laws ofnature, but instead a certain coming together of events which seem purelycoincidental but which speak strongly of God's care and love to the personconcerned. Does God really marshall such natural occurrences in these ways? Oris it rather that God sensitizes or inspires the person to whom he/she wishes tocomm unicate the divine active presen ce in w hatever naturally o ccurs, by m eans ofthe laws of nature we normally experience, and those higher laws of which wehav e no adequate understanding? In either case w e are dea ling with G o d 's intende daction toward a particular individual or group as a perceived response tofaithfulness, openness, prayer, petition. And in either case, we must deal at somejuncture with God's direct action on secondary causes and how that direct actionis effected.

In these personal secondary causal situations, there is always some form ofpersonal relationship between God and the created person—an openness and freeinitiative of God towards the person, and of the person towards God. And thismutual relat ionship is expressed in a whole network of manifestat ions. Further-

more, the person's cooperation is not forced, but free. How does this personalcommunication take place? Something analogous occurs in human relat ionshipsand in human agency involving other persons—acting to have someone else dosomething, ei ther by command, by suggestion, by request , usually based on apreviously established relationship of some sort between the persons. The keyproblem, as always, in this relationship between God and the created personalagent is that of the causal nexus—how does God influence or inspire someone?Oftentimes it is indirect—through an event, another person, reading and reflectingupon scripture, an idea or an emotion. But at some point there must be—at least

according to our analysis so far—some direct connection, communication, orcomponent of divine action with respect to the created agent. There must alwaysbe, it seems, some direct divine communication involved at some stage in thedesignation of a prophet, in the issuance of a call or v ocatio n, and certain ly in veryspecial events like the Incarnation and the Resurrection. How is this direct linkrealized?

And then there is the second situation, God's action through impersonalsecondary causes, in which the agents or instruments are not free to act or not act.

Despite this difference from the previous case, the same issue arises—the way in



256 WILLIAM STOEGER

which God direcUy causes or constrains some created beings to act as secondary

causes.In either case how does God do this? What is the nexus between God and the

secondary causal instruments? We do not know. But perhaps we can begin tounderstand in terms of human agency and action. We do something very similar,do we not? We act through secondary causes . We decide to do something—tobuild a bookcase, to type a letter, to make a pot of coffee. And working throughour bodies—directing our eyes, our hands and our f ingers to perform verycomplex, goal-directed series of operations using tools and instruments, we bringall sorts of secondary causes together to aid in finishing our bookcase, completingthe letter, and br ew ing the coffee. Un doubtedly, G od is able to do the same thing,but with great reverence for both his/her creation and for the freedom andindependence of the persons with whom God is communicating, for the characterand the individuality of the beings, whether they be personal, animate, orinanimate, and their interrelationships, through which he/she is working. Althoughthis is a description of top-dow n causality, which will be brie fly d iscussed later, m ypoint here is not its character but rather whether and how w e can desc ribe o r m od elthe causal nex us betwee n Go d and secondary causal instrum ents. W e understan dsomething about our interaction with the material world around us, because we arematerial (but we certainly do not yet understand the relationship between our

minds and our bodies!). It is considerably more difficult to understand the directcausal nexus between God, who is immaterial and uncreated, and the materialsecondary causes .

And yet a profou nd nexus there must be— wh ether it is mor e "interio r" to thecreated causes, or m ore top-do wn and "e xterio r." I shall very sho rtly sugg est h owthe immanence and transcendence of God may provide the key to understandingthis problem of the "causal joint." 2 8 Before doing so, it is worth pointing out that,as we come to understand that the material and the immaterial are not essentiallydifferent, but intimately united at every level, and how this sameness in difference

functions, we wil l perhaps come to some better appreciat ion of God's directinteraction with secondary causes. This will be paralleled, I hope, by progress inunderstanding how m ind-body issues can be resolved. Both advan ces will help ouranalogy between human agency and divine agency to yield more fruit .

Answering this question "how?" concerning the direct causal connectionbetween God and secondary causes requires a detailed kn ow ledg e and und erstan d-ing of God and of God's causal and personal relationships with persons and withother creatures. Our inability to answer that question reflects the profoundinadequacy of our knowledge of the divine. Still , to the extent that we knowsomething about God—thanks to revelat ion and our reflect ion upon i t—we canm ove in a prom ising direction.

As I have mentioned, this is in the direction of God's immanence andtranscendence, part icularly as they are realized in God's transcendent primarycausality as a cause unlike any other. The key point is that God acts immanently

M

P e a c o c k e , Theolog y for a Scientific Age.



DESCRIBING GO D'S ACTION 257

in nature— in every 4< nook and cranny" of nature, at the core of every being and atthe heart of every relationship— to c onstitute and m aintain it just as it is and just asit evolves. God constitutes things as they are and as they act—with freedom or

without freedom, personal or impersonal—and maintains this consti tut iverel ati on sh ip with them, w ith great effic acy , but also with great reveren ce andrespect for the individuality and character of each and of the network of relation-ships they have with one another. This constitutive presence of God at "the heartof things" is so pervasive that from a strictly scientific perspective we do not noticeit. The re is noth ing we ex perien ce or enco unter, either exterior or interior, that iswithout it . God is fully and actively immanent precisely because God is fullytranscendent.

Transcendence implies complete availability, accessibility, and active

presence at every level—that is , immanence. What is transcendent is not trappedor constrained by a given level of being , a given relationship, or a given perspec-tive, and so is available to all. There are no principles or regularities or relation-ships needed other than the secondary causes, regularities, and relationships whichare vulnerable to scientific and philosophical investigation. But God's transcen-dent/imm anent primary causality is always immediately and immanently endowingthem with existence and with the intricate and d yn am ic o rder and interre lation shipsthey enjoy .

Creation is a limited expression of the divine being. The direct causal nexusis the active, richly differentiated, profoundly immanent presence of God in createdbeings and in their interrelationships. It is at the same time their limited and specificparticipation—inclusion—in God's own existence and interrelationships as Trinity,which is utterly transcendent and immaterial but also radically open to andavailable for the realization of finite possibilities. The presence of God in eachentity constitutes the direct, the immediate, relation ship of tha t entity with G od , andtherefore is the channel of divine influe nce in seconda ry ca uses. This approac h byno means resolves the mystery or answers the question, but it serves to locate it

where the answer almost certainly lies. I shall discuss some of these issues againwhen I deal with God's personal action. Here I have briefly looked at the causalproblems associated with this approach. There I shall focus more on the experienceand intention involved in such modes of divine action.

The final situation in which God has determined an effect through secondarycauses is where either direcdy or indirecUy he/she has rigidly fixed (determined)general patterns of behavior, structures, relationships, constraints—the structureof atoms, for instance, and the periodic table with all the chemical laws embodiedin it, the operation of the "laws of ph ys ics ." Am on g all the po ssible and app aren tlyinternally consistent ways in which physical reality could behave, only this one isrealized. And, if God exists and is the primary cause, he/she must have eitherchosen this realization, or allowed it to develop from some other more primordiallaws.

In either case, God at some point or in some way acts directly to effect them,and continues to act directly and immanently to conserve them. Again, we have thet4 nex us problem," for which we have no real solution— other than the o bservationsm ade above concerning the immanently and transcendently interior active prese nce

of God in all that is . God chose to make the world the way it is , however much



2 58 WILLIAM STOEGER

he/she allowed it to develo p on its ow n. God imp lemen ts that choic e by initiatingand maintaining an existence-endowing (constitutive) relationship with thepossibilities he/she wishes to realize. The choice of a particular instantiation and

its direct implementa t ion—w hatever the num ber of al lowed outcomes— wasnecessary at some level. From revelation, we appreciate some of the motivationsdirecting that choice, in terms of freedom and the primacy of love, dictating aworld in which God remains involved and caring, but in which we remain free andable to freely give or refuse love and service to God and to one an oth er.2 9

7 .3 Top-Down Causality

In this discussion we are already aware of the final problem we shall brieflydiscuss, that of top-down causality. The brief discussion of human agency aboveprovided examples of top-down causali ty—a human being building a bookcase,typing a letter, brewing a pot of coffee—in which an entity of higher complexityor possessing greater versatility determines or causes entities at lower, morefundamental levels to behave in a certain way—in a more organized and coherentway than they would do otherwise. In the hierarchical layers of organization andcomplexity which characterize our universe, top-down causali ty is pervasive.Although some causal influences operate from lower levels of organization to

higher levels, constraining and also enabling what more complex entities do, othercausal influences act from the top down to marshall and coordinate less organizedconstituents into coherent, cooperative action in service of the more complexorganism or system. A precondition for this being possible is the radicalunderdetermination of effects by the "laws of nature" at lower levels (the freedomand the need to establish initial conditions, or boundary conditions)—renderingnature very pliable within certain limits. There is really no problem here—just acharacteristic of reality which requires proper recognition and careful analysis.Obviously in the case of divine action, we have the ultimate case of top-down

causality, in which the essential issues challenging our understanding are thosewhich we have already discussed.

8 Divine Action within the Context of the Personal

The realm of divine action which is especially important for the meaning,orientation, and direction of our lives is that of the personal. In fact, within thecontext of Ch ristian revelation at least, th e focus of divine action is on the personal

and the com m una l— Go d's continual active presenc e with and on behalf of his/herpeople, drawing them closer to God, and sharing the divine l ife ever more fullywith them as individuals and as groups. God takes the initiative in our regard,invites us and en ables us to establish a relationship with him/her, gives life, reveals

2 9 Cf. George F.R. Ellis, 4 The Theology of the Anthropic Principle," in Quantum

Cosmology, 367-405 .



DE S CRIB ING G O D' S ACT IO N 2 5 9

Go dself , heals , punishes, reconciles , forgives , t ransform s, renews, saves— out oflove and care for person s. Th e ultim ate man ifestation of this is in the Incarnation ,and in the life, death, resurrection of Jesus, and sending of the Spirit of the

Incarnate One, wh o is W isdom , W ord, Child of God. I t is only as an afterthought,so to speak, but a very important afterthought, that revelation and our response toit in faith speaks of G od 's creative action with regard to the w hole co ntext withinwhich God personally directed saving and transforming activity takes place. It isobviously important fro m many points of view, but fal ls outside th e primar y fo cusof at tention in much of revelat ion. 3 0

Within the context of our present interest in articulating more adequatelydivine action in light of the self-organizing capabilities of material systems, wem ay think that G od 's person al act ion fal ls outs ide our primary fo cus. There is a

sense in which this is true. But there is also a sense in which it is com pletely fals e.If our understanding of God is primarily as a Trinity of persons—with all that thatimplies within the Christian tradition— then all divine action, how ever imperson alit may seem, in its consequences or manifestations, must be seen in terms of thepersonal, of personal relationships, and of the preconditions for the emergence ofthe personal within the universe. This is certainly true from the standpoint of ourfaith and the knowledge which we have based on divine revelation. However, it isfar from clear simply from the standpoint of the physical and the other natural

sciences, even though there are indications that point in that direction (e.g. , thecoincidences which po int towards an "anthropic principle ," however v acuous theactual logic of those arguments may be without the presupposit ion of God'sexistence). Our procedure is really to take both areas of knowledge seriously andlet them critically interact with one another, as we have already done in dealingwith other issues. What are the consequences of doing so on this subject of thepriority of the personal in divine action and on manifestations of divine action atthe level of the impersonal and inanimate through the underlying physicalconstraints and regularities and the self-organizing capabilities we see in reality?

Th e clearest answer w ould b e that all of what we see m anifeste d in the naturalworld has been established for the purpose of securing the priority and dom inanceof the personal and of personal relationships within creation, and to enable createdpersons to relate freely and lovingly with one anoth er, with th e rest of creatio n, andwith God. Profound as this is, there is nothing new here which we would not have

^ e e Richard J. Clifford, 4,Creation in the Hebrew Bible," in

Physics, Philosophy, andTheology, 15 1-7 0. In say ing this, how ever , we m ust not separate what is personal and

self-conscious from God's action in its deepest form in inanimate creation. The focus of

much of revelation on the person al should not insulate us fro m attending to and celebrating

G od's active presence in all creation. In fact, in light of both what we know from revelation

and from contemporary sciences, part of our commitment must be to emphasize our

pro fou nd unity with the rest of creation, to learn from it by conte mp lating it, and to take a

more enlightened responsibility in caring for it and fostering reverence for it. Though we

must be faithful to revelation in terms of the priority of the personal, we must be faithful to

all that it offers us, and w e cannot continue to indulge in an overwe ening anthropocentrism.




known before delving into the self-organizing behavior of matter . But is there

anything else?Yes, I believe that in George Ellis 's "Christian An thropic Pr inc ipl e," 3 1 we see

a deep compatibility amon g the autonomous ways in wh ich ph ysical, ch em ical, andbiological laws operate at every level of na ture — par ticul arly in the se lf-or gan izingcapabilities of matter and sy stems c om posed of matter at every level. Th e core ofthis compatibility is the relative independence and freedom of created reality toevolve and organize at every level without direct divin e interv ention or inte rfe ren ce(except at the most radical ontological level) with a richness of inherent potentialityand po ssibility. Correlative with this, as I have already mentioned, is G od 's relat ivehidd enn ess in creation; G od has created and is creating it , but at the same time isradically setting it free to become itself, to discover itself, to become conscious of

itself, to becom e free and to become independently personal and social, to discoverits roots and its ultimate origins, to respond freely to the invitation to enter intorelationship with the community and society of persons which is God, its sourceand origin.

In a sense the fact that we are made "in the image and likeness of God"necessi tates an infrastructure l ike we have. One which needed the constantintervention of God — divin e direct action to fill gaps and to negotiate the difficulttransitions between nonliving and living, living and conscious, conscious and

knowing—would be a creation which would be very unfree and incapable ofbecoming i tself , discovering God as a person (and not just as a demiurge andproblem-solver), and entering into a loving relationship with that God . Nor wo uldsuch a creation be very compatible with God's self-communication to it . In shortit would be a creation unw orth y of G od, and one w hich did no t adequ ately refle ctwho God is .

If we take this point of view, then there is on e o ther p oint that fa lls into pla ce.If the personal has priority, then relationships are of the utmost importance. Andwhat we see throughout creation is a reflection of this—the central role that

constitutive relationships play at every level. Entities are as they are at every levelnot just because of the parts that constitute them but because of the relationshipswhich exis t amon g the com pone nts . The w hole is a lways greater than the sum ofthe parts because of these relationships. And the different interactions whichobtain—for instance those of gravitation, electromagnetism, the weak and strongnuclear forces in physics—and the behaviors they al low and forbid help todetermine these interrelationships. We are able to some extent to describe theseregularities, patterns, constraints, and relationships thro ugh the " law s of na tu re " w eformula te .

But, as I have insisted before, these are only imperfect descriptions of theintricate network of regularities, constraints, and relationships which actuallyoperate, linking everything with everything else, but also constituting each entity'sindividuality and relative independence. If there are phenomena which seem to falloutside of the regularities we are able to describe securely, or situations in which

3 1

E l l i s , ' T h eo l ogy o f the Anthropic Principle."



DE S CRIB ING G O D' S ACT IO N 261

they do not seem to hold, then undoubtedly there a re "hig he r" laws at wo rk. T heselaws somehow reflect more fully the dominance of the personal, or the essentialrole of relationships. These in turn ar e mo re intricate, complex , or sub tie, than w e

are yet capable of understanding and modeling, but they would be thoroughlycompatible with the nature of all the entities involved and of their relationshipswith one another, with the personal, and with God, if we were to completelyunderstand those relat ionships .

9 Conclusions

This has been a sketch of my synthesis of a model of God's action in the world,

taking seriously both revelation and the knowledge of reality we have from thesciences. There are aspects of divine action which we are able to understandsomewhat better by letting these two areas of our knowledge critically interact anddialogue with each other. There are other aspects which seem to be thoroughlyresistant to our understanding, particularly that of the nexus between God and thesecondary causes through which God acts or between God and the direct effectsof divine action, as in creatio ex nihilo. The analogue of human agency is of somelimited help here. However, the principal barrier seems to be that we can only

know that critical nexus—an adequate answer to "how" divine causality operatesin this circumstances—if we are divine, or if God reveals such knowledge to us.Otherwise we do not have enough knowledge of the key term in the ne xu s— G od .3 2

s M y special thanks to all those w ho have g iven m e comm ents on a previous draft of

this paper or who have discussed aspects of it with me, especially Stephen Happel, Ian

Barbour, Tom Tracy, Nancey Murphy, George Ellis, Arthur Peacocke, Denis Edwards, Bob

Russell , Wim Drees, and John Polkinghorne.



G O D ' S I N T E R A C T I O N W I T H T H E W O R L D :The Implications of Deterministic "Chaos" and ofInterconnected and Interdependent Complexity 1

Arthur Peacocke

1 Introduction

At the beginning of the seventeenth century, Joh n Do nne lamented the collapse ofthe medieval synthesis but, 2 after that century, nothing could stem the rising tide

of an individualism in which the self surveyed the world as subject over againstobject. This way of viewing the world involved a process of abstraction in whichthe entities and processes of the world were broken down into their constituentunits. These parts w ere conceived as wholes in themselves, whose lawlike relationsit wa s the task of the <4 new ph ilosoph y" to discover. It may be depicted, somew hatover-succinctly, as asking, first, "What's there?"; then, "What are the relations

1This paper is a summ ary and (I ho pe) a clarification and development of some ideas

elaborated more fully in my Theology for a Scientific Age: Beng and Becoming—Naturaland Divine (Oxford: Blackwell, 1990; 2d ed., enlarged, London: SCM Press, 1993 and

Minneapolis, MN: Fortress Press, 1993; references are to the 1990 edition unless otherwise

indicated). It is also developed from a paper entitled, "God's Interaction with a 'Chaotic*

World: Some Scientif ic Reflect ions" (Durham, England: meeting of the Science and

Religion Forum, March 22 ,1 99 1) . A n earlier version and a fuller account of "chaos" theory

in relation to the issues discussed here, and its historical setting, is to be found in a lecture,

"Natural Being and Becoming—The Chrysalis of the Human," given by the author at the

Ge org etow n U niversity Bicentenn ial, April 4-5 , 1989 , and published in ndividuality andCooperative Action, ed. Joseph Earley (Washington , D.C.: Geo rgeto wn Univ ersity Press,

1991), 91 -1 08 . Its present form is the result of further reflection on the issues as a result of

comments made on a draft paper by participants in the Vatican Observatory/Center for

Theology and the Natural Sciences Conference at Berkeley, CA, August 1-7, 1993 on

"Chaos, Com plexity, and Self-Organization: Scie ntific Perspectives on D ivin e A ction"; and

by Brian Austin, Philip Clayton, Steve Knapp, Nancey Murphy, and Iain Paul. I am grateful

to all of these for their helpfu l critiques.

That a "whole-part" (or "downward/top-down") constraining relation (such as that

proposed as illuminating various systems-parts relations, including the brain-body

relat ion— section 3 below ) could provide a clue to how Go d might be con ceived of as

interacting with the world (sections 4.2 and 4.3) was originally expounded by the present

author in lectures given on May 9, 1987, at a Rewley House course of the Department of

External Studies of the University of Oxford.

^ T i s all in pieces, all coherence gone," John Donne in 1611 (in his Anatomie of theWorld, The First Anniversary).



2 6 4 ART H UR R. PE ACO CK E

between what is there?"; and finally, "What are the laws describing theserelations?" To implement this aim a methodologically reductionist approach wasessential, especially when studying the complexities of matter and of living

organisms, and the natural world came to be described as a world of entitiesinvolved in lawlike relations which determ ined the course of events in time.

The success of these procedures has continued to the present day, in spite ofthe revolution in our epistemology of the physics of the sub-atomic worldnecessitated by the advent of quantum theory. For at the macroscopic level that isthe focus of most of the sciences from chemistry to population genetics, theunpredictabilities of quantum events at the sub-atomic level are usually eitherironed out in the statistical certainties of the behavior of large populations of smallentities or can be neglected because of the size of the entities inv olv ed .3 Predictabil-

ity was expected in such macroscopic systems and, by and large, it becamepossible after due sc ientific investigation. H ow ever, it has turned out that science,being the art of the soluble, has concentrated on those phenomena most amenableto such interpretations. What I intend to point to are some developments fromwithin the natural sciences themselves that change this perspective on the naturalworld in a number of ways which might bear significantly on how we can conceiveof God's interaction with the world. After an initial setting of the scene andexposition of the part played until recently by the notions of predictability and

causality in the scientific world-view, I shall focus on recent ideas of deterministic"chaos" (including "order out of chaos") and on whole-part constraint (or"downward/top-down" causation) in interconnected and interdependent complexsystems. Whether or not these new perceptions are of assistance in conceptualizingm ore coherendy and intelligibly than h itherto how God interacts with the world isthen considered.

2 Predictability and Causality

What do the sciences tell us is there in the world? By far the greater proportion ofthe sciences are concerned with the region which lies between the atomic and thecosmological and which manifests a hierarchy of complexities, while at the sametime being a diversity-in-unity. Each "level" of natural complexity usually has acorresponding science that focuses upon it and one "above" focusing on the next,more complex level, which thereby represents a new emerging feature of reality,descriptions of which are often not wholly reducible to those applicable to thelower levels out of which it arose. 4

^There is also the possibility that some quantum events at the micro-level can be

amplified so as to have macro scopic conse quen ces, e.g., in the case o f non-linear dynam ic

systems (see sections 2.4 and 4.1.2).

4 For references on the literature on reductionism, see nter alia the diagram of the

"hierarchy" of scientific disciplines in Peacocke, Theology for Scientific Age, fig. 3, p. 217.

See also, dem, Creation and the World of Science (Oxford: Clarendon Press, 1979), chap.



G O D ' S I N T E R A C T IO N W I T H T H E W O R L D 2 65

The w orld is also— almo st notoriously— in a s tate of continuous flux , and i thas , not surpris ingly, been one of the major preoccupations of the sciences tounderstand the changes that occur at all levels of the natural world. Science has

asked "What is going on?" and "How did these enti t ies and s tructures we nowobserve get here and come to be the way they are?" The object of our curiosity isboth causal explanation of past changes in order to understand the present and alsoprediction of the future course of events, of changes in the entities and structureswith which we are concerned.

The notions of explanation of the past and present and predictability of thefuture are closely interlocked with the concept of causality. For detection of acausal sequence, in which, say, A causes B which causes C and so on, is freque ntlytaken to be an explanation of the pres ent in term s of th e past and also pre dic tive of

the future, insofar as observation of A gives one gro unds fo r inferring that B andC w ill follo w as tim e elapses, as in the original A-B-C.. . succession in tim e.

It has been w idely reco gnized that causality in scientific acco unts of n aturalsequences of events is only reliably attributable when some underlying relation-ships of an intelligible kind between the successive forms of the entities have beendiscovered, over and beyond m ere con junction as such. Th e fund am ental con cernof the sciences is with the explanation of change and so with predictability, andoften therefore with causality. It transpires that various degrees of predictability

pertain to different kinds of natural systems and that the accounts of causality thatare appropriate are correspondingly different .

2 .1 Relatively Simple, Dyna mic, Law-O beying Systems

Science began to gain its great ascendancy in Western culture through thesuccession of intellectual pioneers in mathematics, mechanics, and astronomywhich led to the triumph of the Newtonian system, with its explanation not onlyof man y of the relationships in m any terrestrial system s but, mo re particularly, of

planetary motions in the solar system. Knowledge of both the governing laws andof the values of the variables describing initial conditions apparently allowedcomplete predictability with respect to these particular variables. This led, notsurprisingly considering the sheer intellectual power and beauty of the Newtonianscheme, to the domination of this criterion of predictability in the perception ofwhat science should, at its best, always aim to provide—even though single-levelsystems such as those studied in mechanics are comparatively rare. It alsoreinforced the notio n that scienc e procee ded, indeed should proceed, by breakingdown the world in general, and any investigated system in particular, into itsconstitue nt entities. So it led to a view of the wo rld as m echa nical, determ inistic,and predictable. The concept of causality in such systems can be broadly subsumed

4.1; dem, God and the New Biology (London: Dent, 1986; reprint, Gloucester, MA: Peter

Smith, Magnolia, 1994), chaps. 1 and 2 (references are to 1994 edition); and Ian Barbour,

Reigion in an Age of Science, The Gifford Lectures, vol. 1 (San Francisco: Harper-

SanFrancisco, 1990), 165-72.




into that of intelligible and mathematical relations with their implication of theexistence of som ething analogou s to an underlying m echa nism that generates the se

relat ionships ( the generative mechanism). 5

2.2 Statistical Properties of Assemblies

Certain properties of a total assembly can sometimes be predicted in more complexsystems. For example, the relationships expressed in the gas laws (excluding phasechanges) are still determinable in spite of our lack of knowledge of the directionand velocities of individual molecules. It is well known that the predictability ofevents at the atomic and sub-atomic level has been radically undermined by therealization that accura te determ inations of the values of certain pairs of con jug atequantities (e.g. , mom entum^x)sition and en ergy/tim e) are m utua lly e xclusive. Thisintroduces a fundamental uncertainty (given by the Heisenberg uncertaintyprinciple [HUP]) into the quan titative description of events at this m icro-level andreinforces the unpredictability in many respects, though not in some significantones (e.g. , the classical gas laws) of such macro-systems.

Other related kind s of unpredictability are now also accepted with refe ren ceto other systems at the sub-atomic level, for example in radioactive decay (seesection 4.1.2 [ii], below). All that is known is the probability of a given atom

breaking up in a particular time interval. This exemplifies the current state ofquantum theory, which al lows only for the dependence on each other of theprobable values of certain va riables and so for a looser form of causal coup ling atthis micro-level than had been taken for granted in classical physics. But note thatcausality, as such, is not eliminated, only classical, deterministic (Laplacian)causality.

2 .3 Newtonian Systems Deterministic yet Unpredictable at the Micro-Level ofDescription

That there are New tonian sy stems wh ich are determ inistic yet unpre dictable at themicro-level of description has been a tim e-bo m b ticking awa y u nder the ed ifice ofthe deterministic/predictable paradigm of what constitutes the world-view ofscience since at least the turn of the centu ry. For exa mp le, the French m athem ati-cian Henri Poincar6 pointed out that, since the ability of the (essentially Newto-nian) theory of dynamical systems to make predictions depended on knowing notonly the rules for describing how the system will change with time, but also onknowing the initial conditions of the system, such predictability was extremelysensitive to the accuracy of our knowledge of the variables characterizing those

^ o m Harri, The Principles of Scientific Thinking (London: Macmillan, 1970), chap.

4 .



G O D' S INT E RACT IO N WIT H T H E WO RL D 267

initial cond ition s. 6 Thus, it can be shown that even in assem blies of bo dies obeyin gNewtonian mechanics there is a real limit to the period during which the micro-level description of the system can continue to be specified, that is, there is a limit

to micro-level predictability, the horizon of what Wildman and Russell call"eventual unpredictabil i ty." 7 There is certainly not predictability by us over anindefinite time. 8 This is so, in spite of the determ inistic character of N ew to n's laws,on acco unt of our inability ever to determ ine suff iciently precisely the initialcondit ions.

For example, in a gam e of billiards sup po se that, af ter the first sho t, the ballsare sent in a contin uou s series of collisions, that there are a very large num ber ofballs and that collisions occur with a negligible loss of energy. If the averagedistance between the balls is ten times their radius, then it can be shown that an

error of on e in the 1000th decim al plac e in the angle of the first impac t me ans thatall predictability is lost after 1000 collisions.9 Clearly, infinite initial accuracy isneeded for th e total predictability through infinite time that Laplace assured us waspossible. The uncertainty of movement grows with each impact as the originallyminute uncertainty becom es am plified . So, although the system is determ inistic inprinciple—the constituent entities obey Newtonian mechanics—it is never totallypredictable in practice.

Mo reover, it is not predictable for another reason, for even if per impossible

the error in our kno wled ge of the angle of the first impact were zero, unpredictabil-ity still enters because no such system can ever be isolated completely from theeffects of everything else in the universe—such as gravity and, of course, themechanical and thermal interactions with its immediate surroundings.

Furthermore, attempts to spec ify m ore and m ore finely the initial conditionswill eventually come up against the barrier of the HUP in our knowledge of key

'See , e.g., Henri PoincarS, Science and Method, trans. F. Maitland (London : Thom asNelson, 1914), 68. Earlier considerations of this kind also appear in the works of J.

Hadamard (1898) and P. Duhem (19 06) . For details, se e David Ruelle, Chance and Chaos(Harmondsworth: Penguin Books, 1993), chap. 8, nn. 1 and 3, pp. 175-6.

7 Se e Wesley Wildman and Robert John Russell, "Chaos: A M athematical Introduction

with Philosophical Reflections" (in this volume).8John T . Houg hton, having de fined "chaotic behavior" as "the unpredictable situations

. . . in wh ich give n infinitesimally different starting points, systems can realize very different

outcomes,"(p. 42) later makes the same point as in my text, as follows: "For a chaotic

system , a predictability horizon m ay be defined beyo nd w hich for a given accuracy in the

specification of the initial conditions the behavior of the system cannot be predicted. The

predictability horizon only moves away linearly as the number of decimal places in the

initial specification increases... initial conditions can never be specified absolutely precisely

so that the predictability horizon represe nts a funda me ntal limit to our ab ility to predict"(pp.

48-49). Houghton, "New Ideas of Chaos in Physics," Science and Christian Beief 1 (1989):

41 -51 .

'Michael Berry, "Breaking the Paradigms of Classical Physics from Within," 1983

Cercy Symposium, Logique et TMorie des Catastrophes.




variables characterizing the initial conditions even in these "N ew ton ian " system s.Does this limitation on our knowledge of these variables pertaining to individual"particles" (whether atoms, molecules, or billiard balls) in an assembly reduce the

period of time within which the trajectory of any individual "particle" can betraced? Is there an ultimate upper limit to the predictability horizon set by theirreducible Heisenberg "fuzziness" in the initial values of those key initialparameters to which the eventual states of these systems are so sensitive? Does"eventual unpredictability" prevail—at least with respect to the values of thosesame parameters wh ich characterized the initial conditions and to which the H U Papplied? Th e phy sicist J.T. Houghton thinks so 1 0 and so apparently does another,Joseph Ford, who (to anticipate the next section somewhat) having argued that"chaos is merely a synonym for randomness" goes on to affirm that "we may

legitimately inquire if there is any chaos (randomness) in quantum dynamicsbeyond that of the type contained in the probability density TJ/'I^."11 H o u g h t o n ' scontention does not appear to go beyond the limitations of the italicized conditionand so can be provis ionally a cce pte d, 1 2 since it does not seem to be subject to theoutcome of the debate on quantum chaos (see end of section 2.4 below).

2 .4 "Chaotic" and "Dissipative" Systems

On e of the striking developments in science in recent years ha s been the increa singrecognition that there are many other systems (physical, chemical, biological and

10 Houghton in "New Ideas,*' exp resse s the situation thus: " . . . as soon as the required

specification of the initial conditions [in chaotic systems, defined as in n. 8 above] involves

details of the movements of individual electrons or atomic nuclei [one could add—any

material entity], the Heisenberg uncertainty principle becomes relevant. We then come up

against an inability, not only in practice but in principle, to specify with perfect precision thestate of the system at any given time"(p. 49). The use of "in principle" in this last phrase is

disputed, but whether or not there will prove to be hidden variables, physicists have to

accept that the HU P has to be applied to our kno wle dge of initial c ondido ns.

"Joseph Ford, "What is Chaos, that w e should be m indful o f it?" in The New Physics,ed. Paul Davies (Cambridge: Cambridge University Press, 1989), 365. What Ford is

referring to in the italicized phrase can be expounded as follows based on an editorial

comment by Russel l :

Quantum mechanical systems display an inherent statistical character, represented by

the wave function (\Jj) and computed from its absolute value (^*\Jf). However, the wave

function itself evolves deterministically, according to the Schrodinger equation (in non-

relativistic quantum ph ysic s), and doe s not display the kind of ch aotic b ehavior ty pified b y

the time evolution of even simple (classical) systems such as those represented by the logistic

equation. Whether or not quantum systems do actually display additional statistical behavior

beyond that represented by the wave function—that is, whether or not there is a quantum

version of classical chaos (called "quantum chaos")—is still an open question, as discussed

in the last paragraph of this section.

1 2

A position I myself adopted in Theology for a Scientific Age.



G O D' S INT E RACT IO N WIT H T H E WO RL D 2 69

indeed neurological) which can also in practice become unpredictable in theirmacroscopically observable behavior, even when this is governed by deterministicequations. Basically the unpredictability arises f or us in practice b eca use tw o states

of the systems in question which differ, even only slightly, in their initialconditions eventually generate radically different subsequent states. Broadly thisis often denoted as 'chaotic behavior' (e.g. , see n.8); or 'chaos* is taken asequivalent to ' randomness ' (as with Ford, section 2.3 above and n. l l) . Moreprecise definitions of 'chaos, ' are possible in particular systems and this may beillustrated mathematically by the sensitivity of the eventual reiterated solutions ofthe " logis t ic equation": 1 3

x ^ = k x , ( 1 - x j

to values of the initial con ditio ns (x 0) when the parameter k (which in real systemsoften represents external conditions) is such as to locate the system in the"bifurcation" regime (k=3.0 to 3.58), or in the "chaotic/random" regime (k=3.58to 4). This particular equation has proved to be significant for certain naturalsystems (predator-prey patterns, yearly variation in insect and other populations,etc.) and this combination of an overall influence of environmental factors,"external" conditions, and sensitivity to initial conditions has transpired to beoperative in a very w ide rang e of natural system s. In some of these system s there

can occur an amplification of a fluctuation of the values of particular variables(e.g. , pressure, concentration of a key substance, etc.) pertaining at a micro-levelwithin the system so that the macroscopic state of the system as a whole undergoesa marked transit ion to a new regime of new patterns of, for example, pressure,concentrations, etc. The state of such systems is then critically dependent on theinitial conditions which prevail within the key, transitory fluctuation which issubsequendy amplified. A well-known exam ple is the "butterfly effect" of EdwardLorenz whereby a butterfly dis turbing the air here today is said to affect whatweather occurs on the other side of the wo rld in a m on th 's tim e throu gh am plifica-tions cascading through a chain of complex interactions. Another is the transitionto turbulent flow in liquids at certain combinations of speed of flow and externalconditions. Yet another is the appearance, consequent upon localized fluctuationsin reactant concen trations, of spatial and temp oral pa tterns of conce ntratio n of thereactants in certain, otherwise homogenous systems which involve autocatalyticsteps—as is often the case, significantly, in key biochemical processes in livingorganisms.

One common feature of all these dynamic systems is that they are "non-

linear" with respect to the relation between certain key variables of the system , forexample the fluxes of material or energy and the "forces" controlling them. It isnow realized that the time-sequence of such complex dynamical systems can takemany forms: "limit cycles" such as those which govern the motion of the planetsor the pendulum of a grandfather clock; regular oscillations in time and space with

13 Fo r a detailed discussion o f the logistic equation, see Wildman and Russell, "Chaos."




respect to the concentrations of key constituents in those c hem ical system s alreadymentioned o r with respect to biological populations of predators and prey; systemsthat "fl ip" periodically between two or more al lowed s tates . As a key parameter

increases, all kinds of further com plexit ies can occur with successive bifurcations,and so forth , leading eventually into "chao tic/rando m " regim es.

In the real world most systems do not conserve energy: they are usuallydissipative systems through which en ergy and m atter flow, and so are also open inthe thermodynamic sense. Such systems can often, when non-l inear and farremoved from the s tate of equil ibrium, give rise to the kind of sequence justmentioned. Moreover, non-equil ibrium physics and the discovery of newpropert ies of matter in far-from-equil ibrium condit ions has also led to therecognition that, in such change-overs to temporal and spatial patterns of system

beh avio r we have examples of "symm etry-breaking," and of macroscopic-sca lecorrelations, that is , of self-organization." 1 4 Ilya Prigogine and his colleagues atBrussels have called this "order through fluc tuation s" and "order out of ch ao s,"1 5

perhaps some wh at misleadingly in view of the current usage of the term 'cha os. 'Th e point is that new pa tterns of the constituents of the system in space and timebecome established when a key parameter passes a critical value.

Explicit awareness of all this is only relatively recent in science andnecessitates a re-assessment of the potentialities of the stuff of the world, in which

pattern formation had previously been thought to be confined only to themacroscopically static, equilibrium state. In these far-from-equil ibrium, non-l inear,open systems, matter display s its poten tial to be self-organ izing and thereb y bringto existence n ew forms entirely by the op eration of force s and the m anife station ofpropert ies we thought we already understood. As Crutchfield, et al. put it:"Through amplificat ion of small f luctuations i t [nature] can provide naturalsystems with access to novelty." 1 6

How do the notions of causality and predictability relate to our newawareness of these phenomena? We shall discuss this initially without taking

account of quantum uncertainties. Causality, as usually understood, is clearlyevidenced in the systems just discussed. Nevertheless the identification of thecausal event(s) now h as to be ex tended to include u nob serva ble flu ctuatio ns at themicro-level, whose effects in certain systems may extend throu gh the w ho le systemso as to produce correlations between the values of characteristic parameters which

1 4 See Gregoire Nicolis, "Physics of Far-From-Equilibrium Systems and Self-

Organization," in The New Physics ed. Paul Davies (Cambridge: Cambridge University

Press , 1989), 316-47; and Peacocke, The Physical Chemistry of Biological Organization(Oxford: Clarendon Press, 1989), ch aps. 2 and 4.

1 5 S e e , inter alia, Ilya Prigogine, From Beng to Becoming: Time and Complexity inthe Physical Sciences (San Francisco: Freeman, 1980); dem and Isabelle Stengers, OrderOut of Chaos: Man's New Dialogue with Nature (London: Heinemann, 1984); and

Peacocke, Biological Organization, chap. 2.

1 6

J.P. Crutchfield, et al., "Chaos" (in this volume).



G O D ' S I N T E R A C T I O N W I T H T H E W O R L D 2 7 1

extend over a spatial scale many orders of magnitude greater then that of theoriginal region of fluctuation itself.

The equations governing all these systems are deterministic, which means

that if the initial conditions were known with infinite precision, prediction wouldbe valid into the infinite future, as famously postulated by Laplace. But it is of thenature of our knowledge of the real num bers used to represent initial conditionsthat they have an infinite decimal representation and we can know only theirrepresentation up to a certain lim it. He nce there w ill alwa ys be, for system s wh osestates are sensitive to the values of the parameters describing their initialcondit ions, an "eventual unpredictabil i ty" by us of their future states beyond acertain po int . 1 7 Th e ' 'butterfly effect," the am plificatio n of mic ro-fluc tuation s, turnsout to be but one example of this and we also no te that in such c ases th e prov okin g

fluctuations would anyway be inaccessible to us experimentally. Hence, althoughdeterminis t ic equations govern the t ime-course of these systems, they areunpredictable beyond certain limits because of the inevitably limited accuracy ofour know ledge, m aking them in practice irreducibly unpredictable.

For those dissipative systems that are in regimes in which they could moveto a finite number of possible future states, our lack of precise knowledge of theparameters prevailing in the crucial fluctuation(s) which could provoke symmetry-breaking at the critical value of a key parameter, allows us to affirm only the

probability of future occupancy of any of the possible states. That is , which statewill be occu pied is unpredictable, as well as uncontrollable, and may be said by usto be a matter of "pure chance." Only a detailed knowledge of the particular,individual fluctuation initiating the symmetry-breaking would allow prediction andthat is never going to be observable by us. Hence, in spite of the excitementgenerated by our new awareness of the character of the systems described in thissection, the basis of th e unpred ictability in practice of their overall states is, afterall, no different from that of the eventual unpredictability at the micro-level ofdescription of the Newtonian systems discussed in the previous section (2.3).

W hat will be the effect of quantum (HUP) uncertainties on the predictabilityof the systems displaying "chaotic behavior," that is, hav ing an im m en se sensitivityto initial conditions (to use H ou gh ton 's defin ition)? T he effects of any uncertaintywithin "the type contained in the probability density xj/'ty" would also establish anirremovable horizon of "eventual unpredictability" fo r these "ch aotic " system s— atleast with respect to the level of description of the parameters about which therewas this initial uncertainty. This quantum limit to predictability would also extend,for systems that amplify the effects of fluctuations, to macroscopic states, allowingonly a probabilistic knowledge of which am ong possib le states will actually occur.

But a further question remains, expressed by Ford in the follo w ing term s: "Ifwe exclude from consideration the innate randomness of i\f*\\f and the like [seeprevious paragraph], what op portunit ies for chaos rem ain? " He con tinues, "Th ereare two: randomness in the Schrodinger t ime evolution or f low of the wave

1 7 E.g., the direction of rotation of a B6nard cell in a convecting fluid, or that of a

rotatory w av e pattern in the Belousov-Z habo tinsky reaction.




fu nc tio n or random ness in the quantum eigenvalues, e igenfun ctions andmatrices ." And, he tells us , a "m ajor battle . . . is even now being waged over theexistence of [such] quantum chaos." That being so, it would be unwise to prejudge

the outcome of what Ford also says would be "an earthq uake in the fou nda tions ofphysics ,"18 but concludes that <4 the evidence weighs heavily against quantum chaos[as so de f ine d] . " 1 9

3 Wh ole-Part Constraint (or "Dow nwardITo p-Dow n" Causation)

3.1 General

The notion of causality, when applied to systems, has usually been assumed todescribe "bottom -up" causatio n— that is, the effect on the properties and behaviorof the system of the properties and b ehav ior of its constituent units. However, aninfluence of the state of the system as a whole on the behavior of its componentunits—a constraint exercised by the whole on its parts—has to be recognized. D.C a m p b e l l 2 0 and R.W. Sperry ,2 1 called this "downward" (or " top-down")causation, 2 2 but it will usually be referred to here as "whole-part constraint." For,to take the example of the B6nard phenomenon, beyond the critical point,

individual molecules in a hexagonal "cell," over a wide range in the fluid, m o v ewith a common component of velocity in a coordinated way, having previously

18 Ford, "What is Chaos?," 366.1 9 Ibid., 370. Ford goes on to point out that—even if quantum chaos, as he has just

defined it, does not occur— beca use "quantum mechan ics is firmly rooted in the incomput-

able number continuum," it fo l lows that "if chaos is ubiquitous in nature at the m icros cop ic

level, whether or not nquantum mechanics then there is an incomputable and uncontrolla-ble noise level on the smallest scale" (emphasis added). An irreducible, unpredictability

would then arise from the same considerations as prevailed w ith New tonia n sy stem s, nam ely

on the basis of the infinite decimal representation of real num bers (se e s ec tion 2.3 , and earlier

in this section) and, more generally, of algorithmic complexity theory. (Ibid., 365-70.)

D o n a l d T. Cam pbell, "'Downw ard Causation* in Hierarchically Organized Systems,**

in Studies n he Philosophy of Biology: Reduction and Reated Problems ed. Francisco J.

Aya la and Theod osius Dobzhansky (London: Macm illan, 1974), 179-86.

2 'Roger Sperry, Science and Moral Priority: Merging Mind, Brain, and HumanValues (Oxford: Blackwell , 1983), chap. 6.

2*The "downward/top-down causation" term inology can, I have fou nd, be m isleading

since it is actually meant to denote an effect of the state of the system as a whole on its

constituent parts, such as the constraints on the parts of the boundary conditions of the

system as a whole—more broadly, the constraints of actually being in the interacting, co-

operative network of that particular, whole system. The word 'causation* is not really

appropriate for describing such situations, so—in this paper—I have preferred the usage of

'whole-part consraint,* rather than that of 'downward-* or 'top-down causation,* which I

used more generally in Theology for a Scientific Age.



G O D ' S I N T E R A C T IO N W I T H T H E W O R L D 2 73

manifested only entirely random motions with respect to each other. In suchins tances , 2 3 the changes at the micro-level, that of the constituent units, are whatthey are because of their incorporation into the system as a whole, which is

exerting specific constraints on its units, mak ing th em beh ave oth erw ise than theywould in isolation. Using "boundary con ditions" la ng ua ge ,2 4 one could say that theset of relationships between the constituent units in the complex whole is a new se tof boundary conditions for those units. There is also, of course, the effect on asystem of its total environment (ultimately, the whole universe), since no systemis ever truly isolable though the particular system effects can usually be distin-guished from these.

It is important to emphasize again that recognition of the role of such whole-part constraint in no way d erogates fro m the continued recogn it ion of the effectsof its components on the state of the system as a whole (i.e. , of "bottom-up"effects). But the need for recognition of the former is greater since hardly anyonesince the rise of reductionist scientific m etho dolo gies do ub ts the sig nif ica nc e of thelatter. Indeed this lack of a proper recognition of whole-part constraint hasunfortunately often inhibited the development of concepts appropriate to the morecomplex levels of the hierarchy of natural systems.

On a critical-realist view of the epistemology of the sciences,2 5 this impliesthat the entities to which the theories and experim ental laws refer in our analyses

correspond, however inadequately and provis ionally, to epis temologically non-reducible features of reality, which have to be take n into acco unt w hen the system -as-a-whole is interacting both with its parts and with other systems (includinghuman observers) . These new features may be deemed putat ively to exis t a t thevarious levels being studied; that is , they can also have an ontological reference,however tenta t ive . 2 6 It wo uld then b e legitimate to envisage the postulated realitywhich consti tutes a complex system-as-a-whole (the " top" of the " top-down"

^Another example from another area of s cien ce, a compu ter program med to rearrange

its ow n circuitry through a robot that it itself co ntrols, has been propo sed by Paul D av ies in

The Cosmic Blueprint ([London: Heinemann, 1987], 172-4, fig. 32) as an instance of what

he called "downward causation." In this hypothetical (but not at all impossible) system,

changes in the information encoded in the computer's software (usually taken as the

"higher" level) down wardly caus e m odifications in the com puter's hardware (the "lower"

level)—an example of software-hardware feedback.

2 4 A S does M. Polanyi in

nter alia"Life's Irreducible Structure,"

Science160 (1968):

1308-12 . Se e the account in Peacocke, God and the New Biology, 23-5.

2 5P e a c o c k e , Intimations of Reality: Critical Realism inScience and Reigion (Notre

Dame, IN: University of Notre Dame Press, 1984), chap. 1. See also dem. Theology for aScientific Age 11-19, for references to other authors.

*T his over-brief comm ent refers, of course, to the much debated issue of reductionism

and the possibility of emergent realities at higher levels of complexity. My own views are

expressed nter alia in Theology for a Scientific Age 39-41 ; and God and the New Biology,chaps. 1-2, where references to the extensive literature may be found. See also the next

sec don.




terminology) as exerting a constraint upon its component parts, the realities

postulated as existing at those lower levels—while continuing, of course, to

recognize the often provisional nature of our attempted depictions of realities at all

levels.

3 .2 Evolution

The pattern of "causal" relationships in biological evolution is interesting in thisconnection. We are dealing with a process in which a selective system "edits," asit were, the produ cts of direct phy sico-ch em ical causation (i.e. , chan ges in D N A)over periods of time covering several reprod uctiv e gen erations. D. C am pbell give san example of th is : 2 7 the surfaces and m uscle at tachmen ts of the jaw s of a w orkerterm ite are mechanically highly efficient and their operation depe nds on theproperties of the particular protein s of which the jaw s are ma de. The se hav e beenoptimized by natural selection. Any particular organism is only one in a series ofgenerations of populations of termites and it is the increasing efficacy of theproteins in consti tut ing efficient jaws that is operative in selection and therebydetermines the sequences of the DNA units. Yet when one looks at the develop-ment of a single organism, one observes only, with the molecular biologists, thebiochemical processes whereby protein sequences, and so structures, are "read out"

from the DNA sequences. Hence the network of relat ionships that consti tute thetemporal evolutionary development and the behavior pattern of the wholeorganism is determining what particular DNA sequence is present at the controllingpoin t in its genetic material in the evolved organ ism. T his is what Cam pbell called"downward causa t ion."

It is not adequate to describe such complex interlocking networks of eventsand changes operating at different levels as causally connected in a sequential,constant conjunction of events . We seem rather to have here a determination ofform through a flow of information, as distinct fro m a transm ission of energy ,

where " informat ion" is conceived of in a broad enough sense2 8

to include the

2 7Campbel l , "Downward Causation," 181-2.

^The relation between the different usage s of 'information* has been use fully cla rified

by J.C. Puddefoot in "Information and Creation," in The Science and Theology ofInformation, ed. C. Wassermann, R. Kirby, and B. Rordoff ([Geneva: Labor et Fides, 1992],

15). He distinguishes three senses relevant to the present context (my numberings):

©"Information" in the physicists*, communication engineers*, and brain scientists*

sense, that of C .E. S han non — the sen se in wh ich "information*' is related to the probability

of one outcome, or case selected, out of many, equally probable, outcomes or cases. In this

sense it is, in certain circumstances, the negative of entropy.

(ii)"Information" in the sense of the Latin nformo,-are meaning "to give shape or

form to." Thus, "information" is "the action of informing with some active or essential

quality [sense ii]," as the noun corresponding to the transitive verb 'to inform', in the sense

(ii) o f ' T o giv e 'form' or formative principle to; hence to stamp, impress, or imb ue with

some specific quality or attribute" (quotations from the Shorter Oxford English Dictionary




selective input from the environment towards molecular structures—for example,the DN A sequences in the termite jaw exam ple. Such d eterm inative relations m ayoperate between two different kinds of " level" in nature. The determination of

form by fo rm requires a f low of information, in this case, between lev els .2 9

3 .3 The Brain, Mental Events, and Consciousness

It is in terms such as these, relevant to our later considerations of God's interactionwith the world (section 4) that some neuro-scientists and philosophers have cometo speak of the relation between mental events experienced as consciousness andthe physico-chemical changes at neurons that are th e triggers of obs erv able actionsin those living organisms whose brains are sufficiently developed that it is

appropriate to attribute to them some kind of consciousness. As John Searle hasrecently put it:

Co nscio usn ess . . . is a real property of the brain that can cause things tohappen. My conscious attempt to perfo rm an action such as raising m y armcauses the movement of the arm. At the higher level of description, theintention to raise my arm causes the movement of the arm. At the lowerlevel of description, a series of neuron firings starts a chain of events thatresults in the contraction of the muscles. . . the sam e sequenc e of events has

two levels of description. Both of them are causally real, and the higherlevel causal features are both caused by and realized in the structure of thelower level elements . 3 0

For Roger Sperry and Donald MacKay, "mental events" for human beingsare the internal descr iption s w e offer of an actual total state of the brain. The totalbrain state acts as a constraint on what happens at the more micro-level of theindividual neurons; thus what occurs at this m icro-lev el is wh at it is be cau se of theprevailing state of the whole. There is operative here, it is being suggested, awhole-part constraint of one "level" upon another, from that of the brain state as

on Historical Principles).(iii)'Tnformation" in the ordinary sense of "that of which one is apprised or told"

(Shorter Oxford, sense 1.3).

Puddefoot points out that "information (i)" is necessary to shape or give form, as

"information (ii)," to a receptor. If that receptor is the brain of a human being, then

'inform ation (iii)" is con vey ed. In this paper the term "information" (and its associates) is

being broadly used to represent this whole process of (i) becoming (i i i)—and only

modulating to (iii) when there is a specific reference to human brain processes.

Although in actual natural systems, there is never a flo w o f inform ation without som e

transfer of energy, however small, the concept of nformation is clearly distinguishable from

that of energy.^ . M . M acKay, 'T he Interdependence of Mind and Brain," Neuroscience 5 (1980):

1389-91 .

^ohn Searle, Minds, Brains, and Science(Cambridge, MA: Harvard University Press,

1984), 26 (emphasis added).




a whole to that of the individual neurons. Descriptions of the total brain state inpurely neurological terms would be exceed ingly com plex and, indeed , con sideringthe complexity of the brain, may never be forthcoming in anything other than

broad terms. The causal e ffectiv ene ss of the wh ole brain state on the actual statesof its component nerves and neurons is probably better conceived of in terms ofthe transfer of inform ation rather than of en ergy, in the w ay a progr am repre sent-ing a certain equation, say, controls the chips in a computer—but this whole areaof investigation is still very much sub judice. (For example, is there a 1:1correlation between brain states and mental states? Can a me ntal state be "rea lized "in a number of different brain states?)

It seems that, with the evolution of brains, this kind of whole-part constrainthas become more and more s ignificant in the evolutionary development, as the

whole state and behavior of the individual organism itself plays an increasing role.This has also, as we saw, introduced an elem ent of flexib ility into the ev olutiona ryprocess. Furthermore, since the brain-in-the-body is a dissipative system, it nowbecomes possible to env isage that the actual succession of states of the brain m ayprove in practice not to be describable in terms of currently available scientificconcepts. This would then point to the need fo r som e higher-level conc epts (thosecalled "mental"?) to denote and explicate sequences of events in the brain and the"whole-part constraints" operating from this level . Furthermore, as Nancey

Murphy has written: "W e attribute freedom to the person inso far as the states of theorganism are attributable to the person as a whole, involving intentions, desires,etc. So if the brain states are not predictable [I would say "describable"] whenconsidered solely at that [holistic] level, we have evidence that higher-level (free)processes are the determinative fac tor ." 3 1

4 God's Interaction with the World in the Light of these Scientific Perspectives

4 .1 Unpredictabilityy Open-Endedness, and Flexibility32

The world appears to us less and less to possess the predictability that has been thepresupposition of much theological reflectio n on G o d' s interaction w ith the wo rlds ince Ne w ton 3 3 We now observe it to possess a degree of openness and flexibility

3 1In a personal note, January 24 , 199 4. S ee also, Peacocke, "Natural Being and

Becoming."

"This section represents an elucidation of Theology for a Scientific Age, 152-6, and

a tightening up of the argument, by making more careful distinctions between "in principle"

and "in practice" unpredictability with respect to deterministic chaos and quantum theory

and to whether or not God or ourselves are under consideration.

3 3 Here, and in what follows, by both 'world* and 'all-that-is* I intend to refer to

everything apart from God, both terrestrially and cosmologically. I regard the world/all-that-

is, in this context, fs an interconnected and interdependent system, but with, of course, great

variation in the strength of mutual inter-coupling. All wave functions, e.g., on ly go



G O D ' S I N T E R A C T IO N W I T H T H E W O R L D287

within a lawlike framework, so that certain developments are genuinely unpredict-ab le by us on the basis of any conceivable science. We have good reasons forsaying, fr om the relevant scien ce and mathem atics, that this unpredictability will,

in practice, condnue.The history of the relation between the natural sciences and the Christian

religion affords m any instances of a hu m an inability to predict being exploited bytheists postulating the presence and activity of God to fill the explanatory gap.However, as these gaps were fi l led by new knowledge, "God" as an explanationbecame otiose. Do w e now hav e to take account of, as it were, permanent gaps inour ability to predict events in the natural world. Does this imply there is a "Godof the (to us) uncloseable gaps'*? There would then be no possibility of such a Godbeing squeezed out by increases in scientif ic knowledge. This raises two

theological questions: (1) "Does God know the outcome of these s i tuations/systems that are unpredictable by us?" and (2) "Does God act within suchsituations/systems to effect the divine wil l?"

4.1.1 Non-Quantum Considerations

W e will first respond to these question s excluding quantum theory considerations.

W ith respect to (1), an omniscient God may be presumed to know, not only all the

relevant, deterministic laws which apply to any system (such as those discussed insections 2.3 and 2.4), but also all the relevant initial conditions of the determiningvariables to the deg ree of precision required to predict its state at any fu tur e time,ho w ev er far ahead, together with the effects of any external influences fro manywhere else in the universe, however small . So there could be no "eventualunpredictability" with respect to such systems fo r an inf inite, om niscie nt G od , ev enthough there is such a l imit ing horizon for f ini te human beings—because of thenature of our know ledge of real num bers and beca use of ineluc table observ ationallimitations. To take a particularly significant ex am ple, divine om niscien ce m ust be

conceived to be such that Go d would know and be ab le to track the min utiae of thetriggering fluctuations in dissipative systems, unpredictable and unobservable byus, whose amplification leads at the macroscopic level to one particular, macro-scopic outcome (e.g. , a symmetry-breaking) rather than another—consequentlyalso unpred ictable by us .

Only if we thus answered (1) affirmatively, could we then postulate that Godmigh t cho ose to influence events in deterministic system s in the wo rld b y cha ng ingthe initial conditions so as to bring about a macroscopic consequence conformingto the divine will and purposes—that is, also to answer (2) affirmatively. Godwould then b e conceived of as acting, as it were, "w ithin " the flexibility we find inthese (to us) unpredictable situations in a way that could never be detected by us.Such a mode of divine action would never be inconsistent with our scientific

asymptotically to zero at infinity—and recall the effe cts of gravity from distant ga laxies eve n

on the collision of bill iard balls (section 2.3 ), not to mention the ecolog ical connec tedness

of terrestrial life within itself and with the state of the earth. (Se e also section 4. 2 and n. 42 .)




knowledge of the situation. In the case of those dissipative system s w hose m acro -states (often involving symmetry-breaking) arise from the amplification offluctuations at the micro-level that are unpred ictable and uno bserva ble by us, Go d

would have to be conceived of as actually manipulating micro-events (at theatomic, molecular and, according to some,3 4 quantum levels) in these initiatingfluctuations in the natural world in order to produce the results at the macroscopiclevel which God wills.

But such a conception of Go d's action in these, to us, unp redic table situatio nswould then be no different in principle from that of God intervening in the orderof nature w ith all the problem s that that evokes for a rationally cohere nt belief inGod as the creator of that order. The only difference in this proposal from that ofearlier ones postulating divine intervention would be that, given our recent

recognition of the actual unpredictability, on our part, of many natural systems,God's intervention would always be hidden from us.

Thus, although at first sight this introduction of unpredictability, open-endedness and flexibility into our picture of the natural world seems to help us tosuggest in new terminolog y how God might act in the world in now unclose able"gaps," the abo ve considera tions indicate that such divin e action wou ld be jus t asmuch " intervention" as i t was when postulated before we were aware of thesefeatures of the world. This analysis has, it must be stressed, been grounded on the

*In a paper in the previous volume in this series ("Divine Action, Freedom, and the

Laws of Nature," in Quantum Cosmology and the Laws of Nature: Scientific Perspectiveson Divine Action, ed. Robert John Ru ssell , Na ncey Murphy, and C J. Isham [Vatican C ity

State: V atican Observatory, 199 3; Berk eley, CA : Center for Th eo log y and the Natural

Sciences, 1993], 185-207), W.P. Alston reverted to an earlier idea of William Pollard, in

Chance and Providence: God's Action in a World Governed by Scientific Law (New York:

Scribner, 1958), that God can act at the quantum level because quantum theory predicts onlyprobabilities of particular outcom es of a given situation. H e w rote, "G od can, con siste nt w ith

quantum theory, do some thing to bring about a physically improbable outcom e in one or

more instances without any violation of physical law" (p. 189). For reasons outside the

scope of this particular paper I am skeptical of this proposal, as I am of the similar on es also

advanced in this volum e by Geor ge E llis ("Ordinary and Extraordinary D ivine A ction : Th e

Nexus of Interaction") and, possibly, also those of Nancey Murphy ("Divine Action in the

Natural Order: Buridan's Ass and Schrodinger' Cat").

Later (p. 190) Alston argues that at levels other than the quantum one—i.e., at levels

where there are genuinely deterministic laws relating outcomes to initial situations—God

could be an additional factor, "a divine outside force," not previously allowed for by the

science involved. But this is vulnerable to the criticism that such a "force" cannot but be in

the natural order to be effective—and therefore amenable to scientific investigation. But it

is these very investigations which unveil the deterministic la ws wh ich d emonstrate that such

arbitrary occurrences do not occur. So such "intervention" is an incoherent idea, as well as

casting doubts on the foundations on which the very existence of a divine creator can be

postulated, na nely the regularity of that ordering of the natural world which the sciences

reveal and from which is inferred that it manifests and expresses an endowed rationality.



G O D ' S I N T E R A C T I O N W IT H TH E W O R L D 2 7 9

assumption tha t God does know the outcome of natural situations that are

unpredictable by us; that is, on an affirmative answer to (1). It assumes total divine

om niscience about al l actual , natural events .

4.1.2 Quan tum Theory Considerations

Consideration of the foregoing in the l ight of quantum theory cannot avoid thecontinuing current disagreements concerning the basis and s ignificance of thequantum uncertainties which are expressed in the HUP, which qualif ies totalpredictability, however interpreted. The broad possibilities may be delineated asfol lows:

(i) There are "hidden variables"—that is, there are und erlying d eterm inistic

laws, unknown to us, which govern the time-course of the precise values of thevariables (momentum, posit ion, energy, t ime, etc . ) appearing in the HUP. Theuncertainties, the "fu zz ine ss, " in our kno w ledg e of the values of these variables ispurely an epistemological l imitat ion on our part , which w ould not also be one foran omniscient God. Such a God would know both these laws and the relevantinitial conditions. Hence the conclusions about how God might interact with theworld which were drawn in the previous section (4.1.1) would still apply.

(ii) No "hidden variables" 35— that is, the epistemo logical limitations

expressed in the H U P can never be obviated, not only in practice bu t also in th eor y,and represent a fundamental uncertainty that inherently exists in the values of thevariables in question— an ontological claim that there is indeterm inism with resp ectto these variables. T he future trajectory of any system will always inherently havethat unavoidable lack of precise predictability, given by the HUP relations, withrespect to these variables—it is genuinely ^deterministic in these respects (if notin all, e.g. , in the statistical properties of the ensemble). Only a probabilisticknowledge of these variables is possible for us, but this limitation is insurmount-able. It represents an "in principle" limitation. This is the majority view of

physicis ts .If this is so, w e would ha ve to conclude that this inherent u np red ictab ility also

represents a limitation of the knowledge even an omniscient God could have 3 6 ofthe values of these variables and so of the future trajectory, in those respects, of thesystem. That is to say, God has so made the quantum world that God has allowedG o d ' s o w n possible knowledge to be thus l imited. In this regard, then, God's

3 5 The positive evidence for the absence of, at least, local "hidden variables" is

discussed in a way accessible to the general reader by John C. Polkinghorne, The QuantumWorld (Harmondsworth: Penguin Books, 1986), chap. 7. Whether or not such "hidden

variables" can, more generally, be regarded as absent is sti l l a much discussed question,

though the majority view is against their existence.

3 6 See also Peacocke, Theology for a Scientific Age 122, for a discussion of G od 's

"self-limitation."




omniscience is "self-l imited." 3 7 G od 's kn ow ledge wi th respect to HUP var iablesin future states would be the ma xim um it could b e com pared with ours, but wo uldnevertheless still be only probabilistic. M ore ov er, if th e future, as I and others ha ve

argued38

has no ontological status—that is, does not exist in any sense— then it hasno content of ev ents for God to know, so it logically cannot be known even to anomniscient Go d, who kno ws all that it is pos sible to kno w . Acc ording to this view ,God knows the fu ture definitively only by predict ion on the basis of God'somniscient know ledge of all determining laws and an infinitely precise knowledgeof all initial relevant conditions (as in 4. 1.1 , ab ov e); or probabilistically in the caseof quantum-dependent events (for God cannot predict in detail the outcome of in-principle unpredictable s i tuations, on the no-hidden -variables a ssump tion). Thisconclusion about the basis of God's foreknowledge would still apply, even if it isthought that God acts in the world by altering the initial conditions of a train ofevents (including possibly individual quantum events, as other authors in thisvolume have proposed [see n.33]) to obtain the outcome God wills and so mustforesee .

An easily envisaged example, related to the relations expressed in the HUP,is afforded by radioactive decay, in which a quantum event has an observablemacroscopic outcome in the decay of the atoms. In this case, the foregoing isarguing that God do es no t kn ow which of a million radium atoms will be the next

to disintegrate in, say, the next 10"3

seconds, but only (as we ourselves) what theaverage number will be that will break up in that period of time. There is no factof the matter about which atom will decompose at a particular future mo me n t for

God to know . The proposal of "self-l im it ing" om niscience m eans that God has somade the natural order that it is, in principle, impossible, even for God, as it is forus, to predict the precise, future values of certain variables—which is what I take"in principle" to mean in this context . God's omniscient knowledge of theprobabilities of these future values will, of course, always be maximal.

Hence, in the case of systems sensitive to initial conditions, the introduction

of quantum uncertainty introduces an upper limit to predictability with respect to

^See ibid., 91-94 and 121-23. In the latter passage (p. 1 22), I included in the category

of systems whose future states cannot be definitively k now n ev en to God (since they are in

principle unknowable) not only the operation of human free will and (quantum) systems in

the "H eisenbdg" range, but also "certain non-linear systems at the microscopic level." I had

in mind here (and was insufficiently precise in spec ifyin g) those non-linear sy stem s in w hich

ef fec t s o f quantum events can be amplified to the macroscopic level so that, in principle,

knowledge only of the probabilities of occurrence of particular macroscopic states is

possible— know ledge maxim ally avai lable to God. (Such systems w ere mentioned also in

the penultimate paragraph of sect ion 2. 4.) If "quantum chao s," in the strict se nse de fine d by

Ford (end of section 2.4, and n. 11) proves to be possible, further reflection on God's

know ledge of the future states of syste m s in w hich it occurs w ill be n eede d in the light of its

precise epistem ologica l character.

3 8 See Peacocke, Theology for a Scientific Age 128-133, which gives references to

other authors who also hold this view. See also n. 45 below.




certain parameters which cannot be avoided. 3 9 This limit on total predictabilityapplies to God as well as to ourselves, if there are no hidden variables. So theanswer to the theological quesdon (1) then has to be, in the light of such quantum

considerations, that God also cannot know, beyond real limits, the outcomes ofthose situations, the trajectories of those systems which are also in principle (if nohidden variables exis t) unpredictable for us beyond those same l imits . God, ofcourse, know s m axim ally what it is possible to know , nam ely the probabilities ofthe outcomes of these situations, the various po ssible trajectories of such system s.But this does not suffice fo r us to give a clear affirmative answer to question (2)to the effect that God could act in such situations or systems to implement thedivine will.

On this, to some no doubt revisionary, view Go d bestow s a certain auto nom y

not only on hum an beings, as C hristian theology has long recog nized , but also onthe natural order as such to develop in ways that God chooses not to control indetail. God allows a degree of open-endedness and flexibility in nature, and thisbeco mes the natural, structural basis for the flexibility of conscious organisms and,in due course and more speculat ively, possibly for the freedom of the human-brain-in-the-human-body, that is, of persons (see above, end of section 3.3). So itdoes help us to perce ive the natural w orld as a m atrix w ithin w hich op enness andflexibility and , in hum anity , perha ps even freedom could naturally em erge.

4.1.3 Implications of "Chaotic" Determinism

One set of considerations (section 4.1.1, concerned with the infinite decimalrepresentat ion of real numbers and algori thmic complexity) only reinforces therejection of an already long-rejected intervention!sm 40 as the basis for God'sinteraction with the world to influence events. The other set of considerations(section 4.1.2 [ii], concerned with the HUP and its consequences if there are nohidden variables) implies that God cannot know precisely the future outcom e of

quantum dependent s i tua t ions ,4 1

so cannot act directly to influence them in orderto implement the divine purpose and will, as we may be tempted to postulate. Itshould be noted that this does not derogate at all from God having purposes whichare being implemented through the propen sities (to com plexity, self-orga nization ,information-processing, and consciousness) that load, as it were, the dice whosethrows shape the course of natural events.

The above discussion lead s us to infer that this new ly-w on aw aren ess of theunpredictability, open-endedness, and flexibility inherent in many naturalprocesses and systems does not, of itself, help directly to illuminate the "causal

3 9 N o t e that the argument being pursued here doe s not depen d on establishing that

"quantum chaos," in the strict sense of Ford's definition (section 2.4, last par., and n. 12)

actually occurs.

^S ee the comm ents on "divine intervention" at the end of n. 33 above.4 , T h e s e wo uld also include the future trajectories of systems displaying "chaotic"

behavior if "quantum chaos" proves to be theoretically feasible (see end of section 2.4).




joint" of how God acts in the world, that is, the natu re of the interfac e betw een Go dand all-that-is—much as it alters our interpretation of the meaning of what isactually going on in the world. Def inin g the pro blem (a la Au stin Fa rrer) as that of

the "causal join t" between Go d and the world is inappropriate for i t does not dojustice to the many levels in which causality operates in a world of complexsystems interlocking in many ways at many levels. It is to this major feature of theworld as perceived by the sciences that we m ust now turn.

4 .2 Wh ole-Part Constraint as a Mo del for G od's Interaction with the Wo rld

In a num ber of natural situations, interactions w ithin com plex system s constitutedof complex sub-systems at various levels of interlocking organization can best be

understood as a two-way process. Real features of the total system-as-a-whole areconstraints upon events happening within the su b-system s at lower levels— even ts,which, it must be stressed, in themselves are describable in terms of the sciencespertinent to that lowe r level. In the light of this it is suggested that we can properlyregard the world-as-a-whole as a total system so that its general state can be aholis t ic constraint 4 2 upon what goes on at the myriad levels that comprise it . Forall-that-is displays, with wide variations in the degree of coupling, a realinterconnectedness and interdependence at the quan tum , b iologica l, and cos m olo g-

ical levels and this would, of course, be totally and luminously clear to God in alli ts ram ifications and degrees of cou plin g. 4 3

I want now to explore the possibility that these new perceptions of the wayin which levels within this world-system interact with each other (from higher tolower and vice versa) might provide a new resource for thinking about how Godinteracts with that world-as-a-whole. In making such a suggestion I am notpostulating that the world is , as it were "G od 's bo dy," s ince, a lthough the world isnot organized in the way a hum an bo dy is, it is nevertheless a "syste m ." The w orld-as-a-whole, the total world system, may be regarded as " in God,"4 4 though

ontologically distinct from God. For God is uniquely present to it all , all itsindividual component entities, in and at all spaces and all times (in whatever

4 2 A s pointed out by Ru ssell in this context, the notion of w hole-part constraint does

not depend critically on the idea of "boundary conditions" of a complex system, with its

implicit phase-spatial connota tions— and indeed the universe does not have a boundary in

that sense. I am also indebted to him for some of the wording in the sentences that follo w .

°T he interconnectedness and interdependence of all-that-is w ould be infinitely m ore

apparent to God. For God holds it all in existence; is present to all space and time

frameworks of reference; and all-that-is is "in God," on the, properly qualified, "pan-en-

theistic" model which I espouse (see Peacocke, Theology for a Scientific Age 370-72, n . 75,

and associated text, as well as figure 1).

"A "pan en-theistic" view the sense of which I have explicated further, with references

to other authors, in Theology for a Scientific Age (references in n. 42 above).



G O D ' S I N T E R A C T IO N W I TH T H E W O R L D 2 8 3

relat ivis t ic frame of reference 4 5) and has an unsurpassed awareness of itsinterconnected and interdependent unity—even more that we can have of the unityof our own bodies. If God interacts with the "world" at a supervenient level of

total i ty, then God, by affecting the s tate of the world-as-a-whole, could, on themodel of whole-part constraint relationships in complex systems, be envisaged asable to exercise constraints upon even ts in the my riad su b-levels of existen ce thatconstitute that "w orld " without abrogating the laws and regu larities that spe cifica llypertain to them—and this without " intervening" within the unpredictabil i t ies weh a v e n o t e d . 4 6 Particular events might occur in the world and be what they arebecause God intends them to be so, without at any point any contravention of thelaws of physics, biology, psychology, sociology, or whatever is the pertinentscience for the level of description in question.

In thus speaking of God, it has not been possible to avoid talk of God"intending," and so using the language of personal agency. For these ideas ofwhole-part constraint by God cannot be expounded without relat ing them to theconcept of God as, in some sense, an agent, least misleadingly described aspersonal. In thus speaking, we are focusing upon particular events, or patterns ofevents , as expressive of the "purposes" (e .g. , of communication) of God, who isthereby conceived of as in som e sense pe rso na l. Su ch particular intentions of Godmust be distinguished from that perennial sustaining in existence of the entities,

structures, and dynamic processes of the world, which is an inherent componentof all concepts of God as creator. This sustaining is properly regarded as"continuous," an aspect of God as semper creator with respect to the creatio

continua. W hat is being fur the r suggested here is that w e have to envisa ge G od asat any time (and in this sense only, "all the time") being able to exert constraintsupon the world-as-a-whole, so that particular events and patterns of events canoccur, which otherwise would not hav e do ne so. This is usually rega rded as G od 's"providential" action, unhelpful as the distinction between creation and providenceoften proves to be.

4 5For further elaboration of the understanding of God's relation to time assumed in this

point , see Theology for a Scientific Age 128-33.1 there summarized my position in the

following terms: "God is not 'timeless'; God is temporal in the sense that the divine life is

successive in its relation to us—God is temporally related to us; God creates and is present

to each instant of the (physical and, derivatively, psychological) time of the created world;

G od transcends past and present created time: God is eternal," (p. 132) in the sense that there

is no time at which G od does not exist nor will there ever b e a future time at whic h G od doe s

not exist.

For a discussion of the issues concerning the "block universe" model used in

relativistic physics and their implications for the God-time relation, see the illuminating

discussion of Isham and Polkinghorne, 'The Debate over the Block Universe," in QuantumCosmology, 13 5- 44 .1 take the vi ew o f the latter in this debate.

4 6 B o t h of the (for us) practical kind (e.g., chaotic system s) and of the in-principle,

inherent kinds (e.g., certain quantum events).




4.3 Personal Agents as Psychosom atic Unities

The way in wh ich, in the preceding, w e hav e fou nd ourselves drawn tow ards th e

mode l o f personal agency in attempting to explicate God's interaction with theworld is intriguing in the contemporary context—and not only because of itsbiblical and traditional role. For in one particular instance of a system manifestingwhole-part constraint, the hum an-brain-in-the hu m an-b ody , we ha ve an im m edia tesense of the non-reducibil i ty of the whole—in our "consciousness ," as folkpsychology calls i t . 4 7 For, over recent decades, the pressure from the relevantsciences has been inexorably towards viewing the processes that occur in thehuman brain and nervous system, on the one hand, and the content of con-sciousness, our personal, mental experience, on the other, as two facets or

functions of one total unitive process and activity.4 8 We have already seen thatcombining a non-dualis t account of the human person and of the mind-bodyrelation with the idea of whole-part constraint illuminates the way in which statesof the brain-as-a-whole could hav e effects at the level of neurons, and so of bodilyaction; and could actually also be holistic states of the brain-as-a-whole. Suchstates could b e legitimately referred to in non-redu cible m entalist langu age as a realmodality of the total unitive event which is the activity of thinking that isaccomplished by the human-brain-in-the-human-body.

This invoking of the notion of whole-part constraints of brain states as awhole upon the states of the "lower" level of its constituent neurons in giving anaccount of human agency, affords, I would suggest, a new insight into the natureof human agency very pertinent to the problem of how to mod el G od 's interactionwith the world. My suggestion is that a com bination of the recognition of the w aywhole-part constraints operate in complexly interconnected and interdependentsystems with the recognit ion of the unity of the human mind/brain/body event,together provide a fruitful model for i l luminating how we might think of God'sinteraction with the world. According to this suggestion the state of the totality of

the world-as-a-whole (al l- that-is) would be known maximally only to theomniscience of God and would be the field of the exercise of the divine omni-science at G od 's omnicompetent level of com prehensiveness and co m pr eh en sio n.4 9

W hen w e act as personal agents, there is a unitive, un ify ing , cente red con straint onthe activity of our human bodies, which we experience as the content of our

4 7 I am indebted, at this point especially in this paper, to the wording of some

illuminating comments by Philip Clayton.

4 8 S e e , inter alia, Colin Blakemore, The Mechanics of the Mind (Cambridge:

Cambridge University Press, 1976); The Brain: Readings from Scientific American

Magazine (San Francisco: Freeman, 1979); Mind and Brain: Readings from Scienti f ic

American Magazine (Oxford: Freeman, 1992); and the comprehe nsive information in TheOxford Companion to he Mind, ed. Richard L. Gregory (Oxford: Oxford University Press,

1987).

4 9 W it h the qualification of the self-l imitations of divine om niscience and divine

omnipotence already made (See Peacocke, Theology for a Scientific Age, 121-3).



G O D ' S I N T E R A C T IO N W I TH T H E W O R L D 2 8 5

personal subjectivity (the sense if being an "I") in its mo de of w illing action. G odis here being con ceived of as a unifying, unit ive source and centered influen ce onevents on the world . 5 0

W e are here courting the notion that the success ion of th e states of t he systemof the wo rld-as-a-whole is also experienced as a succession by G od, wh o is presentto it all; and that this m ight be mod eled after the way w e presum e a succession ofbrain states constitutes a succession in our thoughts. God would then be regardedas exerting a continuous holistic constraint on the world-as-a-whole in a way akinto that whereby in our thinking we influence our bodies to implement ourintentions. This suggestion is, fo r m e at least, entire ly m etap ho rical, p rov idin g onlya model for God's interaction with the world and thereby enabling us to conceivecoherendy and intelligibly how God might be conceived of as interacting with the

world consistendy with what we know of its nature and with the character of Godalready inferred on other grounds. As such, therefore, it has its limitations,indeed—with al l such at tempts—an inevitably negative aspect . For, in a humanbeing, the "I" does not transcend the body ontologically in the way that Godtranscends the w orld and m ust therefore be an influence on the world-state fro m"outside" in the sense of having a distinctively different ontological status. 5 1 Butat least the suggested model helps us to conceive how God's transcendence andimm anence m ight be held coherently together as a transcendence-in-im man ence.

This now affords a further clue to how that continuing interaction of Godwith the world-as-a-whole which implements particular divine pu rpo ses m igh t bestbe envisaged—n amely as analogous to an input, a flow of information, rather thanof energ y. 5 2 For different, equally probable, macroscopic s tates of a system—andso, in the mod el, of the wo rld-as-a-w hole— can possess th e same en ergy but differin form and pattern, that is, in informa tion content (cf. n.27). Moreover, s ince Godis properly regarded by most theis ts as in some sense "personal ," this "flow ofinformation" may be mo re approp riately envisaged as a me ans of communication

by God of divine purposes and intentions when it is directed towards that level in

the hierarchy of complexity which is uniquely capable of perceiving andrecogniz ing i t , nam ely , hu m ani ty . 5 3

^Do we have here one aspect of humanity as mago del5 1 The "ontological gap at the causal joint." See n. 51 below.

5 2 T O the best of my k no wle dge the first application of the concept of information to

the interaction of God and the world was made by John Bowker in The Sense of God:Sociological, Anthropological, and Psychological (Oxford: Clarendon Press, 1973), chap.

5: "Structural Accounts of Religion." See also the expression in similar terms of this idea,

of G od "informing" the world in a "dow nward /top-down" m anner, by Polkingh orne,

Science and Providence 32 ff.; idem, Reason and Reality: The Reationship betweenScience and Theology (London: SPCK Press, 1991), chap. 3; and Peacocke, Theology fora Scientific Age, 161, 164, 179, and 207.

5 3 T h e conse quen ces o f this I have tried to dev elop in Theology for a Scientific Age

(1993 ed.), Part 3.



286 ARTHUR R. PEACOCKE

5 Conclusion

The foregoing suggests a way in which we could think of divine constraints

(properly called " influences," to cohere with the model of personal agency)making a difference in the world, yet not in any w ay con trary to those reg ularitiesand laws operative within the observed universe, which are explicated by thesciences applicable to their appropriate levels of com plex ity and org aniz ation . Th isholistic m od e of action on and influence in the world is G o d 's alon e and distin ctiveof God. God's interaction with the whole and the constraints God exerts upon itcould thereby shape and direct events at lesser levels so that the divine purposesare no t ultimately frustrated. Such interaction could occur without ever abrogatingat any point a ny of the natural relationships a nd inbuilt flexibilities and freed om soperative at all of the lower levels, and discerned by the sciences and ordinaryhuman experience.

Only G od in the m ode of transcendence is pres ent to t he totality of all-that-is,as well as, in the mode of immanence, to the individual entities that comprisecreated existence. Accordingly, God's experience is of the world-as-a-whole aswell as of individual entities and events within it. Only God could be aware of thedistinctiveness of any state of that totality and which of its states might or mightnot succeed it in time (or whatever is the appropriate dimension for referring to

"succession in God"). This divine knowledge would always be hidden from andeternally opaque to us, existing as we do at levels at which the conceptua l langu agewill never be available for apprehending G od 's ow n "in ner" life. The best we cando, as we have already urged, is to stretch the language of personal experience asthe least misleading option available to us. According to this approach, we are freeto describe any particular events at our own level of existence in the natural termsavailable to us (e.g. , in those of the sciences explaining both the "bottom-up" andwhole-part effects within the natural order); and at the same time we are free toregard at least some of those events, whether private and internal to us or public

and external to all, as putat ively and part ial ly manifest ing Go d's intentions, G od 'sprovidence, and so as being communications from God. For God could havebrought it about that these particular events are what they are and not somethingelse by that overall comprehensive constraining influence which only God canexert (but does not necessarily do so) in a whole-part manner u pon any lower-levelevent occurring in the totality of existing entities in order to implement divineintentions, such as com mu nicating w ith hum anity.

God, I am suggesting, is thus to be conceived of as all the time the continuingsupra-personal, unifying , unitive Ag ent acting, often selectively, upon all-that-is,as God's own self purposes. We must go on recognizing—and this is essential tothe whole proposal— that, in the light of our earlier discussion, it is God who haschosen to allow a degree of unpredictability, open-endedness, and flexibility in theworld God continues to hold in exis tence and through whose processes Godcontinues to create; and that God, so conceived, does not intervene to break thecausal chains that go from "botto m -up," fro m the micro- to the m acro-levels .

What does this imply about the "causal joint" between God and the world?As already mentioned (n.27), in the world we observe through the sciences, we

know of no transfers of information without some exchange of matter and/or



G O D' S INT E RACT IO N WIT H T H E WO RL D 2 8 7

energy, however minimal. So to speak of God as " informing" the world-as-a-whole without such inputs of matter/energy (that is , as not being "intervention")is but to accept the ultimate, ontological gap between the nature of God's own

being and that of the created world, all-that-is apart from God. Hence the presentexercise could be regarded essentially as an attempt, as it were, to ascertain wherethis ontological gap, across which God transmits " information" (i .e . , communi-cates) is most coherently "located," consistently with God's interaction witheverything else having particular effe cts and withou t abrog ating those regularrelationships to which God's own self continues to give an existence which thesciences increasingly discover.

I would want to emphas ize , wi th Gordon Kaufman 5 4 and Maurice Wiles , 5 5

that G od 's action is on the world-as-a-whole, but to stress more strongly than they

do that this maintaining and supporting interaction is a continuing as well as aninitial one, and can be gen eral and particular in its effects. The freedom of God toaffect the world is indeed reinforced and protected in this mod el. For the notio n ofwhole-part constraint no w allow s us to unders tand how initiating divin e action onthe state of the world-as-a-whole can itself have consequences for individualevents and entities within that world. Moreo ver such d ivin e ca usativ e, con strain inginfluence would never be observed by us as a divine "intervention," that is , as aninterferenc e with the course of nature and as a setting aside of its natural, regular

relationships.Th e propo sed m odel allow s the effe cts of natural events, including theunpredictable ones and the outcome of freely-willed human decisions, to worktheir way up through th e hierarchy of comp lexity and so to contribute to the stateof the world-as-a-whole. It therefore also helps u s to m odel m ore co nvin cingly theinteraction, dialogue even, between human decisions and actions, on the one hand,and divine intentions and purposes, on the other. It is in such a context that thenotion of God communicating with humanity can be developed in which thesignificance of religious experience, revelation, the incarnation, prayer, worship,

and the sacraments may be gro und ed.5 6

In conclusion, it would seem that, the unpredictabilities of non-lineardynamic systems do not as such help us in the problem of articulating morecoherendy and intelligibly how God interacts with the world. Nevertheless recentinsights of the natural sciences into the processes of the world, especially those onwhole-part constraint in com plex systems and on the unity of the hum an-b rain-in-the-human-body, have provided not only a new context for the debate about howGod might be conceived to interact with, and influence, events in the world buthave also afforded new conceptual resources for modeling it .

^Gordon D. Kaufman, God the Problem (Cambridge, MA: Harvard University Press,

1972).

55M aurice W iles, God's Action n heWorld: The Bampton Lecture for 1986 (London:

SCM Press, 1986).

^See Peacocke, Theology for a Scientific Age (1993 ed.), Part 3.



P A R T I C U L A R P R O V I D E N C E

A N D T H E G O D O F T H E G A P S

Thom as F. Tracy

1 Posing the Question

The "G od of the gaps" has not fared well in modern theology. This vivid pe jorat ivephrase has come to characterize the result of a theology that eagerly (perhapsdesperately) rushes forwa rd to insert God at those poin ts w here hu m an und erstan d-

ing reaches its limits. The shortcomings of this theological maneuver are well-expressed in some of Dietrich Bonhoeffer's later prison letters. Co m m entin g o n th eexperience of reading a new book on modern physics , he remarked that:

It has again brought home to me quite clearly how wrong it is to use Godas a s top-gap for the incompleteness of our knowledge. If in fact thefrontiers of knowledge are being pushed furthe r and fu rther back (and thatis bound to be the case), then God is being pushed back with them, and istherefore continually in retreat . We are to f ind God in what we kno w, not

in what we don ' t k n o w . . . . That is t rue of the re la t ionship be tween G odand scientific knowledge, but it is also true of the wider human problemsof death, suffering, and guil t . 1

Bonhoeffer contended that the appeal to God at the l imits of humancomprehension (whether scientific or existential) is part of an attack b y "reli gio n"on human maturity and strength, and it is bound to end in embarrassing failure ina world increasingly come of age.

Bonhoeffer ' s warning agains t mot iva t ing re l ig ious fa i th f rom humanexistential boundaries has been largely ignored by contemporary theologians, but

his critique of the God who fills scientific gaps has been almost universallyembraced. It clearly has not been a winning strategy for theologians to pounceupo n points at which scientific explanations are curre ntly inco m plete and insist thathere at last we see the hand of God at work in the world. The all but inevitableresult of this maneuver is nicely illustrated by the fate of Newton's contention thatGod steps in occasionally to correct accumulating inaccuracies in the orbits of theplanets. A ce ntury later, and w ith better calculations in hand , Laplace was ab le tomake his famous remark that he had "no need of that hypothesis ." I t makes nosense to persist in planting the ban ner of theo logy at the bou nda ries of th e k now n

world, only to be perpetually forced into retreat as new territory is opened up tohuman unders tanding.

Dietrich B onhoeffer, Letters and Papers from Prison, ed. Eberhard Bethge, enlarged

ed. (New York: Macmillan, 1979) , 311.



2 9 0 T H O M A S F . T R A C Y

Contemporary theologians, therefore, have been understandably reluctant toadopt an account of Go d's relation to the wo rld that appe als to the incom pletene ssof scientific explanations. Any theological reliance upon gaps in our understanding

of the natural order may look like a return to the discred ited apo loge tic str ateg y thatBonhoeffer described. It is important, on both scientific and theological grounds,not to embrace this conclusion without further reflect ion, however. We need tothink a bit more about the sorts of "gaps" that can occur in scientific understand-ings of the world. And we need to consider the conceptual requirements of atheology which speaks of the God who acts in history.

1.1 Explanatory and Causal G aps

The first point to note is that not all gaps are the same, and it is important to makesome distinctions. In the broadest sense, "explanatory gaps" occur whenever weare unable to give a complete account of the sufficient condit ions for an event.Defined in this way, such gaps are a commonplace of inquiry; indeed, given ourcognitive limits, we cannot fully spell out the sufficient conditions for anything thathappens in the world. The explanatory gaps that are of principal interest for mypurposes are those that occur either wh en (1) w e m ust ac kno w ledge that w e do notyet have theories or explanatory strategies adeq uate to answ er q uestions raised by

our scientific inquiries, or when (2) our theories entail that human knowers will notin principle be able to give a suffic ient explanation of som e of the events that fallwithin the theory's scope. In the discussion that follows, I will refer to gaps thatarise in these two circumstances as, resp ectiv ely, e xp lana tory limits in prac tice andin principle. The question of how to cla ssify any particular instance of expla natoryincompleteness may, of course, be a matter of scientific controversy. I t m ight b eargued, for example, that a putative instance of the second type (a limit inprinciple) is really just an instance of the first (a limit in practice).

Explanatory gaps of this second type may, but need not always, be

understood to reflect "cau sal gaps." Causal gaps are breaks in the order of whatis com m only called "event causation" (or <4 transeunt causation") which occur whenevents are not uniquely determined by their an teceden ts. W her e causal g aps occur,later events cannot be deduced from a description of their antecedents anddeterminis t ic laws of nature. 2 As a result, causal gaps entail a particular sort ofexplanatory gap. 3 It is important to emphasize that the entailment does not run in

2 On covering law, or deductive nomological, explanation see Carl Hempel, Aspectsof Scientific Explanation, and Other Essays in he Philosophy of Science (New York: Free

Press, 1965).

^ote that an event which cannot be explained in terms o f a determ inistic cove ring law

may nonetheless have some other explanation that is sufficient. If the event is an in-

compatibilist free action, for example, it may have an adequate explanation in terms of the

agent's reasons for acting. Further, if on e su bscr ibes to a con ce pt o f "a gent causa tion" wh ich

is irreducible to event causation, then although there cannot be a complete explanation of the

act in terms of antecedent events and the laws of nature, the act will have a cause (i.e., the



PART ICUL AR PRO VIDE NCE 291

the other direction; not all explanatory gaps (even those that reflect limits inprinciple) will indicate the presence of causal gaps, and we must be very cautiousabout concluding from the former to the latter. Hasty inferences of this kind are

one of the fatal shortcomings of a God of the gaps strategy in theology.It now appears that explanatory gaps in principle occur within some of the

most powerful contemporary physical theories . Quantum mechanics and, morerecently, chaos theory provide the two leading candidates . The Heisenberguncertainty principle acknowledges intrinsic limits on our ability to specify thestate (e.g. , both position and momentum) of quantum systems, and therefore toexplain how later states arise from their antecedents. This explanatory incomplete-ness is subject to various interpretations, but it cannot be avoided within currenttheoretical structures, as J. von Neumann has shown. Many physicists are skeptical

about the prospects fo r new theoretical proposa ls that would elim inate indeterm i-nacy and show that it was a function of hum an ignoran ce (i.e., that it reflected anexplanatory limit in practice but not in principle).1 Further, one well-establishedinterpretation of this explanatory incompleteness takes it to reflect a causal gap inthe order of nature. On this view, there is no underlying deterministic process thatwould explain the behavior of the quantum mechanical system; the probabilityequations tell us as mu ch as can be kno wn abou t the relation of past, present, andfuture states of the system. This was Heisenberg's own later understanding of his

uncertainty principle .2

Chaos theory presents a s ignificantly different example of explanatoryincompleteness. A non-linear dynamic system operating according to the laws ofclassical mechanics can display an extraordinary sensitivity to its initial, orboundary, conditions. Initial conditions that are only minutely different canproduce widely divergent states of the system. Our ability to predict these futurestates, therefore, is determined in part by the accuracy of our specification of itsinitial conditions. In order to apply the relevant deterministic laws and predictstates of the system that are significantly distant from the starting point, we would

need to spec ify the initial conditions w ith an accuracy that exceeds o ur epistem iclimits . Once the system has moved through a specific number of "generations"

agent). Th e idea of agent causation is both ancient and controversial. For recent discu ssion s

of it, see Roderick M. Chisholm, "The Agent as Cause," in Action Theory: Proceedings ofthe Wnnipeg Conference of Human Action, ed. Myles Brand and Douglas Walton

(Dordrecht: D. Reidel, 1976), 199-211; and Peter van Inwagen, An Essay on Free Wll(Oxford: Oxford University Press, 1983), 152.

'David Bohm's hidden variable theory is the best known of such proposals. See

Bohm, Causality and Chance inModern Physics (Princeton, NJ: D. Van Nostrand, 1957);

an d dem,Wholeness and the mplicate Order (London: Routledge & Kegan Paul, 1980).2F or an overview of quantum physics and a description of leading interpretations of

indeterminacy see Robert John Russell, "Quantum Ph ysics in P hilosophica l and Th eol ogic al

Perspective," in Physics, Philosophy, and Theology: A Common Quest or Understanding,ed. Robert John Russell, William R. Stoeger, and George V. Coyne (Vatican City State:

Vatican Observatory, 1988), 343-74.



2 9 2 T H O M A S F. T R A C Y

(fixed by the accuracy of our description of the starting point), it ceases to bepredictable for us . Chaos theory, therefore, generates an explanatory gap of thesecond type (i.e. , a gap that cannot in principle be closed). Note that it does so,

however, precisely by carrying a thoroughly determinis t ic analysis as far aspossible, given our cognitive limits. Because the chaotic system is described by adeterministic equation, we have no grounds for claiming that there are underlyingcausal gaps in the system. Thus, while chaos theory and quantum theory bothinvolve explanatory gaps in principle, they differ in that the gaps in chaos theorydo not indicate the presence of causal g aps in cha otic sy stems, wh ereas th e gap s inquantum theory indicate the possible presence of causal gaps in quantum system s.3

It remains to be seen whether either of these contemporary sources ofincompleteness in our understanding of the world has any s ignificance fortheology. That question hinges upon a set of theological considerations to whichwe are about to turn. But it is worth noting two preliminary points. First, if thesescientific theories establish themselves as integral elements in our contemporaryunderstanding of nature, then theologians who wish to develop an account ofG od 's activity in the world will have to take these g aps into a ccou nt. S econ d, wh ena theologian does so, s/he will not simply be returning to the earlier "God of thegaps" theology, which sought to exploit explanatory gaps of the firs t type andclaimed without scientific warrant that these represented causal gaps. Rather, the

theologian will be working with explanatory gaps of the second type, which (exhypothesi) represent fund am ental l imitat ions upon what w e m ay know (within, ofcourse, the terms of the theories that recognize these gaps).

Recall Bonh oeff er's remark that t 4 w e are to f ind God in what w e know , ratherthan what we don ' t know ." O ne effect of quantum mechan ics and chaos theory, ifthey turn out to be co rrect in their essentials, is that they add to our kn ow led ge ofthe world precisely by pointing out limits in principle on what we may know andby explaining why we cannot know it . We cannot draw theological conclusionsdirecdy from this scientific development. But if we are concerned to construct, on

theological grounds, a theistic understanding of the world, it is legitimate toincorporate (along with the rest of what we currently think we know) thisknowledge of our ignorance.

1.2 Theology without Gaps?

There is a second, and crucial , reason contemporary theologians ought notsummarily to dismiss appeal to gaps in scientific accounts of the world: theologymay not be able to get along altogether without gaps. The considerations here are

chaos theory see , e .g . , James P. Crutchf ie ld, e t . a l . , "Chaos" ( in this volume); and

Joseph Ford , "What I s Chaos , that we shoul d be mi ndful o f i t ? , " i n The New Physics e d .

Paul Davies (Cambridge: Cambridge Univers i ty Press , 1989) . See a l so James Gle ick, Chaos:Making a New Science (L ondon: He i nemann, 19 88) ; and Ian Stewart , Does God Play Dice?

The Mathematics of Chaos ( O x f o r d : B a s i l B l a c k w e l l , 1 9 8 9 ) .



P A R T I C U L A R P R O V I D E N C E 2 9 3

explicitly theolog ical, rather than scientific, and they center on the traditional claimthat God acts in the world.

The scriptural sources of Judaism and Christianity (and Islam) are rich in

stories of divin e action. The G od depicted in the biblical narratives does not, likean Aristotelian First M over, rest within a self-con tained perfec tion u nm ov ed by theworld. Rather this God has purposes for the world and acts at particular times andplaces to advance those purposes. As the biblical s tories unfold, God plays astrikingly intimate role in history, engaging individuals and communities in adramatic , unfo lding relat ionship grounded in G od 's ini tia tives and prom ises . T heauthors of the Hebrew Bible present Yahweh as the one who freed their peoplefrom slavery in Egypt and gave them the law, the sam e one wh o h ad earlier enteredinto a covenant relat ion with Abraham and his descendants and who remains

faithful in judgment and mercy throughout the hardships of Israel 's his tory. Thishistory of divine action plays a central role in identifying who God is and inshaping the language and imagination of the biblical religions.

Notwithstanding the prominence of this theme at the foundation of thesereligious traditions, the idea that God acts in history has had an uncertain career inmodern theology. There are many reasons for this: for example, the emergence ofhistorical criticism of the biblical stories, the persuasiveness of Enlightenmentmoral challeng es to the self-interest and special pleadin g that is too ofte n at work

in talk of divine providence. Of principal interest for my purposes, however, arethose misgivings about divine action that are especially tied to the rise of thenatural sciences. The sciences have taught us to look at the world as a law-governed natural order, and they have achieved such impressive results preciselybecause they seek to explain events in terms of their place within this natural order,without reference to any supernatural agency.

Ho w, then, can we understan d God to act within such a wo rld? D o scientificand theological descriptions of the world compete, so that if we explain an eventscientifically we cannot understand it as a particu lar div ine ac tion? Th is con clusio n

may appear inevitable if we take universal causal determinism to be an axiom of"th e m odern , scientif ic wo rldview ," as a succession of influential co ntem porarytheologians have supposed. In such a world there is , in Rudolph Bultmann'sphrase, 4 <no room fo r G od 's work ing," and God can act within the causal series thatconstitutes the history of the universe only by interrupting it in miraculousin te rven t ions . 4 But then, as David Hume saw clearly, we wil l have powerfulepistemic ground s for rejecting claim s about divin e action in history, sinc e it will(always, said Hume) be m ore likely that a miracle rep ort is mistaken or fraud ulen tthan that the otherwise uniform order of the world has be en tem pora rily suspen ded.

Many contemporary theologians have been convinced, therefore, that (1)traditional ways of speaking about divine action in the world require that there be

R u d o l f B u l t m a n n , Jesus Christ and Mythology (New York: Scr i bner , 1958) , 65 . See

a l so Gordo n Kau fman, "On the Mean i ng o f 4 A c t o f G o d , " ' i n God the Problem ( C a m b r i d g e ,

M A : H a r v a r d U n i v e r s i t y P r e ss , 1 9 7 2 ) ; a n d J o h n M a c q u ar r ie , Principles of Christian

Theology, 2d ed . (N ew York: Scr i bner , 1977) .




gaps in the natural order, and that (2) such gaps are at least (a) epistemicallyproblematic, if not (b) incompatible with the m etho ds or ass um ptio ns of th e n atur alsciences, or even (c) conceptually incoherent. 5 I have argued elsewhere that

theologians should not concede either 2(b) or 2(c), and others have effectivelym ade the case that w e need not accept the strong gen eral v ersio n of 2(a) th at H um eput forward . 6 But these respo nses are not alone sufficient, though they are helpf uland important in overcoming theological timidity in the face of faulty philosophyof science or preemptive epistemic vetoes. Questions remain about the relationbetween scientific descriptions of the world as a natural order and theologicalclaims regarding divine action within that world. Do these theological affirmationsrequire incompleteness in scientific explanations, and if so, can it be claimed withany plausibility that our world is incomplete in the right ways?

2 Divine Action and the Order of Nature

I want to consider three important theological strategies for replying to thesequestions, without claiming that these strategies exhaust the alternatives. Two ofthem argue, in q uite different ways, that talk about divine action does not requirethat there be any gaps in the natural order. The first insists that, strictly speaking,

God does not act in the world at all , and it shifts the focus instead to God'senactment of history as a whole. God acts through, but never among or amidst,finite causes, so that the order of nature remains untouched. The second strategy,by contrast, hold s that Go d d oes act in history, but argues that this is possible quitewithout gaps in the natural order. The third approach both affirms divine action inhistory and grants that this requires gaps in the natural order. But it contends thatthe structure of the world is open in ways that are relevant to theology. God'sactivity in the world, therefore, need not take the form a miraculous interruptionof the ordinary course of events.

I will argu e that the first two strategies face telling theological and conceptualobjections. If we think it important to continue to speak of divine action in history,then we have good reason to consider whether the world displays an open andflexible structure that would allow ongoing divine action without disrupting theorder of nature. In making such a world, God would be the creator not only ofnatural law but also of the indeterministic gaps through which the world remainsopen to possibilities not exhaustively specified by its past.

^T hi s l as t , and s t ronges t , c l a i m i s made by Kaufman, "Meani ng o f ' Act o f God. ' "

' See T h om as T racy, "E nact ing Hi story: O gd en and K au fm an on G od ' s M i ghty Ac t s , "

The Journal of Reigion, 64 , no . 1 (January 198 4) . On H um e' s argument , s ee e . g . , W i l l i am

Al s ton , "Di v i ne Act i on: Sha do w or Subs tance ? , " i n The God Who Acts: Philosophical andTheological Explorations, ed . T racy (Uni vers i ty Park , PA: Pennsy l vani a Sta te Uni vers i ty

Press , 1994) .



PARTICULAR PROVIDENCE 295

2.1 The Enactmen t of History

The defining move of the first strategy is to shift the emphasis in talk of divine

action from providence to creation, locating God's act ivi ty solely at the founda-tions of the world. One simple way of carrying out this procedure is exemplifiedby the Deists. Their God brings the world system into being, establishing its initialconditions and the natural laws which structure its develo pm ent. Ha ving gotten theworld going, however, God plays no ongoing role within i ts his tory. ThoughDeists often claimed that this, along with a set of moral teachings, constitutes the"essence" of Chris t ianity, they generally were not concerned with whether theirviews represented an adequate expression of the historic Christian faith. There are,however, theologically much richer ways of carrying out this absorption of

providence into creation, and w e shou ld not ju m p to the conclu sion th at w hene verw e see this m ove w e are witnessing a version of Deism. A p articularly tho rou ghg o-ing and subtle development of this approach can be found in Friedrich Schleier-macher, wh ose theological proposals pro vide the s tart ing point and paradigm forliberal Protestant theolog y. It is worthw hile to conside r S chle ierm ach er's positionon divine action in some detail, since it nicely illustrates the strengths andweaknesses of this overall strategy.

For Schleiermacher, the whole of God's action is contained in the creation

and preservation of the world, and these two forms of divine action are united ina developmental conception of God's continuous creation. On Schleiermacher 'sprinciples, of course, statements about divine action must either be directexpressions of religious feeling or be the result of logically ordered reflectio n u poni t . 7 At the heart of his understanding of religion generally and Christianity inparticular lies the claim that, at its deepest level, human self-consciousnesscoincides with consciousness of G od as the w hen ce fro m w hich w e and ou r wo rldcontinuously receive our being. 8 As he develops this central idea, Schleiermacherm akes tw o furthe r claims that are part icularly pert inent for my p urposes.

First, he insists that no distinction can be made "between the mediate andim m ed iate activit ies of Go d . . . w ithout bringing the Suprem e Being within thesphere of limitation."9 We must not pick out certain events as direct acts of God inthe world and contrast them with ordinary even ts in w hich G od acts thro ugh fin itecauses (i.e., ind irecdy ).10 Rather, God acts in the same way in every event, namely,

7Friedrich Schleiermacher, The Christian Faith, ed . H. R. Mac intosh and J . S . Ste war t

( N e w Y o r k : H a r p er & R o w , 1 9 6 3 ) , 8 1 .

8 N o t e that the c la im about the wo rld ' s dep end enc e upon Go d must be der ived , on

Schleiermacher's principles, from rel ig ious sel f - co ns cio us ne ss . S ee his argum ent , ib id . , 151 -

5 2 .

9 Ib id . , 179 .

1 0 An othe r way of making this point i s to say that, for Schleierm acher , eve ry act of G od

is a basic, or simple act . A basic act i s one that an agent undertakes without having to

perform any prior intentional action as the means to this end. In a game of pool, for example,

I may intentional ly cause on e of the bal l s to drop into a com er p ock et by striking i t wit h the



296 T H O M A S F. T R A C Y

as its absolute ground and source, as the power which posits it in its entirety. Thisdivine creative activity is always direct; each member of a causal series, and notjust the firs t , wil l depend equally and immediately upon God's act ion (hence,

Schleiermacher can say that theological talk of creation has nothing at all at stakein claims about the beginnings of the world). The same must be said of theopera t ion of < 4 free causes" (i.e. , human agents). In the very act of making a freechoice I depend absolutely upon God, and God acts uncondit ionally to consti tuteme as a free f ini te agent who makes that choice.1 1 Every finite entity at everymom ent of its being and activity is the im m ediate result of G od 's creative age ncy .Any other way of understanding God's active relation to the world, Schleiermacheralleges, ends up treating God as one limited agent among others.

Second, not only does each event in the world's history bear a relation ofimmediate and absolute dependence upon God, it also is integrated into a complete(gap free) system of natural relations. It is interesting to note that Schleierm acherprovides theological grounds for this claim; he does not present it as a co nclusionforced upon theology by natural science, though he clearly has the sciences inview.

It is . . . an expedient often adopted by human indolence to attr ibute whatis not un dersto od to the supernatural imm ediately; but this does not at allbelong to the tendency to piety. . . . Where a pious feeling is actually

exis tent , there the interdependence of nature is a lways po sited .1 2

No t only does the pious m ind hav e no need to find gaps among natural causesin which God can act, it has its own reasons to deny that there are such gaps.Schleiermacher insists that religious consciousness achieves its fullest developmentwhen we see the world as a single, integrated "nature-system" to which we belongin a universal solidarity of abso lute depen den ce upon Go d. "D ivin e pre servation ,as the absolute dependence of all events and changes on God, and naturalcausation, as the complete determination of all events by the universal nexus, areone and the sam e thing s imply fro m different points of view." 1 3

The intention of these two moves is clear: they are meant to ensure that noconflict can occur between scientific (or historical) descriptions of the world and

cue ball . Any complex intentional action of this sort must originate in an act which I perform

without having to do anyth ing el se (as an intent ional a ct ion) in order to bring i t about . T his

bas i c in tentiona l act ion (perhaps a m ov em en t o f my b ody ) wi l l be what I do directly, or

immediatey, in contrast to its vario us ndirect, or mediated, resul ts (e .g . , s inking the 8-bal l ,

win n in g the game, w inn ing a bet , e tc . ) . W e can make use o f th i s d i s t inct ion in d i scu ss ing

d iv ine act ion: God act s d i rect ly , or immedia te ly , when God br ings someth ing about a s a

basic div ine act ion, and G od acts indirectly wh en G od d oe s o ne thing by do ing another (e .g . ,

when God act s through crea ted causes ) .

" S c h l e i e r m a c h e r , Christian Faith, 1 7 9 - 8 0 .

1 2 Ib id . , 172 and 174 .

I 3 Ib id. , 17 4 . C om par e Stoe ge r's statement that "the direct causal nexu s is the act ive

richly di f ferent iated , pr ofo un dly im ma nen t pr ese nc e of G od in created being s and in their

i n t e r r e l a t i o n s h i p s . . . . " ( " D e s c r i b i n g G o d ' s A c t i o n , " s e c t i o n 9 ) .



PART ICUL AR PRO V IDE NCE 297

theological talk about God's active relation to created things. Schleiermacher's keystrategy in achieving this result is to deploy his own version of the classicaldistinction between primary and secondary causes. On the one hand, there is the

"horizontal" order of created (secondary) causes, that is , the individuals that intheir activities and relations across time jointly make up our world. On the otherhand, there is the vertical order of divine (primary) causation, God's continuouscreation^jreservation of all finite things. Every event can be understood both interms of its place within the natu re-sy stem of the w orld and in terms of its relationto God 's agency.

Schleiermacher insists that these two orders of causation can and must bekept distinct; it is alwa ys a m istake to offer explanations of events that mix or crossthem. On the horizontal level, our explanation s m ust ex clude refer enc e to God and

app eal on ly to other events in the created order. Schleierm acher aff irm s here aprinciple of explanatory autonomy among events in nature and his tory. On thevertical axis, by con trast, we m ust (a) attribute all events to God's direct creativeagency, and (b) treat them as proceeding from the divine agency in the same way.

We cannot, that is , appeal to divine action to explain any particular event incontrast to any other. Rather, we must strictly maintain the universality anduniformity of God's action. The metaphysical relation of God to created thingsdiffers not at all from case to case, though the particular content of God's action

varies with all the diversity of the created things that God brings to be.1 4

I 4 In a he l pfu l ov er v i e w o f major theo l og i ca l pos i t i on s regardi ng d i v i ne ac t i on , O w en

T ho m as sug ges t s that " the l ibera l v i ew o f the d i v i ne ac t i v i ty in the wo r l d wa s mere l y a

s i mpl i f i ed form of the t radi t i ona l doc tr i ne o f pr i mary and secondary causes w i th mi rac l e s

d e l e t e d " ( O w e n T h o m a s , " I n t r o d u c t i o n , " i n God's Activity in the World [ C h i c o , C A :

Scholars Press , 1983] , 4) . I t i s worth not ing a crucial di f fe ren ce be tw een Sch le ierm ach er and

Aq ui na s , ho we ver , i n addi t i on to thei r v i e w s on m i rac l e s . Aq ui na s a t tempts to sus ta i n the

di s t i nc t i on be tween what God does d i recdy and through i ntermedi ar i e s . God ac t s d i recdy

i n caus i ng and conserv i ng the ex i s t ence o f f i n i t e th i ngs and i n "concurr i ng" wi th the i r

operation. Bu t G od acts indirectly through the f ini te ca us e in pro du cing i t s e f f e c t Se con da ry

causes are the instruments of God's act ion, rather in the way a tool i s the instrument of the

sculptor's art. The ef fect can be at tr ibuted to both the tool and the sculptor , but on di f ferent

l eve ls . No te Stoeger ' s use o f th i s d i s t i nc t i on i n h i s e s say i n th i s vo l u m e , "D escr i b i ng G od ' s

Act i on i n the Wor l d i n L i ght o f Sc i ent i f i c Knowl edge o f Rea l i ty . " L i ke Schl e i ermacher ,

Stoeger contends that we must not think of God as "intervening" in the natural world, but

that w e can "con ceive G od 's cont inuing crea t ive act ion as be ing r eal ized through the natural

unfolding of nature's pote nt ia l i t i es "(sect ion 7) In contrast to Sch le ierm ach er, how ev er ,

Stoege r ho l d s both that ev en t s i n the wor l d are indi rec t d i v i ne ac t s and that w e nev er hav e

exp er i en ce o f G od ' s d i rec t creat i ve ac t i on ( sec t i ons 8 -9 ) . W i thout a d i s t i nc t i on b e tw een

direct and indirect div ine a ction, as I argue be l ow , i t i s d i f f i cu l t t o s ee how one can avo i d the

conc l us i on that G od i s the on l y m etaphysi cal ly rea l cause . C f . Na nc ey Mu rphy o n causa t i on ,

"Divine Act ion in the Natural Order Buridan's Ass and Schrodinger's Cat" ( in this volume) ,

s e c t i o n 2 . 1 . 3 .

On pr i mary and secondary causat i on i n Aqui nas sec , e . g . , E t i enne Gi l son , "T he



2 98 T H O M A S F . T R A C Y

On this account, every event is God's act, and no event or set of events canbe set apart as flowing from the divine agency in a distinctive way. As Schleier-macher put it in the Speeches , "M iracle is s imply the rel igious nam e for ev en t."1 5

Is there any sense, therefore, in which certain events can be singled out as God'sacts? There are at least two carefully circumscribed ways in which this can bedone. First, w e can pick out events a s divine actions in sofar as they play a sp ecialrole in our apprehension of God's universal agency. Here the dis t inctiveness ofthese events consists in their subjective significance to us in awakening God-consciousness . No claim need be made that there is anything objectivelynoteworthy about them, al though there may be. Their importance l ies in thefunction they perform within an his torical community; they are for us thepreeminent acts of God because they happen to evoke in us a part icularly vivid

recognition of God's action. That action, however, is in fact present in all events .Second, an event or set of events may play a distinctive role in God's

purposes fo r the wo r ld . 1 6 The crucial instance of this for Schleiermacher is foundin the l ife of Jesus. Given Sch leierm ache r 's fou nd ing theological principles, h emust formulate his Chris tology in terms of the content and import of Jesus 'consciousness of God; Jesus is the Chris t because he possessed a complete andunimpeded God-consc iousness . 1 7 Note that al though this perfect God-conscious-ness is unique to Jesus alone, it emerges naturally out of human history and

represents the realization of an inherent hu m an p ossib ility. W e ca nno t say tha t G odacts in the life of Jesus Christ in a un iqu e wa y (e.g., as in carn ate deity or by raisin ghim fr om the dead); any such claim is excluded both by Schleiermacher's assertionof the explanatory autonomy of the created order and by his insistence on themetaphysical uniformity of divine action. But we can say that th e life of Jesus plays

Corporea l World and the Ef f i cacy o f Second Causes ," in God's Activity in the World, ed .

Tho mas . For a use of this d istinction to separate the rea lm s of sci en ce and rel ig ion , s ee Ernan

McMull in , "Natural Science and Christ ian Theology ," in Reigion, Science, and the Searchfor Wsdom: Proceedings of a Conference on Reigion and Science, e d . D a v i d B y e r s

( W a s h i n g t o n D . C . : N a t i o n a l C o n f e r e n c e o f C a t h o l i c B i s h o p s , 1 9 8 7 ) .

15 Schleiermacher, On Reigion: Speeches to its Cultured Despisers, t rans. John O m an

( N e w Y o r k : H a r p er & R o w , 1 9 5 8 ) , 8 8 .

"This i s a point that Dav id Gr if f in ove rlo ok s in his cri t ique of the l iberal theologians*

vers ion o f pr imary and secondary causa t ion . He supposes tha t the only sense in which an

event can be a spe cia l act of Go d, i f mir acles are exclud ed, i s in the f irst o f the tw o se ns es I

discuss here. But one can aff irm, as Schleiermacher does , both that (1) God bears the samerelat ion as agent to every event, and (2) G od so d esi gn s and dete rm ines the cou rse o f h istory

that certain events within it m ake an ob jec t ive ly dist inc t ive con tribut ion to the rea l iz at ion of

G od ' s pu rpose s . Th i s avo ids a pure ly subject ive , and therefore re la tive , unders tanding o f

reve la t ion . L ibera l theo log ians a f ter Sch le i ermacher , however , have no t a lways recogn ized

this possibi li ty themselves . For G rif f in 's cri tique se e his "R elat iv ism , D iv i ne Ca usat ion , and

B i b l i c a l T h e o l o g y , " i n God's Activity in the World, e d . T h o m a s , 1 1 7 - 3 6 .

1 7 F o r a l l h s efforts to avo id expos ing theo logy to any r i sk o f empir i ca l contrad ic t ion ,

Schleiermacher at this point i s forced to make strong cla ims about the historica l Jesus.




a specific salvific role in God's purposes for his tory (the whole of which, ofcourse, is enacted by God). 1 8

It becomes evident here that a theolog ical price m ust be paid fo r this strategy

of interpreting all talk of God's action in the world in terms of a continuous divineenactment of his tory. This procedure has the advantage of el iminating anypossibility of conflict between Christian claims about divine action and ourexpanding knowledge of the world. But this immunity from empirical r isk ispurchased at the cost of significant limitations on wh at w e are able to say about anumber of central theological topics.

Firs t , we have just noted that Schleiermacher 's account of divine actionrestricts the rang e of option s av ailable to us in Christology . His strategy ru les outa "high" Chris tology which would affirm that God enters history in Jesus Christ,

joining divinity to humanity in a unique form of divine action. Christian talk aboutthe divinity of Christ mu st signify, rather, the pe rfec tion of his Go d-co nsciou sness,which makes God avai lable to us through him. 1 9 These alternatives paths inChris tology are matters of longstanding and momentous theological debate, andw e m ay hesitate to adopt a general account of divine action that settles this que stionin advance.

Second, within the terms of Schleiermacher 's theology, there can be nointeraction between God and finite persons. W e cannot say, for example, that God

sometimes acts in response to our actions, for that wou ld violate the cardinal tenetof Schleiermacher's theological system, namely, that relation to God is distin-guished from relation of finite things precisely by the utter absence in the formerof any reciprocal influence or initiative on our p a rt .2 0 Further, if the world's historyis to constitute an unbroken continuum of natural causes, then God cannot modifythe course of events once that history is und er w ay. W hatever God m ay intend forany individual (say, that she should ask for in prayer and receive in practice aheightened sense of God's presence) must be "built into" the causal destiny ofhis tory fro m the outset .

Third, it follows that there can be no opposition between the divine and thehuman wills. G od 's action is the unco nditional g rou nd of all our cho ices, an d th ere

1 8 M o r e spec i f i ca l l y , G od e l ec t s that (a ) h i s tory sha ll be ordered as a prog ress i v e

deve l op men t from a " l ower" con sc i o usn ess su bm erge d i n the i mm edi a te v i ta l i t i e s o f an i mal

l i f e t o a fu l l y emergent "hi gher" consc i ousness o f God, and that (b) th i s h i gher con-

sc iousness shal l radiate outward in his tory from i t s f i rs t ful l appearance in Jesus . Langdon

G i l k e y i n Reaping the Whirlwind: A Christian Interpretation of History ( N e w Y o r k :

Seabury , 1976) , 210-213 , reads Schl e i ermacher as put t i ng forward a deve l opmenta l s cheme

of sa l vat i on . A l ong s i mi l ar l i nes , Mi chae l Root prov i des an i l l umi nat i ng account o f the

doctr i ne o f e l ec t i on i n Schl e i ermacher ' s thought . See h i s ar t i c l e , "Schl e i ermacher as

Innovator and Inheri tor: God, Dependence, and Elect ion," Scottish Journal of Theology 4 3 :

8 7 - 1 1 0 .

1 9 S c h l e i e r m a c h e r , Christian Faith, 3 8 5 - 8 9 .

^See Michael Root , "Innovator and Inheri tor ," 96f f . , for a discuss ion of the impact of

this on narrat ive s tructures in Christ ian theology.




is nothin g in the choice that can be attributed to us but not to G od. Schleierm acherseems to hold that human agents freely choose just what God, in the continuouscreation of each individual, "en acts" us as choosing. But this leaves S chleierma cher

in a difficult position in accounting for sin and moral evil, which must now beincorporated into the divine purp oses n ot simply as som ething God permits but assomething God causes. Sin becomes an element in the developmental progressionthat God u ndertakes as the history of creation, an elem ent destined fro m the outsetto be overcome through Chris t .

It is worth mentioning two more general difficulties with the conceptualunderpinnings of Schleiermacher 's proposals . Although Schleiermacher affirmshuman freedom, it is uncertain just what this amounts to, either in relation to finitecauses or in relation to God. If our actions are integrated into a system of naturethat constitutes a determ inistic w hole , then w e can at mo st be f re e in the sense th atwe are at liberty to do what we choose, though our choices are determined by thenexus of antecedent natural causes. And if our actions are themselves ordained byGod, can we any longer regard them as freely undertaken?2 1

This difficulty, however, is quickly swallowed up within a more pervasiveprob lem . It is no t at all clear that, on Schleiermacher's account, there can be active,or effective, finite causes at all. For he insists that God is always the direct causeof the entire existence, activity, and attrib utes of each indiv idua l. W e mu st not, f or

example, distinguish between God's action of preserving the existence of finitethings and G od 's "cooperation" with them in the exercise of their causal po w er s.2 2

It is not altogether clear how to interpret Schleiermacher on these matters, since onhis principles statements that look like metaphysical claims must always be readas expressions of religious feelin g. But he appears to be saying that God do es notmerely sustain the existence and cau sal properties of, say, a fla m e and a kettle ofwater, bringing about the boiling of the water by means of the heat of the flame.Rather, God directly brings about the event of the flame being hot and the event,a short time later, of the water boiling. But if each event in a causal series is entirely

determined by the direct action of God, then there appears to be no causal workdon e by the finite events themselves; they can b e ca uses and effects, but only in thesense that they stand in certain regular relations to each other (e.g., as proposed byHu me and by contem porary counterfactual analyses of causali ty).

2 1 Sc hl e i erm ac he r ' s va r i ous remarks on hu ma n freedom are d i f f i cu l t t o i n terpre t. H e

s p e ak s o f h u m a n a g e n t s a s " f r e e c a u s e s " w h o m o v e t h e m s e l v e s ( s e e Christian Faith, para.

4 9 ) . T h e p o w e r o f s e l f - m o v e m e n t i s e s s e n t i a l t o o u r h u m a n i t y a n d G o d - c o n s c i o u s n e s s , a n d

the causali ty of other l iv in g thing s shou ld be under stood as a dim inis he d form of the "se l f -

ac t i v i ty" that i s present i n human be i ngs . As we have seen , however , he a l so i ns i s t s on the

"com plete determination of a ll events by the univer sal n exu s" (p. 174 ) and con ten ds that the

ac t i v i ti e s o f nature and o f f ree causes are "co mp l e te l y ord a i ned by G od " (p. 18 9) . T h es e

claim s can be cons is ten t on ly i f freedom is und erstoo d in a restr icted sens e (e .g . , as act io n

i n acco rdan ce w i th our be l i e f s and des i res , wh i ch are them se l ve s de termi ned by the causa l

n e x u s ) .

2 2

I b i d . , 1 7 6 .




It appears, therefore, that Schle ierm ach er's position gene rates an "occa sion-alism" in which the only effective agent is the divine a gen t. 2 3 He could avoid thisproblem by making a distinction between God's direct (or basic) action in causing

the continued existence of finite things, and G o d' s indirect action in bringin g abo utcertain events through secondary causes. But Schleiermacher is quite clear aboutrefusing to make this distinction.

There are several good reasons, then, not to pursue Schleiermacher'sparticular version of the strategy.that substitutes God's creative enactment ofhistory for talk of divine action in history. This strategy can be put into play inother ways, of course. But Schleiermacher's theological position was worked outwith remarkable imagination and skill , and if his proposals face deep objections,then this does not bode well for the approach his work exemplifies. A number ofcontemporary theologians have taken positions of this type, and while they avoidoccasionalism and usually deny universal determinism, they are somewhat lesssuccessful than Schleiermacher in generating a coherent account of divine action.It will be helpful here to consider briefly one recent proposal.

In a widely influential essay, Gordon Kaufman has presented an account ofwhat it means to say that God acts. 2 4 He begins, as contemporary discussions ofthis topic often do, by explaining what this notion cannot mean, namely, that Godpe rf or m s part icular actions which affe ct the course of events in the world. The

natural sciences have taught us, he says, to see the world as a unified andautonomous whole. If I read him right, the relevant autonomy here is explanatory;that is , we have learned to explain what happens in terms of causal relations toother entities and events in the world, and not by appeal to any supernaturalpersonal agency. The idea of a direct act of God is unacceptable for us becausesuch an event would involve a gap in the order of nature; it could not besufficiendy explained in terms of antecedent finite events, and so would constitute"an absolute beginning point" for a novel causal series. Warming to the subject,Kaufman declares that such an event is not just epistemically problematic, it is

"literally inconceivable," for the notion of an event without "adequate finitecauses" is "quite as self-contradictory as the notion of a square-circle."2 5

We must, therefore, rigorously avoid talk of divine action in history.Nonetheless, it is open to us to think of history as a who le as G od 's act. In wo rkingout this prop osal, K auf m an draws upon a distinction in action theory be twee n anagent's guiding intention in action, her "master act," and the particular "subacts"by which that intention is carried out. When we speak of divine action, we referfirs t and foremost to God's master act , which is "the whole course of history."26

Understood this way, God's action does not break in upon the world and disrupt

O cc as i o n a l i s m i s the v i ew that f i n i t e ent i t i e s or even t s are on l y " occas i o na l , " rather

than real, causes; that is , their activity is mere ly th e oc ca si on for a div in e ac tion that p ro du ces

the e f f ec t .

2 4 K a u f m a n , " M e a n i n g o f ' A c t o f G o d , ' " c h a p . 6 . A l s o s e e c h a p s . 3 a n d 4 .

2 5 Ib i d . , 130-31 , n . 11 .

26

Ibid., 137.




it , but rather gives history its structure and direction. This theological vision ofhis tory as a s ingle divine action can readily accommodate modern theories ofcosmic and biological evolution, which rec ogn ize the pro gress ive em erg enc e over

time of higher levels of organization out of simpler structures. Theological andscientific descriptions of the world coincide here in a way that is reminiscent ofSchleiermacher's insistence that religious consciousness itself requires that weregard the world as a complete and harmonious nature-system. Kaufman followsSchleiermacher as well in arguing that, although history as a whole is the primaryunit of divine action, w e can non etheless p ick out certain events as hav ing specialsignificance both in moving history toward the ends that God intends and inm aking the divine purposes vis ible to us .

Th is proposal faces some of the same difficult ies that Sch leiermacherencountered, and it generates several new ones of its ow n. Un like Sch leierma cher,Kaufman does not develop an account of God's relat ion to the part icular eventsthat constitute the unfolding course of history, and this leaves us with a series ofpuzzling questions. The re can, of course, be no m aster act w ithout sub-acts to carryit out . What, on Kaufman's account, should we regard as a divine sub-act , andwhat exactly is God's relation to these events—in what way are they Gods acts?On e possible answer to this question would affirm that every event is a divine sub-a c t . 2 7 One could claim that each event in the world's history can be attributed to

God's agency by virtue of proceeding from the original act of creation whichestablished the fundamental structures and direction of cosmic history. 2 8 Just as ahuman agent can act indirectiy by means of a series of instrumental causes, so Godmay be understood to act in every even t that occu rs within u nbro ken causal chainswhich flow fro m the initial creation. T he even t of the sun w arm ing the earth todayis (indirectiy) G od 's act, even th oug h this event is linked to G o d' s (direct) agen cythrough a staggeringly complex and extended series of intermediate events (eachof which also counts as God's act). We can add that God not only initiates theworld's history but also sustains it at every moment. We then could say (contra

Schleiermacher, who rejects the direct/indirect distinction) that God acts in everyevent both direcdy (to sustain all fini te thing s in existen ce) and indirec tly (to brin gabout events here and now through a series of second ary causes stretching b ack toGod's original creative act) .

The difficulty with this construal of Kaufman's proposal is that he explicitlydenies that he is endorsing universal causal determ inism; he con siders determ inismto be incompat ib le wi th genuine human freedom. 2 9 This generates two acute

2 7 Kaufman mi xes toge ther the i deas o f a d i v i ne subact w i th the i dea o f an event that

w e s ingle out as a special act of God , and so he d en ies that ba s ic natural pr oc ess es s ho uld be

regarded as subact s o f Go d ( see , e . g . , i b i d . , 144 ) . He a f f i rm s , ho we ver , that these pr oce sses

f l o w f ro m G od ' s creat i ve i n i t ia t i ve and cons t i tute the bas i c s t ructures that support the

rea l i za t i on o f Go d' s pur pose s a t h i gher l eve l s o f orga ni zat i on .

^"It i s G od 's master act that g iv es the wo rld the s tructure i t has an d gi ve s natural an d

historical processes their direct ion," ibid. , 138.

2 9

Ibid., 133.



PART ICUL AR PRO VIDE NCE 3 0 3

difficulties for his position, however. First, i t contradicts his key argument foreliminating all talk of divine action in th e world. He had contended that every eventmust have adequate causal antecedents in the natural order. But indeterministic

events, including free hum an acts, will not have such antecedents; they will, in fact,be precisely the "beg innin g poin ts for chains of even ts . . . within ongoing naturaland his torical processes" which Kaufman had declared to be inconceivable.3 0 Ifsuch events are admissible in considering free human action, then Kaufman nolonger has any general conceptual grounds for ruling them out in talk of divineaction (though both divine action and free human action may be epistemicallyproblematic).

Second, if the world includes events that are not determ ined by their historicalantecedents, what relation to they bear to God's agency? Each of the options herepresents problems for Kaufman's posit ion. On the one hand, if God determinesthese naturally undetermined events, then God does after all act in history. On theoth er han d, if God does not determine them (as Ka ufm an affirm s is the case forfree hum an actions), then it is not clear w hat place these even ts hav e w ithin G od 'sm aster-act. History is not, in this case, entirely G od 's act, but rather is a c om plextexture of divine initiative, natu ral inde term inac ies, and creatu rely freedom. Giventhe virulent presence of moral evil in the w orld, it certainly app ears that th e acts offree creatures can run counter to the divine intention for history. And these free

acts will set causal series in mo tion which ech o (and perha ps a m plify ) throu gho uthistory, as theological reflections on 'original ' sin suggest. This provides apowerful motive for affirming that God acts in history (viz. , that God does so in

response to human actions); one common telling of the Christian story understandsthe significanc e of Ch rist in just these term s.

Kaufman need not concede this point, however. It is open to him to argue, forexample, that (1) God foreknows the choices of free creatures and builds inappropriate correctives through those parts of the world that are determined byGod's initial creative act, or more generally, that (2) God sets the parameters of

history in such a way that, whatever the details of free human action, God'spurposes will be rea lize d 3 1 Kaufman does not in fact work out these sorts of detailsin his position, and it is worth noting that he finds it difficult entirely to rid hisdiscussion of reference to divine action in his tory. In commenting on God'srelation to individual persons, Kaufman remarks that "certain of [God's] subactsare responsive to our acts; in this w e may rejoice, finding meaning for our lives and

"Ibi d . , 134 .

3 1 T h e first of these two opt ions requires, I be l iev e , that G od ha ve "m idd le kn ow led ge ,"

i .e ., that G od kno w wh at every p oss i b l e f ree created agent w ou l d f ree l y ch oo se to do under

any se t o f c i rcumstance s in whi c h it mi gh t be p l aced . On l y i f G od has such kn ow l e dg e

would God be able to des ign a world that takes our speci f ic free act ions into account . There

are g o o d reasons to doub t , ho we ver , that such kn ow l e dg e i s po ss i b l e (v i z . , bec au se there

m ay be n o t rue counter fac tua l s about f ree ac t s ). W i l l i am A l s ton exp l ores these i s sues i n

"Di v i ne Act i on , H um an F reedo m, and the L a ws o f Nature , " in Quantum Cosmology, 191-

9 9 .



3 0 4 T H O M A S F . T R A C Y

com fort for our souls ."3 2 But if Go d acts on ly to initiate and su stain the w orld , thenGod cannot respond to our actions, though it m ay be p ossib le fo r God to anticipate

them in the design of his tory. And if God does not act in response to human

actions, then only created free agents wil l make any novel contribution to thedirection of history.

Once again, it is clear that a theological price must be paid for avoiding alltalk of God acting in history. Th e precis e character of that cost w ill be determ inedby the particular way in which this overall strategy is carried out, and my briefremarks here do not , of course, exhaust the possibil i t ies .3 3 It is safe to say,however, that this approach will lim it on e's options in Ch ristology , constrict wha tcan be said about God's interaction with human beings, and present certain puzzlesin soteriology. It is possible to do creative theological work within theseconstraints, as Schleiermacher illustrates. But it may not be necessary to acceptthem. Certainly i t can be shown, for example, that Kaufman claims too much(even, as w e have seen, for his ow n p urpo ses) in insisting that an act of G od in theworld is inconceivable. And it is not difficult to make a case that universaldeterminism is neither a necessary presupposit ion nor a well-establishedconclusion of the natural sciences. I will return to this point in considering the thirdstrategy below. It is worth entertaining the que stion, ho we ver, of wh ether w e cou ldspeak of particular div ine action in the world quite apart from there being any gaps

in its natural structure. It is to this question that I now turn.

2.2 Particular Providence without Gaps

W e have already noted one way in which there can be divine action in a thorou ghlydeterministic wo rld, nam ely, in such a world each e ven t (after the initial state of theworld system) can be considered an indirect divine action, brough t about by m eansof an exten ded series of created causes. W e have also seen that there is a limitedsense in which particular events in a deterministic world can be especially

identified as G od 's acts, namely, if they have a notably imp ortant ro le in adva ncingand/or revealing God's purposes. The question I wish to raise here, however, iswhether there is any stronger sense in which particular events in such a world canbe singled out as Go d' s acts. I will consider two proposals that appear to make thisclaim, and argue that each of them is unsuccessful.

In an illuminating essay, Brian Hebblethwaite sets out to defend the idea ofparticular providence against the charge, brought by Kaufman and Wiles, that it

3 2 K a u f m a n , " M e a n i ng o f 4 A ct o f God,"* 146 - 47 .

M a u r i c e W i l e s , in God's Action in he World, ed . Th om as , work s out a proposa l o f

thi s type , draw ing upo n K auf m an 's work . Schu bert Ogden a l so pursues th is bas i c s t ra tegy

in h i s d i sc us s io n o f d iv ine act ion , thoug h he mak es use o f the rather d i f f erent resources

prov ided by Bul tmann and Charles Hartshorne . See Ogden , "What Sense Does i t Make to

Say, 'God Acts in History'?" in The Reality of God, and Other Essays (New York: Harper

& R o w , 1 9 6 6 ) .




involves an untenable com mitm ent to divine intervention in the wo rld .3 4 Hebble-thwaite wants both to affirm that God realizes part icular purposes in nature andhistory, and to deny that this divine action requires that there be gap s in the natural

or historical explanations of events. In making a case for this position, he drawsupon the rather enigmatic rem arks of Austin Farrer about the paradox of "do ubleagency," namely, that a single event can be attributed both to God and to a createdcause. Hebblethwaite suggests that we understand "God's part icular act ion inrelation both to individual lives and to historical developments as taking place inand through regular natural and his torical processes ." 3 5 This is not simply to saytha t G od initiates and sustains the w or ld 's history; that, of course, is just w hatKaufman and Wiles propose. In opposit ion to this absorption of providence intocreation, Hebblethwaite maintains that God is also at work throughout the course

of the world 's his tory, shaping the development of events in specific ways thatrealize the divine purposes. We should not , however, think of this providentialactivity as a matter of occasional supernatural incursions into natural processes. Onthe contrary, Hebblethwaite insists that God acts co ntinu ously "in and thro ug h" thelaw-governed s tructures of the world. God's act ivi ty is universal and immanent,shaping events from within the network of interacting finite causes. Rather thanoverriding the structures of nature, God's guidance of events takes effect throughthe exercise of the creatures ' own powers of operation, so that God "[makes] the

creature make itself at each level of complexity without faking or forcing thes t o r y . " 3 6 In this way, "the whole web of creaturely events is to be construed aspliable or flexible to the prov idential hand of G o d ." 3 7 No gaps are needed here, hecontends, and although there may in fact be gaps in the causal structures of theworld, he endorses the view that "indeterminacy in nature is not to be thought ofas the specific la tching-on point for divine act ion ."3 8

Hebblethwaite presents a theologically appealing picture of God's pervasivecreative role in the w orld's unfolding history, and it seems to me that w e wou ld dowell to aim for something like this in our account of providence. It is not at all

clear, however, that his account can entirely dispense with gaps in the order ofnatural causes . On the one hand, Hebblethwaite wants to say that God's act ionmakes a difference in the way things go in the world; because God acts with thisor that particular purpo se, events dev elop d iffere ntly than they wo uld h av e if G odhad not so acted. But once this is said, we no longer can claim that a complete

account could be given of these events strictly in terms of creaturely agencies. IfGod, in addition to creating and sustaining secondary causes, acts to affect thecourse of events in the world, then God's agency makes a contribution to the

^B ri an Hebbl e thwai t e , "Prov i dence and Di v i ne Act i on , " Reigious Studies, 14, no. 2:

2 2 3 - 3 6 .

3 5 I b i d . , 2 3 4 .

" I b i d . , 2 2 8 .

^ I b i d . , 2 2 6 .

^ I b i d . , 2 3 3 .



3 06 T H O M A S F . T R A C Y

causal nexus, and any account of the relevant events that is couched strictly interms of finite agencies must contain some gaps.

This will be the case even if we envision God to act upon the finite causal

nexus as a whole, rather than affecting it at particular points. There is a helpfuldistinction to be m ade here between (a) overriding the law ful operation of a causalsystem (say, in the miraculous healing of a withered human limb), and (b) settingthat causal system as a wh ole to work in som e particular way (e.g. , in using on e'srestored legs to jump for joy). In the latter case, the processes that constitute thephysiology of the human body operate without causal irregularity, but they aredirected to the agent's purpose; these processes are, as Hebblethwaite suggests,'flexib le or pliable" to th e will of the agent. So perhaps H ebblethwaite is proposingthat we think of God's action on the latter model rather than the former, namely,

that God acts by continuously influencing the causal nexu s of t he w orld as a w ho le,setting it to w ork in the service of God's purposes but doing so in accordance withthe natural structu res that God ha s established for it .

This is an inviting model for divine action, but it does not altogether elim inateexplanatory gaps. How is this divine "influence," this "setting to work," to beunderstood? The claim that God acts in and through, rather than between oramong, created agencies, does not by itself advance the discussion. We still mustconsider the question of what these prepositional phrases mean in this context.

N ote that in the original an alogy, the perso n wh o leaps for joy does have a quitedefinite effect within the causal history of the body. If we think of this person aspossessing free will in the strong, or libertarian, sense, then the agent's free choicewill have necessary but not sufficient conditions in the events leading up to it; thatis, it will constitute a gap in the causal history of th e psy cho ph ysic al syste m . If, onthe other hand, that causal history remains unbroken, then the system is flexibleonly in the sense that (a) it could, if it received different triggering inputs, producea different output, and (b) there are a wide range of such input-output combina-tions.

If G o d' s action in the world is analogous to the hum an ag ent 's bodily action,then particular divine initiatives will involve some ca usal con tributio n wh ich brin gsit about that the w orld-system deve lops in this way rather than that, realizing on eof the possible operations permitted by the structure of the system. This divineinfluence will be part of the causal history of the world, and a description of thathistory w ill be incomp lete if G od 's agency is left out of the account. Hebblethwaiteis quick to disavow any view that has God act at points of causal indeterminacy inthe world, but it is difficult to see another way to sustain his claims about God'songoing providential act ivi ty. 3 9 If each successive state of the world system is

3 9 Cf . Arthur Peacocke ' s , "God' s Interac t i on w i th the Wor l d" ( i n th i s vo l ume) ; and

idem, Theology for a Scientific Age: Beng and Becoming—Natural and Divine (Oxford:

B l ackwel l , 1990) , chaps . 3 and 9 . Peacocke i nv ok es the con cep t o f t op -dow n, or w hol e -par t ,

causat i on i n de ve l op i ng a s i mi lar m od e l o f d i v i ne ac t i on . I t i s i mportant to rem em ber that

this concept i s su gg est ed by the structure of explanation f r e q u e n t l y e m p l o y e d i n a n a l y z i n g

the behav i or o f i nd i v i dua l cons t i tuent s i n organi zed phys i ca l sys t ems . In order to expl a i n



P A R T I C U L A R P R O V I D E N C E 30 7

uniquely determined by its antecedents, then th e system will be flexible only in thesense that it m ay be org anized in the way we h ave jus t discussed, nam ely, that itcould, depending upon the tr iggering inputs i t receives , function in a variety of

ways without breaking down. God's creative action will initiate and sustain theworld's history and determine its direction, but God will not affect events once theare underway.

I want to consider a second, quite intriguing, suggestion about how Godmight b e understood to act in the world without producing or exploiting gaps in itscausal s tructures . In an essay on "Science and God's Action in Nature," JohnCompton suggests a particularly interesting use of the familiar analogy betweenG od 's relation to the world and a hum an ag en t 's relat ion to her b od y .4 0 C o mp t o npoints out that some movements of the body can be described s imultaneously in

two different ways, namely, both as a component physiological process within acomplex organism and as an action undertaken by an ag ent to realize h er pur pos es.Considered strictly as a physiological process, the bodily movement (e.g. , amovement of one 's arm) can be analyzed in detai l as a causal sequence which,given sufficiently good science, may be "explained as completely as is desir ed ."4 1

At the same time, this bodily move me nt is also an intention al ac tion (e.g., of tryingto throw a strike past the batter) which can be described and explained in terms ofthe agent 's reasons and purposes.

The key to Compton's proposal is the claim that these two descriptions/explanations do not in any way compete with each other. Rather, they constitutecoordinated but independent forms of discourse about human beings.

the i r behav i or , we turn not s i mpl y to the i r i mmedi ate causa l antecedent s , but a l so to the

organi zat i on and operat i on o f the sys t em as a whol e , whi ch cons tra i ns the behav i or o f the

part s . Peacocke moves f rom th i s expl anatory procedure to the sugges t i on that here we see

an ontological structure: namely, one in which "the real nature of the system as a whole"

af f ec t s i t s par t s not through an energet ic causal re lat ion but rather through a f low of

i n fo rm at i o n . T h i s pro v i de s the m od e l f or G od ' s ac t i on upo n the wor l d; the wo r l d is " i n

G o d , " w h o a s a h i g h e r - o r d e r w h o l e c o n s t r a i n s t h e w o r l d ' s d e v e l o p m e n t w i t h o u t e n t e r i n g

i nto i t s causa l h i s tory , eve n a t po i n t s o f i nde term i nacy .

Pea cock e's dev elop me nt of this proposal i s richer both sc ient i f ica l ly and the olo gic al ly

than I can con vey here , but i t non ethe l e s s h i nge s on a ser i e s o f probl em at i c c l a i m s: e . g . , the

supposi t ion that top-d ow n explanat ions cann ot be an aly zed in terms of s tructures o f b ot to m -

up expl ana t i on; the m ov e f rom w hol e -p ar t expl an at i on to t reat ing the wh ol e (or the nature

of the sys t e m ) as a cause ; the i dea that the s ta t e o f a sys t e m can be a f f e c t ed by i nforma t i on

without an energet ic interact ion. Each of these c la ims must be expl icated and defended i f we

are to go no t to assert that G od can h av e particular af f ec ts on the world ye t l eav e i ts cau sal

h i s t o r y u n t o u c h e d .

4 0 J o h n C o m p t o n , " S c i e n c e a n d G o d ' s A c t i o n in N a t u r e, " i n Earth Might Be Fair:Reflections on Ethics, Reigion, and Ecology, ed . Ian B arbour (E n gl ew oo d Cl i f f s , NJ:

Prent i ce -Hal l , 1972) .

4 1

I b i d . , 3 7 .



3 0 8 T H O M A S F . T R A C Y

Th e analysis of actions rev eals a different structure and system of relationsfrom the analysis of bodily events. . . . Whereas bodily events sustaincausal connections in space and time, the same events, viewed as an action,

sustain relat ions in a means-ends continuum, with other more inclusiveactions. Similarly, whereas events simply are what they are, actions arealways subject to appraisal and cri t icism as just if ied or u n ju st if ie d , . . . Th eentire logic of bodily events and the logic of actions—each equallyappl icable to me and my behavior— are di f fe ren t .4 2

Each has a complete cast of characters, without the need for interaction with theother s tory, but quite compatible with i t 4 3

Compton seems to hav e something l ike the following in mind. Descriptionsof human beings as biological organisms and as agents of intentional actionscannot confl ict because the vocabularies they use are at every point logicallydistinct. The physiological description speaks of events that can be analyzed intosimpler components and explained in terms of efficient causation within a law-gove rned s tructure. Teleological and evaluative language has no place here. Th eagentic description, on the other hand, speaks instead of acts that have a unitydefined by the agent's intention, that are related to other acts in means/endsrelations, and that are subject to normative assessments. These two vocabulariescannot conflict because they do not make claims that can be aligned with one

another as contradictories. They employ logically distinct subject and predicateconcepts, with the result that w e canno t gen era te sub ject- pre dica te asse rtions in th eone vocabulary that deny what is affirmed in the other. Conceptual confusion,rather than a conflic t of truth claims, is generated when we cross these vocabulariesand try to offer a physiological explanation of events described as intentionalaction or an intentional explanation of events described as a physiological process.Hie solution to the problem s this generates is not to abandon one vocabulary or theother, but rather to pay attention to their logical differences.

This opens up some promising possibil i t ies in theology. Just as efficient-

causal and intentional-teleological vocabularies offer dist inct and non-competingways of talking about human beings, so too will these vocabularies both beavailable in describing the world aro und us. W e can regard events as belongin g toa law governed natural order and also as enacting God's intentions. This freestheology from any need to claim that events which the faithful have come to regardas special divine actions must necessarily, on the physical level, lie beyond thescope of adequate scientific explanation. "God does not need a 4 gap' in nature inorder to act, any more than you or I need a similar interstice in our bodychemis t ry . " 4 4 A single set of events (say, a strong east wind at the Sea of Reeds)can both be explained in terms of deterministic (thou gh un pre dicta ble) m ete oro log -ical conditions and be described as a mighty act of God in freeing the Jews fromslavery in Egypt. Note that this account allows us not only to regard history as a

4 2Ib id . , 38 .4 3Ib id . , 39

"Ibid., 39 and 44.




wh ole as a divine action (G od 's "master act ," as K aufm an put i t) , but also to saythat specific events enact G o d 's p articular purp oses , so that God acts in history aswell . In his own development of these ideas , Compton follows Kaufman in

focusing on God's enactment of his tory as a whole, but I see nothing in hisposit ion that requires this emphasis . 4 5

This approach is ingenious, and its theological applications are enticing. Thefundamental difficulty with i t , however, res ides in the thoroughness with i tdisconnects the two vocabularies that it distinguishes. While there are importantlogical differences between the description of a bodily movement as a physiologi-cal process and as an intentional action, these modes of description and explanationdo interact in important way s and can com e into conflict. This is evident in the factthat certain sorts of causal explanations of a bodily movement are incompatible

with also describing it as an intentional action. If, for example, the movement ofa pe rso n's l im b has as its prox ima te cause a disorder of the nervous system, thenthat behavior can not also be described as an intentional ac tion. The m otion of thelimb is something that happ ens to the agent, not so m ething that s/he does. If bodilymotion is to be intentional action, then the age nt m ust exe rt inten tiona l con trol ove rit, initiating and regulating it for the attainment of her purposes. This is not to say,however, that if we describe the movement as an intentional action, we cannot alsooffer a complete physiological-causal explanation of i t . We need not deny that

intentional actions might be constituted by certain deterministic causal series(though whether such actions can be regarded as free is, of course, a matter ofancient and intractable debate.) But there will, in any case, be some causal seriesthat cannot be intentional actions, given th e structure and history of the o rgan ismin which they occur.

As it happens, Com pton himself a ckno wle dge s this interaction of causal andintentional vocabularies, and so undercuts the foundations of his position. Incommenting on the shortcomings of mind-body dualism, he remarks that:

consciously held reasons and intentions are causes of our action, and they

do eff ectiv ely m od ify bodily conditions . . . these reasons and intentionshave a basis in certain complex states of our brains and nervous systemsthat may, in principle , be analyzed.4 6

Com pton appears to be joining philosophers like Donald Davidson in holdingthat the agent's reasons explain action because they cause it , and they are able tocause it becau se mental states are realized in brain states tha t a re th e prox im al ca us eof the resul t ing bodi ly mot ion. 4 7 This is a plausible and widely held view, andCompton is right that this account of intentional action does not require (as wenoted abo ve) that there be an y gap s in the physiological explanation of action. But,

4 t o m p t o n a l s o f o l l o w s s o m e p r o c e s s t h e o l o g i a n s in su g g e s t i n g th at w e th in k o f t h e

w o r l d a s G o d ' s b o d y . O n e c o u l d m a k e u s e o f h i s a c c o u n t o f c a u s a l a n d t e l e o l o g i c a l

v o c a b u l a r i e s , h o w e v e r , w i t h o u t a d o p t i n g t h i s w i d e r a n a l o g y .

4 6 C o m p t o n , " S c i e n c e a n d G o d ' s A c t i o n , " 4 1 .

4 7 S e e D o n a l d D a v i d s o n , " A c t i o n s , R e a s o n s , a n d C a u s e s , " Journal of Philosophy 6 0

( 1 9 6 3 ) .



31 0 T H O M A S F. T R A C Y

in the first place, position s of this sort directly link physio logical and intentionaldescriptions of action; indeed, the latter depend upon the former. Understood thisway, Compton's analysis of human action no longer provides a conceptual model

that releases us from puzzling over the relation between descriptions of events asdivine actions and scientific descriptions of the causal order of the world. And, inthe second place, action theories of this type are thorough ly determ inistic, tho ughthey may be coupled with a compatibilist position on human freedom. If this istaken over into theology, Compton's posit ion wil l reduce to one that we havealready considered, nam ely, a divine determinism in wh ich, aft er the initial creativ eact, every event will be an indirect act of God, but no event will be a direct divineact in history.

There may, of course, be other ways of defending the claim that particulardivine action in history is possible even in a wo rld w ho se cau sal struc ture is c losedand complete. As I noted in concluding the first section, the difficulties faced byparticular deployments of a theological strategy do not show that the strategy as awhole is doom ed to failure. But in this instance the outlook is bleak. If by an "actof God in history" we mean a divine initiative (beyo nd c reation and conse rvation)that affects the course of events in the world, then it is at least very difficult to seehow such an action could leave a closed causal structure untouched.

2 .3 Divine Action in an Open Wo rld

The upshot of my argument thus far is this. If we wish to affirm not only that Godenacts history (as the first strategy claimed) but also that God acts in history, thenthere are good reasons to think that the world God has made will have an open("gappy") structure. Note that the motivation for this claim is entirely theologicaland conceptual. Nothing has yet been said, in section 2 of this discussion, about thefindings of the contemporary natural sciences. Our task so far has been to see whatclaims we would be led to make about the world if we consistently pursue the

implications of the claim that God acts in history. We can then go on to askwhether these theologically motivated claims are consonant with descriptions ofthe world currently being given by the natural sciences.

I want to turn, then, to the third strategy for understanding divine action. Thisappro ach aff irm s particular divine action in history and ackno wle dges that thisrequires g aps in the natural orde r, but it contend s that the structures of the worldare "op en " in ways that accom m odate divine action w ithout disruption. We needto consider two questions here. First, in what respects must the structures of naturebe open on this view? Second, do the contemporary natural sciences provide

support for the claim that the natural order is open in this way? I noted earlier(section 1.1) two instances of explan atory incom pleteness in principle (rather thanmerely in practice) in contemporary scientific theory, namely, chaos theory andquantum mechanics. We need to ask whether either or both of these explanatorygaps proves helpful in working out this third strategy for conceiving of particulardivine action.

The world will have an open structure in the required sense if (a) the lock-step of complete causal determination (by antecede nt con ditions together w ith th e

laws of nature) is broken at certain points, and (b) these departures from perfect




There is not space here to pu rsue this W hiteheadian alternative in detail, butit is worth noting one important feature of the generalization of freedom into afundamental metaphysical category. Th e con cept of libertarian free do m , as w e just

noted, involves weightier philosophical commitments than the concept of in-deterministic chance: namely, the for m er adds to th e latter the notion of ag ent self-determination. This self-determination cannot be explained in terms of the causalrole of events (say, desires and beliefs) leading up to the choice; the agent's freechoice will hav e necessary b ut not sufficient conditions in these events. But neitheris the agen t's free choice m erely a chan ce even t. Som e libertarians ha ve sugge stedthat here we find a distinctive type of causal relation: "ag ent cau sation " rather than"event, or transeunt, causation." But no one knows quite what to say about agentcausation (who or what is the "agent" who exercises it? how is it that individuals

of this type hav e this powe r?), an d critics sugg est that "age nt c ausa tion" is m erelythe nam e of the central puzzle abo ut freedom, not a solution to it. Whitehead takesthis sort of freedom as the key to understanding all becoming, so that free self-determination (gready diminished though it might be) is part of the explanation ofevery event. In effect, agent causation is made a more basic category than eventcausation, and the latter is understood as an abstraction from the former. This is apowerful idea, but it also leaves the mystery of agent causation unaddressed, andit risks the charge of generalizing a perplexity rather than resolving it . For if we

find it difficult to explicate the notion of indeterministic self-determination in theinstance that is most familiar to us (viz. , in our own free action), then thesedifficult ies are com pou nded wh en we em ploy this concept as a metaphysicalanalogy and extrapolate a modified version of it to the primitive constituents of allthings.

This is not, of course, an exhaustive analysis of process philosophies. Mypoint in making these remarks is simply to suggest that there may be someadvantage to seeing what can be done theologically with the concept of chance;this will involve more modest metaphysical claims and carry a somewhat lighter

burden of argum ent than the appeal to freedom as a general metaphysical category.In exploring the place of chance in the structures of nature, it is important to

distinguish (a) causal chance and (b) various forms of chaotic unpredictabilityfrom (c) indeterministic chance. By causal chance I mean the intersection of causalchains that were previously unrelated and whose particular convergence isimprobable (as when a meteor crashes through someone's roof). These are thesorts of events that insurance com pan ies (wh ich othe rwise are not w ell-know n fo rtheir sense of humor) call "acts of God." Classical physics would describe theseevents as thoroughly determined by the causal nexus, and though they usually

catch us by surprise, w e may b e able to predict them if the relevant causal c hain scome to our attention in advance. It is their relative improbability, and thereforetheir unpredictability in practice, that makes them a suitable paradigm of one kindof chance.

If chance intersections of causal c hain s are usually un pred ictable in pra ctic e,chaotic systems (after a surprisingly small num ber of cycles) are unpred ictable inprinciple. These systems, as we noted above, are so extraordinarily sensitive totheir initial conditions that arbitrarily close starting points for these processes can

produce dramatically divergent outcomes. The results wil l be unpredictable in



PARTICULAR PROVIDENCE 31 3

principle, since it will not be epistemically possible either (a) to specify the initialconditions with full accuracy or (b) to predict their result by considering theoperation of the system un der similar, yet sli gh dy different, initial conditions. This

epistem ic unpredictab ility is vividly illustrated by noting the limits on our abilityto anticipate accurately the behavior even of a rather simple system of masses inmo tion (e.g., the familiar idealized billiard ba lls) op eratin g in com ple te acc ord withthe laws of classical mechanics. A minuscule error in specifying the initial state ofsuch a system (say, in the initial angle of impact) quickly escalates and, after arelatively small number of collisions, leaves us completely unable to predict thefutu re state of the system. In order to predict each p ositio n of the b illiard b alls eve nfor a short time we would need to specify the initial conditions with an accuracythat ut terly exceeds our epis temic rea ch .4 9

This certainly should awaken us from Laplace 's dream of a world that isentirely calculable, and it sugg ests the astonishing fecun dity of the processe s thatstructure our world. But it does not, by itself, generate the ontological opennessthat w ou ld be fruitfu l fo r theology . The reign of causal determinism persis tsunbroken here; the non-l inear equations describing chaotic systems fix exactlywhat each new state shall be, given the immediately preceding state. There isnothing here to suggest that the world's history is not exhaustively specified bypast events conjoined with deterministic cove ring law s. Ch aotic proc esses gene rate

richness and variety in the world, as well as continued surprises for the humanobservers of nature, but they do not allow for novelty, for a future that is notentirely written into the past Rather, the presence of such systems guarantees onlythat we cannot read the future out of the past.

Chaos theory, therefore, reveals that we are behind a "veil of ignorance" withregard to the determining conditions of many events in our world. It is certainlypossible for the theologian to claim that God is at work on the other side of thisveil. Bu t such divine actions are just as much a m atter of miraculou s interventionin natural causal chains as any overtly astonishing mighty act of God in history.5 0

The difference between parting the Red Sea (at least as Cecil B. De M ille depictedit) and making a infinitesimal adjustment in the initial conditions of a chaotic

4 9 "I f the p l ayer i gn ored an e f f e c t ev en as mi n uscu l e as the grav i ta ti ona l a tt ract ion o f

an e lec tron a t the edg e o f the ga l axy , the predi c t i on w ou l d be co m e w ron g a f t er on e mi nu te !"

(Crutch f i e l d , e t a l ., " Chao s") .

M C f . Pea coc ke , "G od ' s Interac ti on , " sec t i on 6 . 1 . , wh ere he ma kes th is sam e po i n t

about divin e intenrention wh ich take place under the co ve r of un predicta bi l i ty . H e ov er loo ks

the d i st inc t ion , how ever , be tw een the de term i ni s t i c unpredi c tabi li t y o f cha ot i c sy s t em s and

the i ndetermi ni s t i c unpredi c tabi l i t y o f quantum sys t em. D i v i ne ac t i on through quantum

i ndetermi nacy need not , a s I w i l l argue shor t l y , i nvo l ve d i v i ne " i ntervent i on , " i n the sense

th at P e a c o c k e d i s c u s s e s .




system is that human observers are unlikely to overlook the former and utterlyunable to detect the latter.5 1

Jo hn Po lking horn e takes a considerably m ore posit ive view of the s ignifi-

cance of chaos theory for efforts to develop a theological view of the world asopen, without disruption, to divine action within it . 4 t The flexibil i ty-within-regularity which chaotic dynamics suggests, does appear appropriate to a worldheld in being by the G od of lov e and faithfulness, wh ose twin gif ts to his creationwill be openness and re liability ."52 This is well-said. But why we should think thatchaotic unpredictability suggests ontological openness? Nancey Murphy points outthe fallacy of employing a "critical realist" principle (viz. , that our knowledgemodels reality) to license the inference from (a) "We cannot predict the outcomeof this system given our limited knowledge of its initial conditions" to (b) t 4 T h e

outco me of this system is not determined by its initial conditions."5 3 Polkinghornedoes appear to make just this argument.5 4 It is worth noting, however, thatPolkinghorne 's claims about chaos and openness in nature are embedded in hislarger program of exploring the idea of "downward em erg enc e" in w hich "the lawsof physics are but an asymptotic approximation to a mo re s ubtle (and m ore supp le)w h o l e . " 5 5 On this view, deterministic laws would turn out to be abstractions thathave limited applicability, and the deeper story about the natural order wouldinvolve the openness of which Po lking horn e spea ks. If this view were vindicated ,

then chaos theory co uld b e regarded as an instance of it. But it is hard to see whywe should run the inf erenc e in the other direction, that is , from chaos theory to am ore holistic view . For ch aos theory, as we have noted, is quite prepared to e xplainunpredictability entirely as a function of its determ inistic eq uations.

We need to look beyond chaotic unpredictability toward indeterministicchance, then , if the w orld is to be "open" in the requisite sense. And here quantummechanics holds great in tere st. 5 6 If, by virtue of claiming that God acts in history,

5 l Pe r h a ps Go d ha s g o o d r ea s o ns to a c t in bo th the s e w a y s . Th e w o nd r o u s a c t in na tur e

c o m m a n ds o ur a t ten t io n a nd pr o v ide s a m e a n s o f s e l f -r e v e la t io n fo r the d iv ine a g e nt . T he

undetectable contr ibution to a ch ao tic sy s te m a l l ow s G od to sha pe the d irect io n of eve nt s in

the wor ld without undercutting our e ffo rts to understand the wo r ld as a la wf ul natural ord er .

M ur phy d i s c us s e s the la tte r po in t in " D iv in e A c t io n ."

^ J o h n P o l k i n g h o r n e , " A N o t e o n C h a o t i c D y n a m i c s , " Science and Christian Beief1 , no . 2 (1 9 8 9 ) : 1 2 6 .

5 3 M u r p h y , " D i v i n e A c t i o n . "

^ Po lk ing ho r ne , Science and Providence: God's Interaction with the World ( L o n d o n :

S P C K P r e ss , 1 9 8 9 ) , 2 9 ; a n d idem, 4 T h e L a w s o f N a tu r e a n d th e L a w s o f P h y s i c s " i n

Quantum Cosmology, 441 .

" P o l k i n g h o r n e , " T h e L a w s o f N a t u r e a n d t h e L a w s o f P h y s i c s , " 2 .

" i t i s wo r th no t ing tha t we s ho u ld no t a s s ume tha t i f inde te r min i s t i c c ha nc e a ppe a r s

a ny whe r e in the wo r ld , i t w i l l do s o o n l y d e e p wi th in the unde r ly ing s tr uc ture o f th ing s . I f ,

a s a ppe a r s l ike ly , phy s ic a l s y s te ms a t h ig he r l e v e l s o f o r g a n iz a t io n d i s p la y pr o pe r t i e s tha t

cannot be reducrd to ( i .e . , exp la ine d ex ha ust ive ly in term s of) the propert ies o f the ir s im ple r

consti tuents , then i t i s a t leas t po ss i b l e that indete rm inism s m ay appear at these h ig her le ve ls



P A R T I C U L A R P R O V I D E N C E 315

we have some stake in the idea that the world displays an open structure, thenquantum mechanics may appear to be the good luck of theology. I want toemphasize, however, that physical theory at this level does not provide us with a

ready-made metaphysic that theologians can borrow. On the contrary, quantummechanics challenges our ability to gene rate any ontolog ical sch em e that satisfiesthe mathematics of this science. 5 7

Among physicis ts and philosophers of science there are many competinginterpretations of the statistical character of the regularities at this level of nature.It has been argued, for exa m ple, that this featu re of quan tum phy sics mig ht refle ct(a) the presence of hidden determining variables or (b) epistemic limits in principleon scientific observ ation/interac tion with the world or (c) genuine indeter m inisticchance in na ture . 5 8 The first of these alternatives, however, has been undercut by

Bell 's theorem, which shows that the spin correlat ions predicted by quantummechanics are incompatible with deterministic hidden-variable theories that denyinstantaneous action at a distance. With accumulating experimental resultsconfirming the predict ions of quantum mechanics , there is a growing consensusthat classical deterministic explanations for these systems are no longer a viablea l te rna t ive . 5 9 In the familiar Newtonian world at the macroscopic level we finddiscrete entities with determ inate prop erties in teracting in abs olu te spac e and time.Now at the quantum level we find a world of non-locali ty and non-separabil i ty,

where particles that have o nce interacted con tinue to constitute a single system oflinked probabilities even when vastly separated. In contemplating the world

as we l l . T hese ques t i ons about the l ocat i on and causa l ro l e o f chance i nvo l ve a s i gn i f i cant

e m p i r i c a l c o m p o n e n t w h i c h m u s t w a i t u p o n d e v e l o p m e n t s i n t h e r e l ev a n t s c i e n t i f ic

disc ipl ines . But i t i s safe to say that current sc ient i f ic thinking i s recogniz ing a more subt le

and exten s ive interplay of order and chan ce, regular s tructure and f le xib i l i ty , than had b ee n

i m a g i n e d e v e n t w o d e c a d e s a g o , m u s t le s s i n t h e e r a o f u n c h a l l e n g e d N e w t o n i a n

detenni n i sm. See , e . g ., Geo rge F . R . E l l i s , "Ordi nary an d E xtraordi nary D i v i n e Act i o n: T he

Nexus o f Interac t i on" ( i n th i s vo l ume) , s ec t i on 2 .

^ T h i s p o i n t i s w e l l - m a d e b y R u s s e l l i n , " Q u a n t u m P h y s i c s , " 3 5 3 - 5 4 .

5 8 S e e B a rb o u r, Issues in Science and Reigion ( N e w Y o r k : H a rp e r & R o w , 1 9 7 7 ) ,

chap. 10 , s ec t i on 3 ; and dem, Reigion in an Age of Science, T h e G i f f o r d L e c t u r e s, 1 9 8 9 -

199 1, vo l . 1 (San Francisco: HaiperSanFrancisco, 19 90 ) , chap . 4 , sect io n 1 . Se e a l so Ru sse l l ,

" Q u a n t u m P h y s i c s , " 3 4 8 - 5 0 ; a n d M a x J a m m e r , The Philosophy of Quantum Mechanics:The Interpretation of Quantum Mechanics in Historical Perspective ( N e w Y o r k : W i l e y ,

1 9 7 4 ) .

w S e e J o h n S . B e l l, Speakable and Unspeakable in Quantum Mechanics: CollectedPapers on Quantum Philosophy ( C a m b r i d g e : C a m b r i d g e U n i v e r s i t y P r e s s , 1 9 8 7 ) ; J a m e s T .

C u s h i n g a n d E r n a n M c M u l l i n , e d s . , Philosophical Consequences of Quantum Theory:Reflections on Bel's Theorem (Notre Dame, IN: Uni vers i ty o f Notre Dame Press , 1989) ;

R J . G . H u g h e s , The Structure and Interpretation of Quantum Mechanics ( C a m b r i d g e , M A :

Harvard Uni vers ity Press , 198 9) ; and M i cha e l L . G . Red head , Incompleteness, Nonlocality,and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics ( O x f o r d :

C l a r e n d o n P r e s s , 1 9 8 7 ) .




according to quantum mechanics , we quickly encounter the l imits of our (non-mathematical) imaginations, for fam iliar (deterministic) m acros cop ic relationship sare simply unable to provide coherent models of nature at this level.

The open-endedness and conceptual strangeness of the scientific discussionshould keep us cautious in our theological uses of this science: theological meta-physics should not rush in where physicists fear to tread, altho ugh in the discu ssionof these matters the boundary between physics and metaphysics has also beencrossed repeatedly from the scientific side.6 0 B ut if, as I have suggested, theologyhas an interest in an open-structured world, and if at least one widespreadinterpretation of current physical theory describes such a world, then it is legitimateto explore ways in which these theological and scientific descriptions of the wo rldmight cohere. Without attempting to discuss current scientific theory in detail, I

want to comm ent on two conditions, in addition to ind eterm inism , that wo uld needto be satisfied if quantum mechanics is to provide the sort of openness that issought by our third theological approach to divine action.6 1

First, the indeterministic chance that appears in quantum mechanics wouldneed to be embedded in an ordered structure. The presen ce of c han ce even ts in theworld will be of limited help to theology if these events simply represent randomdisruptions of otherwise orderly natural processes. Events of this sort could not begiven a coherent place in a scientific description of the world; the w orld w ould not

so much h ave an open structure as an incomplete one. If we are to understand Godto have an ongoing and pervasive role in contributing to the direction of events,then the world must be structured in a way that is both ope n and ord ered , sm oo thlyintegra t ing chance and law. 6 2 This condition does appear to be satisfied by theprobabilistic distribution of indeterministic chance in quantum mechanics.

^ C o n s i d e r , e . g ., E i n s t e i n ' s i n s i s te n c e t ha t q u a n t u m m e c h a n i c s m u s t b e i n c o m p l e t e

( s i nce God does not p l ay d i ce w i th the uni verse ) or , on the s i de o f i nde termi ni sm, Werner

Hei senberg ' s l a t er wr i t i ngs on the uncer ta i nty pr i nc i p l e ( e . g . , Physics and Beyond:Encounters and Conversations [ N e w Y o r k : H a r pe r & R o w , 1 9 7 1 ] ) . P h y s i c is t s h a v e n o w

bec om e qui te bo l d i n the ir foray s i n to me taph ys i c s : e . g . , s e e John B arrow and Frank T i p l er ,

The Anthropic Cosmological Principle (Oxford: Oxford Uni vers i ty Press , 1986) . In T i p l er ' s

la te st b o o k , t h e o l o g y b e c o m e s " a b r a n ch o f p h y s i c s " (The Physics of Immortality: ModernCosmology, God, and the Resurrection of the Dead [ N e w Y o r k : D o u b l e d a y , 1 9 9 4 ] , i x . ) .

6 1 T hese are the second and th i rd condi t i ons that I noted above i n de f i n i ng the sor t o f

openness i n nature that i s requi red by a theo l ogy whi ch a f f i rms that God ac t s i n the wor l d

wi thout d i srupt i ng i t s i mmanent order .

®It i s notable that creat ion myth s of t en portray ch ao t ic d i sorder as th e po w er that m ust

be subdued by the gods i f a wor l d i s t o be formed i n whi ch human be i ngs can l i ve . At the

s a m e t i m e , h o w e v e r , h u m a n a t t e m p t s t o s e e k d i v i n e g u i d a n c e h a v e o f t e n i n v o l v e d t h e u s e

of some randomi z i ng process whi ch creates an "openi ng i n the wor l d , " beyond the reach o f

imm ediate hum an control, in wh ich the go ds ca n act . (Consid er , e .g . , the remark in Pro verb s

1 6 : 3 3 , 4 T he l o t s may be cas t i n to the l ap , but the i s sue depends whol l y on the L ord . ") On

the accoun t I a m e x p l o r i n g , b o t h o f t h e s e a n c ie n t r e l i g i o u s i m p u l s e s c o n t a i n s o m e w i s d o m ;

G od creates a wor l d o f ordered i ndeterm i nac i e s , a wor l d o f boun ded but op en pos s i b i l i t i e s .




Quantum events are not uniquely specified by antecedent conditions, but theirprobabilities are lawfully ordered and predictable.

Second, indeterministic chance at the quantum level would need to make a

difference in the way events unfold in the world. Chance will be irrelevant tohistory if its effects, when taken together in probabilistic patterns, disappearaltogether into wider deterministic regularities. It is commonly said that this is thecase with quantum indeterminacies, since the statistical patterns of these eventsgive rise to the deterministic structures of macroscopic processes.

Does this entirely undercut the usefulness of quantum chance for atheological proposal of the third type? Remember that the theological strategy wehave been considering seeks to say both that (a) God performs particular actionswhich turn events in a direction that they would not have gone otherwise, and that

(b) these actions need not suspend or disrupt the o rder of n ature. T he im pulse hereis to portray God as having an ongoing providential role in shaping the world 'shistory, over and above creating it , sustaining it , and establishing its lawfulstructures and initial conditions. But it looks as th ou gh a d efe nd er of th is view w hoturns to quantum m echanics f or scientif ic help will confron t a di lem ma. If G od 'saction at the quantum level remains within the bounds of probabilistic law, thenGod's activity adds nothing to the course of events beyond contributing to higherlevel deterministic re gular ities.63 If, on the other hand, God's action in determining

quantum indeterminacies departs from the lawful probabilities, then we are backto "interventionist" disruptions of the natural order. So it look as though we areleft, after all, with just two possibilities: God acts by establishing and sustaining alawful natural order and God may act by intervening to bring about part iculareffects that "violate" those laws.

Theological appeal to quantum openness can, I think, slip out of thisdilemm a. It will be possible to open up a third alternative if quantum events whichfall within the expected probabilities sometimes have significant macroscopiceffects over and above contributing to the stable properties and law ful relations of

macroscopic entities. Here the discussion turn s on scien tific questio ns th at I c ann otpresume to answer. It is apparent, however, that quantum events can set in motioncausal chains at the mac roscop ic level. We are able, for example, to design deviceswhose outputs are contingent upon chance events at the quantum level (as theuncertain fate of Schrtidinger's cat vividly illustrates). Here we arrange anapparatus that has a quantum event as its "trigger," and which amplifies that eventthrough a simple causal mechanism. There may be mechanisms of this sort, though

" W e co ul d say that the e f f e c t o f Go d' s ac t iv i ty at the quan tum l eve l i s s i m pl y to

produce the s tat i s t ical pat terns which account for the s table propert ies of higher order

enti ties . Mu rphy takes this v iew in sect ion 5 of "D ivi ne A ct i on ." H ow ev er , M urph y d oe s n ot

restr ict G od 's act ion to the bou nds of t hes e s tat is t ical law s; G od can act outs id e the qua ntum

mechani ca l regul ar i t i e s t o br i ng about ex traordi nary event s ( s ec t i on 5 . 2 . 2 ) .



3 1 8 T H O M A S F . T R A C Y

vastly more complex, at work in neurop hysiology and gen et ics . 6 4 More generally,

chaos theory indicates that nature contains d elicately balanced pr ocesses that can

amplify minute differences in initial inputs into dramatically divergent outcomes.

It has been suggested that these system s can be determined by quantum phenom -ena, whose effects they would magnify with a double unpredictability: (1) the

unpredictability of indeterministic chance at the quantum level, and (2) chaotic

unpredictability in the system that conveys the quantum effect. The physics

involved here, however, is relatively new and notably controversial. For example,

it appears that the wave equations at the heart of quantum mechanics do not

generate chaotic behavior, and it remains to be seen whether a single coherent

account can be given of quantum ph ysics and chao s that would allow for a chaotic

amplification of quantum ev en ts. 6 5 Whatever the resolution of this issue, however,

there is reason to think that chance events at the lowest reaches of the world'sorganization can have significant effects on the development of events at the

macroscopic level.

If these two conditions are satisfied (and I have done no more here than to

suggest that they might be), then it is open to us to propose that one w ay in w hich

God may act in history is by determining at least some events at the quantum level.

This provides a means by which God might (as Hebblethwaite suggested) act to

guide the direction of even ts w ithout overriding the structures of nature that God

has established; God's work in creation will then include not only initiating andsustaining the world, but also making an ongoing contribution to the develop m ent

of events within it. This providential determination of otherwise undetermined

events will not transgress natural law; as long as this divine action operates within

the statistical regularities described by the relevant sciences, it will remain hidden

within the order of nature. Nor will G od's activity at the quantum level require that

God act as a quasi-physical force, manipulating sub-atomic "particles" as though

they were determinate entities of the sort envisioned in Bohr's initial (and quickly

abandoned) planetary model of the atom. Rather, God will realize one of the

several potentials in the quantum system (the "wave packet"), w hich is define d asa probability distribution. 66 There is no competition with or displacement of finite

causes here, since there is no sufficient finite cause that could explain why the

"In 4 T h e i s t i c E v o l u t i o n : D o e s G o d R e a l l y A c t i n N a t u r e ? " ( i n Genes, Reigion, andSociety: Theology and Ethical Questions Raised by the Human Genome Project, ed. Te d

Peters, f or thco m i ng , 19 96 ) Rus se l l po i nt s out that quantum event s are a source o f ge ne t i c

mutat ion, and he argues that these m uta t ions play an important ro le in pro vid ing for no ve l ty

i n n a t u r e . T h e b i o l o g i c a l a s s e m b l y o f t h e o r g a n i s m ( th e p h e n o t y p e ) a n d th e p r o c e s s e s o f

natural s e l ec t i on b e tw een org ani s ms can then func t i on as a h i gh l y s i gn i f i cant am pl i f i er o f

i ndetenni n is t ic quantum even t s . In th i s wa y , G od ma y be und ers tood to a f f ec t the cou rse o f

e v o l u t i o n b y d e t e r m i n i n g e v e n t s a t t h e q u a n t u m l e v e l .

" F o r d , " W h a t I s C h a o s ? "

"I am indebted to Barbour for this po int in his wri t ten co m m en ts on an earl ier v er s io n

of th is paper . A l s o see h is co m m en ts on W i l l i am Po l l ard' s prop osa l s (B arbour , Issues in

Science and Reigion, 4 2 8 - 3 0 . ) .




probability function collapses as it does. The world at the quantum level iss tructured in such a way that Go d can continuously affect events withoutdis turbing the immanent order of nature.

This represents one significant wa y in w hich G od can act, but it is im portantto emp hasize that I am not saying that God acts only through the gaps in the causalorder of nature. God creates and conserves all fmite things, establishing the initialcondit ions and laws of nature that s tructure the world 's unfolding his tory. Inreflecting upon God's relation to particular events in the world, therefore, we cansay that (1) God acts direcdy in every event to sustain the ex istence of each entitythat has a part in it , (2) God can act directly to determine various events whichoccur by chance on the finite level, (3) God acts indirectly through causal chainsthat extend from God's initiating direct actions, (4) God acts indirectly in andthrough the free acts of persons whose choices have been shaped by the rest ofGod's activity in the world (including God's interaction with those persons).6 7 T h epicture that emerges here is of pervasive divine action which establishes, sustains,and continuously shapes a wo rld of seconda ry causes and created free agents withan integrity of their own . All of this divine activity can take place w ithout in anyway disrupting the natural order of the world. That said, it should be added thatGod can also (5) act directly to bring a bout even ts that exceed the natural pow ersof creatures, events which not only are undetermined on the finite level, but which

also fall outside the prevailing patterns and regular structures of the natural order.It migh t be objected that this account of divine actio n end s u p po rtray ing Go das one agent josding for influence in the midst of many others on the cosm ic scene.If we go beyond the first mode of action just noted (i.e. , God's activity ascreator/sustainer) and allow the other four, do we reduce the infinite divine creatorto the status of a cosm ic dem iurge? In particular, is this a special problem fo r thesecond m od e of divine action, that is, G od 's activity in the interstices of the naturalorder so as to affect the ong oing course of events? Recall here Schleierm acher 'sclaim that if God is said to bear any relation to events in the world other than that

of being their absolute ground, then God's act ion has been placed among fini teagencies and must share in their limitations.

It is important to point out that this conclusion simply does not fo l low fromthe premises given. God can be the unique, transcen dent creator of all finite thingsand also act direcdy amon g the sec onda ry ca uses that G od has brou ght into being .God's s tatus as f irs t cause—the primary agent whose action founds and sustainsall other agencies— is not jeop ardiz ed here. In cho osing to create a wo rld of fin iteagencies with causal powers of their own, God freely constrains the uses of divinepower out of regard for the integrity of creatures and the intelligibility of theirworld. I see no reason in general to hold that it is som eho w unfitting fo r Go d to actat points of causal indeterminacy in nature. Given the Jewish and Christianaffirmations of G od 's ongoing involvemen t w ith hum an destiny, we migh t expectthat the world God has made will turn out to have an intelligible and consistent

the dis tinction betw een direct , or bas ic , and indirect , or m ediate d, d ivi ne act io ns ,

s e e n . 1 3 a b o v e .




f in i t e su f f i c ien t cause . 7 0 But this maneuver is not available to God since, ex

hypothesis there is nothing at all (i .e. , no non-divine actuality) that existsindependent of God's creative activity. If there are to be events that are not

determined by any event or agent, including th e divine agent, we m ust non ethelesssay that they exist by God's will.

In trying to make sense of this, it will be helpful to distinguish between (1)the act of causing or sustaining the existence (ex nihilo) of some individual I atsome t ime t and (2) the act of causing / to possess the property P at f. 7 1 Indistinguishing these two acts, I am not saying that it is po ssib le fo r / to exist at t buthave no properties at all . Go d m ust ca use the existenc e of som ething in p articular.Indeed, if P is an essential property of / , then God cannot cause / to exist at t if /is not P at t. But it does no t foll ow fro m this that God directly causes / to have the

property P at Som e other even t or agent could be the pro xim ate cau se of I beingPatt t even though God is the direct cause of the existence of / at t.

This is the case, for example, i f God chooses to bring about some eventindirectly, that is , through secondary causes. Recall for a moment our earlierdiscussion of Sch leierm acher 's drif t toward occasionalism. Wh at was needed , Isuggested, was a distinction between the direct divine action of causing theexistence of a finite cause and effect (say a source of fire and a kettle of boilingwater) and the indirect act of causing the water to be heated by m eans of the fla m e.

God directly brings about the existence of all the entities involved in this causaltransaction. But God does not directly cause the water to boil.So too, God might cause the existence of entities (or of the linked systems of

indeterminate proto-entities that quantum mechanics suggests to us) but leave thesuccessive states of the entity (or system ) u p to probab ilistically structur ed cha nce ,so that not even God determ ines the next state of affairs. 7 2 God would both be the

^ o t e th at i f h u m a n b e i n g s a r e a g e n t - c a u s e s , t h e n w h e n w e a c t f r e e l y w e c a u s e t h er e

to be even t s wh i ch do not hav e suf f i c i ent anteceden t even t - cau ses . B ut these even t s

no neth e l e s s are de term i ned , v i z . , by the agent .

7 1 W e m ust a l so d i s t i ng ui sh tw o senses o f "caus i ng to ex i s t . " In on e fami l i ar sens e ,

f inite agencies can cause existence; i .e . , they can cause changes i n var i ous cons t i tuent s o f the

wor l d whi ch somet i m es lead to the form at i on or des t ruc t ion o f cont i n gen t i ndi v i du a l s , a s i n

birth and death . God , by co ntrast , ca us es to be ex nihilo; this act is not a s p e c i e s o f c h a n g e ,

s ince there i s nothing to ch an ge unt i l G od cr eates . I t i s in this di s t in ct ive ly the olo gic al se ns e

that I am speaking o f G od cau s i ng e x i s t en ce . T h i s can on l y b e a d i rec t d i v i n e ac t and , m os t

the i st s ha ve he l d , i s requi red a t eve ry m om en t to sus ta in the ex i s t en ce o f each f i n i t e th i ng .

G o d can a l so cau se ex i s t e nc e i n the f ir s t s ense , and m ay d o so i ndi rec tl y , i. e . , by wo rki n g

through creaturely intermediaries , as (once again) in birth and death.

^ a n I n w a g e n , in " T h e P l a c e o f C h a n c e in a W o r l d S u s t a i n e d b y G o d , " i n Divine andHuman Action, ed . T h om as Morr i s ( I thaca , N Y: Corn e l l Un i vers i ty Press, 198 8) , exp l ores

a re l a t ed but even more puzz l i ng ques t i on . He cons i ders whether God, i f f aced w i th an

i nf i n i ty o f d i f f erent but equa l l y acceptabl e poss i b l e i n i t i a l s ta t e s for the uni verse , mi ght

s i mpl y decree "L et on e o f th is s e t be" w i thout de term i ni ng wh i ch w ou l d be ac tu a l i zed . T h i s

i s not s imp ly to ch o os e on e of thes e a l terna t ives arbitrarily , i . e . , wi th out ha vin g any r easo n



3 2 2 T H O M A S F . T R A C Y

absolute ontological ground of every event and bring into being a world thatincludes within its structure an important place for indeterministic chance. Godcould then choose whether or not to d eterm ine these finite indeterminacies in light

of their impact on the course of events in the world.7 3

In this way, God's creativework would include a continuous involvement in history, and the open potentiali-ties of nature would emerge and be elaborated w ithin the ong oing prov idential car eof God.

3 Conclusion

I have done no more here than to sketch the outline of such a proposal, and thereis a great deal more to be said on both the theological and scientific sides of them a t t e r . 7 4 My aim has been to carry the discussion far enough to illustrate theadvantages and vulnerabilities of this third way of developing the idea of divineaction . This approach avoids the crippling conceptual d ifficult ies that beca m eapparent when we took a closer look at two examples of the second s trategy,part icular providence "without gaps"; i f we affirm that God performs part icular

to prefer i t to the others . Nor i s i t to resort to a random select ion procedure, a div ine co in

toss. Rather i t i s to decree that on e of them shall be ac tual ize d with out sp ec i fy ing w hic h. V an

Inwagen thinks this i s possible , but I am not at a l l sure that i t i s . After a l l , none of the

al ternat ives wi l l be actual ized unless God actual izes i t ; there i s no other agent on the scene

to do the job.

P e a c o c k e s u g g e s t s t ha t t he o u t c o m e s o f q u a n tu m u n c e rt a in t ie s w o u l d b e u n k n o w n

even to God before they actua l ly occur , and therefore tha t God would no t be in a pos i t ion

to use them to in f lu enc e the cour se o f even ts (Pea cock e , " Go d' s In teract ion ," sect ion 6 .1 . ) .

On e class ica l response to the related puzz le about d iv ine for ek no w led ge and hum an free dom

appl ies to this problem as wel l : i f God ex ists outs ide t ime, then the whole of h istory i s

available to G o d ' s k n o w l e d g e s i m u l t a n e o u s l y . S e e , e . g . , N o r m a n K r e t z m a n n a n d E l e o n o r e

Stump, "Eternity," Journal of Philosophy 79 (1981): 429-58 . If God ex ists in t ime, there are

a variety of strategies of response. If nature includes amplifiers of quantum events in the way

I sugges ted , I see no reason tha t God would no t know th i s and unders tand the prec i se

re la t ion o f quantum inputs to macroscop ic outputs ; even i f God does no t know what the

input wi l l be in case s le f t to chanc e , Go d wi l l certa in ly kno w the input wh ene ver G od

de ter m ine s i t . F ina l ly , it i s a l so pos s ib le for G od to determine en ou gh quantum indeter-

minacies to guarantee that they wi l l a f fect the course of events in the way God intends.

Murphy , a s we have seen , ho lds tha t God determines all s u c h e v e n t s .

7 4 T h e bes t kn ow n presenta t ion o f a pos i t io n tha t ma kes use o f quantum indeter-

mina cies is that of Pollar d (iChance and Providence) , w ho conte nds tha t d iv i ne pro v ide nce

is exercised though the de term inat ion of all quantum events . See Murphy ' s remarks on the

relation of her proposal in Chance and Providence to Po l lard ' s pos i t ion (Murphy , "Div ine

Action," sect ion 6 .4 . ) . See a lso Donald MacKay, Science, Chance and Providence ( O x f o r d :

O x f o r d U n i v e r s i t y P r e s s , 1 9 7 8 ) ; D a v i d J . B a r t h o l o m e w , God of Chance ( L o n d o n : S C M

Press , 1984 ) ; and Kei th Ward , Divine Action (London: Co l l ins , 1990 ) , chap . 5 .



PART ICUL AR PRO V IDE NCE 323

actions which affect the course of events in the w orld , then it certainly app ears thatwe must also grant that there will be gaps in the explanation of these events in thesciences. Moreover, unlike the firs t s trategy, God's "enactment of history," this

third approach allows us to speak not only of God's enactment of history throughthe creation and preservation of the world, but also of divine action in historywhich shapes the unfolding course of events without disrupting the structures ofnature. This is a theologically important result; talk of particular divine action inthe world has played an undeniably important role in the history of Jewish,Christian, and Islamic thought, and it continues to figure prominendy in rel igiouslife (e.g. , the life of worship and prayer) within these traditions. If the thirdtheological strategy is sustainable, then we need not conclude that our "modern,scientific worldview" requires us to abandon or radically reinterpret this

l anguage . 7 5

These theological gains bring with them some vulnerabilities, however. Fornow we have tied theological reflection to interpretations of contemporaryscientific work, and this means that we must give up the perfect neutrality onscientific matters that is the hallmark of the first strategy. I have argued that atheological proposal of the third type will find quantum mechanics more helpfulthan ch aos theory. W hile both fields present us with explanatory gaps in principle,chaotic unpredictability em erge s from precisely the sort of determ inistic a nalysis

which breaks down in quantum mechanics . Chaos, therefore, appears to be asource of epistemic but not ontological ope nne ss. By co ntrast, o ne w idely acce ptedinterpretation of the statistical character of quantum mechanics takes it to reflectindeterminacy in nature. Of course, quantum mechanics can be interpreted in morethan one way, and the development of this science is by no means complete. Inaddition, the theological usefulness of quantum mechanics hinges in part onempirical questions about whether quantum indeterminacies are entirely"dampened o ut" in determin istic regularities at a higher level, or whether they aresometimes "am plified " by part icular causal mechan isms in nature. We noted that

chaotic processes may play a very significant role in this regard, but that thescience involved here is new and quite uncertain.

It is clear, then, that the third approach exposes our account of God's activerelation to the world to some degree of empirical risk. Modern theologians havebeen notably averse to running such risks, particularly in light of the embarrassinghistory of theological resistance to new scientific developments. As we saw inconsidering the first approach to divine action, however, there is also a price to bepaid if we try to guarantee at the outset that no conflict can occur between

7 5 Th er e are, o f course, important theologica l que st ions ra ised by the lang ua ge o f d iv ine

act ion in history , and these qu est io ns m ay lead to pro posa ls for rev is ion or to a pre fere nce

for a the o log y o f the f irs t type . See , e . g . , Maurice W i les , "Div in e Act ion: S om e Mora l

Considerat ions," and James Gu stafson , "Alternat ive C on ce pt i on s of G od," both in The GodWho Acts ed. Tracy . I do not cla im to have sett led these theologica l quest ions, but only to

have opened up some "conceptua l space" in which they can be debated on theological

grounds without fac ing an immedia te sc i ent i f i c veto .



D IV IN E A C T IO N IN T H E N A T U R A L O R D E R :Buridan 's Ass and Schrodinger ' s Cat

Nancey Murphy

1 Introduction

In the Medieval period, especially after the integration of the lost works ofAristode into Western thought, God's acdon in the world could be explained in away perfectly consis tent with the scientif ic know ledge of the dm e. H eaven was a

part of the 'physic al" cosmos. G od 's agents , the angels , controlled the m ovem entsof the "seven planets," which, in turn, gav e natu re its rhyth m s. B ut m ode rn sciencehas changed all that, primarily by its dependence on the notion of laws of nature.

For Isaac Newton and other architects of the modern scientif ic worldview, the"laws of nature" were a direct expression of God's wil l—God's control of al lphysical processes. However, today they are generally granted a status independentof God, not only by those w ho den y the very exis tence of God, but also by m anyChristians, who seem to suppose that God, like a U.S. senator, must obey the laws

once they are "on the bo ok s." C onsequently, for mo dern thinkers , deism has beenthe most natural view of divine action: God creates in the beginning—and laysdown the laws governing all chan ges a fter that— then takes a rest for the du ration.

Not all modern theologians have opted for this deistic account, but in manycases the only difference has been in their additional claim that God sustains theuniverse in its existence. Those who have wanted (or who have believedChris t ianity needed) a more robust view of God's continued part icipation in thecreated order have been forced to think in term s of interven tion: G od occasion allyacts to bring abo ut a state of affairs different from that which would have occurred

naturally.1

It is an ironic bit of history: the laws that once served as an account ofG od 's universal govern ance of nature have bec om e a competing fo rce, constrain-ing the action of their very creator.

The series of conferences for which this essay was written involve a re-evaluation of the modern understanding of divine action in l ight of more recentscience. Ch aos theory has been prop osed as an imp ortant avenue for a new viewof divine action. 2 However, this essay grows out of a recognition that the turn to

A u t h o r s r e p r e s e n t e d i n t h is v o l u m e ar e s o m e o f a s m a l l n u m b e r o f m o r e r e c e n t

t h i n k e r s w h o h a v e s o u g h t non-interventionist account s o f spec i a l d i v i ne ac t s .

2 Joh n Polkingh orne i s the m ost important propon ent of thi s v ie w . Se e , e .g . , hi s Scienceand Providence: God's Interaction with the World ( B o s t o n : S h a m b h a l a , 1 9 8 9 ) ; a n d idem,"L aws o f Nature and L aws o f Phys i c s , " i n Quantum Cosmology and the Laws of Nature:Scientific Perspectives on Divine Action, ed . Rober t John Ru sse l l , Na nc ey Murp hy , and C .

J . I sham (Vat i can C i ty Sta te : Vat i can Observatory , 1993; B erke l ey , CA: Center for

T h e o l o g y a n d t h e N a t u r a l S c i e n c e s , 1 9 9 3 ) .



3 2 6 N A N C E Y M U R P H Y

chaos and complexity has not solved the problem in the way it was intended.Furthermore, wh ile the recognition of top-down causation is an important advancein our understanding of natural processes, as well as an important ingredient that

must go into any new theory, it is not in itself an adequate account of divinea c t i o n . 3 So the main goal of this paper is to provide an alternative account ofcausation and divine action that is both theologically adequate (consistent withChristian doctrine and adequate to Christian experience), and consistent withcontemporary science.

1.1 Preview of the Argum ent

Following a brief critique of the most promising account of divine action based onchaos theory, I shall attempt to set out in advance the criteria a theory of divineaction needs to meet. It is my contention that the problem of divine action is, atbase, a metaphysical pro ble m — on e that cannot be solved by anything less radicalthan a revision of our understan ding of natural causation. O ne w ay to und erstandthe nature of metaphysics is as a set of interrelated theories about reality that are ofthe broadest possible scope, and thus d escriptive or explan atory of the ph eno m enadescribed by all other branches of know ledge. My goa l, then , is to prov ide a theo ryof causation that takes account of phenomena germane to both science and

theology. Thus, in section 2, I propose criteria of adequacy drawn from boththeology and science.Section 3 surveys relevant changes in metaphysical views of matter and

causation, in particular contrasting the Aristotelian hylomorphic conception withthe early modern corpuscular theory. This background is intended to put inquestion current metaphysical assumptions about the nature of matter and ofnatural causes. This section also considers consequences of recent developmentsin science for rethinking these metaphysical issues.

Section 4 advances a proposal. I shall argue that any adequate account of

divine action must include a "bottom-up" approach: if God is to be active in allevents, then God must be involved in the most basic of natural events. Currentscience suggests that this most basic level is that of quantum phenomena.Consequences of this proposal need to be spelled out regarding the character ofnatural laws and regarding G od 's action at the m acro scop ic lev el in gene ral an d thehuman level in particular.

In section 51 attempt to answer som e of the objections that hav e been raisedagainst theories of divine action based on quantum indeterminacy, and also toshow that this proposal meets the criteria of adequacy set out in section 2.

3Arthur Peacocke i s t o be credi t ed w i th the mos t compe l l i ng account s to date o f the

ro le o f top-down causati on i n acco unt i n g for G od ' s con t i nui ng ac t i on . S ee h i s Theology fora Scientific Age: Beng and Becomng—Natural and Divine 2d ed . , en l arged , (M i nn eap ol i s ,

M N: Fortress Press , 19 93 ) . I o w e a great deb t to Pe ac oc ke 's thou ght throu ghou t this pape r .



D I V I N E A C T I O N IN TH E N A T U R A L O R D E R 32 7

1.2 Chaos Theory: The Road Not Taken

O ne proposed solution of the problem of divine action in the natural wo rld is Joh n

Polkinghorne 's suggestion that God works within the indeterminacy of chaoticsystems. Complex systems, being highly sensitive to initial conditions, areinherently unpredictable, since significant variations in initial conditions fallbeneath the threshold of measurement. Polkinghorne argues from this fact to theclaim that the futures of such systems are truly "open," and hence that God canoperate within them w ithout contravening the laws of nature.

I c laim (1) that the argument from unpredictabil i ty to indeterminacy isfal lacious; (2) that the at tempt to f ind indeterminacy between the quantum andhuman levels is unnecessary if we hav e already mad e al lowan ce for Go d's act ion

at the most basic levels of organization; but (3) that the unpredictability recognizedby chaos theoris ts is nonetheless extremely important for an account of divineaction. If we begin with the hypothesis that God works at the quantum level, it isnot necessary—in fact it is cou nterp rodu ctive— to argue fo r causal indeterm inismat higher levels of organization (excluding the human level) s ince God's wil l isassumed to be exercised by means of the macro-effects of subatomic manipula-tions.

Polkinghorne, in speaking of chaotic systems, says:

W e are neces sarily ignora nt of how such system s will beh ave . If you area realist and believe, as I believe, that what we know (epistemology) andwhat is the cas e (ontolog y) are closely linked to each other, it is natural togo on to interpret this state of affairs as reflecting an intrinsic openness inthe behavior of these systems. 4

No w , let us grant the realist thesis that what w e kno w is (u nprob lem atically)linked to what is the case. Let P stand for any proposition, then *X knows tha t P 'entails P. So far so good.

But Polkinghorne ' s a rgument i s not f rom the content of some known

proposition P to the character of the world; it is rather an argument from thecharacter of our knowledge of P to the character of the world. Take any P that is astatement abo ut t he future (chaotic) state of a chaotic system: what the unpredict-ability amounts to is that for any person, X, and for any P, it is not the case that Xknows that P. This implies nothing at all about the world's likeness to P.

To make such an argument is comparable to confusing a modal qualif ier ,which qualifies a propo sition as a whole, with a property of an object described bythat proposition. 'Possibly there are unicorns' does not entail that there are possibleunicorns—that is, entities that are both unicorns and possible. Neither does 'Theoutcome of chaotic processes are inherently unpredictable ' imply that there areoutcom es that are indeterminate.

Is this move in Polkinghorne 's thought s imply an instance of using a badargument for a position that m ay well be defe nsible on other g roun ds? I think no t.The grounds upon which chaos theoris ts argue for the unpredictabil i ty of future

4

Polk inghorne, Science and Providence 29 .




states depend upon the assumption that the future states are determined by initial

conditions in so sensitive a manner that we cannot measure them. So the systems

are presumed to be determined at a very precise level— small changes produce

large effects .So what chaos shows is not that there is genuine indeterminacy in the

universe, but rather that we have to make a more careful distinction betweenpredictability (an epistemological concept) and causal determinism (an ontologicalconcept) . In a s imilar way, the phenomenon of quantum indeterminacy forcedearlier physicists to distinguish between ontological and epistemologicalindeterminacy. That the consensus no w is in fav or of an ontolo gica l interp retatio ndoes not obliterate the distinction; a fortiori i t does not provide warrant forobliterating the distinction between ontological indeterminism and epistemologicalunpredictability in this case.

Furthe rmo re, i t is not clear to m e that Polk ingho rne 's posit ion w ould solvethe problem even if the argument for indeterminacy were valid. Let us take aspecific case. Suppose Father Murphy is playing billiards in a high-stakes game inthe hop e of winning enough to get his school out of debt. Let us also sup pos e thatGod intends him to win, and in order to do so must bring about his getting aparticular ball in the pocket.

Murphy takes aim, hits the cue ball and the cue ball hits the #2 ball, which

undergoes several more coll is ions. Polkinghorne rightly points out that we areunable to predict whether the ball will fall into the appropriate pocket. But what,exactly, could it mean to say that the outcome is open ? D oes it m ean und eterm ined,tout court? Does it mean not uniquely determined by the laws of motion? I takethis latter to be Polkinghorne's meaning, since I find it hard to imagine what itwould mean to say that it is totally undetermined, and also because he sees suchthings as slight environmental influences as important to the outcome in suchcases. So what we might better say is that there are a range of outcomes that areconsistent with the laws of motion.

No w, how does God effe ct one of these possible outcom es? Polking hornesuggests that in some cases God's input might be a non-energetic contribution ofinformation. But to whom or what is the information contributed? How is i tconveyed without any energy at all . And in what sense does this proposal avoid4<turning God into a demiurge, acting as an agent among other agents?"5 Polking-horne quotes John V. Taylor with approval , when he writes:

fl]f we think of a Creator at all, we are to find him always on the inside ofcreation. And if God is really on the inside, we must find him in theprocess , not in the g aps .6

I suggest that Polkinghorne has not provided a clear account of how G odworks on the inside, in the process.

^ i d . , 3 3 .

6 J o h n V . T a y l o r , The Go-Between God (L ondon: SCM Press , 1972) , 28 , quoted i n

P o l k i n g h o r n e , Science and Providence, 3 1 .



DIVINE ACT IO N IN T H E NA T U RA L O RDE R 329

This raises the question of how God could work "on the inside." I take it thatif God is to do so, the it is necessary that God work on the inside of all createdentities—w hich m ust mean in turn that G od w orks w ithin the smallest c onstituents

of macro scopic entities, since these smallest constituents are entities in their ow nr i g h t . 7 If we begin with this hypothesis, it is not necessary—in fact it iscounterproductive—to argue for causal indeterminism at higher levels oforganization (excluding the human. level) s ince God's wil l is assumed to beexercised by m eans of the m acro-effe cts of subatomic manipulat ions.

2 Criteria of Adequacy for a Theory of Divine Action

The theory of causation and divine action to be pre sente d her e migh t be con strue das metaphysical—that is , m etascien tific and m etatheological. As such, its prim aryconfirmation should come from its consis tency with both science and theology,and especially from the fact that it solves problems that have arisen at the interfacebetween these two sorts of disciplines. To solve such problems is no smallaccomplishment, and insofar as this proposal could be shown to solve problemsthat its competitors cannot solve, it would have a high degree of acceptability.8

7 I t i s i n t eres t i ng to specul a te about the meani ng o f the d i s t i nc t i on be tween God

wor ki ng "on the i ns i de" versu s "from the out s i de . " W e can g i ve a c l ear sen se to "from the

i n s i d e " w h e n w e a re s p e a k i n g o f m a c r o s c o p i c e n ti ti e s a n d G o d w o r k i n g w i t h i n t h e m b y

ma ni pu l a t i ng cons t i tuent qua ntum ent i t ie s , s ince the quan tum ent i t i e s are " i ns i de" o f themacroscopi c ent i ty . B ut can we make sense o f a d i s t i nc t i on be tween the i ns i de and out s i de

of the quantum ent i t i e s them se l v es? I f Go d has no phys i ca l l ocat i on , l i tera l ly speak i ng , ye t

w e say that G od i s omni pr esent and i mm anen t in a l l o f creat ion , perhaps w e are as sum i ng

that a d i sembodi ed agent ' s presence i s t o be de f i ned i n t erms o f the agent ' s causa l

e f f i ca cy — w he re ve r G od ac t s , there G od i s . T hu s , t o say that G od w orks w i th i n quan tum

ent i t i e s w ou l d be equi va l ent to say i n g that Go d a f f ec t s quantum ent i t i e s .

i dea l l y , one woul d l i ke to be ab l e to show that such a proposa l i s progress i ve i n the

sense def ine d by Imre Lakatos. He proposed that a sc ien t i f ic research prog ram is pro gre ss iv e

i f i t can be de ve lop ed in such a w ay that i t s theoret ical cont ent ant ic ipates the disc ov ery ofn o v e l facts . A s imi lar cr i ter ion co u ld be de vis ed for me taph ysica l theories: that they

anti ci pate and so l ve pr obl e ms i n o ther d i sc i p l i nes . T ha t i s, a me taph ys i ca l theory shou l d be

counted pro gres s i ve i f it turns out to conta i n resou rces for so l v i n g conc eptua l or em pi r i ca l

probl ems i n or be tween o ther d i sc i p l i nes that i t was not or i g i na l l y des i gned to so l ve .

L a k a t o s ' s s c i e n t i f i c m e t h o d o l o g y i s f o u n d i n " F a l s i f i c a t i o n a n d t h e M e t h o d o l o g y o f

Scientif ic Research Programmes," in Criticism and the Growth of Knowledge, ed. I . Lakatos

a n d A l a n M u s g r a v e ( C a m b r i d g e : C a m b r i d g e U n i v e r s i ty P r e ss , 1 9 7 0 ) , 9 1 - 1 9 6 . S e e m y

adaptat i on o f h i s work i n "E vi dence o f Des i gn i n the F i ne -T uni ng o f the Uni verse , " i n

Quantum Cosmology.




2.1 Theological Requirements

To do justice to the Christian tradition, a theory of divine action ought to be

consistent with widely accepted form ulations of key Christian doctrines, and — thisis at least as important—it must constitute suitable presuppositions for Christianpractice.

2.1.1 Doctrine

I take it that one desideratum for theological construction is always to see whatsense can be given in each age to traditional form ulatio ns. Only if the form ulatio nsof the past turn out to be hopelessly unintelligible should they be rejected orradically changed. God's continuing action in the created world has been spokenof in a number of different wa ys— as sustenance, providence, co ntinuing creation.O ne traditional set of terms w ill turn ou t to b e particu larly useful: God's cont inuingwork understood as sustenance, governance, and cooperation.9 The sense that canbe given to these terms by means of the proposal in this paper will become clearas we go along.

An additional doctrinal requirement, I suggest, is that an account of divineaction throughout the hierarchy of levels of complexity must show forth God's

consistency. Thus, if the paradigm of divine action for Christians is found in thestory of Jesus, we should expect that same divine m oral character to be m anife sted,analogously, in God's act ion within sub-human orders . I shall c laim that therelevant feature of God's act ion in Chris t , displayed analogously throughout thewhole, is its non-c oercive character.

2.1.2 Presuppositions for Christian Practice

The following seem to be required of any account of divine action that would be

supportive of Christian belief and practice:

2.1.2.1 Special Divine Acts*

Th e first requirement is that we be able to distinguish in a m ean ing ful w ay betw eenevents that are in some way special acts of God, and others that are not. Thisrequirement is not met easily, since both doctr ine and logic su gge st tha t if G od actsat all, God is acting in everything that happens.

There are at least three reasons for needing to distinguish special divine acts.Firs t , our knowledge of a person comes primarily from the person's act ions,

*T hese t erms go back a t l eas t t o Augus t i ne , who formul ated the d i scuss i on o f grace

an d f ree w i l l us i ng the con cep t s o f pro v i de nce , sus ta i n i ng ac t i v i ty , gover na nc e and

cooperat i on . T he t erms have been used f requent l y i n subsequent d i scuss i ons o f d i v i ne

a c t i o n .

l 0 M y use o t' ' spec ia l * here correspo nds to that o f "ob jec t i ve l y sp ec i a l d i v i n e ac t s" as

d e f i n e d i n R u s s e l l ' s " I n t r o d u c ti o n " t o th i s v o l u m e .



D I V I N E A C T I O N I N T H E N A T U R A L O R D E R 3 3 1

including speech acts . Knowledge of God, therefore, must come primarily fromseeing what God has done. However, it is well-recognized that the sum total of theevents known to us so far (both natural and historical) provide at best an

ambiguous tes t imony to the character of God.1 1

So we need at least to be able todistinguish between God's acts and the actions of sinful creatures; ideally we oughtto be able to m ake sense of reco gnizin g certain historical eve nts as actions of Go dthat are especially revelatory of God's character, intentions, and providence.

A second reason for needing to distinguish between divine actions andnatural even ts is to suppo rt the practice of petitionary pra yer. If there is no sensein wh ich G od m ay be expected to bring about a state of affairs that wo uld no totherwise hav e occurred, then the practice of petit ionary prayer is gro un dle ss .1 2

An even more pressing reason for needing to distinguish a special class of

divine actions is that to fail to do so makes God entirely responsible for everyevent, and thus exacerbates the prob lem of evil. As Po lking horn e arg ues, theod icyrequires a "free-process defe nse," as well as a free-will d e fe n s e . 1 3

Notice, though, that a concept of the autonomy and regularity of naturalprocesses is not merely a parallel to the theo dicis t 's do ctrine of f ree will; it is aprerequisite for it as well. In order to make intelligent, free decisions and takeresponsibility fo r our action w e m ust live in a world w here outcomes of our actionsare often predictable, and this in turn requires that the universe exhibit law-like

regularity.

2.1.2.2 Extraordinary Divine Acts

Many modern and contemporary Christians would be satisfied with an account ofcausation and divine action that met all of the above requirements. However,earlier Christians would have insisted as well that th ere be roo m in such an acco un tfor something on the order of miracles. I prefer not to use the term 'miracle 'because it is now so closely associated with the idea of a violation of the laws of

nature. I believe it could be sho w n that the primary reason fo r current reje ction ofmiracles, in fact, has been this very definition.

So on e reason for going against the Enlightened consensus and including asa second requirement for a theory of divine action that it leave room for what Ishall call extraordinary acts of God is that the modem rejection of such acts wasbased on a mistaken view of the nature of m iracle s. A second is that elim inatio n ofall such events from Christian history leaves too little: the resurrection is anextraordinary act of Go d if ever th ere w as on e. Ye t, as Paul a sserts, if Christ is not

1 1 See , e . g . , Dav i d Hume' s cr i t i ques o f the argument f rom des i gn i n DialoguesConcerning Natural Reigion, a n d J o h n W i s d o m ' s p a r ab l e, " G o d s , " Proceedings of theAristoteian Society, 1 9 4 4 - 5 .

1 2 S e e m y " D o e s P r a y er M a k e a D i f f e r e n c e ? " i n Cosmos as Creation: Theology andScience in Consonance, e d . T e d P e t er s ( N a s h v i l l e , T N : A b i n g d o n P r e s s, 1 9 8 9 ) , 2 3 5 - 4 5 .

1 3

S e e P o l k i n g h o r n e , Science and Providence 6 6 - 6 7 .




development of empirical science. 1 6 No revised account of divine action that

undercuts the practice of science will be acceptable.

2.2.3 Metascientific FactorsI have been careful in the two preceding subsections to speak of " the law-likecharacter" of the natural world, not of the existence of law s of n ature. W hile m anyscientists assum e that there must in s om e sens e be such laws—that they must havesome sort of existence7— I do not believe such a view is either a necessaryprerequisite for doing science or necessarily supported by the fi nd ing s of sc ien ce .1 8

Thus, I shall argue that the "de-ontologizing" of the "laws of nature" is a helpfulmove in understanding divine agency.

3 Metaphysical Considerations

I claimed above that nothing short of a revision of current metaphysical notionsregarding the nature of matter and causation is likely to solve the problem of divineaction. In this section we survey some important changes in the history ofmetaphysics as background, and then attempt to see where we are now and where

we mu st go in our thinking about causes .

3.1 From Aristotle to Newton

On e of the m ost s tr iking changes from medieval (A ris totel ian) hylom orphism tomodern corpuscular ism (£ 1& Descartes and Newton) regards the "powers" ofmaterial things to m ove themselves or to ch ang e in other w ays. O f co urse Aristo tleand Newton would both agree that horses, for example, are material bodies, andhorses, obviously, can move. So the question is a deeper one about the nature of

matter itself.For Aristotelians, all individual substances were constituted by two

principles: matter and form. Individual substances could b e arranged hierarchicallywith the mo re com plex at the top. For the higher b eings, the matter of w hich theywere composed was already "en-formed" by the forms of lower reali t ies . Thelowest entities in the hierarchy of existents were th e fo ur ele m ent s: ea rth, w ater, air,and fire. But these elements were them selves constituted by forms (of earth, water,air, or fire) and "prime m atter ." Prim e matter , however, was assumed to exist on ly

1 6 See Ian Barbour, ssues in Science and Reigion ( N e w Y o r k : H a r p er & R o w , 1 9 6 6 ) ,

4 6 .

1 7 S e e , e . g . , P a u l D a v i e s , The Mind of God: Science and the Search for UltimateMeaning ( N e w Y o r k : S i m o n & S c h u s t e r , 1 9 9 2 ) .

, 8 Fo r a d i scuss i on o f th i s i s sue , s e e W i l l i am Stoeg er , "Contemp orary Ph ys i c s and the

Onto l og i ca l S ta tus o f the L aws o f Nature , " i n Quantum Cosmology. See a l so B as C . van

Fraassen , Laws and Symmetries ( O x f o r d : C l a r e n d o n P r e s s , 1 9 8 9 ) .



D I V I N E A C T I O N IN T H E N A T U R A L O R D E R 3 3 5

as ingredient in the four elements (and hence as a basic ingredient in all highersubstances), so it was only a theoretical construct within the system.

How ever, in Ar istotle 's system , prim e ma tter, were it to exist ind ependen tiy

of all forms, would be entirely passive since it is form that gives individualcharacteristics to existent beings, including whatever powers and actions arenatural to that species of existent. Co nve rsely, since all existent m aterial b eing s a reen- formed matter, all material beings have certain inherent powers and certain"m otions" that are natural to them. Even stones, simp le objects compo sed prim arilyof the element earth, have the intrinsic power to seek their natural position, whichis at the center of the cosm os. That is why rocks fal l when drop ped, and s ink w henplaced in water. So in this worldview, while prime matter is passive, it does notexist as such. All material beings ( ''primary sub stances"), in contrast, have inherent

powers to act in their own characteristic ways. The self-moving capacities ofanimals and hum ans need no special explanation.

In contrast, Ren6 Descartes, Thomas Hobbes, Newton, and other earlymodern thinkers developed a worldv iew in which material bod ies we re inh erentlypassive or ine rt All macroscopic phenomena, including the movements of animalsand hum an bodies, were manifestations of matter in m otion. Acc ording to Ho bbes,all that exist are "bodies." Bodies move. In doing so they move other bodies; thatis all that happens. 1 9

We can describe this change by making use of terms coined by BaruchSpinoza. He dis t inguished between immanent causes , which produce changeswithin themselves, and transeunt causes, which produce changes in something else.The change from the Aristotelian to the New tonian world views included a chang efrom a world fdled with immanent causes to one in which all causes, whenproperly understood, are transeunt causes. A ccordin g to New ton, all mo tion in theuniverse w as introduced " fro m the outs ide" by Go d. The laws of nature were, inthe first instance, laws of m otion that determined the patterns of mo tion after thatinitial impetus.

It has been argued that Newton had theological motives for developing theinert ial view of matter . 2 0 One motive was what might be called Calvinisttheological maximalism—to give as much credit to God as possible for whateverhappens. So Newton ascribed all motive power to God. Second, this view of thephysical universe made an obvious argument for the existence of God: someonehad to have set it in motion in the beginning.

So a second chan ge in the understanding of causes, from Aristotle to Newton,regards the question of what it is that causes cause. For Aristotle causal analysiswas given of substances and their modification (including locomotion). ForNew ton causal analyses are g iven of changes, and changes are ultimately changesin motion.

l 9 T h i s s u m m a r y o f H o b b e s ' s m a t er i al is m is W a l l a c e M a t s o n ' s , A New History ofPhilosophy, v o l . 2 ( S a n D i e g o , C A : H a r c o u rt B r a c e J o v a n o v i c h , 1 9 8 7 ) , 2 8 8 .

2 0 S e e E u g e n e K l a a r e n , Reigious Origins of Modern Science: Beief in Creation in

Seventeenth-century Thought (Grand Rap i ds , MI: E erdm ans , 197 7) .




3 .2 Current Assumptions

I submit that since the demise of the New tonian wo rldview , p hilosoph ical accou nts

of causation have not kept pace with sc ience. Th e question of the innate po we rs ofmatter is litde addressed these days by either scientists or philosophers, 2 1 and itseems a crucial preliminary question for locating God's action in the physicaluniverse. Yet, if scientists after New ton are willing to do w ithout N ew to n's versionof the Prime Mover, they must be assuming, contra Descartes and Newton, thatmatter is inherently active. 2 2 So what is the ultimate source of the world'sprocesses? Do we look to the beginning, in the Big Bang; or do we look instead tothe basis of all processes in the smallest constituent events? Are quantum eventsbrought about by transeunt causes or by imm anent causes?

N or is it clear w hat an swer is to be given today to the question of wh at it isthat causes cause. It is more common now to speak of events or states of affairs,rat he r th an objects, as the effec ts of causes. Supp ose w e describe an event as achange from o ne state of affairs S! to another S 2 . Then, is it S 2 or the change fromS, to S 2 that requires causal explanation? And is Sj the cause, or merely a necessarycondition? Scientific language is not consistent here. When there is a regularconnection between states of type 1 and states of type 2 we are inclined to speakof S, as the cause of § . However, if there is no such regularity we have two

options. The first is always to look for an additional factor to label as the cause. Ifnon e can be foun d w e speak of S 2 as random—and in such cases some would saythat the event is uncaused.

Furthermore, it is necessary to distinguish between entropy- increasingchanges and entropy-decreasing changes. Entropy- increasing changes require noadditional explanation; here Sj is an adequate explanation of S 2 (or of the changeto SJ. Entropy-decreasing changes require an exchange with the environment,which is sometimes designated the cause, and the status of S X is reduced to that ofa necessary condit ion.

An other com plication: it is also possib le to treat the "laws of natu re" as themost significant "ingredient" in a causal explanations, in which case Sj isdesignated as the set of initial conditions. This tend enc y has been fur the red by Ca rlHempel 's influential nomological account of explanation, wherein a causal

2 1 However , Richard Tay lor c la ims tha t there remain two important ph i lo sophica l

quest ions regarding caus at ion that ha ve not be en sat isfactor i ly reso l ved . On e i s wh ether the

co nc ep t of pow er or causal ef f ic ac y i s a f ter a l l essent ia l , and w hethe r there i s a f ter a l l any

k ind o f necessary connect ion between a cause and i t s e f f ec t . The Encyclopedia ofPhilosophy, 19 67 ed. , s .v . "C ausat ion," by R. Ta ylor.

2 2 S e e W o l f h a r t P a n n e n b e r g , Toward a Theology of Nature: Essays on Science andFaith, ed . T ed Peters (Lo ui sv i l l e , KY : W estminster /John Kn ox Press , 199 3 ) , esp . ch ap . l ,

4

T h e o l o g i c a l Q u e s t i o n s t o S c i e n t i s t s . "



338 N A N C E Y M U R P H Y

the laws of nature could " ex ist" indep enden tly of either the m ind of G od o r of thereality that instantiates them. Still , Stoeger's account leaves unanswered thequestion of wh at accounts for the objective regularities an d relation s in natu re if not

pre-existent laws. To this question we return in section 4.

3 .4 Pointers Tow ard a New Meta ph ysic

An absolutely crucial development in contemporary understandings of the natureof reality regards its non-reducible hierarchical ordering in terms of increasinglycomplex systems. In some ways this recognition represents a return to theAristotelian view that the form (organization, functional capacities) of an entity isequally constitutive of reality as is the stuff of which a thing is made.

The recognition of top-down causation is integral to this view. Thehierarchical conception of reality suggests that an investigation of causation andthe role of div ine action begin at either the top or the bottom of the hierarch y, orboth. The present s tate of our kno wled ge gives primacy to bottom -up causation;it is not clear whether this is an accident resulting from the long dominance ofreductionis t thinking, or whether bottom-up influences do in fact play a moredecisive role in events than do top-down influences. In any case, no account ofwhat makes things happen can neglect what we no w take to the lowest level of th e

hierarchy—the quantum level .This level is odd from the point of view of a causal analysis: quantum eventsdo no t obey deterministic laws. Individual eve nts violate the principle of sufficien treason, which expresses our expectation that things happen when and as theyhappen due to some specific cause; that we should be able to give a reason whythis happ ened no w , rather than later or not at all . So here is a radical incom plete-ness in our know ledge at this mo st bas ic level. Th ere is a metaph ysical ga p that w ehunger to fill—by means of hidden variables, or layers of the implicate order, orsome other means.

4 A Proposal

Let me summarize the requirements and hints so far assembled for an account ofdivine action. W e are looking for a way to m ake sense of the traditional claim thatGod not only sustains all things, but also cooperates w ith and gov erns all createdentities. This account needs to be consistent with other church teaching; it needsto leave room fo r special divine acts for both doctrinal and practical reasons; and

it must not exacerbate the problem of evil.It also needs to be consistent with science in the sense of saving the

phenomena, and must not undercut the practice of science. However, I claim thatit need not be consistent with metaphysical assumptions about matter andcausation, w hich seem at present to be in great disarray.

Finally, a revised metaphysical account of causation that includes divineaction as an integral part needs to take into account the recent recognition of thenon- reducible hierarchy of complexity; this suggests two likely starting points,

based on either top- down or bottom-up causation.



DIVINE ACTION IN THE NA TUR AL ORDER 339

4.1 Top-Down Causation: Another Road Not Taken

Peacocke has very helpfully explored the topic of top-down causation and i ts

possibilities fo r a theory of divine actio n. T he co nce pt of top -do w n c aus ation itselfis crucially important for a nu m ber of reas ons. It exp lains how hu m an free agencyis possible within a highly deterministic un iver se. H en ce, it is an im po rtant elem entin any account of divine action, s ince God's influence on human consciousnessw ou ld othe rw ise have no po ssible influence on the rest of the cosm os. I t is a lsonecessary simply to understand the relations among the various levels ofcom plexity in the natural w orld.

However, I have serious reservations about the adequacy of an account ofdivine action in terms of top-dow n causation alone. I shall disc uss to p- do w n effects

in the human realm below, so here m y focus will be on pu rported top-d ow n effectson the non -hum an wo rld. Th e clearest account given so far of how G od operatesis by analogy to human (top-down) agency in the inanimate world. However, thisanalogy does not solve the problem because hum an ag ency is brough t to bear onthe natural w orld via bodily action. Since God has no body, w e get no help withthe question of how God brings it about that events obey his will. This pushes usto consider whether God's causal relation to the world is like the causal relationbetween a human mind and the body. But Peacocke rightly rejects any dualis t ic

account; and if we understand mental events as a function of the operation of theorganism at a high level of organization, we again have trouble applying theaccount to God—God would then be the world-mind or the world-soul.

Ordinari ly we invoke the concept of top-down causation when we findprocesses that cannot be described or understood in abstraction from the wholesystem, comprised of the affected enti ty in i ts environment. However, in suchcases, it app ears that th e effect of the environment is always mediated by specificchanges in the entity itself. For example, team spirit only affects an individualinsofar as s ights and sounds emanating from the other people affect the individ-

ual's sensory organs. Environmental factors affec t individual organisms by m eansof, say, foo d surpluses or shortages, w hich in turn a ffec t an anim al only insofa r asit doe s or does not eat.

So top-down causation by God should also be expected to be mediated byspecific changes in the affected entities, and this returns us to the original questionof how and at what level of organization God provides causal input into thesystem. I suggest w e turn to a bottom-up account as the most plausible supplemen tto Peacocke 's top-down approach.

4.2 Overview of Mo des of Divine Action

In brief, the follow ing is my p osition . In addition to creation and sustenan ce, Godhas two modes of action within the created order: one at the quantum level (orwhatever turns out to be the most basic level of reality) and the other throughhum an intelligence and action. The apparently random events at the quantum levelall involve (but are not exhausted by) specific, intentional acts of God. God'saction at this level is limited by two factors. First, God respects the integrity of the

entities with which he cooperates—there are some things that God can do with an




electron, for instance, and many other things that he cannot (e.g. , m ak e it hav e th erest-mass of a proton, or a posit ive charge). 2 7 Second, within the wider range ofeffects allowed by God's action in and through sub-atomic entities, God restricts

his action in order to prod uce a world thatfor all we can tell is orderly and law-likein its operation. The exact possibilities for God's action within higher reaches ofthe natural order by means of cooperation with and governance of sub-atomicentities are highly debatable and will be considered below. But I hope to show thatby taking quantum events as the prim ary locus fo r divine action it will be po ssibleto meet m any of the theolog ical ne eds placed upo n such a theory witho ut r unn inginto insuperable theological or scientific objections.

In the follow ing sections I address each of three regimes m entioned above:the quantum level , the regim e of law-like behavior, and the human realm , askingin each case what are the possibilities for divine gov ern an ce and co op era tion . Sin cethe levels are interrelated, the position outlined for each regime will haveconsequences throughout .

Divine action in the regime of law needs to be understood in terms of bothbottom-up and top-down comp onents. For exa mp le, I shall suggest that there is ananalogy between God's respecting the "natural rights" of humans and a similarrespect for the inheren t rights of low er entities to be wh at they are. So calculatingthe possibilities for divine interaction with macroscopic objects involves the

interaction of top-down and bottom -up inf luen ces with the G od-giv en charac teris-tics and potentialities of those beings.Most of what I shall have to say about God's mode of action at the human

level will be non-controversial. Insofar as it presents anything new, it will be byapplying the results of my proposal regarding bottom-up causation at this level.

4.3 God's Action at the Qua ntum Level

The first question to raise with regard to the quantum level is this: Does God

produce solely and directly all the events (phenomena) at this level, or are theentities endowed with "powers" of their own? In other words, I am raising here thequestion introduced in section 3 — the activity or passivity of matter— but relatingit specifically to the mo st basic entities in the physical unive rse and their relationto God. There are two possible answers: either God is the sole actor at this level orthe entities (also) have their own (God-given) powers to act.

I believe we can rather quickly dismiss the first option on theologicalgrounds. To say that each sub-atomic event is solely an act of God would be aversion of occasionalism , with all the attendant theo logical difficulties mentionedabove: it exacerbates the problem of evil; it also comes close to pantheism, andconflicts with what I take to be an important aspect of the doctrine of cre-ation—that what God creates has a measure of independent existence relative toGod, notwithstanding the fact that God keeps all things in existence. To put the

2 7 T h e ser . se i n wh i ch G od "cannot" do a ll th i ngs w i th an e l ec t ron is exp l a i ne d i n

s e c t i o n 4 . 3 .



DIVINE ACTION IN THE NATU RA L ORDER 341

point another way, if God were completely in control of each event, there wouldb e no-thing for God to keep in existence. To create something, even so lowly athing as an electron, is to grant it some measure of independence and a nature of

its own, including inherent powers to do some things rather than others.Th ese considerations lead to the conclusion that it is necessary for theological

reasons to grant that every created entity, however small and ephemeral, has anexistence independent of God. To be is to be determinate, and to be determinate isto hav e certain innate prope rties, including actual or potential behav iors.

Now, the peculiarity of entities at the quantum level is that while specificparticles have their distinguishing characteristics and specific possibilities foracting, it is no t possible to predict exactly when they will do whatever they do. Thisallows us to raise another question: Is the when: (1) completely random and

undetermined; is it (2) internally determined by the entity itself;2 8 is it (3) externallydetermined by the ent ity's relations to som ething else in the physical sy ste m ;2 9 or,finally (4) is it determined by God?

To make sure that these four options are distinguished clearly, allow me topresent an analogy. A medieval philosopher by the name of Buridan is supposedto have hypothesized that if a starving donkey were placed midw ay between twoequal piles of hay it would starve to death for want of sufficient reason to chooseon e pile rather than the other. I am supposing that entities at the quan tum level are

miniature "Bu ridian" asses. The asses have the "po w er " to do one thing rather thananother (walk to one of the piles of hay). Th e question is what induc es them to ta keone course of action rather than the other (or to take a course of action at aparticular dme rather than another or not at all). By hypothesis, there is nothingexternal to determine the don key 's choice (no diffe ren ce in the piles of hay ). A lso,by hypothesis, there is nothing internal (no sufficient reason) to determine thechoice.

Insofar as epistemological interpretations of quantum theo ry and th e que st fo rhidden variables are rejected, we are left with the conclusion that there is no

"sufficient reason" either internal or external to the entities at this level todetermine their behavior. While these issues are still open, many physicists haverejected both epistemolog ical interpretations and at least local hidden variables.

By process of elimination, this leav es optio ns 1 and 4: complete randomnessor divine determination. The fact that the inventor of Buridan's ass believed thedonkey would starve illustrates the philosophical assumption that all events musthave a sufficient reason. This same intuition is what has made the apparentrandomness of quantum even ts so difficult for the scientific community to accept.I shall argue that the better option is divine determination. While most of myargument will be for the advantages of this thesis for theology, it is important to

2 8 In Spi noza ' s t erms , i s the ent i ty i t s e l f an " i mmanent cause"?

2 9

T h at i s , m ov ed by a "transeunt cause . "




bear in mind that it has the further advantage of consistency with the principle ofsuff ic ient rea son . 3 0 To put it crudely, God is the hidden variable.

4.3.1 God's Governance, C ooperation, and Sustenance

It is neither theologically nor scientifically problematic to maintain that God'screative activity involves the sustaining in existence of that which has been created.How ever, it pose s an interesting q uestion to see if we can fin d work f or the term s'cooperation* and 'governance'. These terms turn out to be quite valuable here. Myproposal is that God's governance at the quantum level consists in activating oractualizing one or another of the quantum entity's innate powers at particularinstants, and that these events are not possible without God's action. This is the

manner and extent of God's governance at this level of reality.I have already claimed that we need to maintain that all created entities,

despite being sustained by God, are entities in their own right vis-d-vis God. Onlyin this way can w e say that there is a created entity w ith w hich G od can co op era te.God's action is thus limited by or constrained by the characteristic limitations ofthe entities with which he cooperates. This limitation is, in one sense, volun-t a r y — G o d could cause an electron to attract another electron, but so far as weknow has chosen not to do so. In another sense, though, this limitation is a logical

necessity—an electron that attracts electrons is no longer (really) an electron.This principle of G od 's respecting the integrity of the entities he has createdis an impo rtant one. Propo sing i t is in l ine with Polkin gho rne 's speaking of "fr eeprocesses" in nature. I further suggest, on the strength of a similar analogy with thehum an realm, that w e speak of all created entities as having "natural rights," whichGod respects in his governance. This is the sense in which his governance iscooperation, not domination.

4.3.2 God 's Bottom-Up Causation

The rationale for proposing this bottom-up account of divine governance is basedupon what remains true about reductionism and determinism, even after recentcriticisms of these positions are taken into account. The theological goal is to finda modus operandi for God at the macro-level—the level that most concerns us inour Christian lives. The ontological reductionist thesis seems undeniable—macroscopic objec ts a re composed of the entities of atomic and subatomicphys ic s . 3 1 This being the case, much (but not all) of the behavior of macro-levelobjects is determined by the behavior of their smallest constituents. Therefore,

God's capacity to act at the macro-level must include the ability to act upon themost basic constituents. This is a conceptual claim, not theological or scientific.

^ H o w e v e r , th i s i s pr o b a b ly a mino r po in t , s inc e it no t c l e a r wha t the pr inc ip le i t s e l f

i s b a s e d u p o n .

3 1 Th is po in t s tands e v e n fo r tho s e w ho wa n t to a dd a m ind o r s o u l to the hum a n bo dy

in order to gr,t a l iving person: the body i s s t il l no th ing but a c o m ple x o r g a n iz a t io n o f it s

mo s t ba s ic phy s ic a l pa r ts .



DIVINE ACTION IN THE NA TUR AL ORDER 345

At this level we have to consider a similar set of questions as we did inconsidering Go d' s relation to entities at the quan tum level. But these que stions arecomplicated by relations to answers given at the quantum level.

Let us take a very simple example of a m acro-level entity: a billiard b all. T heball is composed of cellulose structures; cellulose in turn is composed of carbon,hydrogen, and oxygen. The stability of the elements and their ability to form thisco m po un d are effec ts of overall patterns in the behavio r of the con sti tuentsub-atomic entities. The characteristics of the wood itself (e.g. , the grain anddensity) are the result of past biological pro cesses, sim ilarly grounde d in (but notuniquely determined by) the behavior of the quantum-level enti t ies . Thecharacteristics of the wo od giv e rise to s om e of the c harac teristics of the ball itse lf,such as its elasticity. Others, such as its shape and size are effects of the manu fac-

turing process, and perhaps other accidents since then. So past environmentalinfluences hav e interacted with influences determined in a bottom-up m anner bycharacteristic behaviors of its constituents.

To be a billiard ball is to have a set of inherent properties that allow for acharacteristic range of behaviors and interactions with other entities in theenvironment .

Ho w d oes God act with respect to billiard balls? Is the rolling of a billiard ballalways, som etimes, or never the result of divine action? T o be consistent with th e

above analysis we mu st say that divin e action is always a necessary con dition, butnever a sufficient condition for such an event. The continued existence of the ballis dependent upon God acting in regular ways at the quantum level (e.g., governingthe movements of the electrons in its atoms). But such patterns of action give riseto an entity capable of interacting in some ways (but not others) with theenvironment One of the "capacities" with which the ball is endowed by virtue ofits constitution is to lie still until struck; another is to roll when struck by the cuestick. So th e rolling of the ball (ordinarily) w ill be a joint effect of an impact andof God's sustaining the ball ' s characteris t ics "from below."

O ne might now ask how this account differs from a s tandard modern accountof God sustaining entities in existence whose behavior is determined by the lawsof nature, in particular the laws of motion. The differences are subt le . 3 5 First, Godis not merely keeping the ball in existence; God is maintaining its typicalcharacteristics through intentional manipulation of its smallest constituents. Thisfu lf ill s the theological re quire m ent that Go d be unde rstood as acting within allmacro-level events. Second, the behavior of the ball and its characteristicinteractions with the environment are not determined externally by laws "outthere," but are inherent characteristics, emergent from the behavior of itsconstituent part s. 3 6 And, third, within the limits provided by the "natural rights" oftho se consti tuents , God could effe ct extraordinary behaviors or interactions b ygoverning the constituents in atypical ways. A philosopher once wrote that it is notimpossible for all the atoms in a billiard ball to "go on a spree" so that the ball

M A n d of course they are i n tended to be subt l e . T h e go a l here i s t o pro duc e an acco unt

of d i v i n e ac t i on that do es not co nf l i c t w i th obse rvat i on s .

3 6

T here may be except i ons here , such as the l aw o f grav i ty .




would suddenly move without any outs ide force. The account of divine actiongiven here entails that such things are possible, b ut if they h appe n the y are n ot theresult of chance synchronization of random vibrations, but rather of intentional

orchestration of the vasdy many micro-events .3 7

4.4.2 God and the Laws of Nature

I have already suggested that we view the statistical laws of quantum mechanicsas summaries of patterns in God's action upon quantum entities and processes. Inlight of this claim, what are we to say about the laws of nature above the quantumlevel but below the human level?

To say that these laws are nothing but summaries of individual acts of God

is to ignore the fact that God's actions at the quantum level constitute macro-levelentities that hav e their own distinct m anners of op eration . M athem atical desc riptionof the typical behaviors of these entities yields our "laws of nature."

Notice that at this point I am not saying anything new or unorthodoxscientif ical ly. I am simply assuming what has turned out to be true aboutreductionism. Macro-level objects are complex organizations of their most basicconstituents (this is analytic). To a great extent,3 8 the behavior of the whole isdetermined by the behavior of its parts. So the laws that describe the behavior of

the macro-level entities are consequences of the regularities at the lowest level,3 9

and are indirect though intended consequences of God's direct acts at the quantumlevel. What is unorthodox (scientifically) is the grounding I have given to thestatistical regularities in the behav ior at the quantum level.

Now, if the behavior of macro-level enti t ies is dependent upon God'ssustaining their specific characteristics by means of countless free and intentionalacts, why do natural processes look so much like the effect of blind and whollydeterminate forces? Since we have undermined the s tandard modern answer—determination by the laws of nature—a different account must be provided. The

account to be given here is theolog ical: one of G od 's chief p urpo ses is (must ha vebeen) to produce a true cosmos—an orderly system. If we ask why God purposedan orderly universe we might speculate that it is for the intrinsic b eau ty and interestof such a cosmos; we could ground this speculation in our own aestheticappreciation and in the supposition that our appreciation is an aspect of the imago

Dei.

An equally significant explanation is the necessity for such order andregularity so that intelligent and responsible beings such as ourselves might existto "know, love, and serve him." The law-like character of the universe is a

necessary prerequis i te for the physical exis tence of systems as complex as our

3 7 T h e contentious point here has to do w ith the question w hether or not quantum

effects necessarily "wash out" at the macro-level. I am assuming that they need not. See

section 5.4.

"That is, within the limits circumscribed by top-down causation.3*This is lrue even if the laws at higher leve ls cannot be derived mathematically from

the laws of quantum mechanics.



DIVINE ACT IO N IN T H E NAT URAL O RDE R 347

bodies; it is also necessary for intelligence. There could not, of course, be brainscapable of investigating the cosmos without the cosmos being orderly; but if, per

contra, suitably complex beings did exist in a chaodc environment they would be

unable to develop intel l igence. A fortiori they would not be able to makeresponsible fre e choices. Free agency requires a background of law-like processesso that the effects of one 's acuon can be predicted.

But how law-like does the cosmos have to be? There is a vast continuumbetween total chaos (which is actually unimaginable—think of the difficulty inproducing a truly random series of numbers) and the absolute regulari ty(determinism) that has often been assumed since the rise of modern science. Theassumptions upon which this paper is based require that at some level a principleof the uniformity of nature must prevail . Otherw ise Go d's govern ance w ould n ot

include intelligent use of cause-effect relations (any m ore th an o urs co uld ), and w ewould be back to occasionalism. But this does not entail that our sciendfic lawscould suffer no exceptions—in fact , I have just been arguing that by tamperingwith initial conditions at the quantum level, God can bring about extraordinaryevents; events out of keeping with the general regularities we observe.

So the question is: To what extent can God bring about such extraordinaryevents without defeating his own purposes? It is obvious that the whole cosmosdoes not fall into chaos if there are occasional exceptions. The more interesting

question is how much disorder is possible without destroying our ability (ormotivation) for intelligent appreciation of the cosmos or our ability to takeresponsibility for our actions.

John Hick has written that God withholds obvious signs of his existence inorder to create epistemic distance, and hence to leav e us fr ee to be lieve or no t in hisexistence. 40 This argument seems to have something right about it—it is certainlythe case that God could act in such a w ay as to m ake i t mu ch m ore difficult to denyhis existence. Yet the argument seems faulty, too. It seems to overlook thetraditional account of disbelief as sin, and the fac t that ev en in the fac e of th e m ost

astounding evidence given by and o n behalf of Jesus, the crowd s largely failed tobelieve. I suggest that God's action does remain largely hidden and is alwaysambiguous—when manifest it is always subject to other interpretations. But thisis not because we would otherwise be forced to believe in God (as Hick claims)and then to obey h im . Rather it is becau se we w ould lose our sense of the reliablebehavior of the environment. When the environment is taken to behave in a set(and therefo re predictable) m anner, w e can m ake responsible choices about howto act within it . If instead we saw the environment as a complex manifestation ofdivine action, we would lose our sense of being able to predict the consequences

of our actions, and would also lose our sense of responsibility for them. So, forinstance, if I carelessly allow my child to fall off a balcony, I would not see myselfas responsible for his injuries since God was there with~all sorts of opportunitiesfor preventing them.

4 0

S e e J o h n H i c k , Evil and the God of Love ( L o n d o n : M a c m i l la n , 1 9 6 6 ) .




These psycho logical requirem ents for responsible action seem to require inturn that extraordinary acts of God be exceedingly rare ( that we not have anyadequate just if icat ion for expecting G od to undo the consequen ces of our wron g

choices) and that they normally be open to interpretation as (somehow) in accordwith "the laws of nature." So God's relation with us requires a fine l ine betweencomplete obviousness and complete hiddenness—the lat ter s ince we could notcom e to kno w Go d w ithout special divine acts.41 T h e difficulty in describing God'saction is that we want to have it both ways: both that there be evidence for divineaction— something that science cannot exp lain— and that there be no conflict withscience. So a suitable theory of how God acts leaves everything as it wasscientifically. But then there is no evidence upon which to argue that such a viewought to be accepted over a purely naturalis t ic account. Perhaps the am bivalence

we find in attempting to provide a description of divine action is rooted in anintentional ambiguity in God's acts themselves.

In summary: I am proposing that the uniform ity of natu re is a divine artifac t.God could prod uce a m acrosco pic world that behaved in mu ch less regular w aysby manipulating quantum events. Ho we ver, th ere are two kind s of limits by wh ichGod abides. The first is respecting the inherent characteristics of created entities atboth the quantum and higher levels—respecting their "natural r ights ." However,within the degrees of freedom sti l l remaining many more s trange things could

happen than what we observe—bill iard balls "going on a spree." So we mustassume that God restricts extraordinary actions even further in order to maintainour ability to believe in an orderly and dependable natural environment.

4.4.2.1 Chao s Theory: A Subsidiary Role

The real val ue of chao s theory f or an accoun t of divine action is that it gives G oda great deal of 4Yoo m" in which to effect specific outcomes without destroying ourability to believe in the natural causal order. The room God needs is not space to

work within a causally determined order—ontological room—but rather room towork within our perceptions of natural order—epistemological room.

It may b e significant that two of Christians' m ost com m on subjec ts for pray erare health and weather. Weather patterns are clearly chaotic, so it is never possibleto claim definitively that a prayer regarding the weather has or has not beenanswered. I suspect that because most bodily states are so finely tuned they tooinvolve chaotic systems. Thus, the recovery from an illness and especially thetiming of recovery cannot always be predicted. So do we pray for these things

4 I H ist oi y , both in scr ipture and e l sew he re , reports frequen t m irac les in anc ient t imes;

re l a t i ve l y f e w are repor ted today , and contem pora ry report s co m e mo re o f t e n f rom l e s s -

edu cated pop ul a t i o ns . M ost com me ntato rs as su me that w e are see i n g a decrease i n

gul l ibi l i ty . I t i s poss ible , though, that there are in fact fewer extraordinary events because ,

wi th our sharpened sense of the order of nature , wi th increased abi l i t i es to make

measurements , our sense o f the order o f nature has become more ragile. A s t e c h n o l o g i c a l

and sc ient i f ic capabi l i t i es to test miracle c la ims have increased, so have our abi l i t i es to cast

doubt upon causa l regul ar i ty .



D I V I N E A C T I O N I N T H E N A T U R A L O R D ER 3 4 9

rather than others becau se w e lack faith that God c ould "b reak a law of na tur e" or

is it rather because of our long exp erien ce w ith a God wh o prefe rs to w ork o n our

behalf "und er the cover of ch aos"?

4.4.3 Top-Down Causation: A Subsidiary Role

The recognition of top-down considerations plays two vital roles in this proposal.In addit ion to the factor to be pursued below—God's top-down influence on thecreated order through human top-down agency—a second is as fol lows: I haveargued that God's action at the sub-atomic level governs the behavior of nature'smost basic constituents, but witho ut violating the ir "natural r igh ts." So in order tounderstand the limits of divine agency at that level an d in all high er levels, w e need

to kno w wh at are the intrinsic capabilities of those entities. H ow eve r, it app ear s thatthe behaviors that are "natural" to an entity (from any level of the hierarchy) arenot s imply given—enti t ies can do more, have more degrees of freedom, whenplaced in a more complex environment. Studying the inherent powers of an entityin isolation will not tell us what it can do when incorporated into a higher regime.For example, humans can eat , move about, make noise, in total isolat ion fromcommunity, but our truly human capacit ies such as language only emerge insociety. A solitary individual, or even an individual who is part of a herd rather

than a society, cannot teach philosophy.There are limits, of course, to the increased freedom that any particularregime can promo te. For example, cats can be taught to play gam es and eat onion swhen incorporated into a household; pet rocks cannot, no matter how stimulatingthe com pany. However, this limitation applies to kno w n regim es. A s Po lking hor nehas pointed out, w e are not w ell-acquainted with the possibilities fo r either hu m anlife or natural events within a regime in which God's will is the dominant factor.Medieval Christians believed that the great chain of being was also a chain ofcommand, broken by human (and angelic) disobedience. Saintly beings repaired

the chain, and hence holy people such as St. Francis could command the animals.While this account does no m ore than Pea coc ke's to exp lain how divine influencesare transmitted to sub-human beings, it does suggest that a phenomenon has beenrecognized throughout Christian history: natural beings and processes operatesomewhat differently in the presence of people imbued with the presence of God.

4.5 Divine Action in he Human Realm

God has a number of ways to affect human beings by means of the spoken andwritten word. But this kind of communication is the transmission of effects vianormal human processes, and we have to ask where these effects originated. Howdoes original comm unication between the divine and human take place?

A theory consistent with the prop osal of this pape r is that Go d affects humanconsciousness by s t imulation of neurons—much as a neurologis t can affectconscious states by careful electrical stimulation of parts of the brain. God's actionon the nervous system would not be from the outside, of course, but by means ofbottom-up causation from within. Such s t imulation would cause thoughts to be

recalled to mind; presumably it could cause the occurrence of new thoughts by




5.1.2 Know ledge of God 's Actions

I have proposed an account that for all practical purposes is observationallyindistinguishable from a naturalistic or deistic account. The built-in ambiguity indis t inguishing intentional act ion of God from natural events—the generalhiddenness of Go d's act ion in random processes and chaotic systems— raises thequestion of how we could ever know of God's action. The answer is that we onlysee God's act ion by observing larger patterns of events . Consider this analogy:Rocks are arranged on a hillside to spell out "Jesus saves." It is obvious whenlooking at the who le that this has been d on e intentionally. H ow ever, investigationof the location of any single rock in the collec tion wo uld not revea l that it had bee n

intentionally placed. Similarly, in the student's account of his revelatoryexperience, die occurrence of the thou ght that he should speak to his acqu ainta nceabout a drinking problem , by itself, wo uld m erely b e odd . It is only beca use of itsoccurrence in conjunction with the other experiences that he took it as possiblyrevelatory. Its revelatory status was confirmed when he acted on it: the acquain-tance confessed to the problem and set out immediately to get help. So God's actsare recognized by the way particular events fit into a longer narrative, andultimately into the great narrative from creation to the eschaton, from Genesis to

Revelat ion.In order to maintain a place for special acts of God, it is important todis t inguish between two classes of events : those that would not have happenedwithout causal input from God (and we are here assuming that all events fall intothis category), and events that count as God's actions. In discussing human actionwe distinguish, from am ong all of the even ts that hu m ans cause, the smaller classof those that express their intentions. Only the latter are described as actions. Soall events are the result of G od 's causal influence; only some events express (to us)God's intentions. It is the latter that ought, strictly speaking, to be called God's

actions.

5.1.3 Prayer

Peti t ionary prayer makes sense on this account, but more so for some kinds ofevents than others. Events that are recognized as possible yet unpredictable (i.e. ,the results of chaotic processes, unpredictable coincidences) are more to beexpected than events that defy the law-like behavior of natural processes.However, prayers for the latter are not out of the question. One condition under

which we might exp ect such pray ers to be answered is when the divine act w ouldserve a revelatory purpose, since, by hypothesis, God must occasionally act inextraordinary ways to make himself known.

It is clear that in cases where outcomes are not predictable (e.g. , weather,healing), one of the most va luab le condition s for recogn izing the action of G od isthat i t consti tutes a meaningful complex of prayer and response. The prayerbeforehand makes i t possible for an unpredictable event—an event that "mighthave happened in any case"—to reveal the purposes of G od . So wh ile prayer m ight



DIVINE ACTION IN THE NATURAL ORDER 353

not be necessary to persuade G od to act, it will be necessary f or us to recog nize the

fact that God is act in g. 4 2

5.1.4 Deism and OccasionalismThe central goal of this paper was to prese nt an acco unt of divin e action that steersa course between deism and occasionalism. I believe that this proposal does so.G od 's action in every event is guaran teed, and so is som e measu re of control ov erthe course of events such that special, even extraordinary, acts are possible. At thesame time, G o d' s decision to cooperate with created entities rather than to overridetheir natural characteristics means that entities above the quantum level, with theirbuilt-in capacities for action, are allowed by God to use them—natural causal

relations are not den ied. It is this "letting be " that provides an explana tion for th efact that the universe do es not appear to m anife st the purp oses of an all-wise andall-po w erful God in all of its details.

5.2 Scientific Criteria

This proposal saves the app earan ce (w ithin limits) of law-g overned proc esses andjustifies scientific research. Ho wev er, the justification is theological: the univ erse

can be expected to be intelligible since it is one of G od 's high pu rposes that it beso. In addition, it saves quantum physics from violation of the principle ofsufficient reason.

5 .3 Objections and Answers

The following are som e of the objections that m ight be raised again st this pro po sal.Others will be addressed in conjunction with the evaluation of competitors insection 5.4.

5.3.1 Ad Hoc-ness

One criticism of this position is that it appears ad hoc: God can make all sorts ofwonderful things happen, but almost never does so. In defense, I claim that theapparent absence of divine action is ethically necessa ry . 4 3 First, unless and until weknow more about how God's acts at the quantum level affect the macro-level, wereally do not know what act ions are possible for God without violat ing God'sethical principles.

Second, the intentional but metaphysically unnecessary decis ion on God'spart to act openly only on rare occasions is necessary if God is to interact withhum ans without destroying their sense of the depe nda bility of the natural orde r and

4 > Th er e are surely other reasons for prayer, as w el l , su ch as build ing a rel atio ns hip wit h

God, and perhaps the pray i ng i t s e l f i n some way contr i butes to br i ng i ng about the des i red

e f f e c t .

4 3

See E l l i s , "Ordi nary and E xtraordi nary D i v i ne Act i on" ( i n th i s vo l ume) .




of their own responsibility. This not only answers the charge in question, but hasthe further advantage of answering the very troubling question raised for Ch ristianswh o believe in providence: W hy would God answ er prayers for small things (cure

of a cold), while apparently refusing to take actions that would prevent muchsuffering (an early death for Hider)?

5.3.2 Uncertainty of Science

It may be said that this proposal is faulty because the science upon which it isbased is controv ersial or likely to change. My reply is that the propo sal is not based

on the particularities of current quantum theory. Its real basis is ontologicalreductionism (a view that is not likely to be overturn ed so long as there is scien ceas we know it) and on the theological claim that God works constantly in allcreatures. I conclude that God therefore works constantly in the smallest or mostbasic of all creatures. This claim will stand, however those most basic constituentsare described.

However, current theories in quantum physics do provide a valuableingredient for this theory of divine action: the currently accepted supposition ofindeterminacy at the quantum level provides a handy analo gue fo r hum an fre ed om ,and thus grou nds fo r the claim that G o d' s action is ana logo usly non-coercive at the

quantum level. I would be sorry to have to give up this element, but it is notessential to the proposal.

5.3.3 Two Languages

How shall we now speak of causes? For any event there will be at least two,usually three, necessary cond itions: the prior state of the system , G od 's influe nce,and often influences from the environment. Our s tandard practice in answeringquestions about causes is to select from a set of necessary and jointly sufficient

conditions the one that is most relevant to our purposes. On this account, everyevent can be considered from the point of view of science, and the naturalconditions (previous state and environment) will then be cited as causes. Everyevent can l ikewise be considered from a rel igious point of view, where God'saction is the relevant factor.

It might be said that this position is a version of a "two - lan gua ge" solution,similar to som e strategies fo r answer ing the prob lem of fr ee will and deter m inism .However, the difference is that divine action and natural causation, on the viewproposed here, are no longer opposing accounts (as are free do m and determ inism ),since neither the natural nor the divine condition for an event is assumed to be asufficient condit ion.

I claim that this way of speaking about causes is not only consistent with ournormal linguistic practice, but also reflects a common way of speaking of divineaction in scripture. For e xam ple, Josep h says to his brothers: "A nd now do no t b edistressed, or angry with yourselves, because you sold me here; for God sent mehere to preserve life" (Gen. 45:5). The full account of the event involves bothhuman and divine agency. Joseph emphasizes God's providence while recognizing

at the same time that his brothers can indeed be held accountable.




5.3.4 God's Lack of Knowledge

Peacocke claims that God's action at the quantum level is forestalled by the fact

that particular events are as unpredictable to God as they are to us. My proposalevades this difficulty since by hypothesis these events are not random; they arem anifestat ions of divine w il l.

5 .4 Advantages Over Previous Proposals

The theorist in this area whose work comes closest to mine is W.G. Pollard, whosuggested that God w orks through manipulation of all sub-atom ic e ve n ts. 4 4 Pollardhas been cri t ic ized by both David J . Bartholomew and Barbour for providing an

account w hereby all events are determined by divine action. Such an account, theysay, in incom patible with hum an freedom. M y account avoids this prob lem , firs t ,by qual i fy ing bot tom-up divine inf luences by means of top-down causa t ion. 4 5

Second, and more imp ortantly, my account of G od 's respect for the natural r ightsof al l creatures leaves room for genuine human freedom.

Another criticism of Pollard is that he takes God's action at this level to beconstrained within fixed statistical laws. However, I concur with Bartholomew,who claims that Pollard's work involves a misunderstanding of the very nature of

statistical laws.4 6

The constraints upon God's act ion that I propose come instead from God'scommitment to respect the innate characteristics with which he has endowed hiscreatures. This seems to leave som e room for Go d to m aneu ver at the m acro-lev el,but, as I mention below, the exact amount of room is difficult to ascertain. Thissame factor (constraint) allows m e to answ er a cha rge B artholom ew m ake s againstDonald MacK ay. MacK ay claims that God is in detailed control of the beh avior ofall elementary particles.47 But if this is the case, Bartholomew asks, why does Godappear to act in such a capricious manner? 4 8 My answ er: Go d's control is l imited

by his choice to cooperate with rather than over-ride created entities.So we have returned to the issue of findi ng an acco unt of how God acts that

produces a result between two extremes: On the one hand, the account must notlead us to expect God to have total control of every outcome. If so, it would denyhuman freedom, clash with the apparent randomness and purposelessnessmanifested in some aspects of nature, and leave God entirely responsible for all ofthe evil in the world. On the other hand, such an account must not lead to the

4 4 W i l l i a m P o l l a r d , Chance and Providence: God's Action in a World Governed byScientific Law ( N e w Y o r k : S c r i b n e r , 1 9 5 8 ) .

4 5 B arbour has a l ready noted the need for th i s qua l i f i ca t i on i n h i s d i scuss i on o f

Po l l ard' s pos i t i on i n ssues in Science and Reigion, 4 3 0 .

4 6 S e e D a v i d J . B a r t h o l o m e w , God of Chance ( L o n d o n : S C M P r e s s , 1 9 8 4 ) , 1 2 7 - 2 8 .

4 7 S e e D o n a l d M a c K a y , The Clockwork Image: A Christian Perspective on Science( D o w n e r s G r o v e , I L : I n t e rV a r s i ty , 1 9 7 4 ) .

4 8

B a r t h o l o m e w , God of Chance, 2 5 .




conclusion that God has no room within created processes intentionally toinfluence the course of events. I believe that my account successfully steers

be tween these two extrem es . 4 9

5.5 Unanswered Questions

The most serious weakness of this paper is in describing the consequences of thetheory of divine action at the quantum level for events at the macro-level. What,exactly, are the possibilities for God's determining the outcomes of events at themacro-level by governing the behavior of sub-atomic entities? What exacdy are thelimits placed upon God's determination of macro-events by his decis ion not toviolate the natures of these entities? Is this a broad opening for divine action, or a

very narrow window? T he an swer depen ds on sorting out issues in the relation ofquantum physics to the rest of science. Polkinghorne states that:

The re is a particular difficulty in using quantum indeterminacy to describedivine action. Conv entional qu antum theory contains m uch co ntinuity an ddeterminism in addition to its well-known discontinuities and indeter-minacies. The latter refer, not to all quantum events, but only to thoseparticular events which qualify, by the irreversible registration of theireffects in the macro-world, to be described as m easure m ents. O ccasions of

measurement only occur from time to time and a God who acted throughbeing their determinator would also only be acting from time to time. Suchan episodic account of providential agency does not seem altogethertheologically sat isfactory. 5 0

Polkingho rne w ould include among these possible instances of m eanin gfuldivine action, I believe, cases where sensitivity of chaotic systems to initialconditions involves changes so slight as to fall within the domain of quantummechanics. Th e classic example of a macroscopic system that "m easu res" qua ntumev en ts is Schrt tdin ger 's poor cat, w hose life or death is m ade to depe nd o n the

status of one quantum event.Against Polkingho rne's view, Rob ert Russell w ould argue that the im portant

fact that has been overlooked here is the extent to which the general character ofthe entire macroscopic world is a function of the character of quantum events.Putting it playfully, he points out that the whole cat is constituted by quantum

events!W e can imagine in a straightforward w ay G od 's e ffec t on the quantum event

that the experimental apparatus is designed to isolate; we cannot so easily imaginethe cum ulative effec t of G od 's act ion on the innumerable quantum events that

49li also avoi ds the interventionist overtones of B ar th olo m ew 's s ug ges t io n that i t mig ht

be be t te r to a s s ume tha t Go d l e a v e s mo s t qua ntum e v e nts to c ha nc e a nd o n ly a c t s upo n

o c c a s i o n t o d e t e r m i n e s o m e s p e c i f i c o u t c o m e . S e e ib i d ., 1 3 0 .

4

® P o l k i n g h o m e , " M e t a p h y s i c s o f D i v i n e A c t i o n . "




constitute the cat 's existen ce. Y et this latter is equally th e realm of d ivine ac tio n.5 1

I have been assuming Russell 's position throug hou t this pap er. Y et even if R ussellis correct, there still remains a question. Does the fact that God is affecting the

whole of reali ty ( the whole cat) in a general way by means of operation in thequantum rang e allow fo r the sort of special or ext rao rdin ary div ine a cts that I claimChristians need to account for? Or would such special acts be limited to the fewsorts of instances that Polkinghorne envis ions? 5 2

A second open question comes from our lack of knowledge regarding thepossibilities for top-down causation, and the role of "holist laws." In particular, welack knowledge of the possibil i t ies of divine top-down causation and of thepossible behavior of natural entities within a regime constituted by the fullpresence and action of God. We have a glimpse of this regime in the resurrection

of Jesus, and a hint from Paul that the w hole co sm os awa its such a tra nsfo rm ation.Are there states in between this final state, in which God will be all in all, and thepresent s tate of God's hiddenness in natural processes? Do the extraordinaryevents surrounding the lives of Jesus and th e saints represent su ch an interm ediateregime?

Finally, it has been the consistent teaching of the ch urch that G od resp ects thefreedom and integrity of his human creatures . I have proposed as an axiom of mytheory of divine action that God respects the "natural rights" of entities at the

quantum level as well. Is it, then, the case that all created entities have intrinsiccharacters that God respects in his interaction with the world? And what does Goddo when the rights of creatures at different levels of the hierarchy come intoconflict? The claim that God acts consistently throughout the hierarchy ofcomplexity has consequences regarding what sort of thing God should and shouldnot be expected to do with creatures within the interme diate realm betw een hu m an sand quarks. For instance, it would be consistent with m y prop osal for G od to cau seBuridan's ass to eat, but not to cause Balaam's ass to speak. Does our experienceof God's action in our lives bear out such a distinction, and does this distinction

help explain why some prayers are answered and others not?My hope is that despite these unanswered questions, the forego ing proposal

provides insights that are worthy of further pursuit . 5 3

5 1 S e e R u s s e l l , " Q u a n t u m P h y s i c s i n P h i l o s o p h i c a l a n d T h e o l o g i c a l P e r s p e c t i v e , " i n

Physics, Philosophy, and Theology: A Common Quest for Understanding, ed. Ru ssell,

W i l li am R. Stoeger . , and Geo rge V . Co yn e (Vat i can C i ty Sta te : Vat i can Obser vatory , 198 8) ,

3 4 3 - 6 8 .

5 2 M y ho pe i s that th i s qu es t i on can b e addressed a t a future con fere nce .

thank al l con fere nce participants for their re sp on ses to this pap er. St ev e H ap pe l an d

B ob Ru ssel l were especial ly di l igent cr it ics . Bo b al so ne ed s to be thank ed for the trem end ou s

amount o f ed i tor i a l work he has done i n put t i ng toge ther th i s vo l ume and i t s predecessor .



O R D I N A R Y A N D E X T R A O R D I N A R Y D IV IN E A C T I O N :The Nexus o f In te rac t ion

George F.R. El l i s

0 Prologue

This paper touches controversial issues, and some of the possibilities discussed willundoubtedly make some readers uncomfortable. This is because i t takes seriouslyin a par t icular way both the h is tor ic Chris t ian message and a modern sc ient i f ic

perspect ive , emphas iz ing the i r cogni t ive c la ims as I unders tand them from aQuaker pe rspec t ive . The reade r may no t sha re th i s doub le commi tment .Nevertheless the argument is logically and epis temologically sound; the unease isat a theological and/or metaphysical level . This issue wil l be discussed briefly inthe las t main section. However, a full t reatment cannot be given here; an in-depthjus t i f ica t ion for the v iew taken wi l l be g iven in a for thcoming work.1

For the moment I make the in i t ia l c la ims tha t : (1) there a re o ther types ofknowledge besides that given by the "hard" sciences, for example, that given by

phi losophy, theology, humanis t ic , and ar t i s t ic d isc ip l ines—the task is to f ind aviewpoint that does just ice to these issues as well as to hard science, in acompa t ib le way ; (2 ) the hypo the t i co-deduc t ive me thod used to suppor t theview po int presented here is essential ly the same as that und erlying o ur acceptanceof modern science; and (3) the main themes proposed, controversial as they are,are supported by as much or indeed more evidence (admittedly of a more generalform than tha t used by phys ics a lone) than many of the themes of moderntheore t ica l phys ics .

The requirement in order to approach the material fair ly is an open mind in

looking at the various logically possible options, rather than s imply selecting onepart icular metaphysical s tance on an a priori basis . The important point is that wehave to ado pt som e metaphys ica l pos i t ion ; we shou ld do so here in a cons ideredw a y .

1 Introduction

This paper is la rge ly a response to Nancey Murphy 's contr ibut ion to th is volume,

"Divine A ct ion in the Natu ra l O rde r : Buridan 's Ass and Schrodinger 's C at * Th at

N a n c e y M u r p h y a n d G e o r g e F . R . E ll is , On the Moral Nature of the Universe:Cosmology, Theology, and Ethics ( M i n n e a p o l i s : F o r t r e s s P r e s s , 1 9 9 6 ) d e v e l o p i n g t h e m e s

o u t l i n e d i n E l l i s , Before The Beginning: Cosmology Explained ( N e w Y o r k : B o w e r d e a n / -

B o y a r s , 1 9 9 3 ) .



3 6 0 G E O R G E F . R . E L L I S

paper is revolutionary because it represents a conservative interpretation of theChristian faith 2 which, unlike most other such interpretations, takes the content ofmodern science seriously as part of the task of constructive theology. The

viewpoint here will be to basically agree with Murphy's paper, and comment onsome specific issues raised by its thesis.

Accepting the main thesis of that paper, the themes I would like to discussfurther are: (a) the issue of capricious a ction; (b) the issue of top-dow n causationthrough intention, and the particular causal nexus of the action; and © the issue ofevidence for the position stated.

As regards (a), one of the main problems for the proposal is the charge ofcapriciousness in God's action, in terms of God deciding now and then to actcontrary to the regular patterns of events but often deciding not to do so. Onewould like to have articulated some kind of criterion of choice underlying suchdecisions, and then an analysis given of how that criterion might work out inpractice. This ha s to take very seriously indeed the issue of evil, pain, and sufferingas experienced in the present-day world, of God's acceptance and al lowance ofhorrors of al l kinds, which one might a priori presume he/she could and wouldpreve nt if he/she so desired. If the usual Christian view is to make sense, there hasto be a cast-iron reason why a merciful and loving God does not alleviate a lotmore of the suffering in the world, if he/she has indeed the power to do so. This

leads to the question of when divine action may be expected to take place, in eitheran "ordinary" or an "extraordinary" man ner. Th us, on e needs to characterize thoseconcepts, and have some kind of criterion as to when each may be expected.

On e possible appro ach to this rang e of issues is to em phasiz e the possibilityof another domain of response of matter to life than usually encountered, assugges ted by John Polkinghorne: 3 that matter might respond directly to God-centered mind s through laws of causal behavior that are seldom tested (see section4.4 below). Then the distinction between ordinary and extraordinary actionbecomes the question of whether we have entered this domain or not. This may

provide a partial answer.As regards (b), a central them e in Peaco cke 's w riting ,4 the issue is what type

of top-down causation might occur, and wh ere the causal nexu s could b e wh ereby

^ a t i s , i t i s i n agreem ent w i th centur i e s -o l d aspec t s o f the Chr i s t ian t radit ion . Se e ,

e . g . . Dictionary of Christian Spirituality, e d . G o r d o n W a k e f i e l d ( L o n d o n : S C M P r e s s,

1989) ; and Deni s E dwards , Human Experience of God (Ramsey , NJ: Paul i s t Pres s , 1983) .

However i t i s certainly not fundamental i s t in i t s at t i tude; rather i t i s in agreement wi th the

ki nd o f moderni z i ng approach advocated by Pe ter B erger i n h i s superb book, A Rumor ofAnges: Modern Society and the Rediscovery of the Supernatural ( N e w Y o r k : D o u b l e d a y ,

1 9 6 9 ; r ep r in t . N e w Y o r k : A n c h o r B o o k s , 1 9 9 0 ) .

3 S e e J o h n P o l k i n g h o r n e , " G o d ' s A c t i o n i n t h e W o r l d , " CTNS Bulletin 10, no. 2

(Spring 1990) , 7; dem. Science and Providence: God's Interaction with the World ( L o n d o n :

S P C K P r e ss , 1 9 8 9 ) ; a n d W i l l i a m S t o e g e r " D e s c r i b i n g G o d ' s A c t i o n i n t h e W o r l d in t h e

L i g h t o f S c i e n t i f i c K n o w l e d g e o f R e a l i t y " ( in t hi s v o l u m e ) .

4

See Arthur Peacocke , "God' s Interac t i on w i th the Wor l d" ( i n th i s vo l ume) .



O R D I N A R Y A N D E X T R A O R D I N A R Y D I V IN E A C T I O N 3 6 1

this top-down acdon could be initiated in the physical world. I will particularlycontrast general top-d ow n influenc es which al ter condido ns over a wid e range ofevents (as in many of the examp les given by Bernd-Olaf K upp ers5) with specific

top-down actions, which are very focused in their aim and influence. I will argueth k th e latter is what is required for the Christian tradition to make sense, and thatit requires something like the special action m ention ed in Mu rph y's p ape r. This isprobably related to the issue of free-w ill .6

Regarding the specific causal nexus, my view is in agreement with that ofRobert Russell, William Pollard, and others, and recently supported and well-discussed in Thomas Tracy's paper "Part icular Providence and the God of theGaps ." 7 The relevant points are: (b l) the need for so m e kind of "g ap " in the strictlycausal chain fro m physical c au se to eff ect if specific divine action in the world is

to be possible in a meaningful sense (I believe it m ay well be that on e can m ak e th esame claim in respect to individual actions with a connotation of personalresponsibility); (b2) the inability of deterministic ch aos to pro vid e a so lution to thisproblem of causal gaps; and (b3) the fact that quantum uncertainty does indeedhave this potential.

Overall these contentions are supp ortive of the argu m ent in M ur ph y's pap er.As regards (c) , while "proof ' wil l not be available, one would l ike some

broad brush-stroke defense of the position presented in terms of general lines of

evidence.8

Th e main point here is that, as emp hasized in M urp hy 's present paper,one of the needs is to satisfy the Christian tradition in terms of doctrine andpractice; but then the issue is, Whose doctrine? Whose practice? What is thefoun dation for choosing and sup port ing one part icular brand of tradit ion?

Either one goes here for a rather inclusive, b road-stream interpretation wh ichaims to be widely acceptable across the many varieties of Christian tradition, andtherefo re wil l inevitably be regarded as "w eak " by man y of them; or one aim s tobe m ore particular and detailed in term s of dev eloping the view of som e particularbranch of that tradition in depth. But then the product becomes rather exclusive in

its nature, and may be regarded as irrelevant by others. In either case the issuebecomes that of validating what is claimed to be true by the chosen traditions ordoctrines, in the light of manifest errors, in many cases, in what has been claimedin the p ast.

To cope with the issue of inclusivity, one can suggest that this defenseshould, first, have a broad base aimed at validating a religious worldview in

5 B e m d - 0 1 a f K U p p e r s , " U n d e r s t a n d i n g C o m p l e x i t y " ( i n t h i s v o l u m e ) .

'See , e .g . f Rog er Penrose, The Emperor's New Mind: Concerning Computers, Minds,and the Laws of Physics (Oxford: Oxford Uni vers i ty Press , 1989) ; and E uan Squi res ,

Conscious Mind in the Physical World (B r i s to l : A da m Hi l ger , 199 0) .

7 I n t h i s v o l u m e .

t f . Murphy , "E vi den ce o f De s i g n in the F i ne -T un i i . o f the Un i verse , " i n QuantumCosmology and the Laws of Nature: Scientific Perspectives on Divine Action, ed . Rob er t

J o h n R u s s e l l , N a n c e y M u r p h y , a n d C J . I s h a m ( V a t i c a n C i t y S t a t e : V a t i c a n O b s e r v a t o r y ,

1 9 9 3 ; B e r k e l e y , C A : C e n t e r f o r T h e o l o g y a n d th e N a t u ra l S c i e n c e s , 1 9 9 3 ) .



3 6 2 GEORGE F.R. ELLIS

general, strongly supported by widely acceptable evidence; second, support a morespecifically Christian view developed as a second stage of the argument, refiningits methods, detail, and evidence; and with support for a particular tradition

developed in the third stage. I shall m ak e som e com m ents alon g these lines at theend. The proposal ma de here is that the idea of top-dow n causation, with differe ntlayers of description, effective laws, me anin g, and eviden ce, is the best fram ew orkfor understanding and testing the overall scheme suggested.

2 Emergent Order and Top-Down Action

As explained clearly by Kuppers and Peacocke, in hierarchically structuredcomplex systems we find both top-down action and emergent order.

First, the hierarchical structure introduces levels of emergent order, asdescribed so ably by Arthur Peacocke: 9 irreducible concepts used to describe thehigher levels of the hierarchical order are simply inapplicable at the lower levelsof order. Thus, different levels of order and description are required, allowing newmeanings to emerge at the higher levels of description. (Note that these aredifferent-level descriptions of the same physical system, applicable at the sametime.)

Second, this s tructure enables top-down action to take place wherebyinteractions at the lower levels cannot be predicted by looking at the structure atthat level alone, for it depends on, and can only be understood in terms of, thestructures at the higher levels.

In the specific case of biology, we find, beautifully described by NeilCampbell, a hierarchical structure as depicted in Figure 1 (on following page). A sexpressed by Campbell :

With each upward step in the hierarchy of biological order, novel proper-ties emerge that were not present at the simpler levels of organization.

These emergent properties arise from interactions betwe en the com pon ents.. . . Unique properties of organized matter arise from how the parts arearranged and interact . . . [consequendy] we cannot ful ly explain a higherlevel of organization by breaking it down to its parts. 1 0

Indeed not only are such different levels of descrip tion perm itted, they are requ iredin order to make sense of what is going on. This is true not only of biologicalsystems: Kupp ers shows convincingly that such em ergent properties are imp ortanteven in a physical system such as a gas, being m ediated by the sy ste m 's structural

' P e a c o c k e , ' G o d ' s I n te ra c ti o n. "

, 0

N e i l A . C a m p b e l l , Biology ( R e d w o o d C i ty , C A : B e n j a m i n C u m m i n g s , 1 9 9 1 ) , 2 - 3 .




conditions and boundary conditions (as discussed further below). 1 1 Ian Barbour 1 2

and Peacocke 1 3 develop the theme of em ergence in depth.

E c o s y s t e m I

B i o l o g i c a l C o m m u n i t y c o m m u n i t y s t r u c t u r e

S p e c i e s

P o p u l a t i o n

O r g a n i s m

O r g a n S y s t e m s nO r g a n s organism structure

T i s s u e s

C e l l s

O r g a n e l l e s mM o l e c u l e s ce l l

A t o m s structure

Ions and e l ec t rons

Figure 1: B i o l o g i c a l l e v e l s o f e m e r g e n t o r d e r .

In a biological system, the two crucial levels of order are that of the cell andthe individual organism; at each of the se leve ls there is a higher lev el of auto no m yof cohe rent action than at any of the other levels. A biologist regards individuals

as the elementary c om pon ents of a population, and cells as "elementary com po-nents" of the individual, while (broadly speaking) a microbiologist regardsmolecules and a biochemist, ions and electrons, as the elementary components. Aphysicist would continue down the hierarchical scale, reducing these to quarks,gluons, and electrons.

2.1 Hierarchies of Software: Digital Com puters

A particularly clear exa m ple is given by m odern digital com puters, w hich ope rate

through hierarchies of software: from the bottom up there are m achine language

n K t l p p e r s , " U n d e r s t a n d i n g C o m p l e x i t y . "

, 2 Ian Barbour, Reigion in an Age of Science, T h e G i f f o r d L e c t u re s , 1 9 8 9 - 1 9 9 1 , v o l .

1 ( S a n F r a n c i s c o : H a r p e r S a n F r a n c i s c o , 1 9 9 0 ) .

l3Peaoocke, Theology or a Scientific Age: Beng and Becoming—Natural and Divine

( O x f o r d : B l a c k w e l l , 1 9 8 7 ) .




(expressed in binary digits) , assembly language (expressed in hexadecimal),operating system and programming language (expressed in ASCII), andapplication package (e.g., word processor) levels of software. At every level there

is a completely determ inistic type of beha vior desc ribed by algor ithm s app licableat that level. All of this is realized in terms of the m otio n of elec tron s flo w ing in theintegrated circuits as determined by the laws of physics. This is where the actualaction takes place, but it does so according to plans implemented at the higherlevels of structure, and thereby effects actions that are meaningful at the higherleve l s . 1 4

L e v e l n

L e v e l 4

L e v e l 3

L e v e l 2

L e v e l 1

Figure 2: Ge ner i c Hi erarchi ca l S truc ture o f a Com puter .

Logically, a digital computer consists of a hierarchy of n different virtualmachines M,, each with a different machine language L n . 1 5 Its generic structure isexpressed in Figure 2 (above).

1 4 F o r a very clear expo si t ion of the hierarchical s tructuring in mo der n digi ta l com pu ter

s y s t e m s , s e e A n d r e w S . T a n n e n b a u m , Structured Computer Organization ( E n g l e w o o d

Cl i f f s , NJ: Prent i ce Hal l , 1990) .

1 5

I b i d . , 2 - 3 .



O R D I N A R Y A N D E X T R A O R D I N A R Y D I V IN E A C T IO N 3 6 5

L e v e l 6

L e v e l 5

L e v e l 4

L e v e l 3

L e v e l 2

L e v e l 1

L e v e l 0

A p p l i c a t i o n p a c k a g e

( e . g . , w o r d - p r o c e s s o r )

P r o b l e m - o r i e n t e d l a n g u a g e

le v e l ( e .g . , C o r Ba s ic )

A s s e m b l y l a n g u a g e l e v e l

O p e r a t i n g s y s t e m m a c h i n e

l e v e l

C o n v e n t i o n a l M a c h i n e

l e v e l

M i c r o p r o g r a m m i n g l e v e l

D i g i t a l l o g i c l e v e l

T r a n s l a t i o n ( c o m p i l e r )

T r a n s l a t i o n ( c o m p i l e r )

Tr a ns la t io n (a s s e mble r )

Partial interpretation

( o p e r a t i n g s y s t e m )

Interpretat ion

( m i c r o p r o g r a m )

D i r e c t l y e x e c u t e d b yha r dwa r e

Figure 3: Ty pic a l Hie r a r c h ic a l S tr uc tur e o f a D ig i ta l Co mpute r .

H ie physical computer Mx

does the actual calculation in ma ch ine lang uag e Lt

; eachvirtual computer runs programs either by interpreting them in terms of the lowermachine languages, or translating them into these lower languag es (e.g. , pro gram sin Lj are either interpreted by an interpreter running on L u or are translated to L^.Each computer's machine language (at each level in the hierarchy) consists of allthe instructions the computer can execute at that level. However, only programswritten in language Lj can be directly carried out by the electronic circuits, without



366 GEORGE F.R. ELLIS

the need for intervening translation or interpretation. In contemporary multilevelmachines, the actual levels realized are show n in Figu re 3 (on preceding page)}6

Th e logical connections between th e different levels in the computer, and the

resulting machine languages at each level, are tightly controlled by the machinehardware and software. In particular, given the machine, the program loaded intoparticular memory locations, and the data resident in memory, each high-levelinstruction will result in a unique series of actions at the digital (hardware) level,which in turn will result in a uniq ue series of conseq uence s at each of the hig herlevels. ConsequenUy the machine language at each level also has a tight logicalstructure with a very precise set of op eratio ns resulting fro m each statem ent in thatlanguage. Th e detailed relation of operation s fro m high to low levels, and at eachlevel, will depend on the actual memory locations used for the program and data;but the logical operation is independent of these details. 1 7

In biological systems, with hierarchical levels as indicated above, the samekind of logical structure holds; however the "languages" at the higher levels aremuch less tightly structured than in the case of the computer,1 8 and the linksbetween different levels correspondingly less rigid.

2.2 The Physical Med iation of Top-D own Action

Consider now how the hierarchically structured action is designed to occur, inphysical terms. We can represent this as follows: for a structured hierarchicalphysical system 5, made up of physical p articles interacting on ly throug h physicalforces , top-down and bottom-up action are related as shown in Figure 4 (o n

following page).

The boundary B separates the system S from its environm ent E. Interactionwith the outside world (the environment) takes place by inform ation/ene rgy/m atterflow in or out through the boundary, and is determined by the boundary condit ionsat B. The structure of the system is determined by its structural conditions, which

can be expressed as constitutive relations between the parts. I distinguish herestructural conditions, fixed by the initial state of the physical system but thenremaining constant in a stable physical system (e.g., the structure of a computer asdetermined by its manufacture), and initial conditions and boundary conditions asusually understood in physics (e.g., the initial state of motion of a fluid in a cell andtemperature conditions imposed at the cell boundaries over a period of time). 1 9

, 6 I b i d „ 4 - 7 .

, 7 T h e s e s t ruc tures and the ir i n t ercon nec t i on s are descr i bed i n cons i derab l e de ta il i n

T a n n e n b a u m ' s b o o k .

, 8 T h e ma jor aim of the A l (art i fi c ia l inte l l ige nce ) m ov em en t i s to arrive at a

corresp ond i ng l y l o os e s t ruc ture i n the com pu ter ' s h i gher - l eve l l angu ages .

"Kl i ppe i s ' s concept o f "boundary condi t i on" conf l a t e s these three ra ther d i f f erent

c o n c e p t s . S e e " U n d e r s t a n d i n g C o m p l e x i t y . "




T o p -

D o w n

VI *

* Level of Meaning N* Level of Law N

* Leve l o f Meaning N,

* Leve l o f Law N,

Lowest l eve l

Constituents

Microscopic laws

Bottom-

U p

• Environment

E

Boundary B

Figure 4: T o p - D o w n a n d B o t t o m - U p C a u s a l I n t er a c ti o n s i n a G e n e r i c H i e r a rc h i ca l

S y s t e m . / i s t h e i n i t ia l s t a t e o f t h e c o n s t i t u e n t s a n d F t h e fi n a l s t at e ; t h e m i c r o s c o p i c

l a w s o f t h e s y s t e m d e t e r m i n e t h e m o v e m e n t f ro m / t o F . ( F o r b r e v i t y o n l y t w o o f t h e

l e v e l s o f m e a n i n g a n d l a w h a v e b e e n s h o w n ; o r d i n a r i l y t h e r e w i l l b e m a n y . )

2.2.1 Classical Physical Systems

Examples: (1) the atmosphere; (2) an aircraft; (3) a digital computer.

In these systems, the acdon is stricdy deterministic, though not necessarilypredictable. 20 (This is ensured in designed systems such as (2) and (3), in order toobtain reliability; any quantum uncertainties are damped out, by design.)

A: Top-do wn acdon hap pen s by mean s of states at the higher-level initiatingcoordinated action at the bottom level, which is governed by the basic causalrelat ions underlying the system. The bottom-level components act on each otherby regular physical laws, the resulting final state at the bottom level thendetermining conditions at the higher levels, because they define conditions at thehigher levels through their aggregation (or "coarse-graining") properties. The lasttwo s teps are what is m eant by 'bottom -up causa tion' in these contexts .

The coordination of act ion occurs through the s tructural arrangement andinterconnection of lower-level entities (e.g. , transistors, capacitors, etc.) to formhigher-level entities (e.g. , com puters, television sets, etc.). Because the sema ntics

2 0 I f t h e c o m p u t e r o u t p u t w e r e p r e d i c t a b l e i n a n y s i m p l e r w a y w e w o u l d n o t n e e d t o

r u n t h e c o m p u t e r p r o g r a m .



368 GEO RGE F.R. ELLIS

of the higher level are intrinsic to its natu re, the langu age (vocabu lary and syntax)at each level cannot be reduce d to that at a lower level, even though wh at hap pen sat each higher level is uniq uely determ ined by the coo rdinated action taking pla ce

at the lower-levels, where it is fully described in terms of the lower-levellanguages. Thus, the whole s tructure shows emergence of new propert ies (at thehigher levels) not reducible to those of the constituent parts.Examples: (I) lowering the undercarriage in an aircraft (realized by gas particlesexerting forces on a piston in a cylinder); and (2) a computer reading out a text fdeand printing it on the screen (realized by electrons impinging on the screen).

What happens to a given system is controlled by the initial state along withthe boundary condidons. The system bou ndary is either: (i) closed (no inform ationenters); or (ii) open (information enters; possibly also mass, energy, momentum).In the latter case we have to know what information enters in order to determinethe future state of the system.

B: The final state attained at the bottom level is uniquely determined by theprior state at that level (the initial conditions) and the incoming information at thatlevel—that is , by the "boundary condit ions" (assuming a given system structureand given microlaws). This determines uniquely what happens at the higher levels.We assume that a unique lower-level s tate determines uniquely the higher-levelstates through appropriate coarse-graining. When this is not true, the system is

either ill-defined (for example, because our description has o mitted som e "h id de n"variables), or incoherent (because it does not really constitute a "system"). Weexclude these cases . N ote that the loss of inform ation im plied in the definition ofentropy results beca use a particular higher-lev el state can corre spond to a num berof different lower-level states (each of which leads to that single higher-levelstate.).

Note 1: This statement does not contradict the idea of top-down causation.An y given macro-state at the top level will correspond to a restricted (perhaps evenuniqu e) set of conditions at the basic level. It is through determining a set of micro-

states as initial conditions at the bottom level, corresponding to the initial macro-state, that the top-level situation controls the evolution of the system as a whole inthe future. How uniquely it does so depends on how uniquely the top-level statedetermines a s tate at the b otto m .2 1

Note 2: At the higher levels, the statement analogous to B may or may not betrue (i.e. , the system may or may not be causally determinate when regarded as amachine at a higher level); this depends on what micro-information is lost inform ing the macro-variables at the higher levels , from the micro-variables .

Note 3: Although the bottom-level system is determinate, prediction of whatwill happen is in general not possible even at the bottom level, because of thepossibility of chaotic behavior (sensitive dependence on initial conditions).

2 1 Or, equi va l ent l y , i t does so dependi ng on how much i nformadon o f the mi cros ta tes

i s l o st by g iv i ng onl y a top- l eve l desc r i pt i o n— thi s i n form at i on l os s de f i n i ng the entropy o f

the m acr osco pi c s ta te .




2.2.2 Quantum Physical Systems

In a system where quantum effects are s ignif icant , 2 2 we have a new element:

C: The bottom-level evolution is indeterminate in a quantum system, althoughthe statistical properties of its evolution are determined. This lower-levelindeterminacy may or may not result in significant higher-level indeterminacy,dep end ing on the system structure. .

In many cases the properties at some higher level may be effectivelydeterminate (the quantum uncertainties being washed out). However, this is nottrue when there is a sufficiently powerful amplifier in operation (e.g. , photo-multipliers in a telescope which allow detection of individual photons), orsufficiendy sensit ive dependence on ini t ia l condit ions. 2 3 This theme has been

deve loped by Russe l l . 2 4 He points out that quantum physics both produces themacroscopic world in all its properties and affects the macroscopic world(occasionally) through a single quantum event. Schrttdinger's cat represents bothaspects: it has bulk properties, such as volume, because of quantum statis-tics—based on the Pauli exclusio n prin ciple — and it lives or dies bec aus e of asingle radioactive event. The latter (macroscopic effects due to a single q uantumevent) may well only happen during a "measurement"; the problem in decidingwhether or not this is the case is that "me asur em ent" in quantum theory proper is

not yet a well defined conce pt. Ho we ver, this effe ct is quite sufficient to allow theeffects we have in mind in this paper.

2.2.3 Smple Biological Systems

By this we mean systems in the biological hierarchy at the level of an individualorganism or lower.

Examples: (4) a m osqu ito; (5) a dog ; and (6) a pe rso n.2 5

In these examples complex neural systems convey, route, and filter

information in a hierarchically structured way so as to allow maximal local

^ I n th is pa pe r the pr ime qua ntum e f f e c t c o ns ide r e d i s that o f in de te r m ina c y (w h ic h i s

c lo s e l y r e la te d to the pr o b le m o f me a s ur e m e nt ) . The r e ar e o the r e qua l ly impo r ta nt a s pe c ts

of quantum theory— Ferm i vs . Bo se stat is tics , non loca l i ty , e tc . ; but they d o not se em to bear

d ir e c t ly o n the a r g um e nt a t ha nd , e x c e p t pe r ha ps tha t o f no n - lo c a l i t y .

2 3 T h e s e a re r e a l ly t w o w a y s o f s a y i n g th e s a m e t h i n g .

2 4 S e e R o b e r t J o h n R u s s e l l , " Q u a n t u m P h y s i c s i n P h i l o s o p h i c a l a n d T h e o l o g i c a l

Perspective," in Physics, Philosophy, and Theology: A Common Quest or Understanding,Ro be r t J o hn Rus s e l l , W i l l ia m R. S to e g e r , a nd G e o r g e V . Co y n e , e ds . (V a t ic a n Ci ty S ta te:

V a t i c a n O b s e r v a t o r y , 1 9 8 8 ) .

" in pr inc ip le, the s a me k ind o f des c rip tio n a pp l ie s to c o m ple x b io lo g ic a l s y s te m s , e .g . :

(7 ) pe o p le in a r o o m; and (8 ) a n e c o s y s te m . But s o ma ny e x tr a i s s u e s a r i s e be c a u s e o f s o c ia l ,

ec on om ic , an d pol i t ica l interact ion that i t i s better f irs t to con s ide r and understa nd the

s i m p l e r e x a m p l e s .



3 7 0 G E O R G E F . R . E L L I S

autonomy and yet coordinate overall act i on ,2 6 the whole being coordinated by theextraordinari ly complex s tructure of the brain. 2 7

The fundamental point is that, despite this complexity, if in these systems

what happens macroscopically is determined at the micro-level s imply by theaction of known physical laws, then the analysis is the same as in the case of theclassical or quantum m achin es considered abov e. One can con sider, for exam ple,a moving hum an h and (realized by the motion of electrons and ions in m uscles).

The analysis and examples given above lead to the following proposit ionsabout hierarchically-structured, physically-based systems, even given the highcom plexity of a living system :

Proposition 1: Top-down action underlies meaningful activity, for it enableslower levels to respond coherendy to higher-level states, but does not by itselfimply openness .

Proposition 2: Chaos generates unpredictability, but does not by itselfunderl ie meaningful act ion.

Proposition 3: Quantum uncertainty al lows openness (as i t only makesprobabilistic statements), which can be amplified to macro-levels.

In the latter case, the issue is the nature of this openness: is it trulyindeterminate— representing a rand om proc ess w hose final state is not determ inedby the initial state—or is it in fact determinate, through some hidden variable

presently inaccessible to us? We will return to this later. In any case the aboveanalysis suggests the following spec ulation : M eanin gful physical to p-do wn actionwith open ness in a hierarchical structure can occu r only either (i) via injection ofinformation from outside, that is , by manipulat ion of the boundary condit ions(probably in a very directed manner, conveying specific information to specificsub-components); or (ii) through a process that resolves qua ntum uncertainty at themicroscopic level by a choice of a part icular outcome from all those that arepossible according to quantum laws, thus resolving the uncertainties in a quantummechanical prediction. This effect can then be amp l i f ied , 2 8 or it could be effective

at the larger scale becau se it takes place in a coordin ated way at the m icro-lev el (asin superconductivi ty).

Note to (i): Bill Stoeg er 2 9 has pointed out that it is essential to be clear aboutwhat is "inside" and what is "outside" the system considered— particularly whennon-local effects occur. A more adequate characterization of a system to better

^ e e Stafford B eer , Brain of the Firm: The Managerial Cybernetics of Organization,2 d . e d . ( N e w Y o r k : J o h n W i l e y & S o n s , 1 9 8 1 ) , f o r a n i ll u m i n a t i n g d i s c u s s i o n .

"See , e . g . , John C . E cc l e s , The Human Mystery ( L o n d o n : R o u t l e d g e & K e g a n P a u l ,

1984) ; or dem. The Wonder of Beng Human: Our Brain and Our Mind ( N e w Y o r k : F r e e

P r e s s , 1 9 8 4 ) ; a n d G e r a l d M . E d e l m a n , Bright Air, Brilliant Fire: On the Matter of Mind( N e w Y o r k : B a s i c B o o k s , 1 9 9 2 ) , fo r c o n t r a s ti n g v i e w s .

"See , e . g . , I . Perc i va l , "Schrodi nger*s Quantum Cat , " Nature 3 5 1 ( 1 9 9 1 ) : 3 5 7 f f .

"D N A responds to quantum event s , a s wh en mutat ions are pro du ced b y s i n g l e ph oton s , w i th

c o n s e q u e n c e s tha* m a y b e m a c r o s c o p i c — l e u k e m i a , f or e x a m p l e . "

" P r i v a t e c o m m u n i c a t i o n .



O R D I N A R Y A N D E X T R A O R D I N A R Y D I V I N E A C T I O N 3 7 1

account for the observed phenomena may result in some of what was "outs ide"being brought " inside" the system. Our comment applies after such adjustmentshave been made.

Note to (ii): The basic point made here is that our present description of thequantum world is essential ly causally incomplete , 3 0 as is clear from everydiscussion of the "measurement process" in s tandard quantum mechanics .Quantum theory determines the statistical properties of measurements, but does notdetermine the result of individual measurements where the initial state is not aneigenstate—a condit ion which includes almost al l measurements . However, aspecific final state does in fact result in each case. T he re is no kn ow n rule th at leadsuniquely from the initial state to th e final state. Th us, the fina l state in alm ost everyspecific case is determined by some feature not described by present quantum

theory, or is uncaused. The present view utilizes the first option.Clearly this speculation contrasts with aspects of the views of Polkinghorne

and Peacocke, but basically agrees with those of Russell, Murphy, and Tracy. Isuggest that it is the logical outcome of any hierarchical structuring in which thebottom, low-level actions are governed by regular physical laws (i.e. , we excludea "vitalist" or "mentalist" interaction not mediated by physics).

3 Ordinary Divine Action

To set the scene, it is convenient to recapitulate some issues covered in many otheressays in this volume. W e need som ehow to divid e Go d' s action in the wo rld intoordinary and extraordinary action. This section concerns that which may beregarded as "ordinary," that is , those actions that are the result of the action ofph ysic al laws alone (G od 's effective action is secondary, through these laws,which are themselves established by his primary a ction ). A th em e at the con clusio nof this section will be that it is reasonable and indeed in line with the religious

worldview to characterize most "ordinary" action as revelatory and sacramental.

3.1 Cosmological

The first domain of action is the cosmological creative act:

Action 1: Creation of the universe, which has two aspects:Action la: Initiation of the laws of physics and of the universe: creation of

basic structure (setting up the regularities that underlie existence).

3 a T hi s i s sue i s s eparate f rom the fur ther thorny probl em of de f i n i ng what a measure -

ment i s , i n a fu l l y quantum sys t em, and when i t w i l l t ake p l ace . See , e . g . , M. A . Morr i son ,

"Altered Sta tes: T he G reat M easu rem ent M ystery , " i n Understanding Quantum Physics: A

User's Manual ( E n g l e w o o d C l i f f s , N J : P r e n t i c e H a l l , 1 9 9 0 ) .



3 7 2 G E O R G E F . R . E L L I S

Action lb: Setting the boundary conditions for the universe: contingentchoice from the possibilities compatible with the basic structure 3 1 fo l lowed by : 3 2

Action 2: Sustaining the universe, through m aintaining the sheer ex istence as

well as the regularity of the universe (as described partially through the laws ofnature we discover); thus underpinning existence in a reliable way.

The initial act of creation, if there was one (i.e., if there was a t=0), mayproperly be regarded as an extraordinary divine act, but in the past rather than thepresent; it has taken place, rather th^n being ongoing. The second (sustaining allevents) is what underlies the predictable nature of the laws of physics, as isrequired for meaningful moral act ivi ty. 3 3

Together these are the prerequisites and basis for ordinary divine action; thatis, divine action carried out through the means of regular laws of behavior of the

phy sical un ivers e. Th e true creativity involve d in these acts is in the selection ofthe laws of physics, and in choosing specific boundary conditions for them(whether in a single universe, or in an ensemble of universes) that enable thedesired results to be attained (cf. the previou s vo lum e in this series).

3 .2 Functional

Th e laws of physics in the existent univ erse pr ov ide th e basis fo r the evolu tion and

functioning of complex systems. They therefore al low ordinary divine action,which is "second-order" or "ind irect" action . Its nature is fashioned by th e laws ofphysics and the boundary conditions; it is understood specifically that divine inputin such "ordinary" action— once the system is runn ing— is to maintain the regularfunctioning of nature in such a way that it is describable by means of scientificlaws, and therefore its results are largely determinate.3 4

In the relation of theoretical biology to funda m ental physics, there are th reemain kinds of issue: the functioning of general living systems, evolution, and theissue of consciousness and free will. We will look at these in turn.3 5

3 l T hi s may or may not i mpl y a spec i f i c event a t t=0 . Cf . the d i scuss i ons i n Physics,Philosophy and Theology; and Quantum Cosmology.

° A s see n f rom wi th i n the uni verse . See n f rom out s i de , th i s m ay we l l be no d i f f erent

f r o m A c t i o n 1 .

3 3 E l l i s , "T he T heo l ogy o f the Anthropi c Pr i nc i p l e , " i n Quantum Cosmology, a n d

Muiphy, "Divine Act ion in the Natural Order Buridan's Ass and Schrodinger's Cat" ( in this

v o l u m e ) .

^Quantum uncer ta i nty and sens i t i ve dependence on i n i t i a l condi t i ons to some extent

l i mi t predi c tabi l i t y and a l l ow for i ndetermi nacy .

^The concerns of thi s sect ion re late to the Anthropic Principle di scussed in Quantum

Cosmology; the po int i s that not eve ry set of law s of phy sics w i l l a l l ow l i f e to fun ct io n.




Action 3: sustaining functioning of general living systems: this can be splitinto three parts : 3 6

Action 3a: sustaining deve lopm ent: growth f rom a s ingle cell to a co m plete

organism; Action 3b: enabling physiological functioning of organisms; Action 3c:enabl ing communi ty funct ional ism/ecology.

The basic mechanisms in all three cases are feedback controls operating inhierarchically-structured complex systems, made of matter functioning accordingto the fundam ental laws of physics, and in the first two cases, organized accord ingto digital ly-coded information contained in DNA.

Hie first and second are highly controlled processes; it is very unlikely thatchaotic mechanisms of any kind can play a sign ificant role here. Indeed the w ho lepurpo se of feedb ack organization is to dam p out any deviat ions from the desired

developmental or physiological path; thus, these processes are usually of an anti-chaotic nature when properly functioning (they efficiently guide the system to adesired final state, despite errors in initial data or disturbances that may occur).W hat doe s occur here is self- orga nization , but based on very sp ecific and highlycontrolled mechanisms (e.g., a reaction-diffusion equation with restricted boundaryconditions, or cells moving over an extra-cellular matrix). Given the laws ofphysics, these mechanisms for the operation of life not only function but in som esense seem to be preferred solutions of the physical equations: experience seems

to show that44

physics prefers l i fe" (e .g. , s imple organic molecules assemblethemselves from an appropriate "primeval soup," providing the basis for morecomplex molecules to form). However, it seems a reasonable view that no specialintervention is required to make all this happen; it is just the wo nder of ordinarydivine action (cf. the next subsection).

The third case, ecology, is less well-controlled (as is well known), and herechaotic effec ts m ay w ell happ en. The m ost s ignificant question (apart fromlearning how to cope with them) is whether this played any significant role inevolutionary processes, for example, by enhancing the range of the environments

to which living beings were subjected. That will be a difficult question to answer;it m ay just as well have placed evolutio n in jeo pa rd y as assisted it in creatin g m or ecomplex be ings .

Action 4: evolution, shaping the nature of things as they are at present.

Here is where the issue of "design" arises, answered in conventionalevolutionary theory by the statement that there is no design, only evolutionaryselection, with evolution—an open-ended feedback process with the goal simplyof survival—being adequate to describe the "design" of all living beings, including

*fcf. Ellis in The Anthropic Principle: Proceedings of he Second Venice Conferenceon Cosmology and Philosophy, ed. F. Bertola and U. Curi (Cam bridge: Cam bridg e

University Press, 1993).




environments, different currents flow and adjust electric potentials. Consequentlymuscles mo ve, allowing limbs to fulfill the intent in the mind and alter conditionsin the physical world. This clearly is a case of d ow nw ard causation fro m the brain

to events in the body.4 2

The issue is how the mind relates to the brain43

a corequestion in terms of personal existence and meaning. An open-minded investiga-tion must consider four features that might contribute (singly or together):

a) organized complexity,b) chaotic motion ("openness")*.c) quantum uncertainty,d) mental fields.

Explanation via some combination of a, b, and c sees physics based onknown fundamental (microscopic) laws as the basic answer, through al lowing

hierarchically structured organization and so emergence of higher levels oforganization based on lower levels.

View I is that this com plex ity itself is suf fici ent ; no in vok ing of cha os orquantum theory is necessary to attain consciousness and possibly not for free will,even though everything is fully deterministic. This includes the modern "mind isa computer" suggestion (supported by work on neural networks, and theoreticalanalyses such as that of Dennett, 4 4 but challenged by others such as Penrose. 4 5

View II is the same as view I except that one needs the "openness" or

unpredictability allowed by chaos theory, or the indeter m inacy inhe rent in q uan tumtheory (viewed as a purely random process), in order that consciousness canemerge. However, insofar as this is equivalent in the quantum case to adding atruly random variable to the equations, which is then amplified, this does notappear to help with the deeper issues. 4 6 Thus, views I and II perceive standardphysics alone to be the total answer to the basis of consciousness. Mind is anemergent phenomenon, as are the other levels of organization in biology.4 7 Mindis, in a sense, reducible to physics (the emergent order of biological systems,allowed by physics, is completely ruled by micro-level physics even though it

entails and encodes higher levels of order). It is hard to see how free will andmorality can be anything but an illusion on this notion (cf. the discussion oftop-down causation above), part icularly when we remember the development ofthe physical brain through the proc ess of evolution govern ed by rando m m utationand selection through "survival of the fittest." 4 8

^ f . KUppcrs , "Unders tanding Complexi ty"; and Stoeger , "Descr ib ing G od ' s Ac t ion ."

4 3 See , e .g . , Squ ires , Conscious Mind; Dennett , Consciousness Explained; E d e l m a n ,

Bright Air, Brilliant Fire\ E c c l e s , The Human Mystery, and Penrose , The Emperor's NewMind.

" S e e , D e n n e t t , Consciousness Explained.4 3 S e e , P e n r o s e , The Emperor's New Mind.4 6 C f . Tracy , "Parti cu lar Prov id ence and the Go d o f the Gaps" ( in th is v o lu m e) .

4 1See C a m p b e l l , Biology.4 8

S e e E l l i s , Before the Beginning, for further dis cu ssio n.




The basic physical question relating to quantum uncertainty is what, ifanything, determines such apparently uncaused information selection (e.g. , whenan energetic state will decay)? It m ay be truly uncaused (nothing dete rm ines wh at

occurs , it just happens capriciously— the s tandard dog m a of quantum theo ry) orit may in fact be controlled (something determines w hat hap pen s, w e sim ply do notknow what i t is—in effect the hidden variable theory of quantum mechanics . )View IH supports the latter, linking it to the reality of free will and morality (takenas solid experiential data about the real world), 5 4 and accepting as inevitable andeven natural the consequent non-locali ty of causation—an important aspect ofquantum theory .

View IV, based on d entails something like vitalism: known physics, byitself, is not the answer. Some as yet undiscovered feature (thus, not quantum

uncertainty, which is already known) links mind to brain and matter. Perhaps thereis some as yet undiscovered force or f ield (" the mental f ie ld") underlyingconsciousness, which may eventually be discovered and studied as any otherphysical field. How ever, it is difficult to see how this will reso lve th e issue s at stakeunless its equations of motion are quite unlike any we have seen before.

In both latter views, something outside presently known physics acts and hasmaterial effects in the physical world (e.g. , by fixing the time when a quantumdecay takes place, which currendy known quantum theory is unable to do). These

views are probably consistent with proposals such as the radical dualist-interactionist theory of the brain and the self-conscious mind proposed by Eccles.5 5

This kind of view is of course highly controversial. The challenge to those whodisagree is to produce an alternative in which free will in a solely physics-basedhierarchical system (the hum an brain) is not an epipheno men on.

This discussion is relevant to the theme of this pap er in tw o way s. First, w henviewed from within the world, essentially the same issues arise in terms of specialdivine intervention (discussed below ); we m ay w ell expect that an analysis of thetwo issues will be very much in parallel.5 6 Indeed view III is basically consonant

with the view of special divine action in M urp hy 's pa pe r.5 7

Sec ond , and related to the first point, wha t is at stake here is the close dnessor openness of the physical world to other influences—not the ratde of a dice (asin view II) but the intervention of some purposeful consciousness that is notwholly bound into physical systems. 5 8 On the latter views, physics is not all thatcontrols the fun ctionin g of the physica l un iverse: at higher levels of organization ,information is introduced that affects lower levels by top-down action. This theme

^ E l l i s , Before the Beginning.5 5 S e e E c c l e s , The Human Mystery."Al though compl ex probl ems o f dua l i sm then ar i se : i f our mi nds and God' s can both

i n f l u e n c e w h a t h a p p e n s , h o w d o t h e y c o m p e t e f o r s u c h i n f l u e n c e ? T h i s w o u l d h a v e to b e

m od e l e d on the bas i s o f our unders tandi ng o f the ch ose n m od e o f G od ' s ac t i on . Cf . E l l i s ,

" T h e o l o g y o f t h e A n t h r o p i c P r i n c i p le . "

^ M u r p h y , " D i v i n e A c t i o n . "

^T racy , "Part i cu l ar Prov i dence . "



3 7 8 G E O R G E F . R . E L L I S

will be picked up again in the discussion of special divine acdon in the next

section, and later sections will consider how that higher-level information could be

inserted.

3.3 The Divine in the Ordinary

What is miraculous? The birth of a baby; the design and function of a flower or atree; the everyday and the "ordinary":

I like to walk a lone on cou ntry path s, rice plants and w ild grasses on bothsides, putting each foot down on the earth in mindfulness, knowing that Iwalk on the wondrous earth. In such moments, existence is a miraculousand mysterious reality. People usually consider walking on water or in thinair a miracle. But I think the real miracle is not to walk on water or in thinair, but on earth. Every day we are engaged in a miracle which we don'teven recognize: a blue sky, white clouds, green leaves, the black, curiouseyes of a child— our ow n two eyes. All is m iracle .5 9

W hile these features are "ordinary" given our laws of physics and the natureof our universe, which allows or even prefers these events to take place, they arenot ordinary if one considers the ra nge of all possible un iverses. T his is w here the"anthropic" arguments are relevant: most of these possibilities will probably not

be actualized in mo st u niv erses .6 0

Thus, we can be just if ied in regarding these everyday occurrences asextraordinary if we include in our range of concepts an ensemble of uni-verses—real or imagined— in m ost of w hich life is not p os sib le.6 1 It is app ropriatefor the ordinary scientist to forget this while studying what happens within thegiven, taken-for-granted order of thing s in the universe-a s-is. Ho we ver, this issu ecannot be forgotten in studying C osm olog y in its broad s en se ;6 2 remembering thisfrailty of life within the broader framework of possible universes gives ajustification— even within a scientific fram ew or k— fo r a sense of awe and w ond er

at what w e see around us, which is an essential part of many religious world views(the sense of the num inous). Indeed on many such v iews these "ord inary m irac les"are evidence of design, albeit of design of the universe itself rather than directdesign (through specific action) of the objects or beings involved.6 3

*T h i ch Nhat -Hanh, The Miracle of Mindfulness: A Manual of Meditation ( N e w Y o r k :

Rand om Ho use , 1991) , 12 . T hi s i s a l so the s tandard v i ewp oi n t o f n i ne teenth-century l ibera l

Protestantism (cf. Friedrich Schleiermacher, On Reigion: Speeches to Its Cultured Despisers[Cambri dge : Cam bri dge U ni vers i ty P ress , 1988 ] ) , and con t i nue s in mu ch o f c ontem pora ry

theo l ogy , i n par t i cu l ar be i ng par t o f the v i ews o f Peacocke and B arbour .

hav e to adm i t that i t i s a l mos t i m po ss i b l e to mak e th i s s ta t ement prec i se and g i v e

i t a watert ight just i f i ca t ion. I t i s , ho w ev er , high ly plau sible .

6 , C f . the anthropi c d i scuss i on i n Quantum Cosmology.c B y ' C os m ol og y ' I i n t end to re f er to a more com pl e te accoun t o f rea li t y than that

p r o v i d e d b y s c i e n t i f i c c o s m o l o g y . S e e E l l i s , Before the Beginning.< 3

M u r p h y , " E v i d e n c e o f D e s i g n . "




The point is that our attitude to "ordinary" divine action, mediated throughthe laws of physics and their boundary conditions, can take into account both ofthese views: the ordinariness of this action, and also its "miraculous" nature, where

this word reflects both on the probabil i ty of what has happened and on what isachieved by i t . 6 4 The awe and wonder that attracts many people to a scientificcareer need not be totally lost as one immerses oneself in the details of scientifics tudy.

4 Extraordinary Divine Action

W e ma y define extraordinary divine action in the a lready existent univers e, as that

action which: (a) can reasonably be interpreted as expressing the intention of God,that is, it has a revelatory character; and (b) is not pred ictable throug h regular lawsof behavior of matter; that is , the events concerned will not inevitably happen asa result of the laws of logic and physics. 6 5

I identify two main themes here: revelatory insight and the possibility ofmiracles proper, and consider them in turn.

4.1 Revelatory Insight

Th e first aspect is:

Action 6: revelation as to the nature and meaning of reality. This may betaken as having two p arts :

Action 6a: providing spiritual insight; Action 6b: providing moral insight .

4.1.1 Spiritual Insight

Whatever one 's view may be of consciousness and free wil l in general , to make

sense of the standpoint of M urp hy's p ap er6 6

and the broad Christian tradition, theremu st be a possibility of specific ally revelatory proc esses being m ad e acces sible tothe mind of the believer (and the unbeliever) . 6 7

Th e first point is that the existence of such a causal join t or c om m unica tionchannel is required as the foundation of Christian (and other) spirituality, 68 whichwe are taking to be a reality. This requirement underlies any theory of revelationwhatever, for without some such causal nexus, an immanent God, despite his/herimmanence, is powerless to affect the course of events in the world, but is simply

6*T hus , a ll these ev en t s are sub jec t i ve l y spec i a l , i n t erms o f the typ o l o gy o f m od es o f

d i v i ne ac t i on presented i n Russe l l ' s "Introduct i on" to th i s vo l ume .

w I n t erms o f the ty po l og y o f m od es o f d i v i n e ac t ion i n the "Introduct i on , " they are

o b j e c t i v e l y s p e c i a l .

" M u r p h y , " D i v i n e A c t i o n . "

6 7 C f . E l l i s , 4 T h e o l o g y o f th e A n t h r o p i c P r i n c ip l e ."

68

Dictionary of Christian Spirituality, e d . W a k e f i e l d .



3 8 0 GEO RGE F.R. ELLIS

a spectator watching the inevitable unfolding of these events. Such a God has nohandle with which to alter in any way , in the mind s of the faithful, the conclusionof that physical unfolding governed by the physical regularities (the "laws of

nature") that he/s he has called into being and is faithfully maintaining. Here I amrejecting the somewhat paradoxical notion of revelation without special divineac t s . 6 9 While one can certainly envisage people who are unusually receptive orperceptive of God's action through natural processes, they cannot reach that stageof understanding without somehow knowing of the exis tence and nature of God.But this in turn requires some kind of specific revelatory act to convey thoseconcepts, so that faith can be based in personal experience and knowledge ratherthan unsupported imagination, which could arrive at any conclusion wh atever.

The second point is the use made of this capability by the creator. This iswhere various tradit ions diverge, and the posit ion one obtains depends on one 'sview of revelat ion. It could in principle be used to convey info rma tion, images,emotions, instructions, or pre-conceptual intimations of the nature of reality tohumanity. Which of these actually occurs depends on the nature of the revelatoryprocess implemented by the creator, which m ust be com patible with his/her natu reand th e character of his/her action in th e world. As a specific example, consider thetheory of revelation proposed by Denis Edwards. He states:

Only an adequate theology of experience can do justice to the Old and New

Testament understandings that God breaks in on our individual lives, thatthe Spirit moves within us, that G od 's word is communicated to us, and thatw e live in G o d 's prese nce It is possib le to show that wh ile w e do nothave access to G od 's inner being, and while Go d tran scends our intellectualcomprehension, yet we can and do experience the presence and activity ofthis Holy On e in a pre-conceptual w ay .7 0

This experience is the reason why the kind of "causal join t" me ntioned abo veis necessary; it could not plausibly be the result of the blind action of physicalforces alone. How does this happen?

W hen I speak of the exp erienc e of God I will alwa ys m ean pre-con ceptualex pe rie nc e. . . [ this] a llows us to speak of a real hum an aw areness of Godwho yet remains always incomprehensible to our intellects. It is , I willargue, precisely as mystery that we experience God's presence and action.

. . . experience of grace is experience of som ething that transcend s us,which breaks in on our lives in a mysterious way, and which we exp erienc eas a gift given to us. 7 1

This particular view is broadly in agreement, for example, with the Quakerview of the experience of the light of God w ithi n.7 2 Thus, we may take it that the

6 9 S e e , e . g . , M a u r i c e W i l e s , " R e l i g i o u s A u t h o r i t y a n d D i v i n e A c t i o n , " i n God'sActivity in the World, e d . O w e n T h o m a s ( C h i c o , C A : S c h o l a r ' s P r e s s, 1 9 8 3 ) .

^ D e n i s E d w a r d s , Human Experience of God (N ew York: Pau l is t Press , 1983 ) , 5 .

7 1 Ib id . , 13 ; 28 .

7 2 S e e "Cto i s t ian Fa ith and Practi ce in the Exp er ience o f the Soc ie ty o f Fr iends"

(London: Year ly Meet ing o f the Rel ig ious Soc ie ty o f Fr iends , 1972 ) .



O R D I N A R Y A N D E X T R A O R D I N A R Y D I V I N E A C T I O N 3 81

envisaged channel of communication is used at least to convey pre-conceptualintimations of the nature of reality to humankind. It finds its expression in theprofound insights of the mystics and saints, as well as the religious experiences in

the lives of the cound ess faithful, those ordinary peo ple wh o do their best to followtheir understanding of a life of enlightenment.

Th e traditions diverge on the issue of whether more spe cific fo rm s of spiritualrevelations and insights are com m unicated to hum anity (e.g. , St. Paul on the ro adto Damascus; Jesus throughout his life, but specifically in the temptations in thedesert and in the garden of Gethsemane). In the context of the present investiga-tion, we can afford to be ope n-m inde d abou t this; onc e the existence of the c ausallink is established, it could be used for such purposes—if that was spirituallydesirable.

Note 1: In either case, a process of discernment is required on the part of thereceiver to test whether what appears to be some intimation or revelation is indeedso, or if it is a false (perhaps psychologically induced) manifestation. This is anarea that has been considered by the spiritually aware for many centuries, and willnot be discussed further here. 7 3

Note 2: It must be emphasized that the idea of co nvey ing such " inf or m atio n,"wh ere this wo rd is used in the broadest possible sense as indicated above, does notin any way imply a coercive or monarchical use of that capability by the creator.

Indeed it is fully compatible with a view of the un ive rse based on self-sacrifice andkcnosis . 74 Indeed without such a possibility fo r the flow of inform ation, w e c anno thave any reliable idea of the na ture of transce nden t reality. T hus , it is precisely theavailability of the intimations of reality through the envisaged link that enables usto conclude that this reality is better described by the theme of kenosis than by anyother.

The supposition here is that these events proceed through the normalfunctioning of the brain but have an extra, non -inevitab le ch aracter in the se nse thatthey must—if they mean what they appear to mean on the Christian interpreta-

tion—convey information to the receiver that was not explicitly there initially (inan evolutionary perspective). This necessity supports view III above as to thefun ction ing of the brain, as is discussed in the follo win g section. This is then thefoundation of Christian spirituality.

4.1.2 Moral Insight

How ever, the further need for m eaning ful hum an e xistence is for a mo re generallybased understanding of the nature of ethics and morality, as a foundation for moral

^ e e , e . g ., E d w a r ds , Human Experience of God; a n d M u r p h y , Theology in The Ageof Scientific Reasoning (Ithaca , NY: Cornel l Universi ty Press , 1990) , where this topic i s

d i scussed in depth .

7 4 C f . P e a c o c k e , Theology for a Scientific Age; idem "God's Interact ion with the

World"; El l i s , 'Theo logy o f the Anthrop ic Pr inc ip le"; and Murphy and El l i s , Cosmology,

Theology, and Ethics.



3 8 2 GEO RGE F.R. ELLIS

decis ions and the search for meaning. I t can be argued 7 5 that the deeper levels ofethics and morality also should com e through this revelatory channel as intimationsof reality and ethical lightness, rather than through some process based on

evolution of the brain and culture, as envisaged in sociobiology. While themechanism would be closely related to that by which consciousness and free willarise (cf. the previous section), this ethical understanding cannot—by its verynature, in order that it can have ethical meaning—be mandatory; that is , it cannotbe supposed to follow inevitably from the operation of the laws of physics in thebrain. In that case there would be a lack of the ability for free response, which isessential for ethical behavior to have meaning. 7 6 Thus, this should also beclassified—according to the above definit ion—as extraordinary rather thanordinary divine action (but non-disruptive).

4 .2 Miracles Proper

Finally, we com e to the mo st controversial area of all— the possibil i ty o f:Action 7: miracles: special actions of an exceptional kind, so that the physical

outcome is altered from what it would otherwise have been. This could be either:Action 7a: actions not based on ordinary laws of physics, indeed involving

a suspension of those laws; or

Action 7b: actions affecting physical conditions directly,7 7

based on a steeringof what happens consis tent with known laws; for example, through direction ofquantum events , amplified by sensit ive dependence on ini t ia l condit ions tomacroscopic effects.

This is wh ere the traditions differ most, the modern liberal view den ying theirexistence at all , in contrast to many more traditional views. They may or may notoccur (or have occurred in the past); we will return to that issue in the nextsubsection. For the moment we s imply consider this as a possibil i ty in a non-committed, open-minded way. In doing so, we note that act ion 7a is the only

possibility considered in this paper that does not respect the laws of physics;7 8 allthe rest do (they are all strictly com patible with the regularities of those law s).

Considering the first type of exception (7a), these certainly are possible,although there m ay be a problem of in terfac e with the rest of the un iverse: If som eexceptional interaction takes place in a space-time domain £/, then in general these"illegitimate" effects will causally interact with events outside U, eventuallyspreading the consequences to a large part of the universe. Problems could ariseat the interface of the region wh ere the law s of physics hold and the region w he rethey are violated; for examp le, how are energy, m om entum , and entropy balance smaintained there?

7 5 S e e E l l i s , Before the Beginning.7 6 S e e M u r p h y , " D i v i n e A c t i o n " ; a n d E l l i s, " T h e o l o g y o f t h e A n t h r o p i c P r i n c i p le . "

7 7 A p ar t f rom g i v i ng h um ans i ns i ght that l ead s to pur pose fu l ac t ion , as i n Ac t i o n 6 .

7 8 I n t erm s o f the types o f mo de s o f d i v i ne ac t ion , these are obje c t i ve l y special

i n t ervent i on i s t event s .




Leaving this technical issue aside, exam ples of w ha t mig ht co nce iva bly occ urrange from the Resurrection to altering the weather or ma king som eon e w ell if theyare ill . It is here that one needs to distinguish different strands of the Christian

tradition, and the various w ays the y view the question of miracles. So m e will tak eliterally all the miracle stories in the Old and the New Testaments; others willexplain away some, many, or even al l of them. Suppo sing that they do occu r, orhave occurred, one has then to fac e the thorny question s: W hat is the criterion thatjustifies such special intervention? When would they indeed occur? These issueswill be picked up in the next sub-section.

Th e second type (7b) is quite possible in principle too , the classic case beingGo d affecting the weather through th e "butte rfly effect" but within the known lawsof ph ysics. In its eff ect this is similar to the previo us possibility, but of cou rse inpractical terms this has to be seen throu gh the eyes of fa ith: n o physical investiga-tion could ever detect the difference between such action and chan ce effect, evenif it was clear that the desired rain had fallen just after a major prayer meetingcalled to petition God fo r an end to the dro ugh t. Thu s, on e has he re the possibilityof an "unce rtainty e ffe ct" deliberately maintained in order that true faith bepossible . Such intervention would never be scientif ical ly provable. Whether webelieve it takes place or not depends on our overall worldview and experience.7 9

4 .3 Capricious Action or Regular Criteria

The problem of allowing miraculous inte rve ntio n 8 0 to turn water into wine, to healthe sick, to raise the dead, or to alter the weather is that this involves either asuspension or alteration of the natural o rd er .8 1 Thus, the question arises as to whythis happ ens so seldom. If this is allowed at all to achieve some good, why is it notallowed all the time, to assua ge m y toothach e as well as the evils of Au schw itz?

Indeed when we look at the world around, seeing the anguish of Bosnia,Somalia, Mozambique, and so on, and seeing children dying of drou ght an d f am ine

in many parts of the world, we pray "God have mercy on us" and wonder whatwould induce him/her to do so: to relinquish f or a minu te the iron grip of physicallaw held there by his^er apparendy pitiless will. After all, these laws hold in beingthe material in its inexorable course while it is used to destroy and torturehumanity. Here one recalls the unspeakable horrors of "necklacing" in thetownships of South Africa, or the materials used in previous times by clerics of

P e r h a p s th is corresponds to the non -bas i c o bje c t i ve l y spec i a l ev ent s i den t i f i ed in the

t y p o l o g y o f d i v i n e a c t i o n .

" i t i s no t po ss i bl e in the spa ce avai lab le here to do just ice to the deb ates on the

en or m ou s herm eneut i ca l and h i s tor i ca l pro bl em s con cern i ng the mi rac l e s repor ted l y

per formed by Jesus , and the i r re l a t i on not on l y to en l i ghtenment sc i ence but a l so to the

probl ems o f i n t erpre t i ng anc i ent , o f t en contradi c tory , t ex t s .

8 1 Su ch an occurance i s a l l owed and poss i b l e bec au se the l aw s are the exp ress i o n o f the

w i l l o f G o d , w h o c o u l d t h e r e f o r e s u s p e n d t h e m i f h e / s h e w i s h e d . S e e M u r p h y , " D i v i n e

Action.**




many theological persuasions who pitilessly tortured and burnt to death those of

differing views. We even arrive at the extraordinary concept of God holding to

their natural behavior and nature the nails and wood used in the cross at Calvary

to crucify Jesus.Thus, if the usual Christian view is to make sense, there has to be a cast-iron

reason w hy a merciful and loving God does not alleviate a lot more of the sufferingin the world, if he/she has indeed the power to do so, as envisaged in Murphy'spaper. This reason has to be sufficient to outlaw any pity in all these cases, and toprevent the taking of that decision that would end the suffering. This is of coursejust the age-old problem of evil, brou ght to special f oc us by the claim that the law sthat enab le it to take place are the optional choice of G od .

In broad est terms,*2 the solution has to be that greater good c om es out of thearrangement we see, based on the unwavering imposition of regularities all oralmost al l the t ime, even though that conclusion may not be obvious from ourimmediate point of view. For example, death is not so important when life isconsidered in a full perspective that takes into account the pro m ise of resu rrection.More particularly the regularity and predictability gained by the laws of physicsmust be seen as the necessary path to create beings with independent existenceincorporating freedom of will and the possibility of freely making a moral andloving response.* 3 Pain and evil are the price to be paid both fo r the ex isten ce of the

miracle of the ordinary (cf. the previous section) and for allowing the magnificentpossibility of free, sacrificial respo nse. B ut then— if m iracles do oc cur— the issueis why on som e occasions this apparently unchanging law should be broached; thiswould strongly suggest a capriciousness in God's action, in terms of sometimesdeciding to "intervene" but mostly deciding not to do so.

W hat on e would like here—if on e is to mak e sense of the idea of m iracles— issome kind of rock-solid criterion of choice underlying such decisions to act in amiraculous manner,* 4 for if there is the necessity to hold to these laws during thetimes of the persecutions and Hitler 's Final Solution, during famines and floods,

in order that true morality be possible, then how can it be that sometimes this ironnecessity can fade away and allow turning water to wine , or the raising of La zaru s?Here as before I am not going to deal directly with the enormous hermeneuticalproblems of interpreting texts on miracles. Instead I am asking a different kind ofquestion . If w e are to be able to m ake any sense wh atsoever of these m iracles, whaton e would like to have is some kind of almost inviolable rule that such exceptions

° C f . S t o e g e r , " D e s c r i b i n g G o d ' s A c t i o n ."

" S e e J oh n H i c k , Evil and the God of Love ( N e w Y o r k : M a c m i l l a n , 1 9 7 7 ) ; M u r p h y ,

" D i v i n e A c t i o n " ; S t o e g e r , " D e s c r i b i n g G o d ' s A c t i o n " ; a n d E l l i s , " T h e o l o g y o f t h e

Anthropi c Pr i nc i p l e . "

M T h e s e are cr it er ia f rom our li mi t ed v i ew poi n t , be i ng appl i ed to G od ' s a c t i v i ty .

Stoeger points out we must real ize that in considering this , what appears to us to be

i n t e r v e n t i o n m a y n o t b e s o f r o m G o d ' s v i e w p o i n t ; a n d t h a t w h i l e i n s o m e s e n s e t h r o u g h

reve l a t i on , God has g i ven us acces s to h i s / her po i nt o f v i ew , th i s i s on l y a l i mi t ed acces s .



O R D I N A R Y A N D E X T R A O R D I N A R Y D I V I N E A C T IO N 385

shall not take place unless the most unusual circumstances arise—something likethe fo llowing :

Assertion 1: Exception al div ine action (7) can take place only in the case of

events that m ake a uniq ue and vital difference to the future evolution of humanityas a whole, and/or its understanding of the action of G od , sign ifica nd y influ encin gthe entire future of humankind.

This does not include making rain in a drought-s tr icken area, s toppingslaughters, or saving children from starvation, but could include the Resurrectionof Christ as one of the most important way s of God com m unicating with hum anityabout the nature of l i fe here and after . I t could just conceivably include some"steering" of biological evolution at vital jun ctu res (cf. 4) in a way compatible withthe laws of phy sics (cf. 7b) , although in that case it would b e imp ossible to p rov e

that this steering had ever happened; believing this to be so would be an act offai th. The al ternative, suggested in my previous p ap er ,8 5 is :

Assertion la: Exceptional divine action (7) never takes place, but action (6)does. Then extraordinary divine action m ust alw ays be in the form of provisio n ofpre-images of right action or of ultimate reality, as freely attested in the spiritualtradition, thereby guiding and assisting free agents as they struggle to understandthe world; the "miraculous" option, al though possible , would not be used. Thisview somewhat assuages the problem of evil in that the charge of capriciousness

is removed: the same laws always hold—implemented in order that freedom andmorality can exis t Regularity is always there, and the "rights of matter" are alwaysrespected.

I suggest that what is needed here is a testing and examination of suchpossible views, looking again, systematically, at th e different kinds of claims aboutt4 miraculous" intervention and whether they would or would not be permitted bythe criterion being considered, and what the moral and religious implications are(a centuries-old debate). As emphasized previously, this would be tantamount tochoosing between various viewpoints on the nature of Chris t ianity. My own

present preference has been made clear above: I would exclude interventions 7aand 7b, because otherwise the charge of capriciousness becomes almost over-w h e l m i n g . 8 6 Should one hold the opposite view, adopting a criterion somethinglike that sugg ested, it is imp erative to clarify what "essential" means in this context.

Stoeger raises the issue of a category of events which we call "miracle,"which of itself does not necessarily have a determinative influence on the courseof history, but seemingly involves abrogation or at least a transcending of the lawsof nature, and functions as a s ign of something deeper or more l ife-giving in asituation or in reality than is otherwise apparent. Most of Christ's miracles were inthis category— as are other claimed healings. Their main purpose was not, or is not,the healing or transforming act itself, but rather the manifestation of the deeperlevel of reality which otherwise would be hidden (e.g., Jesus' cure of the paralytic

M E l l i s , ' T h e o l o g y o f t h e A n t h r o p i c P r i n c ip l e ."

"Apart from a point mad e by W il lem D rees about "respect ing the integri ty o f sc i en ce ,"

re l evant to 7a . See Wi l l em Drees , "Gaps for God?" ( i n th i s vo l ume) .



3 8 6 G E O R G E F . R . E L L I S

as a sign of his power to forgive sins). My suggestion would be that insofar asthese events actually happen—obviously an issue for debate—they belong tocategory 6 rather than 7.

T he ab ov e criterion relates tot4

miraculous" events (7). Similar questions arisein regard to the provision for moral and spiritual visions to people (cf. 6): Whatdetermines when this is done and when not? It may perhaps be suggested here thatthese are always available to those willing to hea r, w ho p atien tly wa it on G od . T hisis a partial answer, as one can suggest that somedmes compelling visions areindeed m ade available (cf. S t Paul or George Fox) that are not given at other dm es,an d t ha t a recurrin g feat ure of spiritual life are the "desert" time s when suchsustenance is not forthcoming. There may well be good spiritual reasons for this,but this too needs clarification. Thus, to complete the picture one would require

some kind of criterion app licable in these cases too. This ma y be already imp licitin the literature on Christian spirituality, but it ne ed s t o be draw n out a nd exp licatedin the present context.

4.4 An Alternative Domain of Action

There is one alternative way to avoid the charge of capriciousness. This is toconsider the possibility that within the laws gov ernin g the b eha vior of m atter, the re

is hidden another domain of response of matter to life than usually encountered:matter might respond directly to God-centered minds through laws of causalbehavior, or there m ay be dom ains of resp ons e of matter encom passed in ph ysicallaws, but they are seldom tested b ecau se such Go d- centered m inds a re so seldo me n c o u n t e r e d . 8 7 Then the distinction between ordinary and extraordinary actionbecomes a question of whether or not we hav e entered this dom ain. W hat h as beenclassified as "extraordinary" action above would be "ordinary" action but in adifferent set of circumstances lea ding to a diff eren t kind of respon se and beha viorwhere God-centered thought dominates and matter responds. Thus, we have the

possibility:Action 7c: existence of a new order, a new regime of behavior of matter (cf.

a phase transition), where apparently different rules apply (e.g. , true top-downaction of mind on matter), when the right "spiritual" conditions are fulfilled.8 8

Thus, the extraordinary would be incorporated within the regular behaviorof matter, and neither the violation of the rights of matter8 9 nor the overriding ofthe chosen laws of nature would occur. Thus, the laws and the nature of physicsare respected. The charge of capriciousness would then fal l away, in a wayconsis tent with the views of Murphy's paper. This is related to collapsing thedistinction between the natural and the supern atural, fro m G o d' s point of view . A nexample could be Jesus ' resurrection. Wolfhart Pannenberg suggests that this

" S e e P o l k i n g h o r n e , Science and Providence; a n d S t o e g e r , " D e s c r i b i n g G o d ' s

A c t i o n . "

M I n R us se l l ' s t erms , th is i s a " t i me -depen dent mi rac l e . "

• ' M u r p h y , " D i v i n e A c t i o n . "



3 8 8 G E O R G E F . R . E L L I S

initiated in the world (whatever interpretation one may give to the concept ofspecial divine action).

It is essential here to distinguish two rather different kinds of downward

causation. Firs t ly, there is generic downward causation: this influences a wholerange of events through alteration of operational conditions in a region (e.g. ,variat ion in temp erature or pressure or m agnetic f ields affects the way matterresponds.) Most of the examples mentioned by Kuppers are of this kind.9 1 Thiskind of general top-do wn influen ce al ters condit ions over a wide range of eventsin a region , and affects them all.

By contrast, there is specific or directed downward causation, whichinfluences very specific events as occurs , for example, in the human body orcomplex machinery and is essential to their functioning. Instances include brainaction to move a specific muscle in the body, a command to a computer thatactivates a particu lar relay or sen sor, or hitting a specific typewriter or o rgan keythat effects the desired result. In each of these cases a very specific local change inenvironment (current f low, pH levels , e tc . ) is effected, which causes proximateevents to proceed in a specific way that is very localized and directed. This ispossible through specific com m unication channels (nerves in a hum an bo dy, bu slines in a computer, wires in a telephone exchange, or fiber optics in an aircraft)conveying messages from the command center to the desired point of act ivi ty.9 2

The point here is that setting boundary conditions at the beginning of theuniverse can achieve generic dow nw ard action but not specific act ion. An eventsuch as influencing a mental state requires specific acts, changing circumstancesin a locally highly specific way, rather than an overall change in the boundaryconditions (a chan ge in temperature, for example). I reject the possibility of settingspecial initial conditions at the beginning of the unive rse (t=0) to m ak e this ha pp en .While this is theoretically possible, it would amount to solving the problemsinvolved in a reversal of the arrow of time. It would require setting preciselycoordinated initial conditions over a wide area of the universe so as to come

together at the right time and place in such a way as to achieve the desired effect,despite all the interactions and interfering effects that will have taken place fromthe hot early universe, where the mean free path even for neutrinos is extremelysmall, up to the present day, where the possibility of agents acting with free willimplies an essential unpredictability in the environment within which this distanteffect wil l be propagating. This tuning would in fact be impossible to accom-plish—with the usual arrow of time—for one highly specific event, let alone awh ole series of such events , each to be accomplished indepen dend y. Accordingto Ol iver Penrose , 9 3 this feature is the essential foundation of the second law ofthermod ynam ics, based on a lack of correlation s in initial co ndi tion s in the past (incontrast to the existence of such correlations in the corresp ond ing final c ond itions

9 1 K U p p e r s , " U n d e r s t an d i n g C o m p l e x i t y . "

w C f . B e e r, Brain of the Firm.9 3 01 i ver Penrose , "Foundat i ons o f S ta t i s t i ca l Mechani cs , " Reports on Progress in

Physics 4 2 ( 1 9 7 9 ) : 1 9 3 7 - 2 0 0 6 .



390 GEORGE F.R. ELLIS

No te that this would not mean that Go d in som e se nse ca lculates the effect ofwhat would happen via specific neural s dm ula do ns and then delicately on e by on eacts in just the right way in each neuron; rather we must see how we act down-

wards on our own neurons. W e think things, plan, im agine, and the d elicate cau salchannels set up for that purpose convey these intentions in such a way that theappropriate neurons fire as required. On this analogy we would envisage Godthrough the mode of transcendence planning certain pre-images, emotions, orwhatever to be made available to us . The appropriate communication channelswhich are in place by means of divine immanence allow this intention to becommunicated to the appropriate neurons, quantum uncertainty being the featurethat allows this to happen at any desired place and time without violating knownphysical laws. Thus, we would envisage the conscious part of his/her intentionalaction being similar to ours: the intention is formed consciously, the details takecare of them selves.

Now, this sounds very s trange from the viewpoint of physics alone.However, that is not our s tart ing point . Following Murphy, I am assuming onestream of thought within the variety of traditional Christian positions, anddeveloping its logical implications. Thus, the underlying assumption is:

1: The immanent God is present everywhere and yet, as transcendent God,maintains the natu re of physical entities, ensuring their regular, law-like behav ior

according to the description of local physical laws. In particular he/she causesquantum action to take place in a law-like way, according to the known nature ofquantum physics .

Then the possibilities are:2a: God determines the actual realization of quantum outcomes from the

possible ones, ch oos ing a specific result in each quantum measurement (which isundetermined by the im posed p hysical laws). There is an openne ss in the sy stem ,and God uses it to input the desired information. Or:

2b: These outcomes really are "uncaused," in that God chooses not to

determ ine which of the possible outco m es eventuates. God rattles dice each timeto determine the actual outcome from those that quantum theory allow s, refrain ingfrom ma king a choice. There is an openness in the system, and God uses it to inputrandom noise, or possibly a com bination of these positions. In any of these cases,the issue is not wh ether there is divine action at the quantum level, (for eff ect iveimmanence ensures that there is 9 7 ), but rather, what use is made of this divineaction at the quantum level?

Alternative 2a envisages coherent information input through this action,actualizing top-down action in a purposeful manner. Alternative 2b rejects this asa useful channel of action. The action still takes place, but is specifically structuredso as not to be purposeful. In that case, it seems that the only channel formeaningful top-dow n action of the required k in d 9 8 is through altering the boundaryconditions of the system S. But this in turn has to happen through some physical

^ M u r p h y , " D i v i n e A c t i o n . "

w

P e a c o c k e , " G o d ' s I n t e r a c t i o n w i t h t h e W o r l d . "



3 9 2 GEO RG E F.R. ELLIS

confrontation with the moral and spiritual order of ultimate reality, which exertsits influence on hum ans in a persuasive rather than coercive manner. Thu s, w hilethe upward and dow nw ard causal a cdo n is fairly rigid at the lower levels, it is not

so at the higher ones. At the lower levels the interconnecting laws of acdon arethose of physics, which are inviolate as long as special divine actions 7a are nottaking place (and we have assumed they do not occur), while at the moral levelsthey are of the nature of persuasion and invitation, allowing choice and freerespon se. This is their essential ch aracter.

Le v e l 1 : Sp ir i tua l / r e l ig io us

Sp ir i tua l v a lue s :

ke no s i s in r e la t io n to tr a ns c e nde nc e

L e v e l 2 : M o r a l / e t h i c a l

Eth ic a l v a lue s :

ke no s i s in r e la t io n to o the r s : s e r v in g

L e v e l 3 : S o c i a l a n d e c o l o g i c a l

P o l i t i c a l , e c o n o m i c i n t er a c ti o n s:

c o m m u n i t y a n d e c o s y s t e m k e n o s i s

Leygl 4; Personal/individual (psychological)C o n s c i o u s n e s s , c h o i c e : f r e e w i l l

r e s p o n s i b i l i t y , k e n o s i s / s e l f

L e v e l 5 : B i o l o g i c a l

L e v e l s o f b i o l o g i c a l o r g a n i z a t i o n : l i f e

s e l f - o r g a n i z a t i o n , e v o l u t i o n

L e v e l 6 : P h y s i c a l

Le v e l o f phy s ic a l e n t i t i e s a nd a c t io n

r e g u la r i t i e s o f phy s ic a l la w

• D a t a 1

• D a t a 2

- D a t a 3

• Da ta 4

Da ta 5

• D a t a 6

Figure 5: Hie r a r c h ic a l s tr uc tur ing o f me a n ing a nd mo r a l i ty in the Un iv e r s e .

To p-do wn a nd bo t to m-up a c t io n o c c ur a s in the o the r h ie r a r c h ic a l ly s tr uc tur e d

s y s te m s , l e a d in g to e m e r g e n t me a n i ng a t the h ig he r l e v e l s a s ind ic a te d . Th e da ta a t

e a c h l e v e l mus t be in te r ms o f the k in ds o f c o nc e pt s a nd m e a n ing s a ppr o pr ia te at tha tl e v e l .

In assessing this proposal relative to its comp etitors, there are separate dataof different types appropriate to each level in the hierarchy. At each level thescheme suggested is indeed supported by a considerable volume of data , andprovides an overall coherent scheme in agreement with those data (but not

uniquely indicated by those at the physical level alone). However, choice of the




whole structure is a metaphysical choice based on recognidon of the appropriate-ness and lightness of what is presented, justified ultimately by the "good fruits"associated with this worldview. The further key element is dealing with apparent

counter-evidence, for otherwise the proposal is vulnerable to the charge of beingbased on selected evidence only, ignoring awkward evidence pointing in otherd i rec t ions . 1 0 5

A defense can be built on the lines indicated in Murphy's paper and mypaper : 1 0 6 essentially, the overall scheme prop ose d is only pos sible, in term s of tru lyallowing free will an d full moral choice, if the possib ility of evil is allowed as w ell,with full acceptance of its consequences. This is both the "free-process" defenseof Polkinghorne and the traditional free-will defense.

One's assessment of what has been suggested here will depend on one's prior

assumptions. If on e accepts that the traditional re ligiou s view ( sum m arized abo ve)is correct and, additionally, that the modern scientific view is correct, then onearrives fairly uniquely at the scheme suggested here (the essential element ofchoice is identifying the theme of kenosis as fundamental , 1 0 7 as against, forexample, monarchical themes.). This leads to a holistic view, as sketched above,which accords with the data at all levels, once the apparent counter-evidence hasbeen evaluated in the light of overall constraints on what is possible in view ofGod's ultimate aim in creating a universe where free moral response is possible.

Two further points are of interest.First, from this foundation I suggest that we arrive at the necessity for anupwards openness, in correspondence with the downwards openness fundamentalto the proposa l. Th e possibility of free moral choice requires "gaps" in the system,as discussed by Tracy. Indeed the downward causation is not rigid but involvespersuasion rather than coercion, as mentioned above. Correspondingly, the upwardcausation must be open; this is required for the system to be consistent. 1 0 8

Thus, on this view, rather than searching for the "gap" allowed by quantumuncertainty as a place where divine action can take place, we invert the argument:

we demand that there must be such an openness in physical laws, in order thatmorality can be possible and that special divine action (as described above) cantak e place. That is , just as one d em ands certainty in physical proc esses at themacroscopic level, as discussed by Murphy, so that moral response is possible,additionally one demands causal gaps (as described by Tracy) at the microscopiclevel, so that top-down causation can lead to an openness in upward emergentproperties and allow the kind of revelatory possibilities envisaged in this article.Thus, in a sense one predicts the necessity for an openness. While it may be that

, 0 5 S e e A n t h o n y N . F l e w , Thinking about Social Thinking: Escaping Deception,Resisting Sef-Deception (London: Harper Co l l ins , 1991 ) , for a d i scu ss ion o f the dangers o f

s u c h s e l e c t i v e c h o i c e s .

l 0 6 S e e Murphy , "Div ine Act ion"; and El l i s , 'T he o l og y o f the Anthr op ic Pr inc ip le ."

1 0 7 Cf. El l i s , Before the Beginning; and dem "T heo logy o f the An throp ic Pr inc ip le ."

, 0 8 This i s rea l ly an a spect o f W. Ross -Ashby ' s " law o f requ i s i t e var ie ty ." See h i s

Introduction to Cybernetics (London: Chapm an & Hal l , 195 6); and Beer, Brain of the Firm.




However, a different possibility is the existence of an alternative domain ofaction in the physical world, coming into effect in those cases where wills are inconce r t wi th God . 1 1 1 This preserves a f ixed order of behavior in the universe

without "miraculous" intervention, but al lows "special act ion" to becomecomm onplace where the conditions for this alternative orde r exist. This possibilityneeds further exploration to make clear the criteria that could govern such a "phasechange" and to characterize some of the features of the new domain of action thatcould then arise. Experimental data relevant to this situation would appear to berather few; the motivation for its acceptance on other grounds would then have tobe compel l ing.

Clearly, the proposal that quan tum unce rtainty p rov ides the n ecessary causalgap is highly controversial. H ow ever, if one take s into accou nt th e data as a wh ole

and seriously attempts a holistic combination of both the religious and scientificviews, this suggestion becomes less scandalous and, indeed, the necessity ofmicroscopic uncertainty in physical laws virtually becomes a prediction of theunders tanding a t ta ined. 1 1 2

l eadi ng to s i gn i f i cant var i a t i ons o f the theme proposed i n Murphy' s paper .

1 " P o l k i n g h o r n e , Science and Providence; S t o e g e r , " D e s c r i b i n g G o d ' s A c t i o n . "

1 I 2 I t h a n k a l l t h e m e m b e r s o f t h e s e c o n d V a t i c a n O b s e r v a t o r y / C T N S c o n f e r e n c e f o r

the s t imulat ing interact ion wi th them that has led to the thoughts presented in this paper . I

am part i cu l ar l y grate fu l t o B i l l S toeger , B ob Russe l l , and Nancey Murphy for de ta i l ed

c o m m e n t s o n t h e m a n u s c r i p t , w h i c h h a v e l e d t o m a j o r i m p r o v e m e n t s .



L I S T O F C O N T R I B U T I N G P A R T I C I P A N T S

W illem Drees, Center for the Study of Science, Soc iety, and Relig ion (Be zinn ings -

centrum). Free Universi ty, Amsterdam, The Netherlands.

Denis Edwards , Lecturer in Systemauc Theology, St. Francis Xavier Seminary,Adelaide College of Divinity, Flinders University, Adelaide, South Australia.

George F.R. Ellis, Professor of Applied M athematics , University of Cap e Tow n,Rondebosch, South Afr ica .

Langdon Gi lkey , Professor Emeritus of Systematic Theology, The Divinity

School, University of Chicago, Chicago, Illinois, USA.

Stephen Happel , Associate Professor of Religion and Culture, Chair of theDepartment of Religion and Religious Education, The Catholic University ofAmerica, Washington, D.C. , USA.

Michael Heller, Professor of Philosophy, Pontif ical Academy of Theology,Cracaw, Poland.

Bernd-Olaf Kuppers, Professor of Philosophy, Institut fur Philosophie, Friedrich-Schiller-Universitat Jena, Germany.

J i i rgen Mol tmann, Professor Emeritus Evangelisch-theologische Fakultat derEberhards-Karl-Universit&t, Tubingen, Germany.

Nancey Murph y, Associate Professor of Christian Philosophy, Fuller TheologicalSeminary, Pasadena, California, USA.

Arthur Peacocke, Director of the Ian Ramsey Centre, Oxford, England, WardenEmeritus of the Society of Ordained Scientists, and formerly Dean of ClareCollege, Cambridge, England.

John Charlton Polkinghorne, President, Queens' College, University ofCambridge , Cambridge , England.

Rob ert Joh n Russell, Professor of Theology and Science In Residence, Graduate

Theological Union, Founder and Director, The Center for Theology and the

Natural Sciences, Berkeley, California, USA.

W illiam R. Stoeger, S J . , Staff Astrophysicist and Adjunct Associate Professor,Vatican Observatory Research Group, Steward Observatory, Universi ty ofArizona, Tucson, Arizona, USA.

Thom as F. Tracy, Professor of Religion and Chair, Department of Philosophy and

Religion, Bates College, Lewiston, Maine, USA.



I N D E X

absolute dependence 5, 28, 296

act of God 12,213, 295, 298, 301, 302, 304, 308, 310, 313, 332, 340, 344

see also divine acdonactive information 154, 155ad hoc 249, 353a ge nc y 4 - 6 , 8 , 9 , 2 1 , 2 2 , 2 7 , 2 8 , 1 2 7 , 1 4 7 , 1 4 9 - 1 5 6, 1 6 7 , 1 6 9 , 1 9 5 -1 9 8 , 22 5 , 2 4 4,

248, 249, 255, 256, 258, 261, 283, 284, 286, 293, 296- 298,301-303, 305, 306, 320, 333, 334, 339, 347, 349, 355, 356see also divine action, free agent, human agency

Albert the Great 187algori thmic complexity 81, 272, 281

algorithmic compressibility 109, 117 see also compressibilitya m p l i f y 1 3 , 7 1 , 2 7 1 , 3 0 3 , 3 1 8

an alo gy 8 , 1 2 , 1 3 , 9 8 , 1 4 0 , 1 4 7 , 1 6 7 , 1 6 9 , 1 7 0 , 1 8 2 , 1 9 1 , 2 0 6 , 2 5 1 , 2 5 6 , 3 0 6, 3 07 ,

309, 312, 339-342, 351, 352, 390anthropic principle 115, 258, 260, 350, 372, 373, 377, 379, 382, 384, 385,

391, 393and- reduc t ion i sm 94 ,154aperiodic motion 44argum ent for the exis tence of God 335Aristotelianism 26, 240Aris totle 178,192, 216, 325, 334, 335arrow of time 117, 388assemblies 27, 266, 267astronomy 1, 265a t h e i s m 5 , 1 0 , 1 1 , 2 0 7

a tt rac to rs 15, 39-4 7 ,49 , 55 , 57-60 , 65 , 6 8 ,7 1 ,7 9 , 15 1 , 15 3 , 15 4 , 18 2"dim ensio n" of the at tractor 46

autonomy 23, 169,174, 187, 188, 202, 217, 281, 297, 298, 301, 331, 363, 370axiological gap 121

backw ard orbit 63, 66, 67 see also orbitbanding 63, 66, 67basic act 12, 295basin of attraction 39beginning of t ime 247

Bell 's theorem 315Belousov-Zhabotinsky reaction 136, 271B6nard instability 135, 233, 272Bible 3 , 5 ,6 ,13,166, 246, 259, 293, 380, 387Bie l 196,198

bifurcation 15, 16, 58-61, 63, 64, 168, 182, 200bifurcation cascade 61, 64-66, 68bifurcation diagram 60, 65, 67, 68

billiards 37, 267, 328



4 0 0 INDEX

bio logy 1 -3 ,8 ,1 3 , 14 , 17-21 , 24 ,47 , 93-95 , 97-9 9 ,10 5 , 119 , 123 ,125 - 130-140 ,143, 166, 179, 181-186, 198, 206, 214, 234, 241, 243, 244,

249, 253, 255, 260, 265, 268, 270, 272-274, 282, 283, 302,308, 318, 345, 362, 363, 366, 369, 372, 375, 385, 392

b iologica l complex ity 21 ,9 5 , 97 , 98 ,1 29 ,1 33 , 234biological sciences 2,139, 206

Birch, John 7block universe 171, 283Bonaventure, St . 160bottom-up causali ty 11,12, 22, 30, 153, 225, 228, 320, 366, 392boundary condit ion 100, 101, 236 see also initial conditionsbrain 2 , 3 ,1 1 , 28 , 3 1 ,4 6 ,9 3 , 94 , 96 , 97 ,1 05 , 168- 170, 234, 263, 272, 274-276,

281, 284, 285, 287, 309, 349, 350, 370, 374, 375, 377, 381,382, 388, 389, 391, 393

bridge laws 96Brillouin 155, 226Brownian mot ion 35Brusse ls s choo l 1 32 ,13 4 ,1 36

Buridan's ass 152, 167, 209, 278, 297, 325, 341, 357, 359, 372

butterfly effect 16,17, 81 , 82 , 230Cano 196Cantor set 16, 68-70Casel 196causality 5, 7, 10, 12, 13, 17, 22-24, 26-28, 108, 124, 125, 142, 150- 154, 156,

162, 167, 168, 170, 172, 173, 183, 188, 192, 193, 205, 206,2 0 8 , 2 1 4 , 2 1 7 , 2 1 8 , 2 2 0 , 2 3 4 , 2 4 0 , 2 4 2 , 2 4 6 -2 4 8 , 2 5 2 -2 5 4 , 2 5 6 -258, 261, 264- 266, 270, 272, 282, 291, 300

causa l cha ins 20,124-126,192, 255, 286,302, 312, 313, 317, 319

causal gaps 290-292, 361, 393causal joint 151,198, 228, 285, 379

causal nexus 27, 196-199, 236, 252-254, 256, 257, 296, 300, 306, 312, 360,3 6 1 , 3 7 9 , 3 8 7

causal structure 29, 310chance 19-21, 23, 29, 35, 100,110, 111, 114, 120, 123-127, 132- 134,136, 140-

143, 152, 166, 170, 184, 185, 192, 267, 271, 278, 291, 311,312, 314-322, 346, 355, 356, 374, 376, 383

chaos 1, 3, 9, 11, 13-17, 20, 21, 25- 29, 35-37, 40, 41, 43, 46-50, 75, 107, 109,110, 112, 113, 115, 119, 121, 124, 142, 150, 152, 153, 157,166, 167, 169, 170, 173, 181, 182, 184, 205, 207, 214, 225-228, 230, 267, 268, 270- 272, 276, 280, 281, 291, 292, 310,

313, 314, 318, 323, 325- 328, 347, 348, 361, 370, 375c ha os t he o ry 9 , 1 4 , 1 6 , 1 7 , 25 , 2 9 , 4 6 , 4 9 , 1 1 0 , 1 1 2 , 1 1 9 , 1 5 2 , 1 5 3 , 1 5 7 , 1 6 6 ,

1 6 7 , 1 6 9 , 1 7 3 , 2 2 8 , 2 3 0 , 2 9 1 , 2 9 2 , 3 1 0 , 3 1 3 , 3 1 4 , 3 1 8 , 32 3 , 3 2 5-327, 348, 375

chaotic attractor 40-46



INDEX 401

chaotic dynamics 13, 22, 30, 37,49, 53,151, 314chaot ic e lements 20,121chao dc inf la t ionary cosmology 19 ,11 4chaotic processes 223, 224, 230- 232, 313, 323, 327, 352chaot ic randomness 17 ,74 -76chaotic regime 53, 63chaotic systems 14-16 ,22 -24 ,26 ,37 , 39 ,4 3 , 49 ,1 49 ,1 52 -1 55 , 157 , 167 ,169 ,

170 ,173 ,206 ,21 .8 ,227 ,228 ,268 ,283 ,292 ,312 , 313 , 327 , 348 ,356

chemis t ry 1 ,14,17,18, 21 ,42, 93 , 94 ,96, 67 , 100, 101, 123,126, 128, 133,135-138, 140, 141, 150, 181-184, 215, 199, 233, 241, 243, 244,

248, 253, 257, 260, 264, 268-270, 274, 275, 308Christ 24, 28, 31, 158, 160, 163, 164, 166, 171, 195, 201, 203, 213, 252, 293,

298-300, 303, 330, 332, 385see also Jesus, Logos, Wisdom, Word

Chris t iani ty 84,180,189,193, 212, 293, 295, 325, 385Christian belief 153, 239, 241, 267, 314, 330Christian practice 330Christian tradition 30, 31,171, 187, 224, 330, 360, 361, 379, 383, 389

Christology 165, 248, 298, 299, 304

church 1-3, 142, 252, 338, 357circumincessio 161classical mechanics 95, 108, 291, 313closed universe 5cobw eb diagram 50, 70complementari ty 155, 167

complexity 1, 3, 10, 13-15, 17, 18, 21, 25, 29, 31, 41, 93-95, 97-99, 110, 129,131,133-135,140,141,143,157,169, 170, 174, 180-183, 185,202, 208-210, 223, 228, 234, 258, 263, 264, 270, 272, 273,276, 281, 285- 287, 305, 326, 330, 333, 339, 344, 351, 357,363, 366, 370, 374, 375, 388

comprehensibility of the world 110, 118compressibility 20, 107, 109,115, 117, 118 see also algorithmic compressibilitycomputability 18, 93computational complexity 81confirmation 13, 185, 241, 329

consciousness 5,15,18,23,94,139,140, 143, 149, 153, 155, 158, 172, 178- 180,

199, 201-203, 212, 219, 220, 234, 242, 243, 246, 250, 253,259, 260, 275, 281, 295, 296, 298-300, 302, 339, 349, 350,361, 372, 374-377, 379, 382, 389-392

consonance 140, 147, 173, 331

contingency 23, 101-105, 170, 171, 191, 192, 194, 207, 216-218, 225, 233, 247,

3 1 7 , 3 2 1 , 3 7 2continuum problem 81convection pattern of fluid 46convergence 51, 52, 54, 56, 57, 192, 206, 231, 312



4 0 2 INDEX

cooperation 23, 30, 121, 186, 187, 190, 192, 194,195,197, 199, 201, 202, 255,

330, 333, 340, 342, 344, 351cosm olog y 1-3 , 6, 7, 9, 10, 14, 19, 111 -114, 148, 156, 158, 160, 167, 171, 178,

200, 214, 225, 232, 240, 247, 248, 258, 278, 283, 303, 314,3 1 6 , 3 2 5 , 3 2 9 , 3 3 4 , 3 3 7 , 3 5 0 , 3 5 9 , 3 6 1 , 3 7 2 , 3 7 3 , 3 7 8 , 3 8 1 , 3 9 1

Big Bang cosmology 10,160, 242, 249, 336cosmic e lements 20,121cosmological principle 111, 113,118, 226, 316modern cosmology 6 , 316

Couet te ce l l 44 ,46

creado n 3 - 5 , 8 , 1 0 , 1 1 , 2 1 - 2 4 , 2 6 , 3 0 , 1 0 7 , 1 0 8 , 1 1 0 , 1 1 2 , 1 1 4 , 1 2 0 , 1 4 0 - 1 4 3 , 1 4 8 ,1 5 1 , 1 5 4 , 1 5 5 , 1 5 7 , 1 5 8 , 1 6 0 - 1 6 8 , 1 7 0 - 1 7 4 , 1 8 0 - 1 8 2 , 1 8 6 , 1 8 7 ,189- 192, 195, 198, 202, 203, 206- 210, 213, 215, 225, 232,240, 244-248, 251, 253, 256, 257, 259, 260, 264, 274, 283,295- 297, 300, 302, 305, 310, 314, 316, 318, 323, 328-332,335, 339, 343, 352, 371, 372, 394

creatio continua (continuous creadon) 10, 23, 166, 171, 175, 208, 209, 283,295, 297, 300, 330

creatio ex nihilo (creadon from nothing) 27, 30, 245, 246, 252, 261, 321crea t iv i ty 21,47,139-143, 217, 218, 372

creator 3, 4, 20, 21, 118, 120, 123, 138-142, 150, 156, 157, 162, 213, 245, 247,248, 278, 283, 294, 311, 319, 320, 325, 328, 380, 381, 391critical realism 21, 22, 26,148, 227, 232, 273

de Donder 132de Groot 132deism 5,10, 11, 21, 24, 142, 207, 295, 325, 332, 352, 353demiurge 120, 260, 319, 328

density of periodic points 16depth 25, 213, 220, 359, 361, 363, 381design 4, 5,18, 100, 118, 194, 303, 304, 317, 329, 331, 361, 367, 373, 378determinism 7,13-15, 17, 26, 29, 35, 36, 49,75-77, 84, 152,156, 219, 232, 240,

281, 293, 301, 302, 304, 310, 311, 313, 315, 320, 324, 328,342, 344, 347, 354, 356 see also metaphysical determinism

dialectic 25,179, 202, 211, 217different ia l equat ion 38 ,1 09digital computer 41, 364, 367

direct act 12, 252, 301directionality 200discernment 241, 252, 381discrete time 38disorder 71, 72, 129

dissipative s tructures 21,44, 134-138, 182, 242, 276divine action 1-9, 11-14, 17, 21-23, 25-31, 49, 83-86, 147, 148, 150, 152, 156,

157, 158, 161, 163, 166-174, 177, 180, 187, 189, 190, 192,

194 -199 ,202 ,207 ,2 23-2 26 ,22 8 ,229 ,231-2 36 , 240 , 241 , 244 ,



INDEX 403

248-259, 261, 277, 278, 287, 293-299, 301- 306, 309, 310,313-316, 318, 319, 321-323, 325-327, 329- 334, 338-340,343-351,353- 357,359 -361,371 -373,377 - 380, 382, 383, 385,

387, 388, 390, 391, 393, 394see also agent, extraordinary divine acuon, indirect divine action,ordinary divine action, particular divine action, special divineaction, trinitarian divine action

d iv in i ty 189 ,191 ,196 , 299divine dance 161divine fecundity 161divine foreknowledge 280, 322divine freedom 164, 198

divine immanence 5, 26, 240, 390divine omnipotence 284divine omniscience 168, 277, 279, 284divine preservation 4

divine providence 23,150,155, 166, 172, 177, 194, 196, 293, 322divine sovereignty 320divine temporality 180, 181, 199, 200, 202divine transcendence 187, 189- 191, 198, 199

DNA 18-20, 97,98, 101, 104, 126, 127, 154, 168, 233, 235, 236, 274, 275,373, 374double agency 9, 150, 333double causality 205, 252, 254downward causation 18, 94-97, 99, 100, 167, 374, 375, 388, 393downward emergence 153dr ipp ing fauce t 38 ,45 ,46dualism 154, 220, 234, 309, 377dual-aspect monism 22

dynamical chaos 15, 37, 39,43,44, 181, 184, 214, 266, 269dynamics 8, 10, 13-15, 21, 22, 27, 30, 37-39, 45, 102, 105, 114, 151, 154, 157,

158, 160, 161, 172, 173, 181, 184, 185, 194, 199, 213, 314,240, 241, 252, 257, 264, 265, 268, 269, 283, 287, 291, 314

ecology 51, 131,307, 373effectiveness of mathem atics 19 ,10 7

emergence 18, 31, 94-97, 99, 100, 105, 119, 123, 124, 127, 134,136, 137, 139,

191, 200, 242, 249, 250, 259, 293, 302, 363, 368, 375, 394emergent order 362, 363, 375, 394upwards emergence 394

energetic transactions 155energy surface 44

entropy 20, 21, 46, 72, 96, 128-132, 135, 143, 180, 181, 185,274, 336, 368, 382environment 7, 12, 13, 16, 17, 20, 23, 24, 26, 101, 126, 127, 131, 134, 150, 153,

168, 186, 187, 198, 203, 212, 234-236, 273, 275, 336, 339,345, 347-349, 354, 366, 388, 391



4 0 4 INDEX

epis temology 21,147,148, 227, 264, 273, 327, 350, 376epistemic limit 279

epis temic views of explanation 26, 223

equat ions of mot ion 15, 39 ,41,108, 377equilibrium structures 21, 56eschatology 24, 209

eschatological horizon 209e t e rn i t y 2 4 , 1 5 9 , 1 6 8 , 1 7 1 , 2 0 9 , 2 4 5ethics 228, 307, 337, 359, 381, 382, 391eventual unpredictabil i ty 73-76,79, 271 see also unpredictabilityevil 4 , 8 , 2 9- 31 ,1 68 ,1 90 , 200, 300, 303, 331, 333, 338, 341, 347, 356, 360, 384,

385 393-395

evolution 3, 8, 14, 15, 20, 21, 28, 38, 45, 47, 93, 97, 110, 112, 119, 126, 127,130-134 ,136-140 ,171 ,179 ,183-186 ,200 , 206 , 208 , 213 , 217 ,241, 242, 250, 268, 271, 274, 276, 302, 318, 368, 369, 372-375, 382, 385, 391, 392

E x o d u s 3 , 1 7 1 , 1 7 2

explanation 10,15,18, 19, 23, 25, 26, 29, 30, 36, 37, 96, 102-104, 109, 118,125,147 ,149-151 ,172-174 ,186 ,192 ,198 , 223 , 227-232 , 246 , 247 ,265,277,290-292,306- 310,312,323, 335-337, 346, 350, 353,

3 7 4 - 3 7 6e x po n en ti al 15 , 3 7 , 4 1 , 5 2 , 7 1 - 7 3 , 8 1 , 1 12extraordinary divine ac t ion 3 0 ,1 71 ,1 9 7, 226, 278, 315, 359, 379, 385

see also divine action

faith 1, 3, 5, 6, 24, 142, 150, 153, 178, 189, 190, 195, 198, 213, 224, 249, 259,289, 295, 296, 299, 300, 332, 336, 349, 360, 380, 383, 385,387, 391

far-f rom-equi l ibr ium sys tems 18 1,18 7, 199, 270Fe igenbaum cons tan t 61 ,62 ,64 , 68-70fine-tuning 111, 113, 361finitude 195, 214first caus e 4f ixed po in t 3 9 ,4 4 ,4 5 , 55 , 56 , 58-60fixed t ime delays 4 5flexibility 9, 23, 29, 141,150, 168, 172-174, 202, 225, 244, 276- 278, 281, 286,

294, 305-307, 314, 315flow 15, 28, 35, 37, 38, 41, 43-46, 130, 131, 135, 168, 169, 201, 232, 237, 252,

269-271, 274, 275, 285, 302, 307, 366, 375, 381, 388fluc tua tion 16 ,4 3, 54 , 56-58, 64 ,9 7 , 136-138, 269- 271fluid motion 15, 36, 37, 44, 46f o l d 2 , 4 0 , 4 1 , 4 3 , 4 6"for tu i tous" phenomena 37forward orbit 55, 68frac ta l 15, 41 4 9, 6 1

free agent 83



I N D E X 405

fr ee will 15, 36, 4 8 ,1 1 9 , 140, 225, 226, 232, 280, 291, 306, 311, 330, 331, 354,372, 374, 375, 377, 379, 382, 388, 392, 393, 395

freedom 4, 7, 17, 21, 23, 29, 38, 41, 46, 134, 141, 142, 164-166, 168-170, 174,175, 183, 187, 190-196, 198, 200, 217, 219, 220, 233, 244,247, 256-258, 260, 276, 278, 281, 287, 300, 302, 303, 310-312, 320, 322, 333, 348, 349, 351, 354-357, 376, 384, 385

fundamenta l cons tants 114,123, 251fundamenta l l aws 19 , 99 ,1 03 ,1 77 , 251 , 373

general theory of relat ivi ty 107,112

g e o me t ry 3 5 , 3 9 , 4 0 , 4 6God 3-8, 10, 12, 13, 17, 20-31, 83, 110, 118-120, 123, 138-142, 150-152, 154-

174,177,180,189-203,205- 213, 216-220, 223-226, 228, 232,234-236,239-241,243- 261, 263-265, 273, 276-287, 289-296,295- 314,316-322,321-335,337- 357, 360, 361, 375, 379-381,383-387, 389, 390, 395

God and chance 140God of the gaps 171, 198, 289, 291, 320, 361God:world: :mind:body 85

God's action 2, 3, 8, 10, 12, 19, 21, 26-28, 30, 31, 110, 139, 150, 152, 166,1 6 9 , 1 7 0 , 1 7 2 , 1 8 7 , 2 0 5 , 2 0 7 , 2 2 3 , 2 2 4 , 2 2 6 , 2 3 3 , 2 3 6 , 2 3 9 -2 4 2 ,248-250,252,256,259,261, 278, 287, 295-301, 304-307, 309,311 ,317 ,319 ,320 ,324-327 ,330 ,332 , 333 , 336 , 340 , 342-344 ,346-349,351-355,357,360,371,375, 377, 380, 384, 386, 387,394, 395

God's body 8 , 309

God's enactment of his tory 294, 309, 323

God ' s fu tu re 210God's interaction 9, 148, 155, 166, 169, 199, 205, 226, 228, 234, 263, 264,275, 276, 281, 282, 284-287, 304, 314, 319, 325, 360

God's master act 301, 302God's personal act ion 255, 257, 259God-world relat ion 24, 205

governance 194, 325, 330, 333, 340, 342, 343, 347, 351grace 8, 171, 172,174, 187, 190- 196, 200, 220, 330, 380Ground of Being 21, 25, 210

heat noise 17Henry of Ghent 196hermeneut ics 178,179, 242hidden variables 268, 281, 338, 341hiddenness 209, 254, 260, 352, 357hierarchy 21 ,31 ,1 33 ,19 9,2 14 ,25 8, 264, 273, 285, 287, 330, 333, 334, 338, 339,

349, 357, 362, 364, 365, 369, 391, 392



4 06 INDEX

history 1, 3, 4, 10, 25, 28, 29, 45, 62, 83, 97, 107 ,11 4, 12 0,1 30 , 1 33 ,1 4 9, 1 51 ,1 5 4 , 1 5 5 , 1 6 0 , 1 6 4 , 1 6 8 , 1 7 2 , 1 7 7 - 1 8 0 , 1 8 2 , 1 8 3 , 1 9 2 - 1 9 5 , 2 0 0 ,202, 206, 207, 209, 211, 212, 214-216, 219, 231, 232, 236,

277,290,293-311,313,314,317-319, 322, 323, 325, 331, 334,335, 343, 348, 349, 385

h o li sm 1 3 , 1 5 0 , 1 5 3 , 1 5 4 , 1 6 7 , 1 6 9 , 1 7 0 , 2 8 2, 2 8 4- 2 8 6, 3 1 4, 3 93 , 3 9 5horizon problem 113

human be ing 93 ,1 39 ,1 57 , 216 , 258 , 275 , 285human agency 4 , 2 7 , 14 7 ,1 49 ,1 51 ,1 5 5 , 167 , 249 , 255 , 256, 258 , 261 ,

284, 339human exper ience 25 ,1 47 ,1 4 9 , 15 9 ,1 9 0 , 219 , 250 , 286 , 360, 380, 381human freedom 4, 7, 17, 29, 83, 84, 164, 169, 170, 174, 183, 200, 300, 302,

303, 310, 311, 322, 333, 354-356human nature 164,165, 198human sciences 26, 239

hylomorphism 334

idealism 154idealizat ion 98,108

imago Dei 285, 346imm anence 5 , 8 , 26 , 13 8, 13 9, 14 2 ,1 98 , 240, 256, 257, 285, 286, 379, 390incarnation 22, 24,166, 172,195, 206, 220, 245, 246, 251, 252, 255, 259, 287incompatibilist 311indeterminism 12, 13, 23,76,77, 119,197, 244, 279, 316, 327- 329, 376

see also metaphysical indeterminism, quantum indeterminacyindirect act 12, 310, 321indirect divine action 197, 297, 304 see also divine actionindividualism 263

inference 104, 205, 231, 314in fin ite 4, 14, 109, 112, 114, 119, 139, 159, 161, 194, 209, 214, 220, 226, 2 47,

267, 271, 272, 277, 281, 319, 321i n f l a t i o n 1 9 , 1 1 2 , 1 1 3in fo rmatio n 1 4-16 , 2 6 -2 8 , 3 5 , 3 6, 3 8 , 4 3 , 4 5 , 4 6 , 9 5 -9 8 , 1 0 4 , 1 0 5 , 1 0 7 , 1 0 8 , 1 1 3 ,

119, 124, 126, 127, 129, 131, 138, 154, 155, 167-170, 183-186 ,1 96 ,22 5 ,226 ,2 35 ,23 6 ,242-2 44 , 253 , 273-276 , 281 , 284 ,285 ,287 ,307 ,328 ,366 ,368-370 ,373 , 376-378 , 380 , 381 , 389 ,3 9 0

initia l conditions 13 ,1 6, 31 ,3 9, 41 , 51-57, 62, 63 ,7 2- 74 , 101, 10 4,1 10 -11 3, 118-120, 154, 167, 181, 225, 229, 230, 232, 244, 258, 265-269,271, 277, 279, 280, 291, 295, 312-314, 317, 319, 327, 328,336, 337, 347, 356, 366, 368, 369, 372, 382, 388see also boundary condit ion

dependence on initial conditions 16, 368, 369, 372, 382instrum ental ism 23, 123, 172, 177, 190, 192-19 7, 202, 220, 250, 251 , 253, 297

instrumental causali ty 192,193

intel l igibil i ty i21, 162,190, 236, 319



INDEX 407

intentional action 29, 295, 296, 307- 309, 311, 352, 390interaction model 9, 24, 205, 206interconnectedness 160, 282

interdependence 161, 275, 282, 296in te rvene 24 , 31 , 83 ,1 16 ,1 49 ,1 89 , 198 , 286interventionism 10-12, 169, 172, 180, 189, 192, 195, 196, 202, 226, 242, 243,

249-251, 260, 278, 281, 305, 313, 325, 343, 344, 356, 373,377, 382-385, 38.9, 395

intrinsic gaps 22,151, 152intrinsic indeterminacy 148intrinsic openness 26, 30, 151, 168, 230, 327

irreversible thermodynamics 20,123, 125, 128,132, 138

Islam 293iterative map 49-75, 81, 104, 227

Jesus 3 ,2 4 ,15 8-1 60 ,164 -16 6 ,17 1 , 17 2 ,1 74 ,19 5 , 203 , 213 , 244 , 245 , 259 , 293 ,298, 299, 330, 347, 357, 381, 383, 384see also Chris t , Logos, Wisdom, Word

Judaism 189, 212, 293

Kantian philosophy 84, 86kenosis 168, 174, 254, 381, 391- 393Kingdom of God 158

laminar 15, 36, 37,45language 6-8, 23, 29, 98, 107, 149, 174, 178-181, 186-189, 191, 192, 194, 197,

199, 202, 216, 224, 240-242, 245, 273, 283, 284, 286, 293,308, 323, 336, 337, 349, 363- 366, 368

Laplacian determinism 15, 36law 2, 3, 7-10, 12, 13, 17-21, 23, 26, 27, 30, 31, 35, 36, 38, 48, 93, 94, 96, 97,

99-105, 108-111, 113-115, 117, 118, 120, 123-125,127,128,130, 131, 136, 138-143, 147, 148, 150, 152, 166, 167, 169,170, 173, 177, 193, 198, 207, 213, 220, 223, 225, 226, 229-232 ,2 34 ,236 ,240 ,24 2-244 ,248-25 1 , 253-255 , 257 , 260 , 261,263-267,273,277-280,283,286, 290, 291, 293-295, 303, 305,308 ,3 11 ,313 ,314 ,31 6-320 ,325-32 8 , 331-335 , 337 , 338 , 340,343-348,349- 353,355,357,360-362, 364, 366, 367, 370-373,375, 376, 378, 379, 382-387, 384, 387- 390, 392-395

laws of nature 2, 3, 7-10, 12,13, 19,110, 113,148,150, 167, 173, 177, 225,240 ,242-244 ,248 ,249 ,251 ,253 ,255 ,278 , 290 , 303 , 311 , 314 ,3 1 9 , 3 2 5 , 3 2 7 , 3 3 1 , 3 3 4 , 3 3 5 , 3 3 7 , 3 3 8 , 3 4 4 -3 4 6 , 3 4 8 , 3 6 1, 3 72 ,385, 386

laws of physics 9, 31, 35, 94, 99, 100, 103-105, 118, 123, 147, 167, 236, 283,

314, 325, 361, 364, 371-373, 378, 379, 382- 385



408 INDEX

Lebesque measure 57, 66, 73levels 18, 23, 31, 46, 98,102, 113, 131, 133, 134, 137, 138,162, 168,170, 172,

177, 178, 1%, 202, 214, 215, 217, 220, 232, 234, 235, 242,

244, 245, 251, 258, 264, 265, 273-275, 278, 282, 283, 286,297, 302, 314, 320, 327, 329, 330, 333, 339, 340, 344, 346,349, 357, 362- 364, 366-368, 370, 375-377, 382, 388, 389,391-394

liberal theology 5, 6, 295

limit 16, 17, 26, 31, 36, 39, 41-45, 117, 147, 154, 208, 217, 223, 232, 236, 267,268, 271, 280, 281, 290, 291, 304, 372

l imi t cyc le 39 ,41 ,42 ,45 , 58 , 64limit point 55, 58, 59, 65

limit question 217log i s t i c map 15 ,16 ,49-75 ,78-82 , 268 , 269

Logos 20, 24 ,121, 170, 208 see also Chris t , Jesus, Wisdom, WordLoren z at tractor 41

mapping 38mater ia l i sm 96,154, 335

mathematics 14-17, 19, 20, 44, 45, 107-110, 115-121, 125, 136, 137, 141, 150,179,181, 183, 230, 265-267, 277, 292, 315, 316, 337, 346mathemat ica l phys ics 116,150, 230mathemat ica l randomness 76-79 see also randommathematical theories 107, 116,120

meaning 7 ,1 6 ,2 0 ,2 6 , 96, 102, 110, 115, 121, 123, 124, 159, 178, 1 80 ,1 81 ,1 8 6,191, 194, 195, 197, 198, 211, 215, 217, 240, 245, 258, 274,282, 293, 303, 320, 328, 329, 334, 337, 344, 362, 366, 375,379, 382, 391, 392, 394

measurement problem 152mechanist ic 75media t ion 23, 24 ,197, 199-203, 366Meixner 132mental 47, 124, 142, 149, 154, 155, 167, 226, 234, 275, 276, 284, 309, 339, 3

75-377, 388metabo l i sm 130 ,185metaphor 21 ,134 ,165 , 174 , 199 , 236metaphysics 7 , 13 ,2 1, 25 , 128, 147, 152, 155, 159, 16 5 ,1 67 ,1 69 ,1 9 0, 215, 216,

315,316, 326, 334, 337, 338metaphysical 4- 6, 14 ,1 7, 2 0- 2 2, 25 , 29, 30, 123, 127, 14 7-1 55 ,16 0, 191, 199,

2 1 5 -2 1 7 , 2 2 7 , 2 2 8 , 2 3 3 , 2 4 0 , 2 9 7 , 2 9 8 , 3 0 0 , 3 1 1 , 3 1 2 , 3 2 6 , 3 2 9 ,334, 338, 359, 393

metaphysical determinism 17, 75-77, 82-85 see also determinismmetaphysical indeterminism 75-77, 82-85 see also indeterminismmetaphysical principle 20,123, 127, 233

m ethod ology 3, 329

mighty acts 294



I N D E X 409

mind-brain problem 3, 94min d 2 , 3 , 8 , 1 1 , 2 2 , 3 7 , 9 4 , 9 7 , 1 02 , 1 05 , 1 18 , 1 20 , 1 26 , 1 5 4 , 1 5 5 , 1 6 1 , 1 6 7 , 1 6 9 ,

174, 188, 189, 194, 198, 216, 220, 224, 225, 234, 249, 256,

272, 275, 280, 284, 296, 308, 309, 334, 337-339, 342, 350,359, 361, 369, 370, 374-377, 379, 386, 387, 389, 391

mind of God 120,194, 334, 337, 338, 389

miracle 5,108, 207, 251, 293, 294, 306, 311, 313, 348, 378, 383, 384, 386, 394m i x i n g 1 6 , 4 3 , 7 2 , 7 3 , 1 1 2Mixmaster program 111

model 8, 9, 17, 22, 24, 28, 38, 41, 103, 104, 107, 111, 112, 116, 117, 135, 158,159, 162, 174, 190, 205-208, 223, 229, 231, 234, 235, 242,251-253, 256, 261, 282-287, 306, 307, 310, 318, 337

model of open l ife processes 206models of chaos 77-82

morali ty 5,168,189,196, 213, 217, 220, 252, 254, 272, 293, 295, 300, 303, 323,

330, 359, 372, 374, 375, 377, 381, 382, 384-386, 391-394Morrison 371, 376moth colony 51, 52, 54, 58, 59,78, 79mutual self-mediadon 23, 24, 200, 201, 203mystery of comprehensibil i ty 118

narrat ive 180,184, 187, 197, 200, 299, 352natural law 19, 30, 99-103, 105, 110, 294, 295, 318, 326, 344natural order 28, 29 ,1 20 , 13 9, 1 41 ,1 52 ,1 67 , 209, 235, 278, 280, 281, 286, 290,

293, 294, 297, 303, 308, 310, 314, 317, 319, 325, 340, 354,359, 372, 383

natural rights 355natura l se lec tion 127 ,13 1, 1 34 ,1 68 ,18 4, 185, 274, 318

natural theology 5,118-120, 211, 212, 215naturalism 7, 25, 26, 215, 223, 232, 233, 236, 237, 348, 352natu re 2 -1 0 ,1 2-1 5 ,1 7 ,19 -21 ,23 -30 ,42 ,47 , 95 , 97 ,10 1-104 , 110 ,113 , 114, 119 ,

123, 139-141, 147-150, 155, 156, 158, 161, 162, 164, 165,167-170, 173, 174, 177, 180, 184, 186, 188-192, 194-199,205-207,209,211-220,223,225,227, 228, 231, 232, 235, 240,242-245,247-255,257,258,261, 270-272, 274, 275, 277, 278,281 ,282 ,284 ,285 ,287 ,290-292 ,294 , 296 , 297 , 300-303 , 305 ,307,308,310-320,322,323, 325-327, 331, 332, 334-338, 341,342, 344-348, 355, 356, 359, 361, 368, 370, 372-374, 376,378-382, 384-387, 390-392, 394

necessity 123, 126, 127, 140, 141, 143, 148, 165, 166, 177, 189, 191,194, 197,

200, 214, 243, 247, 248, 251, 254, 346, 381, 384, 393-395neo-Platonism 178Newtonian mechanics 4,13, 14, 27,107, 142, 157, 216, 224, 265-267, 271, 272,

315, 335, 336Newton's laws 36, 38, 267

noise 17, 43, 272, 349, 390



4 10 INDEX

nomological 290, 336nonchaotic attractors 41non-equil ibrium thermodynamics 14, 19, 21, 47, 114, 120, 121, 132, 134-138,

168, 227, 233, 264, 270, 280, 287, 291, 313novelty 7 ,1 0 , 25, 29 ,4 7 , 168, 185, 214, 219, 220, 242, 248, 249, 270, 313, 318

objecdvity 148observable 169, 170, 226, 269, 271, 275, 280, 332, 344, 376observer43, 111, 157, 376occasionalism 301, 321, 332, 333, 340, 347, 353O k h a m 1 9 6 , 1 9 8

o nto lo gy 6 , 2 1 , 2 3 , 2 5 , 2 6 , 1 4 7 , 1 4 8 , 1 6 7 , 1 7 4 , 1 7 7 , 1 9 1 , 2 0 2 , 2 1 5, 2 16 , 2 2 3, 22 7 ,229-231, 327

ondc views of explanation 26, 223, 230ontological gaps 151ontological indeterminacy 167, 168ontological reductionism 18, 354

open future 24, 206, 219

open system 9, 22-26, 29, 30, 119, 120, 132, 133, 140, 151, 153, 165, 167-170,

172, 173, 206, 209, 210, 214, 218, 219, 224, 225, 227-232,241, 243, 248, 255, 276, 281, 286, 311, 313, 314, 316, 317,323, 327, 370, 376, 377, 390, 393, 394

orbit 15, 38, 39,41,43,44, 50, 55, 58-60, 62, 65, 68-70, 80, 81order 2, 3,13, 20, 22, 25, 26, 28, 29, 31, 35, 94, 96-98, 100,101,103,107, 113,

114, 117, 118, 120, 124, 129, 131, 132, 135, 137-139, 141,143, 148, 150-152, 160, 167, 168, 178, 180, 181, 183, 189,191, 196, 205, 207, 209, 211, 213-215, 217, 219, 220, 224,227 ,2 34-23 6 ,240 ,243 ,24 4 ,246 ,247 , 250-252 , 257, 265 , 270 ,

278, 280, 281, 286, 290, 291, 293, 294, 296-298, 301, 303,305-308,310,311,313-319,325, 328, 331, 332, 338-340, 342,344 ,3 46-34 9 ,352 ,354 ,3 59 ,36 2 ,363 , 367, 368 , 372, 374-376 ,378, 382-386, 389, 391-395

order lines s 16 , 71 , 72 ,1 10 ,1 2 9 , 19 2 , 19 9 , 316, 340 , 343 , 346-348ordinary divine action 371-373, 382 see also divine actionorganized 3 ,71,104,119, 123,127,129, 132, 134, 138,140, 143, 183, 243, 258,

272, 282, 306, 307, 362, 373, 375origin of life 9 3 , 9 5 , 9 7 , 1 8 3 , 1 8 5

osc i l l a t ions 37 ,41 , 44 ,46 ,137 ,181 , 269

panentheism 8, 163pantheism 10, 24, 85, 163, 207, 208, 341paradigm shift 18, 19, 99, 102-104, 227particular divine actions 22, 166, 171-173 see also divine actionpendulum clock 15, 39

perichoresis 24, 161, 171, 208



4 1 2 INDEX

370, 372, 384, 395 see also temporary predictability, totalpredictability

predictable in practice 76predictable in principle 74,76

p rei ma g e 5 5 , 6 8 see also forward orbitprimary causali ty 22,150, 247, 257prime matter 334, 335Prime Mover 336

principle of sufficient reason 233, 338, 342, 353probability 19, 20, 105, 107, 110, 111, 115-121, 125, 132, 133, 135, 136, 141,

170 ,184 ,230 ,236 ,243 ,266 ,268 ,271 , 274 , 291 , 318 , 319 , 379

probab i li st ic compressib il ity 20 ,1 15 ,1 1 7 , 1 18 ,1 20probabil is t ical ly compreh ensible 20probabi l i ty ca lculus 19,110, 111, 115,117probability distribution 116, 318probability space 116

problem of evil 8, 29, 31, 331, 333, 338, 341, 384, 385process philosophy 7, 85, 205

process theology 7, 9, 168, 248proof of God 216

Protes tanism 4,7providence 4 , 9 , 23 , 148, 150-152, 155, 156, 166,167, 171, 172,177,180,192,

194-197, 200, 202, 208, 209, 215, 226, 278, 283, 285, 286,289, 293, 295, 304, 305, 314, 320, 322, 325, 327, 328, 330,331, 354, 355, 360, 361, 375, 377, 386, 387, 395

Pseudo-Dionys ius 160

Quaker 359, 380quantum physics 2, 3, 7, 9-13, 15, 16, 22, 23, 26-31, 36, 37, 43, 80, 93, 108,

1 1 3 - 1 1 5 , 1 1 7 , 1 1 9 ,1 2 6 , 1 4 8 , 1 4 9 ,1 5 2 , 1 5 3 , 1 5 5 - 1 5 7 ,1 6 0 , 1 6 7 ,171 ,173 ,174 ,181 ,197 ,200 ,220 ,223 , 225-228 , 230-233 , 240 ,242 -244 ,248 ,252 ,258 ,264 ,266 ,268 ,270 - 272 , 276-283 , 291 ,292, 303, 310, 313-323, 325-329, 333, 334, 336-348, 350,353-357,361,367, 369- 372, 375-378, 382, 389-391, 393-395

quantum chaos 80, 227, 268, 272

quantum cosmology 2 , 3 , 7 , 9 , 10 ,1 14 ,1 48 ,1 56 ,1 67 , 171 , 200 , 225, 232 , 240 ,

2 4 8 , 2 5 8 , 2 7 8 , 2 8 3 , 3 0 3 , 3 1 4 , 3 2 5 , 3 2 9 , 3 3 4 , 3 3 7 , 3 50 , 3 6 1, 3 7 2,378

quantum field theory 2, 3,155, 231quantum gravity 113quantum indeterminacy 1 1,3 0,7 6,1 52 ,15 3,2 32 ,24 4, 313, 320, 326, 328, 356

see also unpredictabilityquantum level 23 ,27 ,29 -3 1, 80, 1 71 ,17 3, 174, 228, 242, 244, 252, 278, 315,

317-319, 327, 333, 338-347, 353-357, 376, 390quantum non-locali ty 76



INDEX 41 3

quantum theory 27,117,119,148,149,152,155,167, 264, 266, 276-279, 292,315, 341, 354, 356, 369, 371, 375-377, 390

quantum uncertainty 1 2, 27 ,2 8, 43 , 81, 83, 227, 231, 270, 279, 280, 322, 361,

367, 369, 370, 372, 375-377, 389-391, 393, 395quantum world 83,108, 148,149, 152, 227, 279, 371

radioactive decay 15, 36, 266,280, 320random 14, 15-17, 20, 35-37, 41, 43, 49, 51, 52, 71, 74-77, 79, 84, 85, 111,

119-121, 127, 129, 143, 170, 182, 185, 211, 268, 271, 333,341, 356, 376, 394 see also mathematical randomness, strictrandomness

real numbers 27,116, 271, 272, 277, 281realism 21, 22, 26,148,198, 227, 232, 237, 240, 273, 315reductionism 15, 17-19, 22, 47, 93-96, 102-105, 149, 150, 153, 154, 157, 215,

234, 264, 273, 311, 338, 342, 346, 354regime 16,45,46, 52-82, 269, 333, 340, 344, 349- 351, 357, 386, 387regular behavior 97, 386religion 1, 2, 5-7, 120, 128, 142, 161, 171, 177- 181, 184, 187, 189, 191, 193,

211, 215, 216, 223, 224, 237, 239, 240, 247, 248, 263, 265,

273, 277, 285, 294, 295, 298, 307, 315, 318, 324, 331, 334,344, 355, 363, 378religious discourse 211religious experience 160, 219, 252, 287, 350religious knowledge 212, 223, 224religious language 191

resurrection 31,165,174, 220, 255, 259, 316, 331- 333, 357, 383- 386revela t ion 6 ,31,163,165, 166, 178,191,194, 212, 241, 242, 244-246, 251, 253,

256, 258, 259, 261, 287, 298, 314, 331, 333, 350, 352, 371,

379-382, 384, 389, 391, 393Richard of St. Victor 22, 158, 159,163ROssler attractor 42,46 see also cover illustration

sacrament 163,193,195, 251, 371Schmaus 196

Schrttdinger equation 80, 93, 148, 152, 268Schrodinger*s cat 317, 325, 359, 369

science 1- 12 ,1 4, 15 ,1 8, 20, 22, 23, 25-28, 30, 31, 35, 36 ,4 7, 93, 94, 9 6 ,9 9 , 102,1 0 3 , 1 0 8 -1 1 0 , 1 2 0 , 1 2 1 , 1 2 3 , 1 2 5 , 1 2 8 -1 3 0 , 1 3 7 , 1 3 8 , 1 4 0 , 1 4 1 ,148-150 ,153 ,156 ,157 ,166 ,167 , 171-174 , 177-182 ,184- 186 ,188 ,189 ,191 ,197 ,198 ,202 , 207-209 , 211 , 213-219 , 223-227 ,229, 232, 236, 239, 240, 242, 247, 248, 251, 263- 268, 270,272- 275, 277, 278, 283-285, 290, 292, 294, 2%, 298, 307,314- 316, 318, 322- 329, 331, 333- 338, 343, 344, 347, 348,354- 356, 359, 360, 363, 374, 383, 385-387, 394, 395

scientific community 157, 341



INDEX 415

t=0 372, 388teleology 201, 214, 215t e l e o n o m y 1 8 2 , 1 8 3 , 1 8 5 , 1 8 7 , 2 0 1

tempora l i ty 24, 156, 158, 179-182,186,187,199-202, 216, 218temporal 22, 23, 38, 137, 138, 141, 151, 153, 156, 180-185, 187, 202,

207-209, 217, 218, 220, 232, 233, 247, 269, 270, 274, 283temporal critical realism 232temporal order 183tempora l sequence 180,185temporary predic tabil ity 74 ,7 6 see also predictability

tertium quid 16 ,75 , 76

the i sm 6 , 8 -10 , 84 ,140 ,141 ,160 , 207 , 208 , 220

classical theism 6,160 see also process theologytheodicy 168, 331theo logy 1 -12 ,1 7 ,21-2 3 ,26-2 8 ,30 , 75 , 83 -86 ,11 8-1 20 ,12 3 ,1 28 , 142 , 148 , 150 ,

154 ,157-160 ,162-168 , 170-174 ,177-180 , 189 ,192-194 , 196 ,197 ,199 ,202 ,205 ,210-213 ,215 ,216 , 219 , 224 , 225 , 232-234 ,236,239-242,244,246-249,253,256, 258, 259, 263, 264, 268,272-274,276,278-285,287,289-296, 298, 299, 306, 308, 310,313, 315, 316, 318, 323-326, 329, 331, 333, 336, 342, 344,

350, 357, 359-361, 363, 369, 372, 378, 380, 381, 391thermal equil ibrium 130

thermodynamics 11, 20, 21, 26, 72, 96, 100, 123, 125, 128, 130-133, 135, 137,138 , 141 ,150 ,182 , 226 , 388

Thomas Aquinas 4 , 23 , 150,165,187,190, 191, 193, 202, 218, 247Thomism 7, 24, 26, 205, 206, 240time 4, 15, 16, 21, 31, 36-39, 41, 43-46, 95, 99, 101, 103, 107, 108, 112, 114,

117, 119, 123, 124, 130, 132, 134, 136-139, 141, 143, 150,152 ,153 ,168 ,171 ,172 ,177 ,179-186 , 190 ,191 , 200 , 205-207 ,

209-211, 214, 218, 220, 224, 226, 229, 230, 232, 235, 239,242, 243, 247, 249, 253, 257, 260, 264-271, 274, 277, 279,280, 282, 283, 286, 297, 300, 302, 307, 308, 313, 315, 316,321, 322, 325, 332, 333, 341, 353, 355, 356, 362, 366, 374,377, 382-384, 388-390

continuous t ime 38time asymmetry 200timeless 21time series 50, 71

top-down causality 11, 12, 22, 24, 30, 31, 168-170, 183, 206, 233-236, 272, 307,320 , 361 ,366 , 386 , 391 ,392

t o r u s 1 5 , 4 1 , 4 2 , 4 4total predictability 75, 267, 279, 281 see also predictabilitytradition 24, 30, 31,147, 150, 158, 160, 171, 179, 187, 193, 198, 205, 206, 211,

212 ,215 ,224 ,241 ,324 ,330 ,343 , 360-362 , 379 , 383 , 385 , 389transcendence 8, 23, 26, 142, 159, 161, 174, 177, 187, 189-192, 198, 199, 202,

208, 210, 213, 240, 256, 257, 285, 286, 390, 392

transition 15, 18, 36, 44-46, 93, 94, 97, 102, 148,168, 183-185, 269, 386, 387



416 INDEX

Trinity 9, 22,157-163, 166, 170, 171, 173, 245, 257, 259trinitarian divine action 157,158trinitarian theology 22, 157, 158, 160, 163,166, 167, 170-174

tuning constant 16, 51-71, 73-75, 80, 81turbulent 15, 36, 37,45, 51, 269tzimtzum 206

uncertainty principle 12, 21, 28, 36, 37, 43, 116, 125, 136, 148, 226, 227, 231,266-268 ,271 ,279 ,280 ,291 ,316 ,354 , 361 , 370 , 372 , 375-377 ,

389-391, 393-395underdetermination 151,197, 198, 244, 249, 254, 258universe 4 ,5 ,7 ,8 , 10 , 12, 13 ,1 9-2 3, 25, 29 , 31 , 36 ,108 -115 , 11 7-1 21 ,12 3,1 24 ,

1 2 6 , 1 2 7 , 1 3 0 , 1 4 0 -1 4 3 , 1 4 8 , 1 5 5 , 1 5 7 , 1 5 8 , 1 6 0 -1 6 3 , 1 6 5 , 1 6 6 ,168-174, 177, 180, 183, 187, 189, 193, 194, 198, 199, 202,208, 210, 213, 216, 232, 242, 244, 246-249, 253, 258, 259,273, 277, 282, 283, 286, 293, 316, 320, 321, 325, 328, 329,331, 335-337, 339, 340, 344, 346, 353, 359, 361, 371, 372,377-379, 381, 382, 387-389, 392-395

see also cosmology, Big Bang cosmologyunpredictability 14,15,20, 21, 23, 26, 27, 35-37, 39, 41,49,71, 73, 75, 117, 119,

121, 153, 157, 167-174, 192, 200, 218, 223, 227, 228, 231,244 ,266 ,267 ,269 ,271 ,272 ,276-281 , 286 , 287 , 308 , 312-314 ,318, 323, 327, 328, 352, 355, 370, 375, 388see also quantum indeterminacy

unreasonable effectiven ess of mathem atics 19 ,10 7

v alu e 1 6 , 2 5 , 9 8 , 1 0 0 , 1 1 4 , 1 1 6 , 1 17 , 1 21 , 1 28 , 1 2 9 , 1 7 3 , 1 7 4 , 1 8 5 , 1 8 6 , 1 9 1 , 1 9 6 ,199, 213-215, 220, 229, 245, 268, 270, 271, 333, 348