chance, love, and logic : philosophical essays - fels

title: Chance, Love, and Logic :Philosophical Essays

author: Peirce, Charles S.; Cohen, MorrisRaphael; Dewey, John

publisher: University of Nebraska Pressisbn10 | asin: 0803287518print isbn13: 9780803287518

ebook isbn13: 9780585265827language: English

subject Pragmatism, Science--Philosophy, Metaphysics.

publication date: 1998

2

lcc: B945.P43C5 1998ebddc: 191

subject: Pragmatism, Science--Philosophy, Metaphysics.

3

Page iii

Chance, Love, and LogicPhilosophical Essays

Charles Sanders Peirce

Edited and introduced byMorris R. Cohen

with an essay byJohn Dewey

Introduction to the Bison Books Edition byKenneth Laine Ketner

4

Introduction to the Bison Books Edition © 1998 by the University ofNebraska PressAll rights reservedManufactured in the United States of America

The paper in this book meets the minimum requirements of AmericanNational Standard for Information SciencesPermanence of Paper forPrinted Library Materials, ANSI Z39.48-1984.

First Bison Books printing: 1998Most recent printing indicated by the last digit below:10 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging-in-Publication DataPeirce, Charles S. (Charles Sanders), 18391914.Chance, love, and logic: philosophical essays / Charles Sanders Peirce;edited and introduced by Morris R. Cohen; with an essay by John Dewey;introduction to the Bison Books edition by Kenneth Laine Ketner.p. cm.Originally published: New York: Harcourt, Brace and World, 1923.Includes bibliographical references.ISBN 0-8032-8751-8 (pbk.: alk. paper)1. Pragmatism. 2. SciencePhilosophy. 3. Metaphysics. 1. Cohen,Morris Raphael, 18801947. II. Dewey, John, 18591952. III. Title.B945.P43C5 1998

5

191dc2197-53252 CIP

Reprinted from the original 1923 edition by Harcourt, Brace and World,Inc., New York.

6

Page v

INTRODUCTION TO THE BISON BOOKSEDITIONKenneth Laine Ketner

It would be challenging to try to imagine a moreattractive title for a book about philosophy, science,and argumentation than Chance, Love, and Logic, aname that is at once both accurate and charming.Perhaps no other out-of-print book concerningCharles Sanders Peirce (18391914), the founder ofPragmatism, is more deserving of reappearing in printthan this volume.

Dr. Carolyn Eisele, one of the founders of the field ofPeirce Studies and editor of his extensive writings onmathematics and the history of science, 1 oncementioned to me that Morris Raphael Cohen(18801947) had done about as much as any mortalperson to introduce Peirce's path-breaking work tothe wider world where it was, and is, sorely needed.She was well informed; in her academic career atHunter College in New York City, she had beenacquainted with Cohen, who was a remarkable figure

7

in American intellectual history. In fact, Eiseleregarded Cohen as an unheralded hero for hispioneering efforts in bringing Peirce's writings to thepublic. These few introductory paragraphs constitutean outline justification of her assessment and atribute to Cohen's important contribution to Peircestudies.

Chance, Love, and Logic (CLL) was the first anthologyof Peirce's writings that was published after his deathin 1914. As its editor, in light of the page limitationset by his publisher, Cohen chose the contentswisely. He selected two books Peirce published duringhis lifetime.

Uninformed scholars often remark that during hiscareer Peirce published only one book, and that inphotometry.2 This claim, however, is wrong; Cohen'sedition consisting of two books is alone sufficient todemonstrate this fact.

The first such book Cohen selected Peirce entitledIllustrations of the Logic of Science, and it wasserialized in Popular Science Monthly in six separateissues between 1877 and 1878.3 Peirce's logic ofscience (which he had developed as early as 1866)was a study of the

8

Page vi

methods of science prepared by a master of actualscientific methods (namely Peirce himself, who had athirty-year career as a world-class physicist in theUnited States Coast and Geodetic Survey). Today thetopic would be known as the philosophy of science.These six essays were quickly transported to Europe,4 where they no doubt had a strong impact. (But thatis a story for another day.) The second essay in thisseries, "How to Make Our Ideas Clear," is Peirce'sclassic presentation of his Pragmatic Maxim, althoughthere he did not use either "pragmatic" or"pragmatism'' to name the principle (but he had usedthose terms in conversations since at least 1870).After the turn of the century, his original conceptionfor pragmatism had become so misused and abusedby other writers that Peirce declared he would selecta new word for his earlier conception. He chose'pragmaticism'"a word," he said, "that was so ugly itwould be safe from kidnappers." Apparently he wasright. Webster's Unabridged Dictionary of the EnglishLanguage has an entry for 'pragmaticism'it is simply"the philosophy of C. S. Peirce."

Peirce supplied no particular title for the second

10

volume; it was composed of five essays on scientificmetaphysics that appeared serially in The Monistduring 1891 through 1893.5 Students of Peirce'swork usually refer to that volume as "The 189193Monist series on Scientific Metaphysics," a somewhatclumsy phrase. Indeed, Cohen's title would be idealfor the second book, because there Peirce discussedhis hypotheses about the logic of what he calledTychism (Chance), Agapism (Love), and Synechism(Continuity).66 (Peirce preferred to coin newtechnical terms for new hypotheses within science.)Cohen had initially planned for name his editionTychism, Agapism, and Synechism, but Mrs. Cohenpersuaded him (much to the relief of his publisher) totranslate those neologisms into a more standardizedlanguage.7 Apparently Peirce had planned a sixthessay devoted to synechism in The Monist series onscientific metaphysics; however, it was notpublished.88 It is possible that MS 955 is a draft ofthat essay.9

Prior to the publication of CLL, Cohen had organizeda special edition of The Journal of Philosophy,Psychology and Scientific Methods 10 hat wasdevoted entirely to remembering Peirce. It containedarticles by Josiah Royce, John Dewey (whose article

11

was reprinted in CLL), Christine Ladd-Franklin, andJoseph Jastrow and Cohen's trib-

12

Page vii

ute (which included a preliminary bibliography ofPeirce's publications).

In addition to their philosophical compatibility, Cohenalso seems to have admired Peirce as a fellowupstream swimmera person, in other words, who hada great deal to offer society but whose talents andcontributions were underrated by contemporaries. InCohen's case, despite his brilliant mind, as a Jew heencountered the unfortunate prejudices that weremore prevalent in the first half of the twentiethcentury in the United States.

Cohen was born in Minsk, Russia. He received anorthodox rabbinical education and in 1892 moved tothe East Side of New York City, where he entered thepublic school; eventually he qualified for entrance tothe College of the City of New York, in which hebegan classes in the fall of 1895. He won the Wardmedal in his junior year and began to show a strongaptitude for philosophical reflection. In his spare timehe frequented the Columbia University library andbecame an avid self-directed reader in the history ofphilosophy. He made an acquaintance with ProfessorThomas Davidson, who recognized Cohen's gifted

13

mind and helped him cultivate it by opening hisprivate library to Cohen's use. Davidson enjoyed afriendship with three well-known Americanphilosophers: Felix Adler, Josiah Royce, and W. T.Harris. After Davidson's early death, and after a fewyears of teaching in various odd jobs, Cohen wasadmitted to graduate study at Harvard in the fall of1904. He completed his doctoral dissertation in thesummer of 1906. While at Harvard he studied withand enjoyed the friendship of Royce, William James,and Hugo Munsterberg. Moreover, he had the goodfortune of being the roommate of Felix Frankfurter. Itis possible that he crossed paths with Peirce in thoseyears, but if so, I have found no record of it. 11

Peirce's thought was already in the air at Harvard.12It is clear that Cohen was a part of the original groupof faculty and graduate students who undertook thetask of editing and publishing Peirce's manuscripts,which Harvard acquired in 1915. But Cohen was notto be among the number completing that task, whichwas followed, beginning in 1931, by the publicationof Peirce's Collected Papers in eight volumes byHarvard University Press.13 Indeed, in 1923, when itbecame clear that Cohen was about to publishChance, Love, and Logic jointly with Harcourt in New

14

York and Kegan Paul Trench

15

Page viii

Trubner and Company in England (Peirce's Englishdisciple C. K. Ogden 14 was general editor for theHarcourt/Trubner series entitled International Libraryof Psychology, Philosophy, and Scientific Method, inwhich CLL appeared in 1923), Professor JamesWoods, then chairman of philosophy at Harvard, triedto dissuade Cohen from publication. But since all theitems anthologized in CLL were either new orpreviously published in journals from which Cohenhad the necessary permissions, publication was notaverted.

How solid is CLL as a presentation of Peirce's work?The answer is, Surprisingly solid! Although thebibliography, after seventy-five years of vigorousscholarship on Peirce's prodigious output, is nowrecognized as seriously incomplete, the two books byPeirce were very well chosen, and the introductoryand supplementary matter is still effective andinteresting. The volume is a sound beginning forsomeone who needs a short introduction to Peirce'sphilosophy of science and his metaphysics.

And the book has had a strong cultural impact in theseventy-odd years since it first appeared. My favorite

16

example concerns Dashiell Hammett. Hismasterpiece, The Maltese Falcon, contains awellknown interlude. It occurs about halfway throughthe volume, as Sam Spade tells a story about aformer client of his detective agency, Mrs. Flitcraft,who wanted to locate her missing husband. Spadepresents the tale as a way of explaining hisphilosophical outlook on life to BrigidO'Shaughnessey, his client and lover. Early in hisinvestigation of the matter, Spade discovered thatbecause of a chance near-deadly accident, Flitcraftabruptly left his wife and family and moved to a newtown, where, under the assumed name of CharlesPierce, he started a new family entirely separate fromtheir first one but almost identical to it. Students ofHammett's fiction argue that this interlude aboutSpade's philosophy of life was inspired by Hammett'sreading of CLL.15

Cohen's intersection with Peirce's thought continuedthroughout his life. His posthumous work AmericanThought contains a quite defensible discussion ofPeirce's contributions. But perhaps the most enduringlegacy of Cohen's appreciation for the scientificphilosophy of Peirce came in the textbook Cohencoauthored with Ernest

17

Page ix

Nagel, An Introduction to Logic and ScientificMethod. Cohen explains it well in his autobiography.

The need for an adequate textbook of logic hadbecome increasingly manifest to me in the course ofthe years of logic-teaching at City College. Finally Ifound in my brilliant colleague and former student,Ernest Nagel, an ideal collaborator for the writing ofsuch a textbook. Between the two of usthough themajor part of the effort was certainly hiswe managedafter a summer together . . . to get out in 1934 atextbook on logic and scientific method. What we hadtried to produce was a text that would find a place forthe realistic formalism of Aristotle, the scientificpenetration of Peirce (whose philosophical essays I hadedited in 1923), the pedagogical soundness of Dewey,and the mathematical rigor of Russell. If we had notentirely achieved this high objective, we hoped that atleast we had achieved our minimum demand, whichwas inspired by the motto with which FlorenceNightingale transformed modern hospital practice:"Whatever hospitals do, they should not spreaddisease." We hoped we had written a logic text thatwould not infect students with fallacies and confusionsas to the nature of valid or scientific reasoning. Wewere both pleasantly surprised when the book wasadopted as a text in various universities about the

19

country, so that it went through five printings in fiveyears. But we were really nonplussed, some eightyears after publication, when the Army one dayordered 16,000 copies. 16

Anyone with even a slight knowledge of Peirce's workwill recognize his ideas on many pages in "Cohen andNagel," as the book was affectionally dubbed ingraduate schools. A whole generation learned aboutscientific logic from that volume. By this conduit,many of Peirce's most important results aboutscientific method filtered into the general academicconsciousness, but unfortunately, often without beingidentified as arising from Peirce.

This Bison Books edition will keep this valuablecultural resourceChance, Love, and Logicalive forfuture generations. And, who knows? Maybe nextyear the Air Force (which didn't exist in Cohen's time)will order seventeen thousand copies. Maybe thebook will even be found in the suitcase of somefuture airman, to keep her

20

Page x

company during the long trip to Mars and to give hera deeper understanding of the methods that madeher trip possible.

References* = recommended for further reading

Cohen, Morris Raphael

1949. A Dreamer's Journey: The Autobiography ofMorris Raphael Cohen. Boston: Beacon.

1954. American Thought: A Critical Sketch. Editedwith a foreword by Felix S. Cohen. Glencoe IL: FreePress.

Cohen, Morris Raphael, and Ernest Nagel

1934. An Introduction to Logic and ScientificMethod. New York: Harcourt, Brace and Company.

Eisele, Carolyn, ed.

1976. The New Elements ofMathematics by CharlesS. Peirce. The Hague: Mouton.

21

1985. Historical Perspectives on Peirce's Logic ofScience: A History of Science. Berlin: Mouton.

Fisch, Max Harold, general editor.

1982-. Writings of Charles S. Peirce: AChronological Edition. Bloomington: IndianaUniversity Press.

Hall, G. Stanley

1879. "Philosophy in the United States." Mind4:89105 at 1013.

Hammett, Dashiell

1975. The Continental Op. Edited with anintroduction by Steven Marcus. New York: VintageBooks.

Hardwick, Charles S., ed., with the assistance ofJames Cook

1977. Semiotic and Significs: The Correspondencebetween Charles S. Peirce and Lady Victoria Welby.Bloomington: Indiana University Press.

Ketner, Kenneth Laine

1986. A Comprehensive Bibliography of the

22

Published Works of Charles Sanders Peirce. 2d ed.,rev. Bowling Green OH: Philosophy DocumentationCenter.

*1987. "Charles Sanders Peirce." In ClassicalAmerican Philosophy, ed. John J. Stuhr. New York:Oxford University Press.

*1990. Elements ofLogic: An Introduction toPeirce's Existential Graphs. Interactive educationalsoftware. Lubbock: Arisbe Associates. (P.O. Box607, Lubbock TX, 79408).

23

Page xi

Ketner, Kenneth Laine, ed.

*1992. Reasoning and the Logic of Things: TheCambridge Conferences Lectures of 1898 byCharles Sanders Peirce. Cambridge: HarvardUniversity Press.

Ketner, Kenneth Laine, and James Edward Cook, eds.

197579. Charles S. Peirce: Contributions to TheNation. Lubbock: Texas Tech University Press.

Kuklick, Bruce

1977. The Rise of American Philosophy:Cambridge, Massachusetts, 18601930. NewHaven: Yale University Press.

Martin, Richard M., ed.

1979. Studies in the Scientific and MathematicalPhilosophy of Charles S. Peirce: Essays by CarolynEisele. The Hague: Mouton.

Peirce, Charles Sanders

193158. Collected Papers of Charles SandersPeirce. Ed. Charles Hartshorne, Paul Weiss, and

24

Arthur Burks. 8 vols. Cambridge: HarvardUniversity Press. The letterpress edition is out ofprint, but an excellent digital edition is publishedby Intelex, P.O. Box 859, Charlottesville VA,22902-0859.

Robin, Richard S.

1967. Annotated Catalogue of the Papers ofCharles S. Peirce. Amherst: University ofMassachusetts Press.

Samway, Patrick H., ed.

*1995. A Thief of Peirce. Jackson: University Pressof Mississippi.

Turrisi, Patricia Ann, ed.

*1997. Pragmatism as a Principle and Method ofRight Thinking. Albany: State University of NewYork Press.

Notes1. See Eisele's two editions of PeirceNew Elements ofMathematics and Historical Perspectives, plus heressays collected by Martin in Studies.

25

2. The book on photometry is P 118. (Number codessuch as P 107 refer to bibliographic entries forPeirce's lifetime publications as listed in Ketner,Comprehensive Bibliography). On the issue of book-length publications by Peirce that appeared duringhis lifetime, see the introduction to ComprehensiveBibliography.

3. See P 107 and P 11923. In those days PopularScience Monthly resembled the Scientific American ofour period, instead of being something like BoyMechanic.

26

Page xii

4. G. Stanley Hall's article in Mind (which containedtwo pages describing Illustrations) was one suchroute of dissemination.

5. P 439, 474, 477, 480, and 521.

6. For an introduction to Peirce's important method oflogic that he entitled Existential Graphs, see Ketner,Elements of Logic.

7. Cohen, Dreamer's Journey, 201.

8. After 1893, other essays by Peirce appeared inThe Monist: P 525, 620, 637, 107780, 1124, 1125,1126, 1128, 1171, 1175, 1193, 1206, 1207.

9. MS 955 was probably read before a group ofHarvard faculty and graduate students at Harvardprofessor Josiah Royce's home in Cambridge in May1892. On a day prior to that evening lecture, Peircehad read "The Law of Mind" (shortly before itappeared in The Monist) to the Harvard GraduatePhilosophy Club at their invitation. Because Peirce'strip to Cambridge encompassed a few days, it ispossible that he participated in Royce's seminar. MS955 is incompletely published in Robin, Annotated

27

Catalogue, 1.14175; the entire manuscript is quite arewarding read. To obtain a full grasp of Peirce'shypotheses about continuity and the central role thatconcept held in his system of science, one may alsoprofitably compare Peirce's lecture on "The Logic ofContinuity" (Ketner, ed., Reasoning and the Logic ofThings, 24268), especially if considered in the light ofHilary Putnam's important comments on Peirce'sdoctrine of continuity (in the same work, pages 3754and 94102). On Peirce's system of science, seeKetner, "Charles Sanders Peirce," in ClassicalAmerican Philosophy, 1325.

10. Journal of Philosophy, Psychology and ScientificMethods (1916): 70137.

11. This account is adapted from Cohen'sautobiography, A Dreamer's Journey, published in1949.

12. In 1898 when William James tried to arrange alecture series for Peirce, he was barred from theHarvard campus by President Eliot, a longterm enemyof the Peirce family. This is an odd event insofar asEliot had previously earned a reputation as a staunchdefender of academic freedom. Peirce lecturedinstead in 1898 at the Cambridge Conferences, which

28

was housed a few blocks off campus (see theintroduction in Ketner, ed., Reasoning and the Logicof Things). This set of lectures inspired Royce inparticular. The fire of Eliot's wrath was banked by1903, when again at the urging of William James,Peirce was admitted to Harvard Yard, where hedelivered a lecture series on pragmatism thatsupplemented his 1898 Cambridge Conferenceslectures (his Harvard lectures on pragmatism are nowpublished in a thorough edition as Turrisi, ed.,Pragmatism as a Principle and Method of RightThinking). Also in 1903 he delivered a set of lecturesat the Lowell Institute in Cambridge, which wereentitled "Some Topics of

29

Page xiii

Logic Bearing on Questions Now Vexed" (seeKetner, Comprehensive Bibliography).

13. Although valuable and important as an initialresource for study of Peirce, the Collected Paperssuffered from a number of problems, the major onebeing that there were a great many more papersamong Peirce's manuscripts deserving of publicationthan the publishers of Collected Papers could affordto produce. Therefore, as scholars began to return tothe manuscripts not found in Collected Papers, aneed for a fuller edition arose. Indiana UniversityPress has undertaken a series entitled Writings ofCharles S. Peirce: A Chronological Edition, Max Fisch,general editor, which is now in five volumes. Atpresent this continuing series covers Peirce's outputthrough 1886.In addition to Eisele's editions of Peirce, otherstandard volumes covering single orcompartmentalized works by Peirce have appeared.These are Ketner, ed., Reasoning and the Logic ofThings; Turrisi, ed., Pragmatism as a Principle andMethod of Right Thinking; and Ketner and Cook,eds., Charles S. Peirce: Contributions to The Nation.

30

14. Victoria Lady Welby's correspondence with Peirceafter 1900 produced a fruitful conversation. While hewas a student at Cambridge, Ogden was a protégé ofLady Welby, who introduced him to Peirce's work. Inher letter from England to Peirce of 2 May 1911 (seeHardwick, ed., Semiotic and Significs, 13839) sheremarked, "I have found you, I think, a disciple atCambridge. He has been studying with care all Icould show him of your writing on ExistentialGraphs . . . .The name of the recruit is C. K. Ogden,and he is at Magdalene College." Later Ogdencollaborated with I. A. Richards to produce TheMeaning of Meaning (New York: Harcourt, Brace,1927), which included an extensive appendix onPeirce's theory of meaning that eventually influencedWittgenstein through Ramsey, who was quite takenwith Peirce's ideas.

15. See the introduction by Steven Marcus toHammett's The Continental Op, xivxviii.

16. Cohen, Dreamer's Journey, 197.

31

Page xv

TABLE OF CONTENTS

Preface xvii

Introduction

Proem. The Rules of Philosophy

Part I. Chance and Logic (Illustrations of the Logic ofScience.)

1. The Fixation of Belief

2. How to Make Our Ideas Clear

3. The Doctrine of Chances

4. The Probability of Induction

5. The Order of Nature 106

6. Deduction, Induction and Hypothesis 131

Part II. Love and Chance

1. The Architecture of Theories 157

2. The Doctrine of Necessity Examined 179

32

3. The Law of Mind 202

4. Man's Glassy Essence 238

5. Evolutionary Love 267

Supplementary EssayThe Pragmatism of Peirce,By John Dewey

301

Bibliography of Peirce's Published Writings 309

33

Page xvii

PREFACEIn the essays gathered together in this volume wehave the most developed and coherent availableaccount of the philosophy of Charles S. Peirce, whomJames, Royce, Dewey, and leading thinkers inEngland, France, Germany and Italy have placed inthe forefront of the great seminal minds of recenttimes. Besides their inherent value as the expressionof a highly original and fruitful mind, unusually welltrained and informed in the exact sciences, theseessays are also important as giving us the sources ofa great deal of contemporary American philosophy.Because of this historical importance no omissions orchanges have been made in the text beyond thecorrection of some obvious slips and the recasting ofa few expressions in the interest of intelligibility.

In a subject which bristles with suggestions anddifficulties the temptation to add notes of explanationor dissent is almost insuperable. But as such notesmight easily have doubled the size of this volume Ihave refrained from all comment on the text except in

34

a few footnotes (indicated, as usual, in brackets). Theintroduction is intended (and I hope it will) help thereader to concatenate the various lines of thoughtcontained in these essays. I cannot pretend to haveadequately indicated their significance. Great mindslike those of James and Royce have been nourishedby these writings and I am persuaded that they

35

Page xviii

still offer mines of fruitful suggestion. Prof. Dewey'ssupplementary essay indicates their value for thefundamental question of metaphysics, viz. the natureof reality.

Grateful acknowledgment is here made to Mrs. PaulCarus and to the Open Court Publishing Co. forpermission to reprint the essays of Part II from theMonist. The late Paul Carus was one of the very fewwho not only gave Peirce an opportunity to publish,but publicly recognized the importance of hiswritings.

I must also acknowledge my obligation to ProfessorDewey for kind permission to reprint his essay on thePragmatism of Peirce from the Journal of Philosophy,and to the editors of that Journal, ProfessorsWoodbridge and Bush, for permission to reprint somematerial of my own. Part V of the Bibliography wascompiled by Mr. Irving Smith.

MORRIS R. COHENTHE COLLEGE OF THE CITY OF NEW YORK.

36

Page xix

INTRODUCTIONMany and diverse are the minds that form thephilosophic community. There are, first and foremost,the great masters, the system builders who rear theirstately palaces towering to the moon. Thesearchitectonic minds are served by a varied host offollowers and auxiliaries. Some provide thefurnishings to make these mystic mansions of themind more commodious, while others are engaged inmaking their façades more imposing. Some are busystrengthening weak places or building much-neededadditions, while many more are engaged in defendingthese structures against the impetuous army of criticswho are ever eager and ready to pounce down uponand destroy all that is new or bears the mortal markof human imperfection. There are also thephilologists, those who are in a more narrow sensescholars, who dig not only for facts or roots, but alsofor the stones which may serve either for building oras weapons of destruction. Remote from all these,however, are the intellectual rovers who, in theirsearch for new fields, venture into the thick jungle

37

that surrounds the little patch of cultivated science.They are not gregarious creatures, these lonelypioneers; and in their wanderings they oftencompletely lose touch with those who tread thebeaten paths. Those that return to the communityoften speak strangely of strange things; and it is notalways that they arouse sufficient faith for others tofollow them and change their trails into high roads.

38

Page xx

Few nowadays question the great value of thesepioneer minds; and it is often claimed thatuniversities are established to facilitate their work,and to prevent it from being lost. But universities, likeother well-managed institutions, can find place onlyfor those who work well in harness. The restless,impatient minds, like the socially or conventionallyunacceptable, are thus kept out, no matter howfruitful their originality. Charles S. Peirce was certainlyone of these restless pioneer souls with the fatal giftof genuine originality. In his early papers, in theJournal of Speculative Philosophy, and later, in theMonist papers reprinted as Part II of this volume, weget glimpses of a vast philosophic system on whichhe was working with an unusual wealth of materialand apparatus. To a rich imagination andextraordinary learning he added one of the mostessential gifts of successful system builders, thepower to coin an apt and striking terminology. Butthe admitted incompleteness of these preliminarysketches of his philosophic system is not altogetherdue to the inherent difficulty of the task and toexternal causes such as neglect and poverty. Acertain inner instability or lack of self-mastery is

39

reflected in the outer moral or conventionalwaywardness which, except for a few years at JohnsHopkins, caused him to be excluded from a universitycareer, and thus deprived him of much neededstimulus to ordinary consistency and intelligibility. Asthe years advanced, bringing little general interest in,or recognition of, the brilliant logical studies of hisearly years, Peirce became more and morefragmentary, cryptic, and involved; so that James,the intellectual companion of his youth, later found

40

Page xxi

his lectures on pragmatism, ''flashes of brilliant lightrelieved against Cimmerian darkness "a statement notto be entirely discounted by the fact that James hadno interest in or aptitude for formal logical ormathematical considerations.

Despite these limitations, however, Peirce stands outas one of the great founders of modern scientificlogic; and in the realm of general philosophy thedevelopment of some of his pregnant ideas has led tothe pragmatism and radical empiricism of James, aswell as to the mathematical idealism of Royce, and tothe anti-nominalism which characterizes thephilosophic movement known as Neo-Realism. At anyrate, the work of James, Royce, and Russell, as wellas that of logicians like Schroeder, brings us of thepresent generation into a better position toappreciate the significance of Peirce's work, thanwere his contemporaries.

IPeirce was by antecedents, training, and occupationa scientist. He was a son of Benjamin Peirce, the

41

great Harvard mathematician, and his earlyenvironment, together with his training in theLawrence Scientific School, justified his favorite claimthat he was brought up in a laboratory. He madeimportant contributions not only in mathematical logicbut also in photometric astronomy, geodesy, andpsychophysics, as well as in philology. For many yearsPeirce worked on the problems of geodesy, and hiscontribution to the subject, his researches on thependulum, was at once recognized by Europeaninvestigators in this field. The International GeodeticCongress, to

42

Page xxii

which he was the first American representative, gaveunusual attention to his paper, and men like Cellerierand Plantamour acknowledged their obligations tohim.1

This and other scientific work involving finemeasurement, with the correlative investigations intothe theory of probable error, seem to have been adecisive influence in the development of Peirce'sphilosophy of chance. Philosophers inexperienced inactual scientific measurement may naively accept asabsolute truth such statements as "every particle ofmatter attracts every other particle directly as theproduct of their masses and inversely as the squareof the distance," or "when hydrogen and oxygencombine to form water the ratio of their weights isI:8." But to those who are actually engaged inmeasuring natural phenomena with instruments ofprecision, nature shows no such absolute constancyor simplicity. As every laboratory worker knows, notwo observers, and no one observer in successiveexperiments, get absolutely identical results. To themen of the heroic period of science this was nodifficulty. They held unquestioningly the Platonic faith

43

that nature was created on simple geometric lines,and all the minute variations were attributable to thefault of the observer or the crudity of his instruments.This heroic faith was, and still is, a most powerfulstimulus to scientific research and a protectionagainst the incursions of supernaturalism. But fewwould defend it to-day in its explicit form, and thereis little empirical evidence to show that while theobserver and his instruments are always varying, theob-

1 See Plantamour's "Recherches Experimentales sur lemouvement simultané d'un pendule et de sessupports," Geneva, 1878, pp. 34.

44

Page xxiii

jects which he measures never deviate in theslightest from the simple law. Doubtless, as onebecomes more expert in the manipulation of physicalinstruments, there is a noticeable diminution of therange of the personal "error," but no amount of skilland no refinement of our instruments have eversucceeded in eliminating irregular, though small,variations. "Try to verify any law of nature and youwill find that the more precise your observations, themore certain they will be to show irregular departurefrom the law." 2 There is certainly nothing in ourempirical information to prevent us from saying thatall the so-called constants of nature are merelyinstances of variation between limits so near eachother that their differences may be neglected forcertain purposes. Moreover, the approach toconstancy is observed only in mass phenomena,when we are dealing with very large numbers ofparticles; but social statistics also approach constantratios when the numbers are very large. Hence,without denying discrepancies due solely to errors ofobservation, Peirce contends that "we must supposefar more minute discrepancies to exist owing to theimperfect cogency of the law itself, to a certain

45

swerving of the facts from any definite formula."3

It is usual to associate disbelief in absolute laws ofnature with sentimental claims for freedom ortheological miracles. It is, therefore, well to insist thatPeirce's attack is entirely in the interests of exactlogic and a rational account of the physical universe.As a rigorous logician familiar with the actualprocedures by which our knowledge

2 P. 1903 Pp. 162163.

46

Page xxiv

of the various laws of nature is obtained, he could notadmit that experience could prove their claim toabsoluteness. All the physical laws actually known,like Boyle's law or the law of gravitation, involveexcessive simplification of the phenomenal course ofevents, and thus a large element of empiricalinaccuracy. But a more positive objection against thetraditional assumption of absolute or invariable lawsof nature, is the fact that such assumption makes theregularities of the universe ultimate, and thus cuts usoff from the possibility of ever explaining them or howthere comes to be as much regularity in the universeas there is. But in ordinary affairs, the occurrence ofany regularity is the very thing to be explained.Moreover, modern statistical mechanics andthermodynamics (theory of gases, entropy, etc.)suggest that the regularity in the universe is a matterof gradual growth; that the whole of physical natureis a growth from a chaos of diversity to a maximum ofuniformity or entropy. A leading physicist of the 19thCentury, Boltzmann, has suggested that the processof the whole physical universe is like that of acontinuous shaking up of a hap-hazard or chancemixture of things, which thus gradually results in a

47

progressively more uniform distribution. Since DunsScotus, students of logic have known that every realentity has its individual character (its haecceitas orthisness) which cannot be explained or deduced fromthat which is uniform. Every explanation, for example,of the moon's path must take particular existences forgranted. Such original or underived individuality anddiversity is precisely what Peirce means by chance;and from this point of view chance is prior to law.

48

Page xxv

All that is necessary to visualize this is to supposethat there is an infinitesimal tendency in things toacquire habits, a tendency which is itself anaccidental variation grown habitual. We shall then beon the road to explain the evolution and existence ofthe limited uniformities actually prevailing in thephysical world.

A good deal of the foregoing may sound somewhatmythologic. But even if it were so it would have themerit of offering a rational alternative to themechanical mythology according to which all theatoms in the universe are to-day precisely in thesame condition in which they were on the day ofcreation, a mythology which is forced to regard all theempirical facts of spontaneity and novelty as illusory,or devoid of substantial truth.

The doctrine of the primacy of chance naturallysuggests the primacy of mind. Just as law is a chancehabit so is matter inert mind. The principal law ofmind is that ideas literally spread themselvescontinuously and become more and more general orinclusive, so that people who form communities ofany sort develop general ideas in common. When this

49

continuous reaching-out of feeling becomes nurturinglove, such, e.g., which parents have for theiroffspring or thinkers for their ideas, we have creativeevolution.

James and Royce have called attention to thesimilarity between Peirce's doctrine of tychistic-agapism (chance and love) and the creative evolutionof Bergson. But while both philosophies aim torestore life and growth in their account of the natureof things, Peirce's approach seems to me to havemarked advantages, owing to its being in closer

50

Page xxvi

touch with modern physics. Bergson's procedure islargely based on the contention that mechanicscannot explain certain empirical facts, such as thesupposed identity of the vertebrate eye and the eyeof the scallop. But the fact here is merely one of acertain resemblance of pattern, which may well beexplained by the mechanical principles of convergentevolution. Peirce's account involves no rejection ofthe possibility of mechanical explanations. Indeed, bycarrying chance into the laws of mechanics he isenabled to elaborate a positive and highly suggestivetheory of protoplasm to explain the facts of plasticityand habit.4 Instead of postulating with Spencer andBergson a continuous growth of diversity, Peirceallows for growth of habits both in diversity and inuniformity. The Spencerian mechanical philosophyreduces all diversity to mere spatial differences. Therecan be no substantial novelty; only new forms orcombinations can arise in time. The creative evolutionof Bergson though intended to support the claims ofspontaneity is still like the Spencerian in assuming allevolution as proceeding from the simple to thecomplex. Peirce allows for diversity and specificity aspart of the original character or endowment of things,

51

which in the course of time may increase in somerespects and diminish in others. Mind acquires thehabit both of taking on, and also of laying aside,habits. Evolution may thus lead to homogeneity oruniformity as well as to greater heterogeneity. Notonly has Peirce a greater regard than even Bergsonfor the actual diversity and spontaneity of things, buthe is in a much better position than any othermodern phi-

4 pp. 249 ff.

52

Page xxvii

losopher to explain the order and coherence of theworld. This he effects by uniting the medieval regardfor the reality of universals with the modern scientificuse of the concept of continuity. The unfortunate warbetween the pioneers of modern science and theadherents of the scholastic doctrine of substantialforms, has been one of the great misfortunes ofhuman thought, in that it made absolute atomismand nominalism the professed creed of physicalscience. Now, extreme nominalism, the insistence onthe reality of the particular, leaves no room for thegenuine reality of law. It leaves, as Hume had thecourage to admit, nothing whereby the present candetermine the future; so that anything is as likely tohappen as not. From such a chaotic world, theprocedure of modern natural and mathematicalscience has saved us by the persistent use of theprinciple of continuity; and no one has indicated thismore clearly than Peirce who was uniquely qualifiedto do so by being a close student both of DunsScotus and of modern scientific methods.

It is instructive in this respect to contrast the views ofPeirce and James. James, who so generously

53

indicated his indebtedness to Peirce for hispragmatism, was also largely indebted to Peirce forhis doctrine of radical empiricism.5 The latter doctrineseeks to rescue the continuity and fluidity ofexperience from the traditional British empiricism ornominalism, which had resolved everything into anumber of mutually exclusive mental states. It iscurious, however, that while in his psychology Jamesmade extensive use of the principle of continuity, hecould not free himself

5James, Pluralistic Universe, pp. 398400.

54

Page xxviii

from British nominalism in his philosophywitness theextreme individualism of his social philosophy or theequally extreme anthropomorphism of his religion.Certain of Peirce's suggestions as to the use ofcontinuity in social philosophy have been developedby Royce in his theory of social consciousness and thenature of the community;6 but much remains to beworked out and we can but repeat Peirce's ownhope: "May some future student go over this groundagain and have the leisure to give his results to theworld."

It is well to note, however, that after writing thepapers included in this volume Peirce continued to beoccupied with the issues here raised. This he mostsignificantly indicated in the articles on logical topicscontributed to Baldwin's Dictionary of Philosophy.7

In these articles it is naturally the logical bearing ofthe principles of tychism (chance), synechism(continuity), and agapism (love) that is stressed. Touse the Kantian terminology, almost native to Peirce,the regulative rather than the constitutive aspect ofthese principles is emphasized. Thus the doctrine ofchance is not only what it was for James' radical

55

empiricism, a release from the blind necessity of a "block universe," but also a method of keep-

6 Royce, Studies in Good and Evil, and The Problem ofChristianity, esp. Vol. 2. Baldwin (Mental Development)is heavily indebted to Royce in this respect.7 These articles are by-products or fragments of acomprehensive work on Logic on which Peirce wasengaged for many years. For the writing of this book,Royce declared, no greater mind or greater erudition hasappeared in America. Only several chapters seem to havebeen finished, and will doubtless be included with otherhitherto unpublished manuscripts in the complete editionof Peirce's writings that is now being prepared by HarvardUniversity.

56

Page xxix

ing open a possible explanation of the genesis of thelaws of nature and an interpretation of them inaccordance with the theorems of probability, sofruitful in physical science as well as in practical life.So the doctrine of love is not only a cosmologic one,showing how chance feeling generates order orrational diversity through the habit of generality orcontinuity, but it also gives us the meaning of truth insocial terms, in showing that the test as to whetherany proposition is true postulates an indefinitenumber of cooperating investigators. On its logicalside the doctrine of love (agapism) also recognizedthe important fact that general ideas have a certainattraction which makes us divine their nature eventhough we cannot clearly determine their precisemeaning before developing their possibleconsequences.

Of the doctrine of continuity we are told expressly8that "synechism is not an ultimate absolutemetaphysical doctrine. It is a regulative principle oflogic," seeking the thread of identity in diverse casesand avoiding hypotheses that this or that is ultimateand, therefore, inexplicable. (Examples of such

57

hypotheses are: the existence of absolutely accurateor uniform laws of nature, the eternity and absolutelikeness of all atoms, etc.) To be sure, the synechistcannot deny that there is an element of theinexplicable or ultimate, since it is directly forcedupon him. But he cannot regard it as a source ofexplanation. The assumption of an inexplicability is abarrier on the road to science. "The form under whichalone anything can be understood is the form ofgenerality which is the same thing

8 Baldwin's Dictionary, article Synechism.

58

Page xxx

as continuity"9 This insistence on the generality ofintelligible form is perfectly consistent with dueemphases on the reality of the individual, which to aScotist realist connotes an element of will or will-resistence, but in logical procedure means that thetest of the truth or falsity of any proposition refers usto particular perceptions.10 But as no multitude ofindividuals can exhaust the meaning of a continuum,which includes also organizing relations of order, thefull meaning of a concept cannot be in any individualreaction, but is rather to be sought in the manner inwhich all such reactions contribute to thedevelopment of the concrete reasonableness of thewhole evolutionary process. In scientific procedurethis means that integrity of belief in general is moreimportant than, because it is the condition of,particular true beliefs.

IIThis insistence on the continuity so effectually usedas a heuristic principle in natural and mathematicalscience, distinguishes the pragmatism of Peirce from

59

that of his follower James. Prof. Dewey has developedthis point authoritatively in the supplementary essay;but in view of the general ignorance as to the sourcesof pragmatism which prevails in this incurious age,some remarks on the actual historical origin ofpragmatism may be in order. There can be littledoubt that Peirce was led to the formulation of theprinciple of pragmatism through the influence

9lb.10 Baldwin's Dictionary, art. Individual: "Everythingwhose identity consists in a continuity of reactions will bea single logical individual."

60

Page xxxi

of Chauncey Wright.11 Wright who had first handacquaintance with creative scientific work inmathematics, physics, and botany was led by thestudy of Mill and Bain to reflect on the characteristicsof scientific method. This reflection led him to draw adistinction between the use of popular scientificmaterial, by men like Spencer, to construct a myth orpicture of the world, and the scientific use of laws bymen like Newton as means for extending ourknowledge of phenomena. Gravitation as a generalfact had interested metaphysicians long beforeNewton. What made Newton's contribution scientificwas the formulation of a mathematical law which hasenabled us to deduce all the then known facts of thesolar system and to anticipate or predict many morefacts the existence of which would not otherwise beeven suspected, e.g., the existence of the planetNeptune. Wright insists, therefore, that the principlesof modern mathematical and physical science are themeans through which nature is discovered, thatscientific

11 The personal relations between Peirce and Wrightwere thus described by Peirce in a letter to Mrs. Ladd-Franklin (Journal of Philosophy Vol. 13, p. 719): ''It

61

must have been about 1857 when I first made theacquaintance of Chauncey Wright, a mind about on thelevel of J. S. Mill. He was a thorough mathematician.He had a most penetrating intellect.He and I used tohave long and very lively and close disputations lastingtwo or three hours daily for many years. In the sixties Istarted a little club called 'The MetaphysicalClub.'Wright was the strongest member and probably Iwas next.Then there were Frank Abbott, William Jamesand others." "It was there that the name and thedoctrine of pragmatism saw the light." It might beadded that Peirce's tychism is indebted to Wright'sdoctrine of accidents and "cosmic weather," a doctrinewhich maintained against LaPlace that a mind knowingnature from moment to moment is bound to encountergenuine novelty in phenomena, which no amount ofknowledge would enable us to foresee. See Wright'sPhilosophical Discussions1876, also Cambridge Hist. ofAmerican Literature, Vol. 3, p. 234.

62

Page xxxii

laws are the finders rather than merely thesummaries of factual truths. This conception of theexperimental scientist as translating generalpropositions into prescriptions for attaining newexperimental truths, is the starting point of Peirce'spragmatism. The latter is embodied in the principlethat the meaning of a concept is to be found in "allthe conceivable experimental phenomena which theaffirmation or denial of the concept could imply." 12

In the earlier statement of the pragmatic maxim,13Peirce emphasized the consequences for conductthat follow from the acceptance or rejection of anidea; but the stoical maxim that the end of man isaction did not appeal to him as much at sixty as it didat thirty.14 Naturally also Peirce could not follow thedevelopment of pragmatism by Wm. James who, likealmost all modern psychologists, was a thoroughnominalist and always emphasized particular sensibleexperience.15 It seemed to Peirce that such em-

12Monist, Vol. 15, p. 180.13 This volume, pp. 4345.14 "To say that we live for the sake of action would be tosay that there is no such thing as a rational purport."

63

Monist, Vol. XV, p. 175.15 The letter to Mrs. Ladd-Franklin quoted before,explains why James, though always loyal to Peirce andanxious to give him credit whenever possible, could notunderstand the latter's lectures on pragmatism. Peirce'sincidental judgments on others is worth quoting here:"Modern psycholoigsts are so soaked with sensationalismthat they cannot understand anything that does not meanthat. How can I, to whom nothing seems so thoroughlyreal as generals, and who regards Truth and Justice asliterally the most powerful powers in the world, expect tobe understood by the thoroughgoing Wundtian? But thecurious thing is to see absolute idealists tainted with thisdisease,-er men who, like John Dewey, hover betweenAbsolute Idealism and Sensationalism. Royce's opinionsas developed in his World and Individualism areextremely near to mine. His insistence on the elements ofpurpose in intellectual concepts is essentially thepragmatic position."

64

Page xxxiii

phasis on particular experiences endangered theprinciple of continuity which in the hands of men likeWeierstrass had reformed modern mathematics. Forthis reason he began to call his own doctrinepragmaticism, a sufficiently unattractive name, hethought, to save it from kidnappers and frompopularity. He never, however, abandoned theprinciple of pragmatism, that the meaning of an ideais clarified (because constituted) by its conceivableexperimental consequences. Indeed, if we want toclarify the meaning of the idea of pragmatism, let usapply the pragmatic test to it. What will be the effectof accepting it? Obviously it will be to develop certaingeneral ideas or habits of looking at things.

Peirce's pragmatism has, therefore, a decidedlyintellectual cast. The meaning of an idea orproposition is found not by an intuition of it but byworking out its implications. It admits that thoughtdoes not constitute reality. Categories can have noconcrete being without action or immediate feeling.But thought is none the less an essential ingredientof reality; thought is " the melody running throughthe succession of our sensations." Pragmatism,

65

according to Peirce, seeks to define the rationalpurport, not the sensuous quality. It is interested notin the effect of our practical occupations or desires onour ideas, but in the function of ideas as guides ofaction. Whether a man is to pay damages in a certainlawsuit may depend, in fact, on a term in theAristotelian logic such as proximate cause.

It is of interest to observe that though Peirce is anardent admirer of Darwin's method, his scientificcaution makes

66

Page xxxiv

him refuse to apply the analogy of biologic naturalselection to the realm of ideas, in the wholesale anduncritical manner that has lately become fashionable.Natural selection may well favor the triumph of viewswhich directly influence biologic survival. But thepleasure of entertaining congenial illusions mayoverbalance the inconvenience resulting from theirdeceptive character. Thus rhetorical appeals maylong prevail over scientific evidence.

IIIPeirce preferred to call himself a logician, and hiscontributions to logic have so far proved his mostgenerally recognized achievement. For a rightperspective of these contributions we may, well beginwith the observation that though few branches ofphilosophy have been cultivated as continuously aslogic, Kant was able to affirm that the science of logichad made no substantial progress since the time ofAristotle. The reason for this is that Aristotle's logic,the logic of classes, was based on his own scientificprocedure as a zoologist, and is still in essence a valid

67

method so far as classification is part of all rationalprocedure. But when we come to describe themathematical method of physical science, we cannotcast it into the Aristotelian form without involvingourselves in such complicated artificialities as toreduce almost to nil the value of Aristotle's logic as anorganon. Aristotle's logic enables us to make a singleinference from two premises. But the vast multitudeof theorems that modern mathematics has derivedfrom a few premises as to the nature of number,shows the need of formulating a logic or theory ofinference

68

Page xxxv

that shall correspond to the modern, morecomplicated, practice as Aristotle's logic did to simpleclassificatory zoology. To do this effectively wouldrequire the highest constructive logical genius,together with an intimate knowledge of the methodsof the great variety of modern sciences. This is in thenature of the case a very rare combination, sincegreat investigators are not as critical in examiningtheir own procedure as they are in examining thesubject matter which is their primary scientificinterest. Hence, when great investigators likePoincaré come to describe their own work, they fallback on the uncritical assumptions of the traditionallogic which they learned in their school days.Moreover, "For the last three centuries thought hasbeen conducted in laboratories, in the field, orotherwise in the face of the facts, while chairs of logichave been filled by men who breathe the air of theseminary." 16 The great Leibnitz had thequalifications, but here, as elsewhere, his worldlyoccupations left him no opportunity except for veryfragmentary contributions. It was not until the middleof the 19th century that two mathematicians, Booleand DeMorgan, laid the foundations for a more

69

generalized logic. Boole developed a general logicalalgorithm or calculus, while DeMorgan calledattention to non-syllogistic inference and especially tothe importance of the logic of relations. Peirce's greatachievement is to have recognized the possibilities ofboth and to have generalized and developed theminto a general theory of scientific inference. Theextent and thoroughness of his achievement hasbeen obscured by his fragmentary way of writing andby a rather

16 Baldwin's Dictionary, art. Method.

70

Page xxxvi

unwieldy symbolism. Still, modern mathematical logic,such as that of Russell's Principles of Mathematics, isbut a development of Peirce's logic of relatives.

This phase of Peirce's work is highly technical and anaccount of it is out of place here. Such an accountwill be found in Lewis' Survey of Symbolic Logic.17 Irefer to it here only to remind the reader that theIllustrations of the Logic of the Sciences (Part I of thisvolume) have a background of patient detailed workwhich is still being developed to-day.

Symbolic logic has been held in rather low esteem bythe followers of the old classical methods inphilosophy. Their stated objection to it has beenmainly that it is concerned with the minutiae of anartificial language and is of no value as a guide to theinterpretation of reality. Now it should be readilyadmitted that preoccupation with symbolic logic israther apt to retard the irresponsible flight ofphilosophic fancy. Yet this is by no means always anevil. By insisting on an accuracy that is painful tothose impatient to obtain sweeping and comforting,though hasty, conclusions, symbolic logic is wellcalculated to remove the great scandal of traditional

71

philosophythe claim of absolutely certain results infields where there is the greatest conflict of opinion.This scandalous situation arises in part from the factthat in popular exposition we do not have to makeour premises or assumptions explicit; hence all sortsof dubious prejudices are implicitly appealed to asabso-

17 "Peirce anticipated the most important proceduresof his successors even when he did not work them outhimself. Again and again one finds the clue to the mostrecent developments in the writings of Peirce," Lewis'Survey of Symbolic Logic, p. 79.

72

Page xxxvii

lutely necessary principles. Also, by the use ofpopular terms which have a variety of meanings, oneeasily slides from one meaning to another, so that themost improbable conclusions are thus derived fromseeming truisms. By making assumptions and rulesexplicit, and by using technical terms that do notdrag wide penumbras of meaning with them, themethod of symbolic logic may cruelly reduce thesweeping pretensions of philosophy. But there is noreason for supposing that pretentiousness rather thanhumility is the way to philosophic salvation. Man isbound to speculate about the universe beyond therange of his knowledge, but he is not bound toindulge the vanity of setting up such speculations asabsolutely certain dogmas.

There is, however, no reason for denying that greaterrigor and accuracy of exposition can really help us todiscern new truth. Modern mathematics since Gaussand Weierstrass has actually been led to greaterfruitfulness by increased rigor which makes suchprocedure as the old proofs of Taylor's theorem nolonger possible. The substitution of rigorous analyticprocedures for the old Euclidean proofs based on

73

intuition, has opened up vast fields of geometry. Norhas this been without any effect on philosophy.Where formerly concepts like infinity and continuitywere objects of gaping awe or the recurrentoccasions for intellectual violence,18 we are nowbeginning to use them, thanks to Peirce and Royce,in accurate and definable senses. Consider, forinstance, the amount of a priori nonsense whichPeirce eliminates by pointing out

18 Hans Breitmann is symbolic of those who "solvedthe infinite as one eternal sphere."

74

Page xxxviii

that the application of the concept of continuity to aspan of consciousness removes the necessity forassuming a first or last moment; so likewise the rangeof vision on a large unobstructed ground has no linebetween the visible and the invisible. Theseconsiderations will be found utterly destructive of theforce of the old arguments (fundamental to Kant andothers) as to the necessary infinity of time and space.Similar enlightenment is soon likely to result from themore careful use of terms like relative and absolute,which are bones of contention in philosophy butAriadne threads of exploration in theoretical physics,because of the definite symbolism of mathematics.Other important truths made clear by symbolic logicis the hypothetical character of universal propositionsand the consequent insight that no particulars can bededuced from universals alone, since no number ofhypotheses can without given data establish anexisting fact.

There is, however, an even more positive direction inwhich symbolic logic serves the interest of philosophy,and that is in throwing light on the nature of symbolsand on the relation of meaning. Philosophers have

75

light-heartedly dismissed questions as to the natureof significant signs as 'merely' (most fatal word!) amatter of language. But Peirce in the paper on Man'sGlassy [Shakespearian for Mirror-Like] Essence,endeavors to exhibit man's whole nature assymbolic.19 This is closely connected with his logicaldoctrine which regards signs or symbols as one of

19 See Journal of Speculative Philosophy, Vol. 2, pp.155157, article on A New List of Categories in theProceedings of the American Academy of Arts andSciences, Vol. 7, 287298 and article on Sign, inBaldwin's Dictionary.

76

Page xxxix

the fundamental categories or aspects of the universe(Thoughts and things are the other two).Independently of Peirce but in line with his thoughtanother great and neglected thinker, Santayana, hasshown that the whole life of man that is bound upwith the institutions of civilization, is concerned withsymbols.

It is not altogether accidental that, since Boole andDeMorgan, those who have occupied themselves withsymbolic logic have felt called upon to deal with theproblem of probability. The reason is indicated byPeirce when he formulates the problem of probableinference in such a way as to make the old classiclogic of absolutely true or false conclusions, a limitingcase (i.e., of values I and o) of the logic of probableinference whose values range all the way betweenthese two limits. This technical device is itself theresult of applying the principle of continuity to throwtwo hitherto distinct types of reasoning into the sameclass. The result is philosophically significant.

Where the classical logic spoke of major and minorpremises without establishing any really importantdifference between the two, Peirce draws a

77

distinction between the premises and the guidingprinciple of our argument. All reasoning is from someconcrete situation to another. The propositions whichrepresent the first are the premises in the strict senseof the word. But the feeling that certain conclusionsfollow from these premises is conditioned by animplicit or explicit belief in some guiding principlewhich connects the premises and the conclusions.When such a leading principle results in trueconclusions in all cases of true premises, we havelogical deduction of the orthodox

78

Page xl

type. If, however, such a principle brings about atrue conclusion only in a certain proportion of cases,then we have probability.

This reduction of probability to the relative frequencyof true propositions in a class of propositions, wassuggested to Peirce by Venn's Logic of Chance.Peirce uses it to establish some truths of greatestimportance to logic and philosophy.

He eliminates the difficulties of the old conceptualistview, which made probability a measure of ourignorance and yet had to admit that almost allfruitfulness of our practical and scientific reasoningdepended on the theorems of probability. How couldwe safely predict phenomena by measuring ourignorance?

Probability being reduced to a matter of the relativefrequency of a class in a larger class or genus, itbecomes, strictly speaking, inapplicable to singlecases by themselves. A single penny will fall head orit will fall tail every time; to-morrow it will rain, or itwill not rain at all. The probability of ½ or any otherfraction means nothing in the single case. It is only

79

because we feel the single event as representative ofa class, as something which repeats itself, that wespeak elliptically of the probability of a single event.Hence follows the important corollary that reasoningwith respect to the probability of this or thatarrangement of the universe would be valid only ifuniverses were as plentiful as blackberries.

To be useful at all, theories must be simpler than thecomplex facts which they seek to explain. Hence, it isoften convenient to employ a principle of certaintywhere

80

Page xli

the facts justify only a principle of some degree ofprobability. In such cases we must be cautious inaccepting any extreme consequence of theseprinciples, and also be on guard against apparentrefutations based on such extreme consequences.

Finally I should like to emphasize the value of Peirce'stheory of inference for a philosophy of civilization. Tothe old argument that logic is of no importancebecause people learn to reason, as to walk, byinstinct and habit and not by scientific instruction,Peirce admits 20 that ''all human knowledge up to thehighest flights of science is but the development ofour inborn animal instincts." But though logical rulesare first felt implicitly, bringing them into explicitconsciousness helps the process of analysis and thusmakes possible the recognition of old principles innovel situations. This increases our range ofadaptability to such an extent as to justify a generaldistinction between the slave of routine or habit andthe freeman who can anticipate and control naturethrough knowledge of principles. Peirce's analysis ofthe method of science as a method of attainingstability of beliefs by free inquiry inviting all possible

81

doubt, in contrast with the methods of iteration ("willto believe ") and social authority, is one of the bestintroductions to a theory of liberal or Helleniccivilization, as opposed to those of despotic societies.Authority has its roots in the force of habit, but itcannot prevent new and unorthodox ideas fromarising; and in the effort to defend authoritative socialviews men are apt to be far more ruthless than indefending their own personal convictions.

20 Studies in Logic, p. 181.

82

Page xlii

IVNot only the pragmatism and the radical empiricismof James, but the idealism of Royce and the morerecent movement of neo-realism are largely indebtedto Peirce.

It may seem strange that the same thinker should beclaimed as foster-father of both recent idealism andrealism, and some may take it as another sign of hislack of consistency. But this seeming strangeness isreally due to the looseness with which the antithesisbetween realism and idealism has generally been put.If by idealism we denote the nominalistic doctrine ofBerkeley, then Peirce is clearly not an idealist; and hiswork in logic as a study of types of order (in whichRoyce followed him) is fundamental for a logicalrealism. But if idealism means the old Platonicdoctrine that "ideas," genera, or forms are not merelymental but the real conditions of existence, we neednot wonder that Peirce was both idealist and realist.

Royce's indebtedness to Peirce is principally in theuse of modern mathematical material, such as the

83

recent development of the concepts of infinity andcontinuity, to throw light on fundamental questions ofphilosophy, such as relation of the individual to Godor the Universe. At the end of the nineteenth centurymathematics had almost disappeared from therepertory of philosophy (cf. Külpe's Introduction toPhilosophy), and Peirce's essay on the Law of Mindopened a new way which Royce followed in his Worldand the Individual, to the great surprise of hisidealistic brethren. In his Problem of ChristianityRoyce has also indicated his indebtedness to Peircefor his doc-

84

Page xliii

trine of social consciousness, the mind of thecommunity, and the process of interpretation. It maybe that a great deal of the similarity between thethoughts of these two men is due to commonsources, such as the works of Kant and Schelling; butit is well to note that not only in his later writings butalso in his lectures and seminars Royce continuallyreferred to Peirce's views.

The ground for the neo-realist movement in Americanphilosophy was largely prepared by the mathematicalwork of Russell and by the utilization of mathematicsto which Royce was led by Peirce. The logic of Mr.Russell is based, as he himself has pointed out, on acombination of the work of Peirce and Peano. In thiscombination the notation of Peano has proved ofgreater technical fluency, but all of Peano's resultscan also be obtained by Peirce's method asdeveloped by Schroeder and Mrs. Ladd-Franklin. Butphilosophically Peirce's influence is far greater ininsisting that logic is not a branch of psychology, thatit is not concerned with merely mental processes, butwith objective relations. To the view that the laws oflogic represent "the necessities of thought," that

85

propositions are true because " we can not helpthinking so," he answers: " Exact logic will say thatC's following logically from A is a state of things whichno impotence of thought alone can bring about.'' 21"The question of validity is purely one of fact and notof thinking. . . . It is not in the least the questionwhether, when the premises are accepted by themind, we feel an impulse to accept the conclusionalso.

21Monist, Vol. 7, p. 27. Cf. Journal of SpeculativePhilosophy, Vol. 2, p. 207; Popular Science Monthly,Vol. 58, pp. 305306.

86

Page xliv

The true conclusion would remain true if we had noimpulse to accept it, and the false one would remainfalse though we could not resist the tendency tobelieve in it." 22

Since the days of Locke modern philosophy has beenalmost entirely dominated by the assumption thatone must study the process of knowing before onecan find out the nature of things known; in otherwords, that psychology is the central philosophicscience. The result of this has been an almostcomplete identification of philosophy with mentalscience. Nor did the influence of biologic studies ofthe middle of the nineteenth century shake the beliefin that banal dictum of philosophic mediocrity: " Theproper study of mankind is man." The recentrenaissance of logical studies, and the remarkableprogress of physics in our own day bid fair to remindus that while the Lockian way has brought somegains to philosophy, the more ancient way ofphilosophy is by no means exhausted of promise. Mancannot lose his interest in the great cosmic play.Those who have faith in the ancient and fruitfulapproach to philosophy through the doors of

87

mathematics and physics will find the writings ofCharles S. Peirce full of suggestions. That such anapproach can also throw light on the vexed problemof knowledge needs no assurance to thoseacquainted with Plato and Aristotle. But I mayconclude by referring to Peirce's doctrine of ideal asopposed to sensible experiment,23 and to histreatment of the question

22 This vol., p. 15.23 Suggestive for a theory of the metaphysics of fictionsis the suggestion (p. 46) "that the question of what wouldoccur under circumstances which do not actually arise, isnot a question of fact, but only of the most perspicuousarrangement of them." This arrangement is, of course,not merely subjective.

88

Page xlv

how it is that in spite of an infinity of possiblehypotheses, mankind has managed to make so manysuccessful inductions.24 And for the bearing ofmathematical studies on the wisdom of life, thefollowing is certainly worth serious reflection: "Allhuman affairs rest upon probabilities. If man wereimmortal [on earth] he could be perfectly sure ofseeing the day when everything in which he hadtrusted should betray his trust. He would breakdown, at last, as every great fortune, as everydynasty, as every civilization does. In place of this wehave death." The recognition that the death of theindividual does not destroy the logical meaning of hisutterances, that this meaning involves the ideal of anunlimited community, carries us into the heart of purereligion.

24 Pp. 128129, cf. Monist, Vol. 7, p. 206, and LogicalStudies, pp. 175 ff.

89

PROEM:THE RULES OF PHILOSOPHY1

Descartes is the father of modern philosophy, and thespirit of Cartesianismthat which principallydistinguishes it from the scholasticism which itdisplacedmay be compendiously stated as follows:

1. It teaches that philosophy must begin withuniversal doubt; whereas scholasticism had neverquestioned fundamentals.

2. It teaches that the ultimate test of certainty is tobe found in the individual consciousness; whereasscholasticism had rested on the testimony of sagesand of the Catholic Church.

3. The multiform argumentation of the middle ages isreplaced by a single thread of inference dependingoften upon inconspicuous premises.

4. Scholasticism had its mysteries of faith, butundertook to explain all created things. But there aremany facts which Cartesianism not only does notexplain but renders absolutely inexplicable, unless to

90

say that " God makes them so " is to be regarded asan explanation.

In some, or all of these respects, most modernphilosophers have been, in effect, Cartesians. Nowwithout wishing

1 From the Journal of Speculative Philosophy, vol. 2, p.140.

91

to return to scholasticism, it seems to me thatmodern science and modern logic require us to standupon a very different platform from this.

1. We cannot begin with complete doubt. We mustbegin with all the prejudices which we actually havewhen we enter upon the study of philosophy. Theseprejudices are not to be dispelled by a maxim, forthey are things which it does not occur to us can bequestioned. Hence this initial skepticism will be amere self-deception, and not real doubt; and no onewho follows the Cartesian method will ever besatisfied until he has formally recovered all thosebeliefs which in form he has given up. It is, therefore,as useless a preliminary as going to the North Polewould be in order to get to Constantinople by comingdown regularly upon a meridian. A person may, it istrue, in the course of his studies, find reason to doubtwhat he began by believing; but in that case hedoubts because he has a positive reason for it, andnot on account of the Cartesian maxim. Let us notpretend to doubt in philosophy what we do not doubtin our hearts.

2. The same formalism appears in the Cartesian

92

criterion, which amounts to this: " Whatever I amclearly convinced of, is true." If I were reallyconvinced, I should have done with reasoning andshould require no test of certainty. But then to makesingle individuals absolute judges of truth is mostpernicious. The result is that metaphysics hasreached a pitch of certainty far beyond that of thephysical sciences;only they can agree upon nothingelse. In sciences in which men come to agreement,when a theory

93

has been broached it is considered to be on probationuntil this agreement is reached. After it is reached,the question of certainty becomes an idle one,because there is no one left who doubts it. Weindividually cannot reasonably hope to attain theultimate philosophy which we pursue; we can onlyseek it, therefore, for the community of philosophers.Hence, if disciplined and candid minds carefullyexamine a theory and refuse to accept it, this oughtto create doubts in the mind of the author of thetheory himself.

3. Philosophy ought to imitate the successful sciencesin its methods, so far as to proceed only from tangiblepremises which can be subjected to careful scrutiny,and to trust rather to the multitude and variety of itsarguments than to the conclusiveness of any one. Itsreasoning should not form a chain which is nostronger than its weakest link, but a cable whosefibers may be ever so slender, provided they aresufficiently numerous and intimately connected.

4. Every unidealistic philosophy supposes someabsolutely inexplicable, unanalyzable ultimate; inshort, something resulting from mediation itself not

94

susceptible of mediation. Now that anything is thusinexplicable, can only be known by reasoning fromsigns. But the only justification of an inference fromsigns is that the conclusion explains the fact. Tosuppose the fact absolutely inexplicable, is not toexplain it, and hence this supposition is neverallowable.

95

PART ICHANCE AND LOGIC (ILLUSTRATIONS OFTHE LOGIC OF SCIENCE)

96

First Paper:The Fixation of Belief1

I

Few persons care to study logic, because everybodyconceives himself to be proficient enough in the art ofreasoning already. But I observe that this satisfactionis limited to one's own ratiocination, and does notextend to that of other men.

We come to the full possession of our power ofdrawing inferences the last of all our faculties, for it isnot so much a natural gift as a long and difficult art.The history of its practice would make a grandsubject for a book. The medieval schoolman,following the Romans, made logic the earliest of aboy's studies after grammar, as being very easy. So itwas as they understood it. Its fundamental principle,according to them, was, that all knowledge rests oneither authority or reason; but that whatever isdeduced by reason depends ultimately on a premisederived from authority. Accordingly, as soon as a boy

97

was perfect in the syllogistic procedure, hisintellectual kit of tools was held to be complete.

1Popular Science Monthly, November, 1877.

98

To Roger Bacon, that remarkable mind who in themiddle of the thirteenth century was almost ascientific man, the schoolmen's conception ofreasoning appeared only an obstacle to truth. He sawthat experience alone teaches anythinga propositionwhich to us seems easy to understand, because adistinct conception of experience has been handeddown to us from former generations; which to himalso seemed perfectly clear, because its difficultieshad not yet unfolded themselves. Of all kinds ofexperience, the best, he thought, was interiorillumination, which teaches many things about Naturewhich the external senses could never discover, suchas the transubstantiation of bread.

Four centuries later, the more celebrated Bacon, inthe first book of his " Novum Organum," gave hisclear account of experience as something which mustbe open to verification and reëxamination. But,superior as Lord Bacon's conception is to earliernotions, a modern reader who is not in awe of hisgrandiloquence is chiefly struck by the inadequacy ofhis view of scientific procedure. That we have only tomake some crude experiments, to draw up briefs of

99

the results in certain blank forms, to go throughthese by rule, checking off everything disproved andsetting down the alternatives, and that thus in a fewyears physical science would be finished upwhat anidea! " He wrote on science like a Lord Chancellor," 2indeed.

The early scientists, Copernicus, Tycho, Brahe,Kepler, Galileo and Gilbert, had methods more likethose of their modern brethren. Kepler undertook todraw a curve

2 [This is substantially the dictum of Harvey to JohnAubrey. See the latter's Brief Lives (Oxford ed. 1898) I299].

100

through the places of Mars;3 and his greatest serviceto science was in impressing on men's minds that thiswas the thing to be done if they wished to improveastronomy; that they were not to content themselveswith inquiring whether one system of epicycles wasbetter than another but that they were to sit down bythe figures and find out what the curve, in truth,was. He accomplished this by his incomparableenergy and courage, blundering along in the mostinconceivable way (to us), from one irrationalhypothesis to another, until, after trying twenty-twoof these, he fell, by the mere exhaustion of hisinvention, upon the orbit which a mind well furnishedwith the weapons of modern logic would have triedalmost at the outset.4

In the same way, every work of science great enoughto be remembered for a few generations affords someexemplification of the defective state of the art ofreasoning of the time when it was written; and eachchief step in science has been a lesson in logic. Itwas so when Lavoisier and his contemporaries tookup the study of Chemistry. The old chemist's maximhad been, "Lege, lege, lege, labora, ora, et relege."

101

Lavoisier's method was not to read and pray, not todream that some long and complicated chemicalprocess would have a certain effect, to put it intopractice with dull patience, after its inevitable failureto dream that with some modification it would haveanother result, and to end by publishing the lastdream as a fact: his way was to carry his mind intohis laboratory, and to make of his alembics andcucurbits instruments of thought,

3 Not quite so, but as nearly so as can be told in a fewwords.4 [This modern logic, however, is largely the outcome ofKepler's work.]

102

giving a new conception of reasoning as somethingwhich was to be done with one's eyes open, bymanipulating real things instead of words andfancies.

The Darwinian controversy is, in large part, aquestion of logic. Mr. Darwin proposed to apply thestatistical method to biology. The same thing hasbeen done in a widely different branch of science, thetheory of gases. Though unable to say what themovement of any particular molecule of gas would beon a certain hypothesis regarding the constitution ofthis class of bodies, Clausius and Maxwell were yetable, by the application of the doctrine ofprobabilities, to predict that in the long run such andsuch a proportion of the molecules would, undergiven circumstances, acquire such and suchvelocities; that there would take place, every second,such and such a number of collisions, etc.; and fromthese propositions they were able to deduce certainproperties of gases, especially in regard to their heat-relations. In like manner, Darwin, while unable to saywhat the operation of variation and natural selectionin every individual case will be, demonstrates that in

103

the long run they will adapt animals to theircircumstances. Whether or not existing animal formsare due to such action, or what position the theoryought to take, forms the subject of a discussion inwhich questions of fact and questions of logic arecuriously interlaced.

II

The object of reasoning is to find out, from theconsideration of what we already know, somethingelse which we do

104

not know. Consequently, reasoning is good if it besuch as to give a true conclusion from true premises,and not otherwise. Thus, the question of validity ispurely one of fact and not of thinking. A being thepremises and B being the conclusion, the question is,whether these facts are really so related that if A is Bis. If so, the inference is valid; if not, not. It is not inthe least the question whether, when the premisesare accepted by the mind, we feel an impulse toaccept the conclusion also. It is true that we dogenerally reason correctly by nature. But that is anaccident; the true conclusion would remain true if wehad no impulse to accept it; and the false one wouldremain false, though we could not resist the tendencyto believe in it.

We are, doubtless, in the main logical animals, butwe are not perfectly so. Most of us, for example, arenaturally more sanguine and hopeful than logic wouldjustify. We seem to be so constituted that in theabsence of any facts to go upon we are happy andself-satisfied; so that the effect of experience iscontinually to counteract our hopes and aspirations.Yet a lifetime of the application of this corrective does

105

not usually eradicate our sanguine disposition. Wherehope is unchecked by any experience, it is likely thatour optimism is extravagant. Logicality in regard topractical matters is the most useful quality an animalcan possess, and might, therefore, result from theaction of natural selection; but outside of these it isprobably of more advantage to the animal to have hismind filled with pleasing and encouraging visions,independently of their truth; and thus, uponunpractical subjects, natural

106

selection might occasion a fallacious tendency ofthought.

That which determines us, from given premises, todraw one inference rather than another, is somehabit of mind, whether it be constitutional oracquired. The habit is good or otherwise, accordingas it produces true conclusions from true premises ornot; and an inference is regarded as valid or not,without reference to the truth or falsity of itsconclusion specially, but according as the habit whichdetermines it is such as to produce true conclusionsin general or not. The particular habit of mind whichgoverns this or that inference may be formulated in aproposition whose truth depends on the validity ofthe inferences which the habit determines; and sucha formula is called a guiding principle of inference.Suppose, for example, that we observe that arotating disk of copper quickly comes to rest whenplaced between the poles of a magnet, and we inferthat this will happen with every disk of copper. Theguiding principle is, that what is true of one piece ofcopper is true of another. Such a guiding principlewith regard to copper would be much safer than with

107

regard to many other substancesbrass, for example.

A book might be written to signalize all the mostimportant of these guiding principles of reasoning. Itwould probably be, we must confess, of no service toa person whose thought is directed wholly to practicalsubjects, and whose activity moves along thoroughlybeaten paths. The problems which presentthemselves to such a mind are matters of routinewhich he has learned once for all to handle inlearning his business. But let a man venture into anunfamiliar field, or where his results are notcontinually

108

checked by experience, and all history shows that themost masculine intellect will ofttimes lose hisorientation and waste his efforts in directions whichbring him no nearer to his goal, or even carry himentirely astray. He is like a ship on the open sea, withno one on board who understands the rules ofnavigation. And in such a case some general study ofthe guiding principles of reasoning would be sure tobe found useful.

The subject could hardly be treated, however,without being first limited; since almost any fact mayserve as a guiding principle. But it so happens thatthere exists a division among facts, such that in oneclass are all those which are absolutely essential asguiding principles, while in the other are all thosewhich have any other interest as objects of research.This division is between those which are necessarilytaken for granted in asking whether a certainconclusion follows from certain premises, and thosewhich are not implied in that question. A moment'sthought will show that a variety of facts are alreadyassumed when the logical question is first asked. It isimplied, for instance, that there are such states of

109

mind as doubt and beliefthat a passage from one tothe other is possible, the object of thought remainingthe same, and that this transition is subject to somerules which all minds are alike bound by. As these arefacts which we must already know before we canhave any clear conception of reasoning at all, itcannot be supposed to be any longer of muchinterest to inquire into their truth or falsity. On theother hand, it is easy to believe that those rules ofreasoning which are deduced from the very idea ofthe process are the ones

110

which are the most essential; and, indeed, that solong as it conforms to these it will, at least, not leadto false conclusions from true premises. In point offact, the importance of what may be deduced fromthe assumptions involved in the logical question turnsout to be greater than might be supposed, and thisfor reasons which it is difficult to exhibit at the outset.The only one which I shall here mention is, thatconceptions which are really products of logicalreflections, without being readily seen to be so,mingle with our ordinary thoughts, and are frequentlythe causes of great confusion. This is the case, forexample, with the conception of quality. A quality assuch is never an object of observation. We can seethat a thing is blue or green, but the quality of beingblue and the quality of being green are not thingswhich we see; they are products of logical reflections.The truth is, that common-sense, or thought as it firstemerges above the level of the narrowly practical, isdeeply imbued with that bad logical quality to whichthe epithet metaphysical is commonly applied; andnothing can clear it up but a severe course of logic.

III

111

We generally know when we wish to ask a questionand when we wish to pronounce a judgment, forthere is a dissimilarity between the sensation ofdoubting and that of believing.

But this is not all which distinguishes doubt frombelief. There is a practical difference. Our beliefsguide our desires and shape our actions. TheAssassins, or followers

112

of the Old Man of the Mountain, used to rush intodeath at his least command, because they believedthat obedience to him would insure everlastingfelicity. Had they doubted this, they would not haveacted as they did. So it is with every belief, accordingto its degree. The feeling of believing is a more or lesssure indication of there being established in ournature some habit which will determine our actions.Doubt never has such an effect.

Nor must we overlook a third point of difference.Doubt is an uneasy and dissatisfied state from whichwe struggle to free ourselves and pass into the stateof belief; while the latter is a calm and satisfactorystate which we do not wish to avoid, or to change toa belief in anything else.5 On the contrary, we clingtenaciously, not merely to believing, but to believingjust what we do believe.

Thus, both doubt and belief have positive effectsupon us, though very different ones. Belief does notmake us act at once, but puts us into such acondition that we shall behave in a certain way, whenthe occasion arises. Doubt has not the least effect ofthis sort, but stimulates us to action until it is

113

destroyed. This reminds us of the irritation of a nerveand the reflex action produced thereby; while for theanalogue of belief, in the nervous system, we mustlook to what are called nervous associationsforexample, to that habit of the nerves in consequenceof which the smell of a peach will make the mouthwater.

5 I am not speaking of secondary effects occasionallyproduced by the interference of other impulses.

114

IV

The irritation of doubt causes a struggle to attain astate of belief. I shall term this struggle inquiry,though it must be admitted that this is sometimes nota very apt designation.

The irritation of doubt is the only immediate motivefor the struggle to attain belief. It is certainly best forus that our beliefs should be such as may truly guideour actions so as to satisfy our desires; and thisreflection will make us reject any belief which doesnot seem to have been so formed as to insure thisresult. But it will only do so by creating a doubt in theplace of that belief. With the doubt, therefore, thestruggle begins, and with the cessation of doubt itends. Hence, the sole object of inquiry is thesettlement of opinion. We may fancy that this is notenough for us, and that we seek not merely anopinion, but a true opinion. But put this fancy to thetest, and it proves groundless; for as soon as a firmbelief is reached we are entirely satisfied, whetherthe belief be false or true. And it is clear that nothingout of the sphere of our knowledge can be ourobject, for nothing which does not affect the mind

115

can be a motive for a mental effort. The most thatcan be maintained is, that we seek for a belief thatwe shall think to be true. But we think each one ofour beliefs to be true, and, indeed, it is meretautology to say so.

That the settlement of opinion is the sole end ofinquiry is a very important proposition. It sweepsaway, at once, various vague and erroneousconceptions of proof. A few of these may be noticedhere.

116

1. Some philosophers have imagined that to start aninquiry it was only necessary to utter or question orset it down on paper, and have even recommendedus to begin our studies with questioning everything!But the mere putting of a proposition into theinterrogative form does not stimulate the mind to anystruggle after belief. There must be a real and livingdoubt, and without all this discussion is idle.

2. It is a very common idea that a demonstrationmust rest on some ultimate and absolutelyindubitable propositions. These, according to oneschool, are first principles of a general nature;according to another, are first sensations. But, inpoint of fact, an inquiry, to have that completelysatisfactory result called demonstration, has only tostart with propositions perfectly free from all actualdoubt. If the premises are not in fact doubted at all,they cannot be more satisfactory than they are.

3. Some people seem to love to argue a point after allthe world is fully convinced of it. But no furtheradvance can be made. When doubt ceases, mentalaction on the subject comes to an end; and, if it didgo on, it would be without a purpose.

117

V

If the settlement of opinion is the sole object ofinquiry, and if belief is of the nature of a habit, whyshould we not attain the desired end, by taking anyanswer to a question, which we may fancy, andconstantly reiterating it to ourselves, dwelling on allwhich may conduce to that belief,

118

and learning to turn with contempt and hatred fromanything which might disturb it? This simple anddirect method is really pursued by many men. Iremember once being entreated not to read a certainnewspaper lest it might change my opinion uponfree-trade. ''Lest I might be entrapped by its fallaciesand misstatements," was the form of expression."You are not," my friend said, "a special student ofpolitical economy. You might, therefore, easily bedeceived by fallacious arguments upon the subject.You might, then, if you read this paper, be led tobelieve in protection. But you admit that free-trade isthe true doctrine; and you do not wish to believewhat is not true." I have often known this system tobe deliberately adopted. Still oftener, the instinctivedislike of an undecided state of mind, exaggeratedinto a vague dread of doubt, makes men clingspasmodically to the views they already take. Theman feels that, if he only holds to his belief withoutwavering, it will be entirely satisfactory. Nor can it bedenied that a steady and immovable faith yields greatpeace of mind. It may, indeed, give rise toinconveniences, as if a man should resolutelycontinue to believe that fire would not burn him, or

119

that he would be eternally damned if he received hisingesta otherwise than through a stomach-pump. Butthen the man who adopts this method will not allowthat its inconveniences are greater than itsadvantages. He will say, " I hold steadfastly to thetruth and the truth is always wholesome." And inmany cases it may very well be that the pleasure hederives from his calm faith overbalances anyinconveniences resulting from its deceptive character.Thus, if it be true that death is annihila-

120

tion, then the man who believes that he will certainlygo straight to heaven when he dies, provided he havefulfilled certain simple observances in this life, has acheap pleasure which will not be followed by the leastdisappointment. A similar consideration seems tohave weight with many persons in religious topics, forwe frequently hear it said, " Oh, I could not believeso-and-so, because I should be wretched if I did."When an ostrich buries its head in the sand asdanger approaches, it very likely takes the happiestcourse. It hides the danger, and then calmly saysthere is no danger; and, if it feels perfectly sure thereis none, why should it raise its head to see? A manmay go through life, systematically keeping out ofview all that might cause a change in his opinions,and if he only succeedsbasing his method, as hedoes, on two fundamental psychological lawsI do notsee what can be said against his doing so. It wouldbe an egotistical impertinence to object that hisprocedure is irrational, for that only amounts tosaying that his method of settling belief is not ours.He does not propose to himself to be rational, andindeed, will often talk with scorn of man's weak andillusive reason. So let him think as he pleases.

121

But this method of fixing belief, which may be calledthe method of tenacity, will be unable to hold itsground in practice. The social impulse is against it.The man who adopts it will find that other men thinkdifferently from him, and it will be apt to occur to himin some saner moment that their opinions are quiteas good as his own, and this will shake his confidencein his belief. This conception, that another man'sthought or sentiment may be equivalent

122

to one's own, is a distinctly new step, and a highlyimportant one. It arises from an impulse too strong inman to be suppressed, without danger of destroyingthe human species. Unless we make ourselveshermits, we shall necessarily influence each other'sopinions; so that the problem becomes how to fixbelief, not in the individual merely, but in thecommunity.

Let the will of the state act, then, instead of that ofthe individual. Let an institution be created whichshall have for its object to keep correct doctrinesbefore the attention of the people, to reiterate themperpetually, and to teach them to the young; havingat the same time power to prevent contrary doctrinesfrom being taught, advocated, or expressed. Let allpossible causes of a change of mind be removed frommen's apprehensions. Let them be kept ignorant, lestthey should learn of some reason to think otherwisethan they do. Let their passions be enlisted, so thatthey may regard private and unusual opinions withhatred and horror. Then, let all men who reject theestablished belief be terrified into silence. Let thepeople turn out and tar-and-feather such men, or let

123

inquisitions be made into the manner of thinking ofsuspected persons, and, when they are found guiltyof forbidden beliefs, let them be subjected to somesignal punishment. When complete agreement couldnot otherwise be reached, a general massacre of allwho have not thought in a certain way has proved avery effective means of settling opinion in a country.If the power to do this be wanting, let a list ofopinions be drawn up, to which no man of the leastindependence of thought can assent, and let thefaithful be re-

124

quired to accept all these propositions, in order tosegregate them as radically as possible from theinfluence of the rest of the world.

This method has, from the earliest times, been one ofthe chief means of upholding correct theological andpolitical doctrines, and of preserving their universal orcatholic character. In Rome, especially, it has beenpracticed from the days of Numa Pompilius to thoseof Pius Nonus. This is the most perfect example inhistory; but wherever there is a priesthoodand noreligion has been without one this method has beenmore or less made use of. Wherever there isaristocracy, or a guild, or any association of a class ofmen whose interests depend or are supposed todepend on certain propositions, there will beinevitably found some traces of this natural productof social feeling. Cruelties always accompany thissystem; and when it is consistently carried out, theybecome atrocities of the most horrible kind in theeyes of any rational man. Nor should this occasionsurprise, for the officer of a society does not feeljustified in surrendering the interests of that societyfor the sake of mercy, as he might his own private

125

interests. It is natural, therefore, that sympathy andfellowship should thus produce a most ruthlesspower.

In judging this method of fixing belief, which may becalled the method of authority, we must in the firstplace, allow its immeasurable mental and moralsuperiority to the method of tenacity. Its success isproportionally greater; and in fact it has over andover again worked the most majestic results. Themere structures of stone which it has caused to beput togetherin Siam, for example,

126

in Egypt, and in Europehave many of them asublimity hardly more than rivaled by the greatestworks of Nature. And, except the geological epochs,there are no periods of time so vast as those whichare measured by some of these organized faiths. Ifwe scrutinize the matter closely, we shall find thatthere has not been one of their creeds which hasremained always the same; yet the change is so slowas to be imperceptible during one person's life, sothat individual belief remains sensibly fixed. For themass of mankind, then, there is perhaps no bettermethod than this. If it is their highest impulse to beintellectual slaves, then slaves they ought to remain.

But no institution can undertake to regulate opinionsupon every subject. Only the most important onescan be attended to, and on the rest men's mindsmust be left to the action of natural causes. Thisimperfection will be no source of weakness so long asmen are in such a state of culture that one opiniondoes not influence anotherthat is, so long as theycannot put two and two together. But in the mostpriest-ridden states some individuals will be foundwho are raised above that condition. These men

127

possess a wider sort of social feeling; they see thatmen in other countries and in other ages have held tovery different doctrines from those which theythemselves have been brought up to believe; andthey cannot help seeing that it is the mere accidentof their having been taught as they have, and of theirhaving been surrounded with the manners andassociations they have, that has caused them tobelieve as they do and not far differently. And theircandor cannot resist the reflection that there is noreason to rate their

128

own views at a higher value than those of othernations and other centuries; and this gives rise todoubts in their minds.

They will further perceive that such doubts as thesemust exist in their minds with reference to everybelief which seems to be determined by the capriceeither of themselves or of those who originated thepopular opinions. The willful adherence to a belief,and the arbitrary forcing of it upon others, must,therefore, both be given up and a new method ofsettling opinions must be adopted, which shall notonly produce an impulse to believe, but shall alsodecide what proposition it is which is to be believed.Let the action of natural preferences be unimpeded,then, and under their influence let men conversingtogether and regarding matters in different lights,gradually develop beliefs in harmony with naturalcauses. This method resembles that by whichconceptions of art have been brought to maturity.The most perfect example of it is to be found in thehistory of metaphysical philosophy. Systems of thissort have not usually rested upon observed facts, atleast not in any great degree. They have been chiefly

129

adopted because their fundamental propositionsseemed " agreeable to reason." This is an aptexpression; it does not mean that which agrees withexperience, but that which we find ourselves inclinedto believe. Plato, for example, finds it agreeable toreason that the distances of the celestial spheresfrom one another should be proportional to thedifferent lengths of strings which produce harmoniouschords. Many philosophers have been led to theirmain conclusions by considerations like this; but thisis the lowest and least

130

developed form which the method takes, for it is clearthat another man might find Kepler's [earlier] theory,that the celestial spheres are proportional to theinscribed and circumscribed spheres of the differentregular solids, more agreeable to his reason. But theshock of opinions will soon lead men to rest onpreferences of a far more universal nature. Take, forexample, the doctrine that man only acts selfishlythatis, from the consideration that acting in one way willafford him more pleasure than acting in another. Thisrests on no fact in the world, but it has had a wideacceptance as being the only reasonable theory.

This method is far more intellectual and respectablefrom the point of view of reason than either of theothers which we have noticed. But its failure hasbeen the most manifest. It makes of inquirysomething similar to the development of taste; buttaste, unfortunately, is always more or less a matterof fashion, and accordingly, metaphysicians havenever come to any fixed agreement, but thependulum has swung backward and forward betweena more material and a more spiritual philosophy, fromthe earliest times to the latest. And so from this,

131

which has been called the a priori method, we aredriven, in Lord Bacon's phrase, to a true induction.We have examined into this a priori method assomething which promised to deliver our opinionsfrom their accidental and capricious element. Butdevelopment, while it is a process which eliminatesthe effect of some casual circumstances, onlymagnifies that of others. This method, therefore,does not differ in a very essential way from that ofauthority. The government may not have lifted itsfinger to influence my

132

convictions; I may have been left outwardly quite freeto choose, we will say, between monogamy andpolygamy, and appealing to my conscience only, Imay have concluded that the latter practice is in itselflicentious. But when I come to see that the chiefobstacle to the spread of Christianity among a peopleof as high culture as the Hindoos has been aconviction of the immorality of our way of treatingwomen, I cannot help seeing that, thoughgovernments do not interfere, sentiments in theirdevelopment will be very greatly determined byaccidental causes. Now, there are some people,among whom I must suppose that my reader is to befound, who, when they see that any belief of theirs isdetermined by any circumstance extraneous to thefacts, will from that moment not merely admit inwords that that belief is doubtful, but will experiencea real doubt of it, so that it ceases to be a belief.

To satisfy our doubts, therefore, it is necessary that amethod should be found by which our beliefs may becaused by nothing human, but by some externalpermanencyby something upon which our thinkinghas no effect. Some mystics imagine that they have

133

such a method in a private inspiration from on high.But that is only a form of the method of tenacity, inwhich the conception of truth as something public isnot yet developed. Our external permanency wouldnot be external, in our sense, if it was restricted in itsinfluence to one individual. It must be somethingwhich affects, or might affect, every man. And,though these affections are necessarily as various asare individual conditions, yet the method must besuch that the ultimate conclusion of every man shallbe the same.

134

Such is the method of science. Its fundamentalhypothesis, restated in more familiar language, isthis: There are real things, whose characters areentirely independent of our opinions about them;whose realities affect our senses according to regularlaws, and, though our sensations are as different asour relations to the objects, yet, by taking advantageof the laws of perception, we can ascertain byreasoning how things really are, and any man, if hehave sufficient experience and reason enough aboutit, will be led to the one true conclusion. The newconception here involved is that of reality. It may beasked how I know that there are any realities. If thishypothesis is the sole support of my method ofinquiry, my method of inquiry must not be used tosupport my hypothesis. The reply is this: I. Ifinvestigation cannot be regarded as proving thatthere are real things, it at least does not lead to acontrary conclusion; but the method and theconception on which it is based remain ever inharmony. No doubts of the method, therefore,necessarily arise from its practice, as is the case withall the others. 2. The feeling which gives rise to anymethod of fixing belief is a dissatisfaction at two

135

repugnant propositions. But here already is a vagueconcession that there is some one thing to which aproposition should conform. Nobody, therefore, canreally doubt that there are realities, or, if he did,doubt would not be a source of dissatisfaction. Thehypothesis, therefore, is one which every mindadmits. So that the social impulse does not cause meto doubt it. 3. Everybody uses the scientific methodabout a great many things, and only ceases to use itwhen he does not know how to apply it. 4.Experience of the

136

method has not led me to doubt it, but, on thecontrary, scientific investigation has had the mostwonderful triumphs in the way of settling opinion.These afford the explanation of my not doubting themethod or the hypothesis which it supposes; and nothaving any doubt, nor believing that anybody elsewhom I could influence has, it would be the merestbabble for me to say more about it. If there beanybody with a living doubt upon the subject, let himconsider it.

To describe the method of scientific investigation isthe object of this series of papers. At present I haveonly room to notice some points of contrast betweenit and other methods of fixing belief.

This is the only one of the four methods whichpresents any distinction of a right and a wrong way.If I adopt the method of tenacity and shut myself outfrom all influences, whatever I think necessary todoing this is necessary according to that method. Sowith the method of authority: the state may try toput down heresy by means which, from a scientificpoint of view, seems very ill-calculated to accomplishits purposes; but the only test on that method is

137

what the state thinks, so that it cannot pursue themethod wrongly. So with the a priori method. Thevery essence of it is to think as one is inclined tothink. All metaphysicians will be sure to do that,however they may be inclined to judge each other tobe perversely wrong. The Hegelian system recognizesevery natural tendency of thought as logical,although it is certain to be abolished bycountertendencies. Hegel thinks there is a regularsystem in the succession of these tendencies, inconsequence of which,

138

after drifting one way and the other for a long time,opinion will at last go right. And it is true thatmetaphysicians get the right ideas at last; Hegel'ssystem of Nature represents tolerably the science ofthat day; and one may be sure that whateverscientific investigation has put out of doubt willpresently receive a priori demonstration on the part ofthe metaphysicians. But with the scientific methodthe case is different. I may start with known andobserved facts to proceed to the unknown; and yetthe rules which I follow in doing so may not be suchas investigation would approve. The test of whether Iam truly following the method is not an immediateappeal to my feelings and purposes, but, on thecontrary, itself involves the application of the method.Hence it is that bad reasoning as well as goodreasoning is possible; and this fact is the foundationof the practical side of logic.

It is not to be supposed that the first three methodsof settling opinion present no advantage whateverover the scientific method. On the contrary, each hassome peculiar convenience of its own. The a priorimethod is distinguished for its comfortable

139

conclusions. It is the nature of the process to adoptwhatever belief we are inclined to, and there arecertain flatteries to one's vanities which we all believeby nature, until we are awakened from our pleasingdream by rough facts. The method of authority willalways govern the mass of mankind; and those whowield the various forms of organized force in the statewill never be convinced that dangerous reasoningought not to be suppressed in some way. If liberty ofspeech is to be untrammeled from the grosser formsof constraint, then uni-

140

formity of opinion will be secured by a moral terrorismto which the respectability of society will give itsthorough approval. Following the method of authorityis the path of peace. Certain non-conformities arepermitted; certain others (considered unsafe) areforbidden. These are different in different countriesand in different ages; but, wherever you are let it beknown that you seriously hold a tabooed belief, andyou may be perfectly sure of being treated with acruelty no less brutal but more refined than huntingyou like a wolf. Thus, the greatest intellectualbenefactors of mankind have never dared, and darenot now, to utter the whole of their thought; andthus a shade of prima facie doubt is cast upon everyproposition which is considered essential to thesecurity of society. Singularly enough, thepersecution does not all come from without; but aman torments himself and is oftentimes mostdistressed at finding himself believing propositionswhich he has been brought up to regard withaversion. The peaceful and sympathetic man will,therefore, find it hard to resist the temptation tosubmit his opinions to authority. But most of all Iadmire the method of tenacity for its strength,

141

simplicity, and directness. Men who pursue it aredistinguished for their decision of character, whichbecomes very easy with such a mental rule. They donot waste time in trying to make up their minds towhat they want, but, fastening like lightning uponwhatever alternative comes first, they hold to it to theend, whatever happens, without an instant'sirresolution. This is one of the splendid qualities whichgenerally accompany brilliant, unlasting success. It isimpossible not to envy the man who

142

can dismiss reason, although we know how it mustturn out at last.

Such are the advantages which the other methods ofsettling opinions have over scientific investigation. Aman should consider well of them; and then heshould consider that, after all, he wishes his opinionsto coincide with the fact, and that there is no reasonwhy the results of these three methods should do so.To bring about this effect is the prerogative of themethod of science. Upon such considerations he hasto make his choice a choice which is far more thanthe adoption of any intellectual opinion, which is oneof the ruling decisions of his life, to which when oncemade he is bound to adhere. The force of habit willsometimes cause a man to hold on to old beliefs,after he is in a condition to see that they have nosound basis. But reflection upon the state of the casewill overcome these habits, and he ought to allowreflection full weight. People sometimes shrink fromdoing this, having an idea that beliefs are wholesomewhich they cannot help feeling rest on nothing. Butlet such persons suppose an analogous thoughdifferent case from their own. Let them ask

143

themselves what they would say to a reformedMussulman who should hesitate to give up his oldnotions in regard to the relations of the sexes; or to areformed Catholic who should still shrink from theBible. Would they not say that these persons oughtto consider the matter fully, and clearly understandthe new doctrine, and then ought to embrace it in itsentirety? But, above all, let it be considered that whatis more wholesome than any particular belief, isintegrity of belief; and that to avoid looking into thesupport

144

of any belief from a fear that it may turn out rotten isquite as immoral as it is disadvantageous. The personwho confesses that there is such a thing as truth,which is distinguished from falsehood simply by this,that if acted on it will carry us to the point we aim atand not astray, and then though convinced of this,dares not know the truth and seeks to avoid it, is in asorry state of mind, indeed.

Yes, the other methods do have their merits: a clearlogical conscience does cost somethingjust as anyvirtue, just as all that we cherish, costs us dear. But,we should not desire it to be otherwise. The genius ofa man's logical method should be loved andreverenced as his bride, whom he has chosen from allthe world. He need not condemn the others; on thecontrary, he may honor them deeply, and in doing sohe only honors her the more. But she is the one thathe has chosen, and he knows that he was right inmaking that choice. And having made it, he will workand fight for her, and will not complain that there areblows to take, hoping that there may be as many andas hard to give, and will strive to be the worthyknight and champion of her from the blaze of whose

145

splendors he draws his inspiration and his courage.

146

Second Paper:How to Make Our Ideas Clear1

I

Whoever has looked into a modern treatise on logic ofthe common sort, will doubtless remember the twodistinctions between clear and obscure conceptions,and between distinct and confused conceptions. Theyhave lain in the books now for nigh two centuries,unimproved and unmodified, and are generallyreckoned by logicians as among the gems of theirdoctrine.

A clear idea is defined as one which is soapprehended that it will be recognized wherever it ismet with, and so that no other will be mistaken for it.If it fails of this clearness, it is said to be obscure.

This is rather a neat bit of philosophical terminology;yet, since it is clearness that they were defining, Iwish the logicians had made their definition a littlemore plain. Never to fail to recognize an idea, andunder no circumstances to mistake another for it, let

147

it come in how recondite a form it may, would indeedimply such prodigious force and clearness of intellectas is seldom met with in this world. On the otherhand, merely to have such an acquaintance with theidea as to have become familiar with it, and to havelost all hesitancy in recognizing it in ordinary

1Popular Science Monthly, January, 1878.

148

cases, hardly seems to deserve the name of clearnessof apprehension, since after all it only amounts to asubjective feeling of mastery which may be entirelymistaken. I take it, however, that when the logiciansspeak of ''clearness," they mean nothing more thansuch a familiarity with an idea, since they regard thequality as but a small merit, which needs to besupplemented by another, which they calldistinctness.

A distinct idea is defined as one which containsnothing which is not clear. This is technical language;by the contents of an idea logicians understandwhatever is contained in its definition. So that an ideais distinctly apprehended, according to them, whenwe can give a precise definition of it, in abstractterms. Here the professional logicians leave thesubject; and I would not have troubled the readerwith what they have to say, if it were not such astriking example of how they have been slumberingthrough ages of intellectual activity, listlesslydisregarding the enginery of modern thought, andnever dreaming of applying its lessons to theimprovement of logic. It is easy to show that the

149

doctrine that familiar use and abstract distinctnessmake the perfection of apprehension, has its onlytrue place in philosophies which have long beenextinct; and it is now time to formulate the method ofattaining to a more perfect clearness of thought, suchas we see and admire in the thinkers of our own time.

When Descartes set about the reconstruction ofphilosophy, his first step was to (theoretically) permitskepticism and to discard the practice of theschoolmen of looking to authority as the ultimatesource of truth. That done, he

150

sought a more natural fountain of true principles, andprofessed to find it in the human mind; thus passing,in the directest way, from the method of authority tothat of apriority, as described in my first paper. Self-consciousness was to furnish us with our fundamentaltruths, and to decide what was agreeable to reason.But since, evidently, not all ideas are true, he was ledto note, as the first condition of infallibility, that theymust be clear. The distinction between an ideaseeming clear and really being so, never occurred tohim. Trusting to introspection, as he did, even for aknowledge of external things, why should he questionits testimony in respect to the contents of our ownminds? But then, I suppose, seeing men, whoseemed to be quite clear and positive, holdingopposite opinions upon fundamental principles, hewas further led to say that clearness of ideas is notsufficient, but that they need also to be distinct, i.e.,to have nothing unclear about them. What heprobably meant by this (for he did not explain himselfwith precision) was, that they must sustain the testof dialectical examination; that they must not onlyseem clear at the outset, but that discussion mustnever be able to bring to light points of obscurity

151

connected with them.

Such was the distinction of Descartes, and one seesthat it was precisely on the level of his philosophy. Itwas somewhat developed by Leibnitz. This great andsingular genius was as remarkable for what he failedto see as for what he saw. That a piece of mechanismcould not do work perpetually without being fed withpower in some form, was a thing perfectly apparentto him; yet he did not understand that the machineryof the mind can only trans-

152

form knowledge, but never originate it, unless it befed with facts of observation. He thus missed themost essential point of the Cartesian philosophy,which is, that to accept propositions which seemperfectly evident to us is a thing which, whether it belogical or illogical, we cannot help doing. Instead ofregarding the matter in this way, he sought to reducethe first principles of science to formulas whichcannot be denied without self-contradiction, and wasapparently unaware of the great difference betweenhis position and that of Descartes. So he reverted tothe old formalities of logic, and, above all, abstractdefinitions played a great part in his philosophy. Itwas quite natural, therefore, that on observing thatthe method of Descartes labored under the difficultythat we may seem to ourselves to have clearapprehensions of ideas which in truth are very hazy,no better remedy occurred to him than to require anabstract definition of every important term.Accordingly, in adopting the distinction of clear anddistinct notions, he described the latter quality as theclear apprehension of everything contained in thedefinition; and the books have ever since copied hiswords. There is no danger that his chimerical scheme

153

will ever again be over-valued. Nothing new can everbe learned by analyzing definitions. Nevertheless, ourexisting beliefs can be set in order by this process,and order is an essential element of intellectualeconomy, as of every other. It may be acknowledged,therefore, that the books are right in makingfamiliarity with a notion the first step towardclearness of apprehension, and the defining of it thesecond. But in omitting all mention of any higherperspicuity of thought, they

154

simply mirror a philosophy which was exploded ahundred years ago. That much-admired " ornamentof logic "the doctrine of clearness anddistinctnessmay be pretty enough, but it is high timeto relegate to our cabinet of curiosities the antiquebijou, and to wear about us something betteradapted to modern uses.

The very first lesson that we have a right to demandthat logic shall teach us is, how to make our ideasclear; and a most important one it is, depreciatedonly by minds who stand in need of it. To know whatwe think, to be masters of our own meaning, willmake a solid foundation for great and weightythought. It is most easily learned by those whoseideas are meagre and restricted; and far happier theythan such as wallow helplessly in a rich mud ofconceptions. A nation, it is true, may, in the course ofgenerations, overcome the disadvantage of anexcessive wealth of language and its naturalconcomitant, a vast, unfathomable deep of ideas. Wemay see it in history, slowly perfecting its literaryforms, sloughing at length its metaphysics, and, byvirtue of the untirable patience which is often a

155

compensation, attaining great excellence in everybranch of mental acquirement. The page of history isnot yet unrolled which is to tell us whether such apeople will or will not in the long run prevail over onewhose ideas (like the words of their language) arefew, but which possesses a wonderful mastery overthose which it has. For an individual, however, therecan be no question that a few clear ideas are worthmore than many confused ones. A young man wouldhardly be persuaded to sacrifice the greater part ofhis thoughts to save the rest; and the

156

muddled head is the least apt to see the necessity ofsuch a sacrifice. Him we can usually onlycommiserate, as a person with a congenital defect.Time will help him, but intellectual maturity withregard to clearness comes rather late, an unfortunatearrangement of Nature, inasmuch as clearness is ofless use to a man settled in life, whose errors have ingreat measure had their effect, than it would be toone whose path lies before him. It is terrible to seehow a single unclear idea, a single formula withoutmeaning, lurking in a young man's head, willsometimes act like an obstruction of inert matter inan artery, hindering the nutrition of the brain, andcondemning its victim to pine away in the fullness ofhis intellectual vigor and in the midst of intellectualplenty. Many a man has cherished for years as hishobby some vague shadow of an idea, toomeaningless to be positively false; he has,nevertheless, passionately loved it, has made it hiscompanion by day and by night, and has given to ithis strength and his life, leaving all other occupationsfor its sake, and in short has lived with it and for it,until it has become, as it were, flesh of his flesh andbone of his bone; and then he has waked up some

157

bright morning to find it gone, clean vanished awaylike the beautiful Melusina of the fable, and theessence of his life gone with it. I have myself knownsuch a man; and who can tell how many histories ofcircle-squarers, metaphysicians, astrologers, andwhat not, may not be told in the old German story?

158

II

The principles set forth in the first of these paperslead, at once, to a method of reaching a clearness ofthought of a far higher grade than the " distinctness "of the logicians. We have there found that the actionof thought is excited by the irritation of doubt, andceases when belief is attained; so that the productionof belief is the sole function of thought. All thesewords, however, are too strong for my purpose. It isas if I had described the phenomena as they appearunder a mental microscope. Doubt and Belief, as thewords are commonly employed, relate to religious orother grave discussions. But here I use them todesignate the starting of any question, no matterhow small or how great, and the resolution of it. If,for instance, in a horse-car, I pull out my purse andfind a fivecent nickel and five coppers, I decide, whilemy hand is going to the purse, in which way I willpay my fare. To call such a question Doubt, and mydecision Belief, is certainly to use words verydisproportionate to the occasion. To speak of such adoubt as causing an irritation which needs to beappeased, suggests a temper which is uncomfortable

159

to the verge of insanity. Yet, looking at the matterminutely, it must be admitted that, if there is theleast hesitation as to whether I shall pay the fivecoppers or the nickel (as there will be sure to be,unless I act from some previously contracted habit inthe matter), though irritation is too strong a word,yet I am excited to such small mental activity as maybe necessary to deciding how I shall act. Mostfrequently doubts arise from some indecision,however

160

momentary, in our action. Sometimes it is not so. Ihave, for example, to wait in a railway-station, and topass the time I read the advertisements on the walls,I compare the advantages of different trains anddifferent routes which I never expect to take, merelyfancying myself to be in a state of hesitancy, becauseI am bored with having nothing to trouble me.Feigned hesitancy, whether feigned for mereamusement or with a lofty purpose, plays a great partin the production of scientific inquiry. However thedoubt may originate, it stimulates the mind to anactivity which may be slight or energetic, calm orturbulent. Images pass rapidly throughconsciousness, one incessantly melting into another,until at last, when all is overit may be in a fraction ofa second, in an hour, or after long yearswe findourselves decided as to how we should act undersuch circumstances as those which occasioned ourhesitation. In other words, we have attained belief.

In this process we observe two sorts of elements ofconsciousness, the distinction between which maybest be made clear by means of an illustration. In apiece of music there are the separate notes, and

161

there is the air. A single tone may be prolonged foran hour or a day, and it exists as perfectly in eachsecond of that time as in the whole taken together;so that, as long as it is sounding, it might be presentto a sense from which everything in the past was ascompletely absent as the future itself. But it isdifferent with the air, the performance of whichoccupies a certain time, during the portions of whichonly portions of it are played. It consists in anorderliness in the succession of sounds which strikethe ear at different times; and to per-

162

ceive it there must be some continuity ofconsciousness which makes the events of a lapse oftime present to us. We certainly only perceive the airby hearing the separate notes; yet we cannot be saidto directly hear it, for we hear only what is present atthe instant, and an orderliness of succession cannotexist in an instant. These two sorts of objects, whatwe are immediately conscious of and what we aremediately conscious of, are found in allconsciousness. Some elements (the sensations) arecompletely present at every instant so long as theylast, while others (like thought) are actions havingbeginning, middle, and end, and consist in acongruence in the succession of sensations whichflow through the mind. They cannot be immediatelypresent to us, but must cover some portion of thepast or future. Thought is a thread of melody runningthrough the succession of our sensations.

We may add that just as a piece of music may bewritten in parts, each part having its own air, sovarious systems of relationship of succession subsisttogether between the same sensations. Thesedifferent systems are distinguished by having

163

different motives, ideas, or functions. Thought is onlyone such system; for its sole motive, idea, andfunction is to produce belief, and whatever does notconcern that purpose belongs to some other systemof relations. The action of thinking may incidentallyhave other results. It may serve to amuse us, forexample, and among dilettanti it is not rare to findthose who have so perverted thought to the purposesof pleasure that it seems to vex them to think thatthe questions upon which they delight to exercise itmay ever get finally settled; and a positive discovery

164

which takes a favorite subject out of the arena ofliterary debate is met with ill-concealed dislike. Thisdisposition is the very debauchery of thought. But thesoul and meaning of thought, abstracted from theother elements which accompany it, though it may bevoluntarily thwarted, can never be made to directitself toward anything but the production of belief.Thought in action has for its only possible motive theattainment of thought at rest; and whatever does notrefer to belief is no part of the thought itself.

And what, then, is belief? It is the demi-cadencewhich closes a musical phrase in the symphony of ourintellectual life. We have seen that it has just threeproperties: First, it is something that we are aware of;second, it appeases the irritation of doubt; and, third,it involves the establishment in our nature of a rule ofaction, or, say for short, a habit. As it appeases theirritation of doubt, which is the motive for thinking,thought relaxes, and comes to rest for a momentwhen belief is reached. But. since belief is a rule foraction, the application of which involves further doubtand further thought, at the same time that it is astopping-place, it is also a new starting-place for

165

thought. That is why I have permitted myself to call itthought at rest, although thought is essentially anaction. The final upshot of thinking is the exercise ofvolition, and of this thought no longer forms a part;but belief is only a stadium of mental action, an effectupon our nature due to thought, which will influencefuture thinking.

The essence of belief is the establishment of a habit,and different beliefs are distinguished by the differentmodes of action to which they give rise. If beliefs donot differ

166

in this respect, if they appease the same doubt byproducing the same rule of action, then no meredifferences in the manner of consciousness of themcan make them different beliefs, any more thanplaying a tune in different keys is playing differenttunes. Imaginary distinctions are often drawnbetween beliefs which differ only in their mode ofexpression;the wrangling which ensues is realenough, however. To believe that any objects arearranged as in Fig. I, and to believe that they arearranged as in Fig. 2, are

Fig. 1

167

Fig. 2

one and the same belief; yet it is conceivable that aman should assert one proposition and deny theother. Such false distinctions do as much harm as theconfusion of beliefs really different, and are amongthe pitfalls of which we ought constantly to beware,especially when we are upon metaphysical ground.One singular deception of this sort, which oftenoccurs, is to mistake the sensation produced by ourown unclearness of thought for a character of theobject we are thinking. Instead of perceiving that theobscurity is purely subjective, we fancy that wecontem-

168

plate a quality of the object which is essentiallymysterious; and if our conception be afterwardpresented to us in a clear form we do not recognize itas the same, owing to the absence of the feeling ofunintelligibility. So long as this deception lasts, itobviously puts an impassable barrier in the way ofperspicuous thinking; so that it equally interests theopponents of rational thought to perpetuate it, andits adherents to guard against it.

Another such deception is to mistake a meredifference in the grammatical construction of twowords for a distinction between the ideas theyexpress. In this pedantic age, when the general mobof writers attend so much more to words than tothings, this error is common enough. When I just saidthat thought is an action, and that it consists in arelation, although a person performs an action butnot a relation, which can only be the result of anaction, yet there was no inconsistency in what I said,but only a grammatical vagueness.

From all these sophisms we shall be perfectly safe solong as we reflect that the whole function of thoughtis to produce habits of action; and that whatever

169

there is connected with a thought, but irrelevant toits purpose, is an accretion to it, but no part of it. Ifthere be a unity among our sensations which has noreference to how we shall act on a given occasion, aswhen we listen to a piece of music, why we do notcall that thinking. To develop its meaning, we have,therefore, simply to determine what habits itproduces, for what a thing means is simply whathabits it involves. Now, the identity of a habitdepends on how it might lead us to act, not merelyunder such circumstances

170

as are likely to arise, but under such as mightpossibly occur, no matter how improbable they maybe. What the habit is depends on when and how itcauses us to act. As for the when, every stimulus toaction is derived from perception; as for the how,every purpose of action is to produce some sensibleresult. Thus, we come down to what is tangible andpractical, as the root of every real distinction ofthought, no matter how subtile it may be; and thereis no distinction of meaning so fine as to consist inanything but a possible difference of practice.

To see what this principle leads to, consider in thelight of it such a doctrine as that oftransubstantiation. The Protestant churches generallyhold that the elements of the sacrament are flesh andblood only in a tropical sense; they nourish our soulsas meat and the juice of it would our bodies. But theCatholics maintain that they are literally just that;although they possess all the sensible qualities ofwafer-cakes and diluted wine. But we can have noconception of wine except what may enter into abelief, either

1. That this, that, or the other, is wine; or,

171

2. That wine possesses certain properties.

Such beliefs are nothing but self-notifications that weshould, upon occasion, act in regard to such thingsas we believe to be wine according to the qualitieswhich we believe wine to possess. The occasion ofsuch action would be some sensible perception, themotive of it to produce some sensible result. Thus ouraction has exclusive reference to what affects thesenses, our habit has the same bearing as our action,our belief the same as our habit, our

172

conception the same as our belief; and we canconsequently mean nothing by wine but what hascertain effects, direct or indirect, upon our senses;and to talk of something as having all the sensiblecharacters of wine, yet being in reality blood, issenseless jargon. Now, it is not my object to pursuethe theological question; and having used it as alogical example I drop it, without caring to anticipatethe theologian's reply. I only desire to point out howimpossible it is that we should have an idea in ourminds which relates to anything but conceivedsensible effects of things. Our idea of anything is ouridea of its sensible effects; and if we fancy that wehave any other we deceive ourselves, and mistake amere sensation accompanying the thought for a partof the thought itself. It is absurd to say that thoughthas any meaning unrelated to its only function. It isfoolish for Catholics and Protestants to fancythemselves in disagreement about the elements ofthe sacrament, if they agree in regard to all theirsensible effects, here or hereafter.

It appears, then, that the rule for attaining the thirdgrade of clearness of apprehension is as follows:

173

Consider what effects, which might conceivably havepractical bearings, we conceive the object of ourconception to have. Then, our conception of theseeffects is the whole of our conception of the object.

III

Let us illustrate this rule by some examples; and, tobegin with the simplest one possible, let us ask whatwe mean by calling a thing hard. Evidently that it willnot

174

be scratched by many other substances. The wholeconception of this quality, as of every other, lies in itsconceived effects. There is absolutely no differencebetween a hard thing and a soft thing so long as theyare not brought to the test. Suppose, then, that adiamond could be crystallized in the midst of acushion of soft cotton, and should remain there untilit was finally burned up. Would it be false to say thatthat diamond was soft? This seems a foolish question,and would be so, in fact, except in the realm of logic.There such questions are often of the greatest utilityas serving to bring logical principles into sharper reliefthan real discussions ever could. In studying logic wemust not put them aside with hasty answers, butmust consider them with attentive care, in order tomake out the principles involved. We may, in thepresent case, modify our question, and ask whatprevents us from saying that all hard bodies remainperfectly soft until they are touched, when theirhardness increases with the pressure until they arescratched. Reflection will show that the reply is this:there would be no falsity in such modes of speech.They would involve a modification of our presentusage of speech with regard to the words hard and

175

soft, but not of their meanings. For they represent nofact to be different from what it is; only they involvearrangements of facts which would be exceedinglymaladroit. This leads us to remark that the questionof what would occur under circumstances which donot actually arise is not a question of fact, but only ofthe most perspicuous arrangement of them. Forexample, the question of free-will and fate in itssimplest form, stripped of verbiage, is something

176

like this: I have done something of which I amashamed; could I, by an effort of the will, haveresisted the temptation, and done otherwise? Thephilosophical reply is, that this is not a question offact, but only of the arrangement of facts. Arrangingthem so as to exhibit what is particularly pertinent tomy questionnamely, that I ought to blame myself forhaving done wrongit is perfectly true to say that, if Ihad willed to do otherwise than I did, I should havedone otherwise. On the other hand, arranging thefacts so as to exhibit another important consideration,it is equally true that, when a temptation has oncebeen allowed to work, it will, if it has a certain force,produce its effect, let me struggle how I may. Thereis no objection to a contradiction in what would resultfrom a false supposition. The reductio ad absurdumconsists in showing that contradictory results wouldfollow from a hypothesis which is consequentlyjudged to be false. Many questions are involved inthe free-will discussion, and I am far from desiring tosay that both sides are equally right. On the contrary,I am of opinion that one side denies important facts,and that the other does not. But what I do say is,that the above single question was the origin of the

177

whole doubt; that, had it not been for this question,the controversy would never have arisen; and thatthis question is perfectly solved in the manner whichI have indicated.

Let us next seek a clear idea of Weight. This isanother very easy case. To say that a body is heavymeans simply that, in the absence of opposing force,it will fall. This (neglecting certain specifications ofhow it will fall, etc., which exist in the mind of thephysicist who uses the word)

178

is evidently the whole conception of weight. It is afair question whether some particular facts may notaccount for gravity; but what we mean by the forceitself is completely involved in its effects.

This leads us to undertake an account of the idea ofForce in general. This is the great conception which,developed in the early part of the seventeenthcentury from the rude idea of a cause, and constantlyimproved upon since, has shown us how to explain allthe changes of motion which bodies experience, andhow to think about all physical phenomena; whichhas given birth to modern science, and changed theface of the globe; and which, aside from its morespecial uses, has played a principal part in directingthe course of modern thought, and in furtheringmodern social development. It is, therefore, worthsome pains to comprehend it. According to our rule,we must begin by asking what is the immediate useof thinking about force; and the answer is, that wethus account for changes of motion. If bodies wereleft to themselves, without the intervention of forces,every motion would continue unchanged both invelocity and in direction. Furthermore, change of

179

motion never takes place abruptly; if its direction ischanged, it is always through a curve without angles;if its velocity alters, it is by degrees. The gradualchanges which are constantly taking place areconceived by geometers to be compounded togetheraccording to the rules of the parallelogram of forces.If the reader does not already know what this is, hewill find it, I hope, to his advantage to endeavor tofollow the following explanation; but if mathematicsare

180

insupportable to him, pray let him skip threeparagraphs rather than that we should part companyhere.

A path is a line whose beginning and end aredistinguished. Two paths are considered to beequivalent, which, beginning at the same point, leadto the same point. Thus the two paths, A B C D Eand A F G H E (Fig. 3), are equivalent. Paths whichdo not begin at the same point are considered to beequivalent, provided that, on moving either of themwithout turning it, but keeping it always parallel to itsoriginal position, [so that] when its beginningcoincides with that of the other path, the ends alsocoincide. Paths are considered as geometricallyadded together, when one begins where the otherends; thus the path A E is conceived to be a sum of AB, B C, C D, and D E. In the parallelogram of Fig. 4the diagonal A C is the sum of A B and B C; or, sinceA D is geometrically equivalent to B C, A C is thegeometrical sum of A B and A D.

181

Fig. 3

Fig. 4

All this is purely conventional. It simply amounts tothis: that we choose to call paths having the relationsI have described equal or added. But, though it is aconvention, it is a convention with a good reason.The rule for geometrical addition may be applied notonly to paths, but to any other things which can berepresented by paths. Now, as a path is determinedby the varying direction and

182

distance of the point which moves over it from thestarting-point, it follows that anything which from itsbeginning to its end is determined by a varyingdirection and a varying magnitude is capable of beingrepresented by a line. Accordingly, velocities may berepresented by lines, for they have only directionsand rates. The same thing is true of accelerations, orchanges of velocities. This is evident enough in thecase of velocities; and it becomes evident foraccelerations if we consider that precisely whatvelocities are to positionsnamely, states of change ofthemthat accelerations are to velocities.

The so-called ''parallelogram of forces" is simply a rulefor compounding accelerations. The rule is, torepresent the accelerations by paths, and then togeometrically add the paths. The geometers,however, not only use the "parallelogram of forces" tocompound different accelerations, but also to resolveone acceleration into a sum of several. Let A B (Fig.5) be the path

183

Fig. 5

which represents a certain accelerationsay, such achange in the motion of a body that at the end ofone second the body will, under the influence of thatchange, be in a position different from what it

would have had if its motion had continuedunchanged, such that a path equivalent to A B wouldlead from the latter position to the former. Thisacceleration may be considered as the sum of theaccelerations represented by A C and C B.

184

It may also be considered as the sum of the verydifferent accelerations represented by A D and D B,where A D is almost the opposite of A C. And it isclear that there is an immense variety of ways inwhich A B might be resolved into the sum of twoaccelerations.

After this tedious explanation, which I hope, in viewof the extraordinary interest of the conception offorce, may not have exhausted the reader's patience,we are prepared at last to state the grand fact whichthis conception embodies. This fact is that if theactual changes of motion which the different particlesof bodies experience are each resolved in itsappropriate way, each component acceleration isprecisely such as is prescribed by a certain law ofNature, according to which bodies in the relativepositions which the bodies in question actually haveat the moment,2 always receive certain accelerations,which, being compounded by geometrical addition,give the acceleration which the body actuallyexperiences.

This is the only fact which the idea of forcerepresents, and whoever will take the trouble clearly

185

to apprehend what this fact is, perfectlycomprehends what force is. Whether we ought to saythat a force is an acceleration, or that it causes anacceleration, is a mere question of propriety oflanguage, which has no more to do with our realmeaning than the difference between the Frenchidiom "II fait froid " and its English equivalent "It iscold." Yet it is surprising to see how this simple affairhas muddled men's minds. In how many profoundtreatises is not force spoken of as a "mysteriousentity," which seems to be

2 Possibly the velocities also have to be taken intoaccount.

186

only a way of confessing that the author despairs ofever getting a clear notion of what the word means!In a recent admired work on Analytic Mechanics it isstated that we understand precisely the effect offorce, but what force itself is we do not understand!This is simply a self-contradiction. The idea which theword force excites in our minds has no other functionthan to affect our actions, and these actions can haveno reference to force otherwise than through itseffects. Consequently, if we know what the effects offorce are, we are acquainted with every fact which isimplied in saying that a force exists, and there isnothing more to know. The truth is, there is somevague notion afloat that a question may meansomething which the mind cannot conceive; andwhen some hair-splitting philosophers have beenconfronted with the absurdity of such a view, theyhave invented an empty distinction between positiveand negative conceptions, in the attempt to give theirnon-idea a form not obviously nonsensical. The nullityof it is sufficiently plain from the considerations givena few pages back; and, apart from thoseconsiderations, the quibbling character of thedistinction must have struck every mind accustomed

187

to real thinking.

IV

Let us now approach the subject of logic, andconsider a conception which particularly concerns it,that of reality. Taking clearness in the sense offamiliarity, no idea could be clearer than this. Everychild uses it with perfect confidence, never dreamingthat he does not understand it.

188

As for clearness in its second grade, however, itwould probably puzzle most men, even among thoseof a reflective turn of mind, to give an abstractdefinition of the real. Yet such a definition mayperhaps be reached by considering the points ofdifference between reality and its opposite, fiction. Afigment is a product of somebody's imagination; ithas such characters as his thought impresses upon it.That those characters are independent of how you orI think is an external reality. There are, however,phenomena within our own minds, dependent uponour thought, which are at the same time real in thesense that we really think them. But though theircharacters depend on how we think, they do notdepend on what we think those characters to be.Thus, a dream has a real existence as a mentalphenomenon, if somebody has really dreamt it; thathe dreamt so and so, does not depend on whatanybody thinks was dreamt, but is completelyindependent of all opinion on the subject. On theother hand, considering, not the fact of dreaming,but the thing dreamt, it retains its peculiarities byvirtue of no other fact than that it was dreamt topossess them. Thus we may define the real as that

189

whose characters are independent of what anybodymay think them to be.

But, however satisfactory such a definition may befound, it would be a great mistake to suppose that itmakes the idea of reality perfectly clear. Here, then,let us apply our rules. According to them, reality, likeevery other quality, consists in the peculiar sensibleeffects which things partaking of it produce. The onlyeffect which real things have is to cause belief, for allthe sensations which they

190

excite emerge into consciousness in the form ofbeliefs. The question, therefore, is, how is true belief(or belief in the real) distinguished from false belief(or belief in fiction). Now, as we have seen in theformer paper, the ideas of truth and falsehood, intheir full development, appertain exclusively to thescientific method of settling opinion. A person whoarbitrarily chooses the propositions which he willadopt can use the word truth only to emphasize theexpression of his determination to hold on to hischoice. Of course, the method of tenacity neverprevailed exclusively; reason is too natural to men forthat. But in the literature of the dark ages we findsome fine examples of it. When Scotus Erigena iscommenting upon a poetical passage in whichhellebore is spoken of as having caused the death ofSocrates, he does not hesitate to inform the inquiringreader that Helleborus and Socrates were twoeminent Greek philosophers, and that the latterhaving been overcome in argument by the formertook the matter to heart and died of it! What sort ofan idea of truth could a man have who could adoptand teach, without the qualification of a perhaps, anopinion taken so entirely at random? The real spirit of

191

Socrates, who I hope would have been delighted tohave been "overcome in argument," because hewould have learned something by it, is in curiouscontrast with the naive idea of the glossist, for whomdiscussion would seem to have been simply astruggle. When philosophy began to awake from itslong slumber, and before theology completelydominated it, the practice seems to have been foreach professor to seize upon any philosophicalposition he found unoccupied and which seemed a

192

strong one, to intrench himself in it, and to sally forthfrom time to time to give battle to the others. Thus,even the scanty records we possess of those disputesenable us to make out a dozen or more opinions heldby different teachers at one time concerning thequestion of nominalism and realism. Read theopening part of the Historia Calamitatum of Abelard,who was certainly as philosophical as any of hiscontemporaries, and see the spirit of combat which itbreathes. For him, the truth is simply his particularstronghold. When the method of authority prevailed,the truth meant little more than the Catholic faith. Allthe efforts of the scholastic doctors are directedtoward harmonizing their faith in Aristotle and theirfaith in the Church, and one may search theirponderous folios through without finding anargument which goes any further. It is noticeablethat where different faiths flourish side by side,renegades are looked upon with contempt even bythe party whose belief they adopt; so completely hasthe idea of loyalty replaced that of truth-seeking.Since the time of Descartes, the defect in theconception of truth has been less apparent. Still, itwill sometimes strike a scientific man that the

193

philosophers have been less intent on finding outwhat the facts are, than on inquiring what belief ismost in harmony with their system. It is hard toconvince a follower of the a priori method byadducing facts; but show him that an opinion he isdefending is inconsistent with what he has laid downelsewhere, and he will be very apt to retract it. Theseminds do not seem to believe that disputation is everto cease; they seem to think that the opinion which isnatural for one man is not so for another,

194

and that belief will, consequently, never be settled.In contenting themselves with fixing their ownopinions by a method which would lead another manto a different result, they betray their feeble hold ofthe conception of what truth is.

On the other hand, all the followers of science arefully persuaded that the processes of investigation, ifonly pushed far enough, will give one certain solutionto every question to which they can be applied. Oneman may investigate the velocity of light by studyingthe transits of Venus and the aberration of the stars;another by the oppositions of Mars and the eclipsesof Jupiter's satellites; a third by the method of Fizeau;a fourth by that of Foucault; a fifth by the motions ofthe curves of Lissajoux; a sixth, a seventh, an eighth,and a ninth, may follow the different methods ofcomparing the measures of statical and dynamicalelectricity. They may at first obtain different results,but, as each perfects his method and his processes,the results will move steadily together toward adestined center. So with all scientific research.Different minds may set out with the mostantagonistic views, but the progress of investigation

195

carries them by a force outside of themselves to oneand the same conclusion. This activity of thought bywhich we are carried, not where we wish, but to aforeordained goal, is like the operation of destiny. Nomodification of the point of view taken, no selectionof other facts for study, no natural bent of mind even,can enable a man to escape the predestinate opinion.This great law is embodied in the conception of truthand reality. The

196

opinion which is fated 8 to be ultimately agreed to byall who investigate, is what we mean by the truth,and the object represented in this opinion is the real.That is the way I would explain reality.

But it may be said that this view is directly opposedto the abstract definition which we have given ofreality, inasmuch as it makes the characters of thereal depend on what is ultimately thought aboutthem. But the answer to this is that, on the onehand, reality is independent, not necessarily ofthought in general, but only of what you or I or anyfinite number of men may think about it; and that, onthe other hand, though the object of the final opiniondepends on what that opinion is, yet what thatopinion is does not depend on what you or I or anyman thinks. Our perversity and that of others mayindefinitely postpone the settlement of opinion; itmight even conceivably cause an arbitrary propositionto be universally accepted as long as the human raceshould last. Yet even that would not change thenature of the belief, which alone could be the resultof investigation carried sufficiently far; and if, afterthe extinction of our race, another should arise with

197

faculties and disposition for investigation, that trueopinion must be the one which they would ultimatelycome to. " Truth crushed to earth shall rise again,"and the opinion which would finally result frominvestigation does not depend on how anybody mayactually think. But the reality of that which is realdoes depend on the real fact that investigation is

3 Fate means merely that which is sure to come true,and can nohow be avoided. It is a superstition tosuppose that a certain sort of events are ever fated,and it is another to suppose that the word fate cannever be freed from its superstitious taint. We are allfated to die.

198

destined to lead, at last, if continued long enough, toa belief in it.

But I may be asked what I have to say to all theminute facts of history, forgotten never to berecovered, to the lost books of the ancients, to theburied secrets.

"Full many a gem of purest ray serene The dark, unfathomed caves of ocean bear;Full many a flower is born to blush unseen, And waste its sweetness on the desert air."

Do these things not really exist because they arehopelessly beyond the reach of our knowledge? Andthen, after the universe is dead (according to theprediction of some scientists), and all life has ceasedforever, will not the shock of atoms continue thoughthere will be no mind to know it? To this I reply that,though in no possible state of knowledge can anynumber be great enough to express the relationbetween the amount of what rests unknown to theamount of the known, yet it is unphilosophical tosuppose that, with regard to any given question(which has any clear meaning), investigation wouldnot bring forth a solution of it, if it were carried far

199

enough. Who would have said, a few years ago, thatwe could ever know of what substances stars aremade whose light may have been longer in reachingus than the human race has existed? Who can besure of what we shall not know in a few hundredyears? Who can guess what would be the result ofcontinuing the pursuit of science for ten thousandyears, with the activity of the last hundred? And if itwere to go on for a million, or a billion, or any numberof years you please, how is it

200

possible to say that there is any question which mightnot ultimately be solved?

But it may be objected, "Why make so much of theseremote considerations, especially when it is yourprinciple that only practical distinctions have ameaning? " Well, I must confess that it makes verylittle difference whether we say that a stone on thebottom of the ocean, in complete darkness, is brilliantor notthat is to say, that it probably makes nodifference, remembering always that that stone maybe fished up to-morrow. But that there are gems atthe bottom of the sea, flowers in the untraveleddesert, etc., are propositions which, like that about adiamond being hard when it is not pressed, concernmuch more the arrangement of our language thanthey do the meaning of our ideas.

It seems to me, however, that we have, by theapplication of our rule, reached so clear anapprehension of what we mean by reality, and of thefact which the idea rests on, that we should not,perhaps, be making a pretension so presumptuous asit would be singular, if we were to offer ametaphysical theory of existence for universal

201

acceptance among those who employ the scientificmethod of fixing belief. However, as metaphysics is asubject much more curious than useful, theknowledge of which, like that of a sunken reef, serveschiefly to enable us to keep clear of it, I will nottrouble the reader with any more Ontology at thismoment. I have already been led much further intothat path than I should have desired; and I havegiven the reader such a dose of mathematics,psychology, and all that is most abstruse, that I fearhe may already have left me, and that what I amnow writing is for the compositor

202

and proofreader exclusively. I trusted to theimportance of the subject. There is no royal road tologic, and really valuable ideas can only be had at theprice of close attention. But I know that in the matterof ideas the public prefer the cheap and nasty; and inmy next paper I am going to return to the easilyintelligible, and not wander from it again. The readerwho has been at the pains of wading through thispaper, shall be rewarded in the next one by seeinghow beautifully what has been developed in thistedious way can be applied to the ascertainment ofthe rules of scientific reasoning.

We have, hitherto, not crossed the threshold ofscientific logic. It is certainly important to know howto make our ideas clear, but they may be ever soclear without being true. How to make them so, wehave next to study. How to give birth to those vitaland procreative ideas which multiply into a thousandforms and diffuse themselves everywhere, advancingcivilization and making the dignity of man, is an artnot yet reduced to rules, but of the secret of whichthe history of science affords some hints.

203

Third Paper:The Doctrine of Chances1

I

It is a common observation that a science first beginsto be exact when it is quantitatively treated. Whatare called the exact sciences are no others than themathematical ones. Chemists reasoned vaguely untilLavoisier showed them how to apply the balance tothe verification of their theories, when chemistryleaped suddenly into the position of the most perfectof the classificatory sciences. It has thus become soprecise and certain that we usually think of it alongwith optics, thermotics, and electrics. But these arestudies of general laws, while chemistry considersmerely the relations and classification of certainobjects; and belongs, in reality, in the same categoryas systematic botany and zoölogy. Compare it withthese last, however, and the advantage that itderives from its quantitative treatment is veryevident.

204

The rudest numerical scales, such as that by whichthe mineralogists distinguish the different degrees ofhardness, are found useful. The mere counting ofpistils and stamens sufficed to bring botany out oftotal chaos into some kind of form. It is not, however,so much from counting as from measuring, not somuch from the conception of

1 Popular Science Monthly, March, 1878.

205

number as from that of continuous quantity, that theadvantage of mathematical treatment comes.Number, after all, only serves to pin us down to aprecision in our thoughts which, however beneficial,can seldom lead to lofty conceptions, and frequentlydescends to pettiness. Of those two faculties of whichBacon speaks, that which marks differences and thatwhich notes resemblances, the employment ofnumber can only aid the lesser one; and theexcessive use of it must tend to narrow the powers ofthe mind. But the conception of continuous quantityhas a great office to fulfill, independently of anyattempt at precision. Far from tending to theexaggeration of differences, it is the direct instrumentof the finest generalizations. When a naturalist wishesto study a species, he collects a considerable numberof specimens more or less similar. In contemplatingthem, he observes certain ones which are more orless alike in some particular respect. They all have, forinstance, a certain S-shaped marking. He observesthat they are not precisely alike, in this respect; the Shas not precisely the same shape, but the differencesare such as to lead him to believe that forms could befound intermediate between any two of those he

206

possesses. He, now, finds other forms apparentlyquite dissimilarsay a marking in the form of a Candthe question is, whether he can find intermediateones which will connect these latter with the others.This he often succeeds in doing in cases where itwould at first be thought impossible; whereas, hesometimes finds those which differ, at first glance,much less, to be separated in Nature by the non-occurrence of intermediaries. In this way, he buildsup from the study of Nature a new gen-

207

eral conception of the character in question. Heobtains, for example, an idea of a leaf which includesevery part of the flower, and an idea of a vertebrawhich includes the skull. I surely need not say muchto show what a logical engine there is here. It is theessence of the method of the naturalist.2 How heapplies it first to one character, and then to another,and finally obtains a notion of a species of animals,the differences between whose members, howevergreat, are confined within limits, is a matter whichdoes not here concern us. The whole method ofclassification must be considered later; but, atpresent, I only desire to point out that it is by takingadvantage of the idea of continuity, or the passagefrom one form to another by insensible degrees, thatthe naturalist builds his conceptions. Now, thenaturalists are the great builders of conceptions;there is no other branch of science where so much ofthis work is done as in theirs; and we must, in greatmeasure, take them for our teachers in this importantpart of logic. And it will be found everywhere that theidea of continuity is a powerful aid to the formation oftrue and fruitful conceptions. By means of it, thegreatest differences are broken down and resolved

208

into differences of degree, and the incessantapplication of it is of the greatest value in broadeningour conceptions. I propose to make a great use ofthis idea in the present series of papers; and theparticular series of important fallacies, which, arisingfrom a neglect of it, have desolated philosophy, mustfurther on be closely studied.

2 [Later, pp. 170 ff. and 215 ff., it is shown thatcontinuity is also at the basis of mathematicalgeneralization. See also article on Synechism inBaldwin's Dictionary of Philosophy.]

209

At present, I simply call the reader's attention to theutility of this conception.

In studies of numbers, the idea of continuity is soindispensable, that it is perpetually introduced evenwhere there is no continuity in fact, as where we saythat there are in the United States 10.7 inhabitantsper square mile, or that in New York 14.72 personslive in the average house.3 Another example is thatlaw of the distribution of errors which Quetelet,Galton, and others, have applied with so muchsuccess to the study of biological and social matters.This application of continuity to cases where it doesnot really exist illustrates, also, another point whichwill hereafter demand a separate study, namely, thegreat utility which fictions sometimes have in science.

II

The theory of probabilities is simply the science oflogic quantitatively treated. There are twoconceivable certainties with reference to anyhypothesis, the certainty of its truth and the certaintyof its falsity. The numbers one and zero areappropriated, in this calculus, to marking these

210

extremes of knowledge; while fractions having valuesintermediate between them indicate, as we mayvaguely say, the degrees in which the evidence leanstoward one or the other. The general problem ofprobabilities is, from a given state

3 This mode of thought is so familiarly associated withall exact numerical consideration, that the phraseappropriate to it is imitated by shallow writers in orderto produce the appearance of exactitude where noneexists. Certain newspapers which affect a learned tonetalk of '' the average man," when they simply meanmost men, and have no idea of striking an average.

211

of facts, to determine the numerical probability of apossible fact. This is the same as to inquire howmuch the given facts are worth, considered asevidence to prove the possible fact. Thus the problemof probabilities is simply the general problem of logic.

Probability is a continuous quantity, so that greatadvantages may be expected from this mode ofstudying logic. Some writers have gone so far as tomaintain that, by means of the calculus of chances,every solid inference may be represented bylegitimate arithmetical operations upon the numbersgiven in the premises. If this be, indeed, true, thegreat problem of logic, how it is that the observationof one fact can give us knowledge of anotherindependent fact, is reduced to a mere question ofarithmetic. It seems proper to examine thispretension before undertaking any more reconditesolution of the paradox.

But, unfortunately, writers on probabilities are notagreed in regard to this result. This branch ofmathematics is the only one, I believe, in which goodwriters frequently get results entirely erroneous. Inelementary geometry the reasoning is frequently

212

fallacious, but erroneous conclusions are avoided; butit may be doubted if there is a single extensivetreatise on probabilities in existence which does notcontain solutions absolutely indefensible. This is partlyowing to the want of any regular method ofprocedure; for the subject involves too manysubtilties to make it easy to put its problems intoequations without such an aid. But, beyond this, thefundamental principles of its calculus are more or lessin dispute. In regard to that class of questions towhich it is chiefly applied for practical purposes, there

213

is comparatively little doubt; but in regard to othersto which it has been sought to extend it, opinion issomewhat unsettled.

This last class of difficulties can only be entirelyovercome by making the idea of probability perfectlyclear in our minds in the way set forth in our lastpaper.

III

To get a clear idea of what we mean by probability,we have to consider what real and sensible differencethere is between one degree of probability andanother.

The character of probability belongs primarily,without doubt, to certain inferences. Locke explains itas follows: After remarking that the mathematicianpositively knows that the sum of the three angles of atriangle is equal to two right angles because heapprehends the geometrical proof, he thus continues:" But another man who never took the pains toobserve the demonstration, hearing a mathematician,a man of credit, affirm the three angles of a triangleto be equal to two right ones, assents to it; i.e.,

214

receives it for true. In which case the foundation ofhis assent is the probability of the thing, the proofbeing such as, for the most part, carries truth with it;the man on whose testimony he receives it not beingwont to affirm anything contrary to, or besides hisknowledge, especially in matters of this kind." Thecelebrated Essay concerning Human Understandingcontains many passages which, like this one, makethe first steps in profound analyses which are notfurther developed. It was shown in the first of thesepapers

215

that the validity of an inference does not depend onany tendency of the mind to accept it, howeverstrong such tendency may be; but consists in the realfact that, when premises like those of the argumentin question are true, conclusions related to them likethat of this argument are also true. It was remarkedthat in a logical mind an argument is alwaysconceived as a member of a genus of arguments allconstructed in the same way, and such that, whentheir premises are real facts, their conclusions are soalso. If the argument is demonstrative, then this isalways so; if it is only probable, then it is for the mostpart so. As Locke says, the probable argument is "such as for the most part carries truth with it."

According to this, that real and sensible differencebetween one degree of probability and another, inwhich the meaning of the distinction lies, is that inthe frequent employment of two different modes ofinference, one will carry truth with it oftener than theother. It is evident that this is the only differencethere is in the existing fact. Having certain premises,a man draws a certain conclusion, and as far as thisinference alone is concerned the only possible

216

practical question is whether that conclusion is trueor not, and between existence and non-existencethere is no middle term. " Being only is and nothing isaltogether not," said Parmenides; and this is in strictaccordance with the analysis of the conception ofreality given in the last paper. For we found that thedistinction of reality and fiction depends on thesupposition that sufficient investigation would causeone opinion to be universally received and all othersto be rejected. That presupposition, involved in thevery con-

217

ceptions of reality and figment, involves a completesundering of the two. It is the heaven-and-hell ideain the domain of thought. But, in the long run, thereis a real fact which corresponds to the idea ofprobability, and it is that a given mode of inferencesometimes proves successful and sometimes not, andthat in a ratio ultimately fixed. As we go on drawinginference after inference of the given kind, during thefirst ten or hundred cases the ratio of successes maybe expected to show considerable fluctuations; butwhen we come into the thousands and millions, thesefluctuations become less and less; and if we continuelong enough, the ratio will approximate toward afixed limit. We may, therefore, define the probabilityof a mode of argument as the proportion of cases inwhich it carries truth with it.

The inference from the premise, A, to the conclusion,B, depends, as we have seen, on the guidingprinciple, that if a fact of the class A is true, a fact ofthe class B is true. The probability consists of thefraction whose numerator is the number of times inwhich both A and B are true, and whose denominatoris the total number of times in which A is true,

218

whether B is so or not. Instead of speaking of this asthe probability of the inference, there is not theslightest objection to calling it the probability that, ifA happens, B happens. But to speak of theprobability of the event B, without naming thecondition, really has no meaning at all. It is true thatwhen it is perfectly obvious what condition is meant,the ellipsis may be permitted. But we should avoidcontracting the habit of using language in this way(universal as the habit is), because it gives rise

219

to a vague way of thinking, as if the action ofcausation might either determine an event to happenor determine it not to happen, or leave it more or lessfree to happen or not, so as to give rise to aninherent chance in regard to its occurrence.4 It isquite clear to me that some of the worst and mostpersistent errors in the use of the doctrine of chanceshave arisen from this vicious mode of expression.5

IV

But there remains an important point to be clearedup. According to what has been said, the idea ofprobability essentially belongs to a kind of inferencewhich is repeated indefinitely. An individual inferencemust be either true or false, and can show no effectof probability; and, therefore, in reference to a singlecase considered in itself, probability can have nomeaning. Yet if a man had to choose betweendrawing a card from a pack containing twenty-fivered cards and a black one, or from a pack containingtwenty-five black cards and a red one, and if thedrawing of a red card were destined to transport himto eternal felicity, and that of a black one to consignhim to everlasting woe, it would be folly to deny that

220

he ought to prefer the pack containing the largerportion of red cards, although, from the nature of therisk, it could not be repeated. It is not easy toreconcile this with our analysis of the conception

4 Cf. pp. 179 ff. below.5 The conception of probability here set forth issubstantially that first developed by Mr. Venn, in his Logicof Chance. Of course, a vague apprehension of the ideahad always existed, but the problem was to make itperfectly clear, and to him belongs the credit of first doingthis.

221

of chance. But suppose he should choose the redpack, and should draw the wrong card, whatconsolation would he have? He might say that he hadacted in accordance with reason, but that would onlyshow that his reason was absolutely worthless. And ifhe should choose the right card, how could he regardit as anything but a happy accident? He could not saythat if he had drawn from the other pack, he mighthave drawn the wrong one, because an hypotheticalproposition such as, "if A, then B," means nothingwith reference to a single case. Truth consists in theexistence of a real fact corresponding to the trueproposition. Corresponding to the proposition," if A,then B," there may be the fact that whenever suchan event as A happens such an event as B happens.But in the case supposed, which has no parallel as faras this man is concerned, there would be no real factwhose existence could give any truth to thestatement that, if he had drawn from the other pack,he might have drawn a black card. Indeed, since thevalidity of an inference consists in the truth of thehypothetical proposition that if the premises be truethe conclusion will also be true, and since the onlyreal fact which can correspond to such a proposition

222

is that whenever the antecedent is true theconsequent is so also, it follows that there can be nosense in reasoning in an isolated case, at all.

These considerations appear, at first sight, to disposeof the difficulty mentioned. Yet the case of the otherside is not yet exhausted. Although probability willprobably manifest its effect in, say, a thousand risks,by a certain proportion between the numbers ofsuccesses and failures, yet this, as we have seen, isonly to say that it certainly will,

223

at length, do so. Now the number of risks, thenumber of probable inferences, which a man draws inhis whole life, is a finite one, and he cannot beabsolutely certain that the mean result will accordwith the probabilities at all. Taking all his riskscollectively, then, it cannot be certain that they willnot fail, and his case does not differ, except indegree, from the one last supposed. It is anindubitable result of the theory of probabilities thatevery gambler, if he continues long enough, mustultimately be ruined. Suppose he tries the martingale,which some believe infallible, and which is, as I aminformed, disallowed in the gamblinghouses. In thismethod of playing, he first bets say $1; if he loses ithe bets $2; if he loses that he bets $4; if he losesthat he bets $8; if he then gains he has lost 1 + 2 +4 = 7, and he has gained $1 more; and no matterhow many bets he loses, the first one he gains willmake him $1 richer than he was in the beginning. Inthat way, he will probably gain at first; but, at last,the time will come when the run of luck is so againsthim that he will not have money enough to double,and must, therefore, let his bet go. This will probablyhappen before he has won as much as he had in the

224

first place, so that this run against him will leave himpoorer than he began; some time or other it will besure to happen. It is true that there is always apossibility of his winning any sum the bank can pay,and we thus come upon a celebrated paradox that,though he is certain to be ruined, the value of hisexpectation calculated according to the usual rules(which omit this consideration) is large. But, whethera gambler plays in this way or any other, the samething is true, namely, that if he plays long

225

enough he will be sure some time to have such a runagainst him as to exhaust his entire fortune. Thesame thing is true of an insurance company. Let thedirectors take the utmost pains to be independent ofgreat conflagrations and pestilences, their actuariescan tell them that, according to the doctrine ofchances, the time must come, at last, when theirlosses will bring them to a stop. They may tide oversuch a crisis by extraordinary means, but then theywill start again in a weakened state, and the samething will happen again all the sooner. An actuarymight be inclined to deny this, because he knowsthat the expectation of his company is large, orperhaps (neglecting the interest upon money) isinfinite. But calculations of expectations leave out ofaccount the circumstance now under consideration,which reverses the whole thing. However, I must notbe understood as saying that insurance is on thisaccount unsound, more than other kinds of business.All human affairs rest upon probabilities, and thesame thing is true everywhere. If man were immortalhe could be perfectly sure of seeing the day wheneverything in which he had trusted should betray histrust, and, in short, of coming eventually to hopeless

226

misery. He would break down, at last, as every goodfortune, as every dynasty, as every civilization does.In place of this we have death.

But what, without death, would happen to everyman, with death must happen to some man. At thesame time, death makes the number of our risks, ofour inferences, finite, and so makes their mean resultuncertain. The very idea of probability and ofreasoning rests on the assumption that this number isindefinitely great. We are thus landed

227

in the same difficulty as before, and I can see butone solution of it. It seems to me that we are drivento this, that logicality inexorably requires that ourinterests shall not be limited. They must not stop atour own fate, but must embrace the wholecommunity. This community, again, must not belimited, but must extend to all races of beings withwhom we can come into immediate or mediateintellectual relation. It must reach, however vaguely,beyond this geological epoch, beyond all bounds. Hewho would not sacrifice his own soul to save thewhole world, is, as it seems to me, illogical in all hisinferences, collectively. Logic is rooted in the socialprinciple.

To be logical men should not be selfish; and, in pointof fact, they are not so selfish as they are thought.The willful prosecution of one's desires is a differentthing from selfishness. The miser is not selfish; hismoney does him no good, and he cares for what shallbecome of it after his death. We are constantlyspeaking of our possessions on the Pacific, and of ourdestiny as a republic, where no personal interests areinvolved, in a way which shows that we have wider

228

ones. We discuss with anxiety the possible exhaustionof coal in some hundreds of years, or the cooling-offof the sun in some millions, and show in the mostpopular of all religious tenets that we can conceivethe possibility of a man's descending into hell for thesalvation of his fellows.

Now, it is not necessary for logicality that a manshould himself be capable of the heroism of self-sacrifice. It is sufficient that he should recognize thepossibility of it, should perceive that only that man'sinferences who has it are really logical, and shouldconsequently regard his own

229

as being only so far valid as they would be acceptedby the hero. So far as he thus refers his inferences tothat standard, he becomes identified with such amind.

This makes logicality attainable enough. Sometimeswe can personally attain to heroism. The soldier whoruns to scale a wall knows that he will probably beshot, but that is not all he cares for. He also knowsthat if all the regiment, with whom in feeling heidentifies himself, rush forward at once, the fort willbe taken. In other cases we can only imitate thevirtue. The man whom we have supposed as havingto draw from the two packs, who if he is not alogician will draw from the red pack from mere habit,will see, if he is logician enough, that he cannot belogical so long as he is concerned only with his ownfate, but that that man who should care equally forwhat was to happen in all possible cases of the sortcould act logically, and would draw from the packwith the most red cards, and thus, though incapablehimself of such sublimity, our logician would imitatethe effect of that man's courage in order to share hislogicality.

230

But all this requires a conceived identification of one'sinterests with those of an unlimited community. Now,there exist no reasons, and a later discussion willshow that there can be no reasons, for thinking thatthe human race, or any intellectual race, will existforever. On the other hand, there can be no reasonagainst it; 6 and, fortunately, as the wholerequirement is that we should have certain

6 I do not here admit an absolutely unknowable.Evidence could show us what would probably be thecase after any given lapse of time; and though asubsequent time might be assigned which thatevidence might not cover, yet further evidence wouldcover it.

231

sentiments, there is nothing in the facts to forbid ourhaving a hope, or calm and cheerful wish, that thecommunity may last beyond any assignable date.

It may seem strange that I should put forward threesentiments, namely, interest in an indefinitecommunity, recognition of the possibility of thisinterest being made supreme, and hope in theunlimited continuance of intellectual activity, asindispensable requirements of logic. Yet, when weconsider that logic depends on a mere struggle toescape doubt, which, as it terminates in action, mustbegin in emotion, and that, furthermore, the onlycause of our planting ourselves on reason is thatother methods of escaping doubt fail on account ofthe social impulse, why should we wonder to findsocial sentiment presupposed in reasoning? As for theother two sentiments which I find necessary, they areso only as supports and accessories of that. Itinterests me to notice that these three sentimentsseem to be pretty much the same as that famous trioof Charity, Faith, and Hope, which, in the estimationof St. Paul, are the finest and greatest of spiritualgifts. Neither Old nor New Testament is a textbook of

232

the logic of science, but the latter is certainly thehighest existing authority in regard to the dispositionsof heart which a man ought to have.

V

Such average statistical numbers as the number ofinhabitants per square mile, the average number ofdeaths per week, the number of convictions perindictment, or, generally speaking, the numbers of x'sper y, where the x's

233

are a class of things some or all of which areconnected with another class of things, their y's, Iterm relative numbers. Of the two classes of things towhich a relative number refers, that one of which it isa number may be called its relate, and that one perwhich the numeration is made may be called itscorrelate.

Probability is a kind of relative number; namely, it isthe ratio of the number of arguments of a certaingenus which carry truth with them to the totalnumber of arguments of that genus, and the rules forthe calculation of probabilities are very easily derivedfrom this consideration. They may all be given here,since they are extremely simple, and it is sometimesconvenient to know something of the elementaryrules of calculation of chances.

RULE I. Direct Calculation.To calculate, directly, anyrelative number, say for instance the number ofpassengers in the average trip of a street-car, wemust proceed as follows:

Count the number of passengers for each trip; add allthese numbers, and divide by the number of trips.

234

There are cases in which this rule may be simplified.Suppose we wish to know the number of inhabitantsto a dwelling in New York. The same person cannotinhabit two dwellings. If he divide his time betweentwo dwellings he ought to be counted a half-inhabitant of each. In this case we have only todivide the total number of the inhabitants of NewYork by the number of their dwellings, without thenecessity of counting separately those which inhabiteach one. A similar proceeding will apply wherevereach individual relate belongs to one individualcorrelate exclu-

235

sively. If we want the number of x's per y, and no xbelongs to more than one y, we have only to dividethe whole number of x's of y's by the number of y's.Such a method would, of course, fail if applied tofinding the average number of street-car passengersper trip. We could not divide the total number oftravelers by the number of trips, since many of themwould have made many passages.

To find the probability that from a given class ofpremises, A, a given class of conclusions, B, follow, itis simply necessary to ascertain what proportion ofthe times in which premises of that class are true, theappropriate conclusions are also true. In other words,it is the number of cases of the occurrence of boththe events A and B, divided by the total number ofcases of the occurrence of the event A.

RULE II. Addition of Relative Numbers.-Given tworelative numbers having the same correlate, say thenumber of x's per y, and the number of z's per y; it isrequired to find the number of x's and z's togetherper y. If there is nothing which is at once an x and az to the same y, the sum of the two given numbers

236

would give the required number. Suppose, forexample, that we had given the average number offriends that men have, and the average number ofenemies, the sum of these two is the average numberof persons interested in a man. On the other hand, itplainly would not do to add the average number ofpersons having constitutional diseases and overmilitary age, to the average number exempted byeach special cause from military service, in order toget the average number exempt in any way, sincemany are exempt in two or more ways at once.

237

This rule applies directly to probabilities, given theprobability that two different and mutually exclusiveevents will happen under the same supposed set ofcircumstances. Given, for instance, the probabilitythat if A then B, and also the probability that if Athen C, then the sum of these two probabilities is theprobability that if A then either B or C, so long asthere is no event which belongs at once to the twoclasses B and C.

RULE III. Multiplication of Relative Numbers.Supposethat we have given the relative number of x's per y;also the relative number of z's per x of y; or, to take aconcrete example, suppose that we have given, first,the average number of children in families living inNew York; and, second, the average number of teethin the head of a New York childthen the product ofthese two numbers would give the average numberof children's teeth in a New York family. But thismode of reckoning will only apply in general undertwo restrictions. In the first place, it would not betrue if the same child could belong to differentfamilies, for in that case those children who belonged

238

to several different families might have anexceptionally large or small number of teeth, whichwould affect the average number of children's teethin a family more than it would affect the averagenumber of teeth in a child's head. In the secondplace, the rule would not be true if different childrencould share the same teeth, the average number ofchildren's teeth being in that case evidentlysomething different from the average number ofteeth belonging to a child.

239

In order to apply this rule to probabilities, we mustproceed as follows: Suppose that we have given theprobability that the conclusion B follows from thepremise A, B and A representing as usual certainclasses of propositions. Suppose that we also knewthe probability of an inference in which B should bethe premise, and a proposition of a third kind, C, theconclusion. Here, then, we have the materials for theapplication of this rule. We have, first, the relativenumber of B's per A. We next should have therelative number of C's per B following from A. But theclasses of propositions being so selected that theprobability of C following from any B in general is justthe same as the probability of C's following from oneof those B's which is deducible from an A, the twoprobabilities may be multiplied together, in order togive the probability of C following from A. The samerestrictions exist as before. It might happen that theprobability that B follows from A was affected bycertain propositions of the class B following fromseveral different propositions of the class A. But,practically speaking, all these restrictions are of verylittle consequence, and it is usually recognized as aprinciple universally true that the probability that, if A

240

is true, B is, multiplied by the probability that, if B istrue, C is, gives the probability that, if A is true, C is.

There is a rule supplementary to this, of which greatuse is made. It is not universally valid, and thegreatest caution has to be exercised in making use ofita double care, first, never to use it when it willinvolve serious error; and, second, never to fail totake advantage of it in cases in which it can beemployed. This rule depends upon the fact

241

that in very many cases the probability that C is trueif B is, is substantially the same as the probability thatC is true if A is. Suppose, for example, we have theaverage number of males among the children born inNew York; suppose that we also have the averagenumber of children born in the winter months amongthose born in New York. Now, we may assumewithout doubt, at least as a closely approximateproposition (and no very nice calculation would be inplace in regard to probabilities), that the proportionof males among all the children born in New York isthe same as the proportion of males born in summerin New York; and, therefore, if the names of all thechildren born during a year were put into an urn, wemight multiply the probability that any name drawnwould be the name of a male child by the probabilitythat it would be the name of a child born in summer,in order to obtain the probability that it would be thename of a male child born in summer. The questionsof probability, in the treatises upon the subject, haveusually been such as relate to balls drawn from urns,and games of cards, and so on, in which the questionof the independence of events, as it is calledthat is tosay, the question of whether the probability of C,

242

under the hypothesis B, is the same as its probabilityunder the hypothesis A, has been very simple; but, inthe application of probabilities to the ordinaryquestions of life, it is often an exceedingly nicequestion whether two events may be considered asindependent with sufficient accuracy or not. In allcalculations about cards it is assumed that the cardsare thoroughly shuffled, which makes one deal quiteindependent of another. In point of fact the cards

243

seldom are, in practice, shuffled sufficiently to makethis true; thus, in a game of whist, in which the cardshave fallen in suits of four of the same suit, and areso gathered up, they will lie more or less in sets offour of the same suit, and this will be true even afterthey are shuffled. At least some traces of thisarrangement will remain, in consequence of whichthe number of ''short suits," as they are calledthat isto say, the number of hands in which the cards arevery unequally divided in regard to suitsis smallerthan the calculation would make it to be; so that,when there is a misdeal, where the cards, beingthrown about the table, get very thoroughly shuffled,it is a common saying that in the hands next dealtout there are generally short suits. A few years ago afriend of mine, who plays whist a great deal, was sogood as to count the number of spades dealt to himin 165 hands, in which the cards had been, ifanything, shuffled better than usual. According tocalculation, there should have been 85 of thesehands in which my friend held either three or fourspades, but in point of fact there were 94, showingthe influence of imperfect shuffling.

244

According to the view here taken, these are the onlyfundamental rules for the calculation of chances. Anadditional one, derived from a different conception ofprobability, is given in some treatises, which if it besound might be made the basis of a theory ofreasoning. Being, as I believe it is, absolutely absurd,the consideration of it serves to bring us to the truetheory; and it is for the sake of this discussion, whichmust be postponed to the next number, that I havebrought the doctrine of chances to the reader'sattention at this early stage of our studies of the logicof science.

245

Fourth Paper:The Probability of Induction1

I

We have found that every argument derives its forcefrom the general truth of the class of inferences towhich it belongs; and that probability is theproportion of arguments carrying truth with themamong those of any genus. This is most convenientlyexpressed in the nomenclature of the medievallogicians. They called the fact expressed by a premisean antecedent, and that which follows from it itsconsequent; while the leading principle, that every(or almost every) such antecedent is followed by sucha consequent, they termed the consequence. Usingthis language, we may say that probability belongsexclusively to consequences, and the probability ofany consequence is the number of times in whichantecedent and consequent both occur divided bythe number of all the times in which the antecedentoccurs. From this definition are deduced the followingrules for the addition and multiplication of

246

probabilities:

Rule for the Addition of Probabilities.Given theseparate probabilities of two consequences havingthe same antecedent and incompatible consequents.Then the sum of these two numbers is the probabilityof the consequence,

1 Popular Science Monthly, April, 1878

247

that from the same antecedent one or other of thoseconsequents follows.

Rule for the Multiplication of Probabilities.Given theseparate probabilities of the two consequences, " If Athen B," and "If both A and B, then C." Then theproduct of the these two numbers is the probability ofthe consequence, " If A, then both B and C."

Special Rule for the Multiplication of IndependentProbabilities.Given the separate probabilities of twoconsequences having the same antecedents, "If A,then B," and " If A, then C." Suppose that theseconsequences are such that the probability of thesecond is equal to the probability of theconsequence, " If both A and B, then C." Then theproduct of the two given numbers is equal to theprobability of the consequence, " If A, then both Band C."

To show the working of these rules we may examinethe probabilities in regard to throwing dice. What isthe probability of throwing a six with one die? Theantecedent here is the event of throwing a die; theconsequent, its turning up a six. As the die has six

248

sides, all of which are turned up with equalfrequency, the probability of turning up any one is1/6. Suppose two dice are thrown, what is theprobability of throwing sixes? The probability of eithercoming up six is obviously the same when both arethrown as when one is thrownnamely, 1/6. Theprobability that either will come up six when theother does is also the same as that of its coming upsix whether the other does or not. The probabilitiesare, therefore, independent; and, by our rule, theprobability that both events will happen together isthe product of their several probabilities, or 1/6 X1/6. What

249

is the probability of throwing deuce-ace? Theprobability that the first die will turn up ace and thesecond deuce is the same as the probability that bothwill turn up sixes namely, 1/36; the probability thatthe second will turn up ace and the first deuce islikewise 1/36; these two events first, ace; second,deuce; and, second, ace; first, deuce areincompatible. Hence the rule for addition holds, andthe probability that either will come up ace and theother deuce is 1/36 + 1/36, or 1/16 .

In this way all problems about dice, etc., may besolved. When the number of dice thrown is supposedvery large, mathematics (which may be defined asthe art of making groups to facilitate numeration)comes to our aid with certain devices to reduce thedifficulties.

II

The conception of probability as a matter of fact, i.e.,as the proportion of times in which an occurrence ofone kind is accompanied by an occurrence of anotherkind, is termed by Mr. Venn the materialistic view ofthe subject. But probability has often been regarded

250

as being simply the degree of belief which ought toattach to a proposition, and this mode of explainingthe idea is termed by Venn the conceptualistic view.Most writers have mixed the two conceptionstogether. They, first, define the probability of anevent as the reason we have to believe that it hastaken place, which is conceptualistic; but shortly afterthey state that it is the ratio of the number of casesfavorable to the event to the total number of casesfavorable or contrary,

251

and all equally possible. Except that this introducesthe thoroughly unclear idea of cases equally possiblein place of cases equally frequent, this is a tolerablestatement of the materialistic view. The pureconceptualistic theory has been best expounded byMr. De Morgan in his Formal Logic: or, the Calculus ofInference, Necessary and Probable.

The great difference between the two analyses is,that the conceptualists refer probability to an event,while the materialists make it the ratio of frequency ofevents of a species to those of a genus over thatspecies, thus giving it two terms instead of one. Theopposition may be made to appear as follows:

Suppose that we have two rules of inference, suchthat, of all the questions to the solution of which bothcan be applied, the first yields correct answers to81/100, and incorrect answers to the remaining9/100; while the second yields correct answers to93/100, and incorrect answers to the remaining7/100. Suppose, further, that the two rules areentirely independent as to their truth, so that thesecond answers correctly 93/100 of the questionswhich the first answers correctly, and also 93/100 of

252

the questions which the first answers incorrectly, andanswers incorrectly the remaining 7/100 of thequestions which the first answers correctly, and alsothe remaining 7/100 of the questions which the firstanswers incorrectly. Then, of all the questions to thesolution of which both rules can be applied

253

Suppose, now, that, in reference to any question,both give the same answer. Then (the questionsbeing always such as are to be answered by yes orno), those in reference to which their answers agreeare the same as those which both answer correctlytogether with those which both answer falsely, or

of all. The proportion of those whichboth answer correctly out of those their answers towhich agree is, therefore

This is, therefore, the probability that, if both modesof inference yield the same result, that result iscorrect. We may here conveniently make use ofanother mode of expression. Probability is the ratio ofthe favorable cases to all the cases. Instead ofexpressing our result in terms of this ratio, we maymake use of anotherthe ratio of favorable to

254

unfavorable cases. This last ratio may be called thechance of an event. Then the chance of a trueanswer by the first mode of inference is 81/19 and bythe second is 93/7; and the chance of a correctanswer from both, when they agree, is

255

or the product of the chances of each singly yieldinga true answer.

It will be seen that a chance is a quantity which mayhave any magnitude, however great. An event inwhose favor there is an even chance, or 1/1, has aprobability of 1/2. An argument having an evenchance can do nothing toward reenforcing others,since according to the rule its combination withanother would only multiply the chance of the latterby 1.

Probability and chance undoubtedly belong primarilyto consequences, and are relative to premises; butwe may, nevertheless, speak of the chance of anevent absolutely, meaning by that the chance of thecombination of all arguments in reference to it whichexist for us in the given state of our knowledge.Taken in this sense it is incontestable that the chanceof an event has an intimate connection with thedegree of our belief in it. Belief is certainly somethingmore than a mere feeling; yet there is a feeling ofbelieving, and this feeling does and ought to vary

256

with the chance of the thing believed, as deducedfrom all the arguments. Any quantity which varieswith the chance might, therefore, it would seem,serve as a thermometer for the proper intensity ofbelief. Among all such quantities there is one which ispeculiarly appropriate. When there is a very greatchance, the feeling of belief ought to be very intense.Absolute certainty, or an infinite chance, can neverbe attained by mortals, and this may be representedappropriately by an infinite belief. As the chancediminishes the feeling of

257

believing should diminish, until an even chance isreached, where it should completely vanish and notincline either toward or away from the proposition.When the chance becomes less, then a contrarybelief should spring up and should increase inintensity as the chance diminishes, and as the chancealmost vanishes (which it can never quite do) thecontrary belief should tend toward an infiniteintensity. Now, there is one quantity which, moresimply than any other, fulfills these conditions; it isthe logarithm of the chance. But there is anotherconsideration which must, if admitted, fix us to thischoice for our thermometer. It is that our belief oughtto be proportional to the weight of evidence, in thissense, that two arguments which are entirelyindependent, neither weakening nor strengtheningeach other, ought, when they concur, to produce abelief equal to the sum of the intensities of beliefwhich either would produce separately. Now, wehave seen that the chances of independentconcurrent arguments are to be multiplied togetherto get the chance of their combination, and,therefore, the quantities which best express theintensities of belief should be such that they are to be

258

added when the chances are multiplied in order toproduce the quantity which corresponds to thecombined chance. Now, the logarithm is the onlyquantity which fulfills this condition. There is ageneral law of sensibility, called Fechner'spsychophysical law. It is that the intensity of anysensation is proportional to the logarithm of theexternal force which produces it. It is entirely inharmony with this law that the feeling of belief shouldbe as the logarithm of the chance, this latter beingthe expression of the state of facts which producesthe belief.

259

The rule for the combination of independentconcurrent arguments takes a very simple form whenexpressed in terms of the intensity of belief,measured in the proposed way. It is this: Take thesum of all the feelings of belief which would beproduced separately by all the arguments pro,subtract from that the similar sum for arguments con,and the remainder is the feeling of belief which weought to have on the whole. This is a proceedingwhich men often resort to, under the name ofbalancing reasons.

These considerations constitute an argument in favorof the conceptualistic view. The kernel of it is that theconjoint probability of all the arguments in ourpossession, with reference to any fact, must beintimately connected with the just degree of ourbelief in that fact; and this point is supplemented byvarious others showing the consistency of the theorywith itself and with the rest of our knowledge.

But probability, to have any value at all, must expressa fact. It is, therefore, a thing to be inferred uponevidence. Let us, then, consider for a moment theformation of a belief of probability. Suppose we have

260

a large bag of beans from which one has beensecretly taken at random and hidden under athimble. We are now to form a probable judgment ofthe color of that bean, by drawing others singly fromthe bag and looking at them, each one to be thrownback, and the whole well mixed up after eachdrawing. Suppose the first drawing is white and thenext black. We conclude that there is not animmense preponderance of either color, and thatthere is something like an even chance that the beanunder the thimble is black. But this judgment may bealtered by the next few drawings. When we

261

have drawn ten times, if 4, 5, or 6, are white, wehave more confidence that the chance is even. Whenwe have drawn a thousand times, if about half havebeen white, we have great confidence in this result.We now feel pretty sure that, if we were to make alarge number of bets upon the color of single beansdrawn from the bag, we could approximately insureourselves in the long run by betting each time uponthe white, a confidence which would be entirelywanting if, instead of sampling the bag by 1,000drawings, we had done so by only two. Now, as thewhole utility of probability is to insure us in the longrun, and as that assurance depends, not merely onthe value of the chance, but also on the accuracy ofthe evaluation, it follows that we ought not to havethe same feeling of belief in reference to all events ofwhich the chance is even. In short, to express theproper state of our belief, not one number but twoare requisite, the first depending on the inferredprobability, the second on the amount of knowledgeon which that probability is based.2 It is true thatwhen our knowledge is very precise, when we havemade many drawings from the bag, or, as in most ofthe examples in the books, when the total contents of

262

the bag are absolutely known, the number whichexpresses the uncertainty of the assumed probabilityand its liability to be changed by further experiencemay become insignificant, or utterly vanish. But,when our knowledge is very slight, this number maybe even more important than the probability itself;and when we have no knowledge at all thiscompletely overwhelms the

2 Strictly we should need an infinite series of numberseach depending on the probable error of the last.

263

other, so that there is no sense in saying that thechance of the totally unknown event is even (for whatexpresses absolutely no fact has absolutely nomeaning), and what ought to be said is that thechance is entirely indefinite. We thus perceive thatthe conceptualistic view, though answering wellenough in some cases, is quite inadequate.

Suppose that the first bean which we drew from ourbag were black. That would constitute an argument,no matter how slender, that the bean under thethimble was also black. If the second bean were alsoto turn out black, that would be a secondindependent argument reënforcing the first. If thewhole of the first twenty beans drawn should proveblack, our confidence that the hidden bean was blackwould justly attain considerable strength. Butsuppose the twenty-first bean were to be white andthat we were to go on drawing until we found thatwe had drawn 1,010 black beans and 990 whiteones. We should conclude that our first twenty beansbeing black was simply an extraordinary accident,and that in fact the proportion of white beans toblack was sensibly equal, and that it was an even

264

chance that the hidden bean was black. Yetaccording to the rule of balancing reasons, since allthe drawings of black beans are so manyindependent arguments in favor of the one under thethimble being black, and all the white drawings somany against it, an excess of twenty black beansought to produce the same degree of belief that thehidden bean was black, whatever the total numberdrawn.

In the conceptualistic view of probability, completeignorance, where the judgment ought not to swerveeither toward or away from the hypothesis, isrepresented by the probability ½..3

3 ''Perfect indecision, belief inclining neither way, aneven chance."-Dr MORGAN, p. 182.

265

But let us suppose that we are totally ignorant whatcolored hair the inhabitants of Saturn have. Let us,then, take a color-chart in which all possible colorsare shown shading into one another by imperceptibledegrees. In such a chart the relative areas occupiedby different classes of colors are perfectly arbitrary.Let us inclose such an area with a closed line, andask what is the chance on conceptualistic principlesthat the color of the hair of the inhabitants of Saturnfalls within that area? The answer cannot beindeterminate because we must be in some state ofbelief; and, indeed, conceptualistic writers do notadmit indeterminate probabilities. As there is nocertainty in the matter, the answer lies between zeroand unity. As no numerical value is afforded by thedata, the number must be determined by the natureof the scale of probability itself, and not by calculationfrom the data. The answer can, therefore, only beone-half, since the judgment should neither favor noroppose the hypothesis. What is true of this area istrue of any other one; and it will equally be true of athird area which embraces the other two. But theprobability for each of the smaller areas being one-half, that for the larger should be at least unity,

266

which is absurd.

III

All our reasonings are of two kinds: 1. Explicative,analytic, or deductive; 2. Amplifiative, synthetic, or(loosely speaking) inductive. In explicative reasoning,certain facts are first laid down in the premises.These facts are, in every case, an inexhaustiblemultitude, but they may often

267

be summed up in one simple proposition by means ofsome regularity which runs through them all. Thus,take the proposition that Socrates was a man; thisimplies (to go no further) that during every fraction ofa second of his whole life (or, if you please, duringthe greater part of them) he was a man. He did notat one instant appear as a tree and at another as adog; he did not flow into water, or appear in twoplaces at once; you could not put your finger throughhim as if he were an optical image, etc. Now, thefacts being thus laid down, some order among someof them, not particularly made use of for the purposeof stating them, may perhaps be discovered; and thiswill enable us to throw part or all of them into a newstatement, the possibility of which might haveescaped attention. Such a statement will be theconclusion of an analytic inference. Of this sort are allmathematical demonstrations. But syntheticreasoning is of another kind. In this case the factssummed up in the conclusion are not among thosestated in the premises. They are different facts, aswhen one sees that the tide rises m times andconcludes that it will rise the next time. These are theonly inferences which increase our real knowledge,

268

however useful the others may be.

In any problem in probabilities, we have given therelative frequency of certain events, and we perceivethat in these facts the relative frequency of anotherevent is given in a hidden way. This being statedmakes the solution. This is, therefore, mereexplicative reasoning, and is evidently entirelyinadequate to the representation of syntheticreasoning, which goes out beyond the facts given inthe

269

premises. There is, therefore, a manifest impossibilityin so tracing out any probability for a syntheticconclusion.

Most treatises on probability contain a very differentdoctrine. They state, for example, that if one of theancient denizens of the shores of the Mediterranean,who had never heard of tides, had gone to the bay ofBiscay, and had there seen the tide rise, say m times,he could know that there was a probability equal to

that it would rise the next time. In a well-known workby Quetelet, much stress is laid on this, and it ismade the foundation of a theory of inductivereasoning.

But this solution betrays its origin if we apply it to thecase in which the man has never seen the tide rise atall; that is, if we put m = o. In this case, theprobability that it will rise the next time comes out ½,or, in other words, the solution involves theconceptualistic principle that there is an even chanceof a totally unknown event. The manner in which ithas been reached has been by considering a number

270

of urns all containing the same number of balls, partwhite and part black. One urn contains all white balls,another one black and the rest white, a third twoblack and the rest white, and so on, one urn for eachproportion, until an urn is reached containing onlyblack balls. But the only possible reason for drawingany analogy between such an arrangement and thatof Nature is the principle that alternatives of whichwe know nothing must be considered as equallyprobable. But this principle is absurd. There is anindefinite variety of ways of enumerat-

271

ing the different possibilities, which, on theapplication of this principle, would give differentresults. If there be any way of enumerating thepossibilities so as to make them all equal, it is notthat from which this solution is derived, but is thefollowing: Suppose we had an immense granary filledwith black and white balls well mixed up; andsuppose each urn were filled by taking a fixednumber of balls from this granary quite at random.The relative number of white balls in the granarymight be anything, say one in three. Then in one-third of the urns the first ball would be white, and intwo-thirds black. In one-third of those urns of whichthe first ball was white, and also in one-third of thosein which the first ball was black, the second ballwould be white. In this way, we should have adistribution like that shown in the following table,where w stands for a white ball and b for a black one.The reader can, if he chooses, verify the table forhimself.

wwww.

wwwb. wwbw.wbww.bwww.

272

wwwb. wwbw.wbww.bwww.

wwbb.wwbb.wwbb.wwbb.

wbwb.wbwb.wbwb.wbwb.

bwwb.bwwb.bwwb.bwwb.

wbbw.wbbw.wbbw.wbbw.

bwbw.bwbw.bwbw.bwbw.

bbww.bbww.bbww.bbww.

wbbb.wbbb.wbbb.wbbb.

bwbb.bwbb.bwbb.bwbb.

bbwb.bbwb.bbwb.bbwb.

bbbw.bbbw.bbbw.bbbw.

273

wbbb.wbbb.wbbb.wbbb.

bwbb.bwbb.bwbb.bwbb.

bbwb.bbwb.bbwb.obwb.

bbbw.bbbw.bbbw.bbbw.

bbbb. In the second group, where there is one b, therebbbb. are two sets just alike; in the third there are 4, inbbbb. the fourth 8, and in the fifth 16, doubling everybbbb. time. This is because we have supposed twice asbbbb. many black balls in the granary as white ones; hadbbbb. we supposed 10 times as many, instead ofbbbb.bbbb. 1, 2, 4, 8, 16bbbb.bbbb. sets we should have hadbbbb.bbbb. 1, 10, 100, 1000, 10000bbbb.bbbb. sets; on the other hand, had the numbers of blackand white balls in the granary been even, therebbbb. would have been but one set in each group. Nowsuppose two balls were drawn from one of bbbb. theseurns and were found to be both white, what would be the

274

probability of the next one being white? If the two drawn outwere the first two put into the urns, and the next to be drawnout were the third put in, then the probability of this thirdbeing white would be the same whatever the colors of thefirst two, for it has been supposed that just the sameproportion of urns has the third ball white among those whichhave the first two white-white, white-black, black-white

275

and black-black. Thus, in this case, the chance of thethird ball being white would be the same whateverthe first two were. But, by inspecting the table, thereader can see that in each group all orders of theballs occur with equal frequency, so that it makes nodifference whether they are drawn out in the orderthey were put in or not. Hence the colors of the ballsalready drawn have no influence on the probability ofany other being white or black.

Now, if there be any way of enumerating thepossibilities of Nature so as to make them equallyprobable, it is clearly one which should make onearrangement or combination of the elements ofNature as probable as another, that is, a distributionlike that we have supposed, and it, therefore,appears that the assumption that any such thing canbe done, leads simply to the conclusion thatreasoning from past to future experience is absolutelyworthless. In fact, the moment that you assume thatthe chances in favor of that of which we are totallyignorant are even, the problem about the tides doesnot differ, in any arithmetical particular, from thecase in which a penny (known to be equally likely to

276

come up heads and tails) should turn up heads mtimes successively. In short, it would be to assumethat Nature is a pure chaos, or chance combination ofindependent elements, in which reasoning from onefact to another would be impossible; and since, as weshall hereafter see, there is no judgment of pureobservation without reasoning, it would be tosuppose all human cognition illusory and no realknowledge possible. It would be to suppose that if wehave found the order of Nature more or less regularin the past, this has been by a pure run of luck which

277

we may expect is now at an end. Now, it may be wehave no scintilla of proof to the contrary, but reasonis unnecessary in reference to that belief which is ofall the most settled, which nobody doubts or candoubt, and which he who should deny would stultifyhimself in so doing. The relative probability of this orthat arrangement of Nature is something which weshould have a right to talk about if universes were asplenty as blackberries, if we could put a quantity ofthem in a bag, shake them well up, draw out asample, and examine them to see what proportion ofthem had one arrangement and what proportionanother. But, even in that case, a higher universewould contain us, in regard to whose arrangementsthe conception of probability could have noapplicability.

IV

We have examined the problem proposed by theconceptualists, which, translated into clear language,is this: Given a synthetic conclusion; required to knowout of all possible states of things how many willaccord, to any assigned extent, with this conclusion;and we have found that it is only an absurd attempt

278

to reduce synthetic to analytic reason, and that nodefinite solution is possible.

But there is another problem in connection with thissubject. It is this: Given a certain state of things,required to know what proportion of all syntheticinferences relating to it will be true within a givendegree of approximation. Now, there is no difficultyabout this problem (except for its mathematicalcomplication); it has been much studied,

279

and the answer is perfectly well known. And is notthis, after all, what we want to know much ratherthan the other? Why should we want to know theprobability that the fact will accord with ourconclusion? That implies that we are interested in allpossible worlds, and not merely the one in which wefind ourselves placed. Why is it not much more to thepurpose to know the probability that our conclusionwill accord with the fact? One of these questions isthe first above stated and the other the second, andI ask the reader whether, if people, instead of usingthe word probability without any clear apprehensionof their own meaning, had always spoken of relativefrequency, they could have failed to see that whatthey wanted was not to follow along the syntheticprocedure with an analytic one, in order to find theprobability of the conclusion; but, on the contrary, tobegin with the fact at which the synthetic inferenceaims, and follow back to the facts it uses for premisesin order to see the probability of their being such aswill yield the truth.

As we cannot have an urn with an infinite number ofballs to represent the inexhaustibleness of Nature, let

280

us suppose one with a finite number, each ball beingthrown back into the urn after being drawn out, sothat there is no exhaustion of them. Suppose one ballout of three is white and the rest black, and that fourballs are drawn. Then the table on pages 9596represents the relative frequency of the differentways in which these balls might be drawn. It will beseen that if we should judge by these four balls of theproportion in the urn, 32 times out of 81 we shouldfind it ¼ and 24 times out of 81 we should find it

281

1/2, the truth being 1/3. To extend this table to highnumbers would be great labor, but themathematicians have found some ingenious ways ofreckoning what the numbers would be. It is foundthat, if the true proportion of white balls is p, and sballs are drawn, then the error of the proportionobtained by the induction will be

The use of this may be illustrated by an example. Bythe census of 1870, it appears that the proportion ofmales among native white children under one yearold was 0.5082, while among colored children of thesame age the proportion was only 0.4977. Thedifference between these is 0.0105, or about one in a1oo. Can this be attributed to chance, or would thedifference always exist among a great number of

282

white and colored children under like circumstances?Here p may be taken at 1/3; hence 2p (Ip) is also1/3. The number of white children counted was near1,000,000; hence the fraction whose square-root isto be taken is about 1/2000000 The root is about1/1400, and this multiplied by 0.477 gives about0.0003 as the probable error in the ratio

283

of males among the whites as obtained from theinduction. The number of black children was about150,000, which gives 0.0008 for the probable error.We see that the actual discrepancy is ten times thesum of these, and such a result would happen,according to our table, only once out of10,000,000,000 censuses, in the long run.

It may be remarked that when the real value of theprobability sought inductively is either very large orvery small, the reasoning is more secure. Thus,suppose there were in reality one white ball in 100 ina certain urn, and we were to judge of the numberby 100 drawings. The probability of drawing no whiteball would be 366/1000that of drawing one white ballwould be 370/1000 ; that of drawing two would be185/1000 that of drawing three would be 61/1000;that of drawing four would be 15/1000; that ofdrawing five would be only 3/1000 etc. Thus weshould be tolerably certain of not being in error bymore than one ball in 100.

It appears, then, that in one sense we can, and inanother we cannot, determine the probability ofsynthetic inference. When I reason in this way:

284

Ninety-nine Cretans in a hundred are liars;

But Epimenides is a Cretan;

Therefore, Epimenides is a liar:

I know that reasoning similar to that would carrytruth 99 times in 100. But when I reason in theopposite direction:

Minos, Sarpedon, Rhadamanthus, Deucalion, andEpimenides, are all the Cretans I can think of;

But these were all atrocious liars,

Therefore, pretty much all Cretans must have beenliars; I do not in the least know how often suchreasoning would

285

carry me right. On the other hand, what I do know isthat some definite proportion of Cretans must havebeen liars, and that this proportion can be probablyapproximated to by an induction from five or sixinstances. Even in the worst case for the probabilityof such an inference, that in which about half theCretans are liars, the ratio so obtained wouldprobably not be in error by more than 1/6. So much Iknow; but, then, in the present case the inference isthat pretty much all Cretans are liars, and whetherthere may not be a special improbability in that I donot know.

V

Late in the last century, Immanuel Kant asked thequestion, ''How are synthetical judgments a prioripossible? " By synthetical judgments he meant suchas assert positive fact and are not mere affairs ofarrangement; in short, judgments of the kind whichsynthetical reasoning produces, and which analyticreasoning cannot yield. By a priori judgments hemeant such as that all outward objects are in space,every event has a cause, etc., propositions whichaccording to him can never be inferred from

286

experience. Not so much by his answer to thisquestion as by the mere asking of it, the currentphilosophy of that time was shattered and destroyed,and a new epoch in its history was begun. But beforeasking that question he ought to have asked themore general one, "How are any syntheticaljudgments at all possible? " How is it that a man canobserve one fact and straightway pronouncejudgment concerning another different fact notinvolved in the first?

287

Such reasoning, as we have seen, has, at least in theusual sense of the phrase, no definite probability;how, then, can it add to our knowledge? This is astrange paradox; the Abbé Gratry says it is a miracle,and that every true induction is an immediateinspiration from on high.4 I respect this explanationfar more than many a pedantic attempt to solve thequestion by some juggle with probabilities, with theforms of syllogism, or what not. I respect it because itshows an appreciation of the depth of the problem,because it assigns an adequate cause, and because itis intimately connected-as the true account shouldbewith a general philosophy of the universe. At thesame time, I do not accept this explanation, becausean explanation should tell how a thing is done, and toassert a perpetual miracle seems to be anabandonment of all hope of doing that, withoutsufficient justification.

It will be interesting to see how the answer whichKant gave to his question about syntheticaljudgments a priori will appear if extended to thequestion of synthetical judgments in general. Thatanswer is, that synthetical judgments a priori are

288

possible because whatever is universally true isinvolved in the conditions of experience. Let us applythis to a general synthetical reasoning. I take from abag a handful of beans; they are all purple, and Iinfer that all the beans in the bag are purple. Howcan I do that? Why, upon the principle that whateveris universally true of my experience (which is here theappearance

4 Logique. The same is true, according to him, of everyperformance of a differentiation, but not of integration.He does not tell us whether it is the supernaturalassistance which makes the former process so muchthe easier.

289

of these different beans) is involved in the conditionof experience. The condition of this specialexperience is that all these beans were taken fromthat bag. According to Kant's principle, then,whatever is found true of all the beans drawn fromthe bag must find its explanation in some peculiarityof the contents of the bag. This is a satisfactorystatement of the principle of induction.

When we draw a deductive or analytic conclusion,our rule of inference is that facts of a certain generalcharacter are either invariably or in a certainproportion of cases accompanied by facts of anothergeneral character. Then our premise being a fact ofthe former class, we infer with certainty or with theappropriate degree of probability the existence of afact of the second class. But the rule for syntheticinference is of a different kind. When we sample abag of beans we do not in the least assume that thefact of some beans being purple involves thenecessity or even the probability of other beans beingso. On the contrary, the conceptualistic method oftreating probabilities, which really amounts simply tothe deductive treatment of them, when rightly carried

290

out leads to the result that a synthetic inference hasjust an even chance in its favor, or in other words isabsolutely worthless. The color of one bean is entirelyindependent of that of another. But syntheticinference is founded upon a classification of facts, notaccording to their characters, but according to themanner of obtaining them. Its rule is, that a numberof facts obtained in a given way will in general moreor less resemble other facts obtained in the sameway; or, experiences whose conditions are the samewill have the same general characters.

291

In the former case, we know that premises preciselysimilar in form to those of the given ones will yieldtrue conclusions, just once in a calculable number oftimes. In the latter case, we only know that premisesobtained under circumstances similar to the givenones (though perhaps themselves very different) willyield true conclusions, at least once in a calculablenumber of times. We may express this by saying thatin the case of analytic inference we know theprobability of our conclusion (if the premises aretrue), but in the case of synthetic inferences we onlyknow the degree of trustworthiness of ourproceeding. As all knowledge comes from syntheticinference, we must equally infer that all humancertainty consists merely in our knowing that theprocesses by which our knowledge has been derivedare such as must generally have led to trueconclusions.

Though a synthetic inference cannot by any meansbe reduced to deduction, yet that the rule ofinduction will hold good in the long run may bededuced from the principle that reality is only theobject of the final opinion to which sufficient

292

investigation would lead. That belief gradually tendsto fix itself under the influence of inquiry is, indeed,one of the facts with which logic sets out.

293

Fifth Paper:The Order of Nature1

I

Any proposition whatever concerning the order ofNature must touch more or less upon religion. In ourday, belief, even in these matters, depends more andmore upon the observation of facts. If a remarkableand universal orderliness be found in the universe,there must be some cause for this regularity, andscience has to consider what hypotheses mightaccount for the phenomenon. One way of accountingfor it, certainly, would be to suppose that the world isordered by a superior power. But if there is nothing inthe universal subjection of phenomena to laws, nor inthe character of those laws themselves (as beingbenevolent, beautiful, economical, etc.), which goesto prove the existence of a governor of the universe,it is hardly to be anticipated that any other sort ofevidence will be found to weigh very much withminds emancipated from the tyranny of tradition.

294

Nevertheless, it cannot truly be said that even anabsolutely negative decision of that question couldaltogether destroy religion, inasmuch as there arefaiths in which, however much they differ from ourown, we recognize those essential characters whichmake them worthy to be called religions, and which,nevertheless, do not postulate an

1 Popular Science Monthly, June, 1878.

295

actually existing Deity. That one, for instance, whichhas had the most numerous and by no means theleast intelligent following of any on earth, teachesthat the Divinity in his highest perfection is wrappedaway from the world in a state of profound andeternal sleep, which really does not differ from non-existence, whether it be called by that name or not.No candid mind who has followed the writings of M.Vacherot can well deny that his religion is as earnestas can be. He worships the Perfect, the SupremeIdeal; but he conceives that the very notion of theIdeal is repugnant to its real existence.2 In fact, M.Vacherot finds it agreeable to his reason to assertthat non-existence is an essential character of theperfect, just as St. Anselm and Descartes found itagreeable to theirs to assert the extreme opposite. Iconfess that there is one respect in which either ofthese positions seems to me more congruous with thereligious attitude than that of a theology whichstands upon evidences; for as soon as the Deitypresents himself to either Anselm or Vacherot, andmanifests his glorious attributes, whether it be in avision of the night or day, either of them recognizeshis adorable God, and sinks upon his knees at once;

296

whereas the theologian of evidences will first demandthat the divine apparition shall identify himself, andonly after having scrutinized his credentials andweighed the probabilities of his being found amongthe totality of existences, will he finally render hiscircumspect homage, thinking that no characters canbe adorable but those which belong to a real thing.

If we could find out any general characteristic of the

2 [See Santayana, Reason in Religion.]

297

universe, any mannerism in the ways of Nature, anylaw everywhere applicable and universally valid, sucha discovery would be of such singular assistance to usin all our future reasoning, that it would deserve aplace almost at the head of the principles of logic. Onthe other hand, if it can be shown that there isnothing of the sort to find out, but that everydiscoverable regularity is of limited range, this againwill be of logical importance. What sort of aconception we ought to have of the universe, how tothink of the ensemble of things, is a fundamentalproblem in the theory of reasoning.

II

It is the legitimate endeavor of scientific men now, asit was twenty-three hundred years ago, to accountfor the formation of the solar system and of thecluster of stars which forms the galaxy, by thefortuitous concourse of atoms. The greatestexpounder of this theory, when asked how he couldwrite an immense book on the system of the worldwithout one mention of its author, replied, verylogically, "Je n'avais pas besoin de cette hypothèse-là." But, in truth, there is nothing atheistical in the

298

theory, any more than there was in this answer.Matter is supposed to be composed of moleculeswhich obey the laws of mechanics and exert certainattractions upon one another; and it is to theseregularities (which there is no attempt to account for)that general arrangement of the solar system wouldbe due, and not to hazard.

If any one has ever maintained that the universe is apure throw of the dice, the theologians haveabundantly

299

refuted him. "How often," says Archbishop Tillotson,"might a man, after he had jumbled a set of letters ina bag, fling them out upon the ground before theywould fall into an exact poem, yea, or so much asmake a good discourse in prose! And may not a littlebook be as easily made by chance as this greatvolume of the world? " The chance world here shownto be so different from that in which we live would beone in which there were no laws, the characters ofdifferent things being entirely independent; so that,should a sample of any kind of objects ever show aprevalent character, it could only be by accident, andno general proposition could ever be established.Whatever further conclusions we may come to inregard to the order of the universe, thus much maybe regarded as solidly established, that the world isnot a mere chance-medley.

But whether the world makes an exact poem or not,is another question. When we look up at the heavensat night, we readily perceive that the stars are notsimply splashed on to the celestial vault; but theredoes not seem to be any precise system in theirarrangement either. It will be worth our while, then,

300

to inquire into the degree of orderliness in theuniverse; and, to begin, let us ask whether the worldwe live in is any more orderly than a purely chance-world would be.

Any uniformity, or law of Nature, may be stated in theform, "Every A is B "; as, every ray of light is a non-curved line, every body is accelerated toward theearth's center, etc. This is the same as to say, "Theredoes not exist any A which is not B "; there is nocurved ray; there

301

is no body not accelerated toward the earth; so thatthe uniformity consists in the non-occurrence inNature of a certain combination of characters (in thiscase, the combination of being A with being non-B).3And, conversely, every case of the non-occurrence ofa combination of characters would constitute auniformity in Nature. Thus, suppose the quality A isnever found in combination with the quality C: forexample, suppose the quality of idiocy is never foundin combination with that of having a well-developedbrain. Then nothing of the sort A is of the sort C, oreverything of the sort A is of the sort non-C (or say,every idiot has an ill-developed brain), which, beingsomething universally true of the A's, is a uniformityin the world. Thus we see that, in a world wherethere were no uniformities, no logically possiblecombination of characters would be excluded, butevery combination would exist in some object. Buttwo objects not identical must differ in some of theircharacters, though it be only in the character ofbeing in such-and-such a place. Hence, precisely thesame combination of characters could not be found intwo different objects; and, consequently, in achance-world every combination involving either the

302

positive or negative of every character would belongto just one thing. Thus, if there were but five simplecharacters in such a world,4 we might denote themby A, B, C, D, E, and their negatives

3 For the present purpose, the negative of a characteris to be considered as much a character as the positive,for a uniformity may either be affirmative or negative. Ido not say that no distinction can be drawn betweenpositive and negative uniformities.4 There being 5 simple characters, with their negatives,they could be compounded in various ways so as to make241 characters in all, without counting the charactersexistence and non-existence, which make up 243 or 35

303

by a, b, c, d, e; and then, as there would be 25 or 32different combinations of these characters,completely determinate in reference to each of them,that world would have just 32 objects in it, theircharacters being as in the following table:

Table I.ABCDE AbCDE aBCDE abCDEABCDe AbCDe aBCDe abCDeABCdE AbCdE aBCdE abCdEABCde AbCde aBCde abCdeABcDE AbcDE aBcDE abcDEABcDe AbcDe aBcDe abcDeABcdE AbcdE aBcdE abcdEABcde Abcde aBcde abcde

For example, if the five primary characters were hard,sweet, fragrant, green, bright, there would be oneobject which reunited all these qualities, one whichwas hard, sweet, fragrant, and green, but not bright;one which was hard, sweet, fragrant, and bright, butnot green; one which was hard, sweet, and fragrant,but neither green nor bright; and so on through allthe combinations.

304

This is what a thoroughly chance-world would be like,and certainly nothing could be imagined moresystematic. When a quantity of letters are poured outof a bag, the appearance of disorder is due to thecircumstance that the phenomena are only partlyfortuitous. The laws of space are supposed, in thatcase, to be rigidly preserved, and there is also acertain amount of regularity in the formation of theletters. The result is that some elements are

305

orderly and some are disorderly, which is preciselywhat we observe in the actual world. Tillotson, in thepassage of which a part has been quoted, goes on toask, '' How long might 20,000 blind men whichshould be sent out from the several remote parts ofEngland, wander up and down before they would allmeet upon Salisbury Plains, and fall into rank and filein the exact order of an army? And yet this is muchmore easy to be imagined than how the innumerableblind parts of matter should rendezvous themselvesinto a world." This is very true, but in the actual worldthe blind men are, as far as we can see, not drawnup in any particular order at all. And, in short, while acertain amount of order exists in the world, it wouldseem that the world is not so orderly as it might be,and, for instance, not so much so as a world of purechance would be.

But we can never get to the bottom of this questionuntil we take account of a highly-important logicalprinciple5 which I now proceed to enounce. Thisprinciple is that any plurality or lot of objectswhatever have some character in common (no matterhow insignificant) which is peculiar to them and not

306

shared by anything else. The word "character" here istaken in such a sense as to include negativecharacters, such as incivility, inequality, etc., as wellas their positives, civility, equality, etc. To prove thetheorem, I will show what character any two things,A and B, have in common, not shared by anythingelse. The things, A and B, are each distinguishedfrom all other things by the possession of certaincharacters which may be named A-ness and B-ness.Corresponding to these posi-

5 This principle was, I believe, first stated by Mr. DeMorgan.

307

tive characters, are the negative characters un-A-ness, which is possessed by everything except A, andun-B-ness, which is possessed by everything exceptB. These two characters are united in everythingexcept A and B; and this union of the characters un-A-ness and un-B-ness makes a compound characterwhich may be termed A-B-lessness. This is notpossessed by either A or B, but it is possessed byeverything else. This character, like every other, hasits corresponding negative un-A-B-lessness, and thislast is the character possessed by both A and B, andby nothing else. It is obvious that what has thus beenshown true of two things is mutatis mutandis, true ofany number of things. Q. E. D.

In any world whatever, then, there must be acharacter peculiar to each possible group of objects.If, as a matter of nomenclature, characters peculiarto the same group be regarded as only differentaspects of the same character, then we may say thatthere will be precisely one character for each possiblegroup of objects. Thus, suppose a world to containfive things, a,b,g,d,e. Then it will have a separatecharacter for each of the 31 groups (with non-

308

existence making up 32 or 25) shown in the followingtable:

Table II.ab abg abgd abgde

a ag abd abgeb ad abe abdeg ae agd agded bg age bgdee bd ade

be bgdgd bgege bdede gde

309

This shows that a contradiction is involved in the veryidea 6 of a chance-world, for in a world of 32 things,instead of there being only 35 or 243 characters, aswe have seen that the notion of a chance-worldrequires, there would, in fact, be no less than 232, or4,294,967,296 characters, which would not be allindependent, but would have all possible relationswith one another.

We further see that so long as we regard charactersabstractly, without regard to their relativeimportance, etc., there is no possibility of a more orless degree of orderliness in the world, the wholesystem of relationship between the differentcharacters being given by mere logic; that is, beingimplied in those facts which are tacitly admitted assoon as we admit that there is any such thing asreasoning.

In order to descend from this abstract point of view,it is requisite to consider the characters of things asrelative to the perceptions and active powers of livingbeings. Instead, then, of attempting to imagine aworld in which there should be no uniformities, let ussuppose one in which none of the uniformities should

310

have reference to characters interesting or importantto us. In the first place, there would be nothing topuzzle us in such a world. The small number ofqualities which would directly meet the senses wouldbe the ones which would afford the key to everythingwhich could possibly interest us. The whole universewould have such an air of system and perfectregularity that there would be nothing to ask. In thenext place, no action of ours, and no event of Nature,would have important consequences in such a world.We should be

6 Not in every idea but only in the one so formulated.

311

perfectly free from all responsibility, and there wouldbe nothing to do but to enjoy or suffer whateverhappened to come along. Thus there would benothing to stimulate or develop either the mind or thewill, and we consequently should neither act northink. We should have no memory, because thatdepends on a law of our organization. Even if we hadany senses, we should be situated toward such aworld precisely as inanimate objects are toward thepresent one, provided we suppose that these objectshave an absolutely transitory and instantaneousconsciousness without memorya supposition which isa mere mode of speech, for that would be noconsciousness at all. We may, therefore, say that aworld of chance is simply our actual world viewedfrom the standpoint of an animal at the veryvanishing-point of intelligence. The actual world isalmost a chance-medley to the mind of a polyp. Theinterest which the uniformities of Nature have for ananimal measures his place in the scale of intelligence.

Thus, nothing can be made out from the orderlinessof Nature in regard to the existence of a God, unlessit be maintained that the existence of a finite mind

312

proves the existence of an infinite one.

III

In the last of these papers we examined the natureof inductive or synthetic reasoning. We found it to bea process of sampling. A number of specimens of aclass are taken, not by selection within that class, butat random. These specimens will agree in a greatnumber of respects. If, now, it were likely that asecond lot would agree with

313

the first in the majority of these respects, we mightbase on this consideration an inference in regard toany one of these characters. But such an inferencewould neither be of the nature of induction, norwould it (except in special cases) be valid, becausethe vast majority of points of agreement in the firstsample drawn would generally be entirely accidental,as well as insignificant. To illustrate this, I take theages at death of the first five poets given in Wheeler'sBiographical Dictionary. They are:

Aagard, 48.Abeille, 70.Abulola, 84.Abunowas, 48.Accords, 45.

These five ages have the following characters incommon:

1. The difference of the two digits composing thenumber, divided by three, leaves a remainder of one.

2. The first digit raised to the power indicated by thesecond, and divided by three, leaves a remainder ofone.

314

3. The sum of the prime factors of each age,including one, is divisible by three.

It is easy to see that the number of accidentalagreements of this sort would be quite endless. Butsuppose that, instead of considering a characterbecause of its prevalence in the sample, wedesignate a character before taking the sample,selecting it for its importance, obviousness, or otherpoint of interest. Then two considerable samplesdrawn at random are extremely likely to agree

315

approximately in regard to the proportion ofoccurrences of a character so chosen. The inferencethat a previously designated character has nearly thesame frequency of occurrence in the whole of a classthat it has in a sample drawn at random out of thatclass is induction. If the character be not previouslydesignated, then a sample in which it is found to beprevalent can only serve to suggest that it may beprevalent in the whole class. We may consider thissurmise as an inference if we pleasean inference ofpossibility; but a second sample must be drawn totest the question of whether the character actually isprevalent. Instead of designating beforehand a singlecharacter in reference to which we will examine asample, we may designate two, and use the samesample to determine the relative frequencies of both.This will be making two inductive inferences at once;and, of course, we are less certain that both will yieldcorrect conclusions than we should be that eitherseparately would do so. What is true of twocharacters is true of any limited number. Now, thenumber of characters which have any considerableinterest for us in reference to any class of objects ismore moderate than might be supposed. As we shall

316

be sure to examine any sample with reference tothese characters, they may be regarded not exactlyas predesignated, but as predetermined (whichamounts to the same thing); and we may infer thatthe sample represents the class in all these respects ifwe please, remembering only that this is not sosecure an inference as if the particular quality to belooked for had been fixed upon beforehand.

The demonstration of this theory of induction restsupon

317

principles and follows methods which are accepted byall those who display in other matters the particularknowledge and force of mind which qualify them tojudge of this. The theory itself, however, quiteunaccountably seems never to have occurred to anyof the writers who have undertaken to explainsynthetic reasoning. The most widely-spread opinionin the matter is one which was much promoted byMr. John Stuart Millnamely, that induction dependsfor its validity upon the uniformity of Naturethat is, onthe principle that what happens once will, under asufficient degree of similarity of circumstances,happen again as often as the same circumstancesrecur. The application is this: The fact that differentthings belong to the same class constitutes thesimilarity of circumstances, and the induction is good,provided this similarity is "sufficient." What happensonce is, that a number of these things are found tohave a certain character; what may be expected,then, to happen again as often as the circumstancesrecur consists in this, that all things belonging to thesame class should have the same character.

This analysis of induction has, I venture to think,

318

various imperfections, to some of which it may beuseful to call attention. In the first place, when I putmy hand in a bag and draw out a handful of beans,and, finding threequarters of them black, infer thatabout three-quarters of all in the bag are black, myinference is obviously of the same kind as if I hadfound any larger proportion, or the whole, of thesample black, and had assumed that it represented inthat respect the rest of the contents of the bag. Butthe analysis in question hardly seems adapted to the

319

explanation of this proportionate induction, where theconclusion, instead of being that a certain eventuniformly happens under certain circumstances, isprecisely that it does not uniformly occur, but onlyhappens in a certain proportion of cases. It is truethat the whole sample may be regarded as a singleobject, and the inference may be brought under theformula proposed by considering the conclusion to bethat any similar sample will show a similar proportionamong its constituents. But this is to treat theinduction as if it rested on a single instance, whichgives a very false idea of its probability.

In the second place, if the uniformity of Nature werethe sole warrant of induction, we should have noright to draw one in regard to a character whoseconstancy we knew nothing about. Accordingly, Mr.Mill says that, though none but white swans wereknown to Europeans for thousands of years, yet theinference that all swans were white was "not a goodinduction," because it was not known that color wasa usual generic character (it, in fact, not being so byany means). But it is mathematically demonstrablethat an inductive inference may have as high a

320

degree of probability as you please independent ofany antecedent knowledge of the constancy of thecharacter inferred. Before it was known that color isnot usually a character of genera, there was certainlya considerable probability that all swans were white.But the further study of the genera of animals led tothe induction of their non-uniformity in regard tocolor. A deductive application of this generalproposition would have gone far to overcome theprobability of the universal whiteness of swans before

321

the black species was discovered. When we do knowanything in regard to the general constancy orinconstancy of a character, the application of thatgeneral knowledge to the particular class to whichany induction relates, though it serves to increase ordiminish the force of the induction, is, like everyapplication of general knowledge to particular cases,deductive in its nature and not inductive.

In the third place, to say that inductions are truebecause similar events happen in similarcircumstancesor, what is the same thing, becauseobjects similar in some respects are likely to be similarin othersis to overlook those conditions which reallyare essential to the validity of inductions. When wetake all the characters into account, any pair ofobjects resemble one another in just as manyparticulars as any other pair. If we limit ourselves tosuch characters as have for us any importance,interest, or obviousness, then a synthetic conclusionmay be drawn, but only on condition that thespecimens by which we judge have been taken atrandom from the class in regard to which we are toform a judgment, and not selected as belonging to

322

any sub-class. The induction only has its full forcewhen the character concerned has been designatedbefore examining the sample. These are theessentials of induction, and they are not recognizedin attributing the validity of induction to theuniformity of Nature. The explanation of induction bythe doctrine of probabilities, given in the last of thesepapers, is not a mere metaphysical formula, but isone from which all the rules of synthetic reasoningcan be deduced systematically and withmathematical cogency. But the account of the matterby a prin-

323

ciple of Nature, even if it were in other respectssatisfactory, presents the fatal disadvantage ofleaving us quite as much afloat as before in regard tothe proper method of induction. It does not surpriseme, therefore, that those who adopt this theory havegiven erroneous rules for the conduct of reasoning,nor that the greater number of examples put forwardby Mr. Mill in his first edition, as models of whatinductions should be, proved in the light of furtherscientific progress so particularly unfortunate thatthey had to be replaced by others in later editions.One would have supposed that Mr. Mill might havebased an induction on this circumstance, especiallyas it is his avowed principle that, if the conclusion ofan induction turns out false, it cannot have been agood induction. Nevertheless, neither he nor any ofhis scholars seem to have been led to suspect, in theleast, the perfect solidity of the framework which hedevised for securely supporting the mind in itspassage from the known to the unknown, although atits first trial it did not answer quite so well as hadbeen expected.

IV

324

When we have drawn any statistical inductionsuch,for instance, as that one-half of all births are of malechildrenit is always possible to discover, byinvestigation sufficiently prolonged, a class of whichthe same predicate may be affirmed universally; tofind out, for instance, what sort of births are of malechildren. The truth of this principle followsimmediately from the theorem that there is acharacter peculiar to every possible group of objects.The

325

form in which the principle is usually stated is, thatevery event must have a cause.

But, though there exists a cause for every event, andthat of a kind which is capable of being discovered,yet if there be nothing to guide us to the discovery; ifwe have to hunt among all the events in the worldwithout any scent; if, for instance, the sex of a childmight equally be supposed to depend on theconfiguration of the planets, on what was going on atthe antipodes, or on anything elsethen the discoverywould have no chance of ever getting made.

That we ever do discover the precise causes ofthings, that any induction whatever is absolutelywithout exception, is what we have no right toassume. On the contrary, it is an easy corollary, fromthe theorem just referred to, that every empirical rulehas an exception.7 But there are certain of ourinductions which present an approach to universalityso extraordinary that, even if we are to suppose thatthey are not strictly universal truths, we cannotpossibly think that they have been reached merely byaccident. The most remarkable laws of this kind arethose of time and space. With reference to space,

326

Bishop Berkeley first showed, in a very conclusivemanner, that it was not a thing seen, but a thinginferred. Berkeley chiefly insists on the impossibility ofdirectly seeing the third dimension of space, since theretina of the eye is a surface. But, in point of fact, theretina is not even a surface; it is a conglomeration ofnerve-needles directed

7 [Note that this corollary is itself a theoreticalinference and not an empirical rule.]

327

toward the light and having only their extreme pointssensitive, these points lying at considerable distancesfrom one another compared with their areas. Now, ofthese points, certainly the excitation of no one singlycan produce the perception of a surface, andconsequently not the aggregate of all the sensationscan amount to this. But certain relations subsistbetween the excitations of different nervepoints, andthese constitute the premises upon which thehypothesis of space is founded, and from which it isinferred. That space is not immediately perceived isnow universally admitted; and a mediate cognition iswhat is called an inference, and is subject to thecriticism of logic. But what are we to say to the factof every chicken as soon as it is hatched solving aproblem whose data are of a complexity sufficient totry the greatest mathematical powers? It would beinsane to deny that the tendency to light upon theconception of space is inborn in the mind of thechicken and of every animal. The same thing isequally true of time. That time is not directlyperceived is evident, since no lapse of time is present,and we only perceive what is present. That, nothaving the idea of time, we should never be able to

328

perceive the flow in our sensations without someparticular aptitude for it, will probably also beadmitted. The idea of forceat least, in its rudimentsisanother conception so early arrived at, and found inanimals so low in the scale of intelligence, that itmust be supposed innate. But the innateness of anidea admits of degree, for it consists in the tendencyof that idea to present itself to the mind. Some ideas,like that of space, do so present themselvesirresistibly at the very dawn of

329

intelligence, and take possession of the mind on smallprovocation, while of other conceptions we areprepossessed, indeed, but not so strongly, down ascale which is greatly extended. The tendency topersonify every thing, and to attribute humancharacters to it, may be said to be innate; but it is atendency which is very soon overcome by civilizedman in regard to the greater part of the objectsabout him. Take such a conception as that ofgravitation varying inversely as the square of thedistance. It is a very simple law. But to say that it issimple is merely to say that it is one which the mindis particularly adapted to apprehend with facility.Suppose the idea of a quantity multiplied into anotherhad been no more easy to the mind than that of aquantity raised to the power indicated by itselfshouldwe ever have discovered the law of the solar system?

It seems incontestable, therefore, that the mind ofman is strongly adapted to the comprehension of theworld; at least, so far as this goes, that certainconceptions, highly important for such acomprehension, naturally arise in his mind; and,without such a tendency, the mind could never have

330

had any development at all.

How are we to explain this adaptation? The greatutility and indispensableness of the conceptions oftime, space, and force, even to the lowestintelligence, are such as to suggest that they are theresults of natural selection. Without something likegeometrical, kinetical, and mechanical conceptions,no animal could seize his food or do anything whichmight be necessary for the preservation of thespecies. He might, it is true, be provided with aninstinct which would generally have the same effect;that is to say

331

he might have conceptions different from those oftime, space, and force, but which coincided withthem in regard to the ordinary cases of the animal'sexperience. But, as that animal would have animmense advantage in the struggle for life whosemechanical conceptions did not break down in anovel situation (such as development must bringabout), there would be a constant selection in favorof more and more correct ideas of these matters.Thus would be attained the knowledge of thatfundamental law upon which all science rolls; namely,that forces depend upon relations of time, space, andmass. When this idea was once sufficiently clear, itwould require no more than a comprehensible degreeof genius to discover the exact nature of theserelations. Such an hypothesis naturally suggestsitself, but it must be admitted that it does not seemsufficient to account for the extraordinary accuracywith which these conceptions apply to thephenomena of Nature, and it is probable that there issome secret here which remains to be discovered.

V

Some important questions of logic depend upon

332

whether we are to consider the material universe asof limited extent and finite age, or quite boundless inspace and in time. In the former case, it isconceivable that a general plan or design embracingthe whole universe should be discovered, and itwould be proper to be on the alert for some traces ofsuch a unity. In the latter case, since the proportionof the world of which we can have any experience isless than the smallest assignable fraction, it followsthat

333

we never could discover any pattern in the universeexcept a repeating one; any design embracing thewhole would be beyond our powers to discern, andbeyond the united powers of all intellects during alltime. Now, what is absolutely incapable of beingknown is, as we have seen in a former paper, not realat all. An absolutely incognizable existence is anonsensical phrase. If, therefore, the universe isinfinite, the attempt to find in it any designembracing it as a whole is futile, and involves a falseway of looking at the subject. If the universe neverhad any beginning, and if in space world stretchesbeyond world without limit, there is no whole ofmaterial things, and consequently no generalcharacter to the universe, and no need or possibilityof any governor for it. But if there was a time beforewhich absolutely no matter existed, if there arecertain absolute bounds to the region of thingsoutside of which there is a mere void, then wenaturally seek for an explanation of it, and, since wecannot look for it among material things, thehypothesis of a great disembodied animal, the creatorand governor of the world, is natural enough.

334

The actual state of the evidence as to the limitationof the universe is as follows: As to time, we find onour earth a constant progress of development sincethe planet was a red-hot ball; the solar system seemsto have resulted from the condensation of a nebula,and the process appears to be still going on. Wesometimes see stars (presumably with systems ofworlds) destroyed and apparently resolved back intothe nebulous condition, but we have no evidence ofany existence of the world previous to the nebulousstage from which it seems to have been evolved. Allthis rather

335

favors the idea of a beginning than otherwise. As forlimits in space, we cannot be sure that we seeanything outside of the system of the Milky Way.Minds of theological predilections have therefore noneed of distorting the facts to reconcile them withtheir views.

But the only scientific presumption is, that theunknown parts of space and time are like the knownparts, occupied; that, as we see cycles of life anddeath in all development which we can trace out tothe end, the same holds good in regard to solarsystems; that as enormous distances lie between thedifferent planets of our solar system, relatively to theirdiameters, and as still more enormous distances liebetween our system relatively to its diameter andother systems, so it may be supposed that othergalactic clusters exist so remote from ours as not tobe recognized as such with certainty. I do not saythat these are strong inductions; I only say that theyare the presumptions which, in our ignorance of thefacts, should be preferred to hypotheses whichinvolve conceptions of things and occurrences totallydifferent in their character from any of which we have

336

had any experience, such as disembodied spirits, thecreation of matter, infringements of the laws ofmechanics, etc.

The universe ought to be presumed too vast to haveany character. When it is claimed that thearrangements of Nature are benevolent, or just, orwise, or of any other peculiar kind, we ought to beprejudiced against such opinions, as being theoffspring of an ill-founded notion of the finitude of theworld. And examination has hitherto shown that suchbeneficences, justice, etc., are of a most limitedkindlimited in degree and limited in range.

337

In like manner, if any one claims to have discovered aplan in the structure of organized beings, or ascheme in their classification, or a regulararrangement among natural objects, or a system ofproportionality in the human form, or an order ofdevelopment, or a correspondence betweenconjunctions of the planets and human events, or asignificance in numbers, or a key to dreams, the firstthing we have to ask is whether such relations aresusceptible of explanation on mechanical principles,and if not they should be looked upon with disfavoras having already a strong presumption againstthem; and examination has generally exploded allsuch theories.

There are minds to whom every prejudice, everypresumption, seems unfair. It is easy to say whatminds these are. They are those who never haveknown what it is to draw a well-grounded induction,and who imagine that other people's knowledge is asnebulous as their own. That all science rolls uponpresumption (not of a formal but of a real kind) is noargument with them, because they cannot imaginethat there is anything solid in human knowledge.

338

These are the people who waste their time andmoney upon perpetual motions and other suchrubbish.

But there are better minds who take up mysticaltheories (by which I mean all those which have nopossibility of being mechanically explained). Theseare persons who are strongly prejudiced in favor ofsuch theories. We all have natural tendencies tobelieve in such things; our education oftenstrengthens this tendency; and the result is, that tomany minds nothing seems so antecedently probableas a theory of this kind. Such persons find evidenceenough

339

in favor of their views, and in the absence of anyrecognized logic of induction they cannot be drivenfrom their belief.

But to the mind of a physicist there ought to be astrong presumption against every mystical theory;and, therefore, it seems to me that those scientificmen who have sought to make out that science wasnot hostile to theology have not been so clear-sightedas their opponents.

It would be extravagant to say that science can atpresent disprove religion; but it does seem to me thatthe spirit of science is hostile to any religion exceptsuch a one as that of M. Vacherot. Our appointedteachers inform us that Buddhism is a miserable andatheistical faith, shorn of the most glorious andneedful attributes of a religion; that its priests can beof no use to agriculture by praying for rain, nor to warby commanding the sun to stand still. We also hearthe remonstances of those who warn us that to shakethe general belief in the living God would be to shakethe general morals, public and private. This, too,must be admitted; such a revolution of thought couldno more be accomplished without waste and

340

desolation than a plantation of trees could betransferred to new ground, however wholesome initself, without all of them languishing for a time, andmany of them dying. Nor is it, by-the-way, a thing tobe presumed that a man would have taken part in amovement having a possible atheistical issue withouthaving taken serious and adequate counsel in regardto that responsibility. But, let the consequences ofsuch a belief be as dire as they may, one thing iscertain: that the state of the facts, whatever it maybe, will surely get found out, and no human prudencecan long arrest the triumphal car

341

of truthno, not if the discovery were such as to driveevery individual of our race to suicide!

But it would be folly to suppose that anymetaphysical theory in regard to the mode of being ofthe perfect is to destroy that aspiration toward theperfect which constitutes the essence of religion. It istrue that, if the priests of any particular form ofreligion succeed in making it generally believed thatreligion cannot exist without the acceptance ofcertain formulas, or if they succeed in so interweavingcertain dogmas with the popular religion that thepeople can see no essential analogy between areligion which accepts these points of faith and onewhich rejects them, the result may very well be torender those who cannot believe these thingsirreligious. Nor can we ever hope that any body ofpriests should consider themselves more teachers ofreligion in general than of the particular system oftheology advocated by their own party. But no manneed be excluded from participation in the commonfeelings, nor from so much of the public expression ofthem as is open to all the laity, by the unphilosophicalnarrowness of those who guard the mysteries of

342

worship. Am I to be prevented from joining in thatcommon joy at the revelation of enlightenedprinciples of religion, which we celebrate at Easterand Christmas, because I think that certain scientific,logical, and metaphysical ideas which have beenmixed up with these principles are untenable? No; todo so would be to estimate those errors as of moreconsequence than the truth-an opinion which fewwould admit. People who do not believe what arereally the fundamental principles of Christianity arerare to find, and all but these few ought to feel athome in the churches.

343

Sixth Paper:Deduction, Induction, and Hypothesis1

I

The chief business of the logician is to classifyarguments; for all testing clearly depends onclassification. The classes of the logicians are definedby certain typical forms called syllogisms. Forexample, the syllogism called Barbara is as follows:

S is M; M is P:Hence, S is P.

Or, to put words for letters

Enoch and Elijah were men; all men die:Hence, Enoch and Elijah must have died.

The '' is P" of the logicians stands for any verb, activeor neuter. It is capable of strict proof (with which,however, I will not trouble the reader) that allarguments whatever can be put into this form; butonly under the condition that the is shall mean " is forthe purposes of the argument" or "is represented by."

344

Thus, an induction will appear in this form somethinglike this: These beans are two-thirds white;

But, the beans in this bag are (represented by) thesebeans;

1Popular Science Monthly, August, 1878.

345

\ The beans in the bag are two-thirds white.

But, because all inference may be reduced in someway to Barbara, it does not follow that this is themost appropriate form in which to represent everykind of inference. On the contrary, to show thedistinctive characters of different sorts of inference,they must clearly be exhibited in different formspeculiar to each. Barbara particularly typifiesdeductive reasoning; and so long as the is is takenliterally, no inductive reasoning can be put into thisform. Barbara is, in fact, nothing but the applicationof a rule. The so-called major premise lays down thisrule; as, for example, All men are mortal. The other orminor premise states a case under the rule; as, Enochwas a man. The conclusion applies the rule to thecase and states the result: Enoch is mortal. Alldeduction is of this character; it is merely theapplication of general rules to particular cases.Sometimes this is not very evident, as in thefollowing:

All quadrangles are figures,But no triangle is a quadrangle;Therefore, some figures are not triangles.

346

But here the reasoning is really this:

Rule.Every quadrangle is other than a triangle.Case.Some figures are quadrangles.Result.Some figures are not triangles.

Inductive or synthetic reasoning, being somethingmore than the mere application of a general rule to aparticular case, can never be reduced to this form.

If, from a bag of beans of which we know that 2/3are white, we take one at random, it is a deductiveinference

347

that this bean is probably white, the probability being2/3. We have, in effect, the following syllogism:

Rule.The beans in this bag are 2/3 white.Case.This bean has been drawn in such a way that inthe long run the relative number of white beans sodrawn would be equal to the relative number in thebag.Result.This bean has been drawn in such a way thatin the long run it would turn out white 2/3 of thetime.

If instead of drawing one bean we draw a handful atrandom and conclude that about 2/3 of the handfulare probably white, the reasoning is of the same sort.If, however, not knowing what proportion of whitebeans there are in the bag, we draw a handful atrandom and, finding 2/3 of the beans in the handfulwhite, conclude that about 2/3 of those in the bagare white, we are rowing up the current of deductivesequence, and are concluding a rule from theobservation of a result in a certain case. This isparticularly clear when all the handful turn out onecolor. The induction then is:

348

So that induction is the inference of the rule from thecase and result.

349

But this is not the only way of inverting a deductivesyllogism so as to produce a synthetic inference.Suppose I enter a room and there find a number ofbags, containing different kinds of beans. On thetable there is a handful of white beans; and, aftersome searching, I find one of the bags contains whitebeans only. I at once infer as a probability, or as afair guess, that this handful was taken out of thatbag. This sort of inference is called making anhypothesis.2 It is the inference of a case from a ruleand result. We have, then÷

DEDUCTION.

Rule.All the beans from this bag are white.Case.These beans are from this bag.\Result.These beans are white.

INDUCTION.

Case.These beans are from this bag.Result.These beans are white.\Rule.All the beans from this bag are white.

HYPOTHESIS.

Rule.All the beans from this bag are white.

350

Result.These beans are white.\Case.These beans are from this bag.

We, accordingly, classify all inference as follows:

2 [Later Pierce called it presumptive inference. SeeBaldwin's Dictionary art. Probable Inference.]

351

Induction is where we generalize from a number ofcases of which something is true, and infer that thesame thing is true of a whole class. Or, where we finda certain thing to be true of a certain proportion ofcases and infer that it is true of the same proportionof the whole class. Hypothesis is where we find somevery curious circumstance, which would be explainedby the supposition that it was a case of a certaingeneral rule, and thereupon adopt that supposition.Or, where we find that in certain respects two objectshave a strong resemblance, and infer that theyresemble one another strongly in other respects.

I once landed at a seaport in a Turkish province; and,as I was walking up to the house which I was to visit,I met a man upon horseback, surrounded by fourhorsemen holding a canopy over his head. As thegovernor of the province was the only personage Icould think of who would be so greatly honored, Iinferred that this was he. This was an hypothesis.

Fossils are found; say, remains like those of fishes,but far in the interior of the country. To explain thephenomenon, we suppose the sea once washed overthis land. This is another hypothesis.

352

Numberless documents and monuments refer to aconqueror called Napoleon Bonaparte. Though wehave not seen the man, yet we cannot explain whatwe have seen, namely, all these documents andmonuments, without supposing that he really existed.Hypothesis again.

As a general rule, hypothesis is a weak kind ofargument. It often inclines our judgment so slightlytoward its conclusion that we cannot say that webelieve the latter to

353

be true; we only surmise that it may be so. But thereis no difference except one of degree between suchan inference and that by which we are led to believethat we remember the occurrences of yesterday fromour feeling as if we did so.

II

Besides the way just pointed out of inverting adeductive syllogism to produce an induction orhypothesis, there is another. If from the truth of acertain premise the truth of a certain conclusionwould necessarily follow, then from the falsity of theconclusion the falsity of the premise would follow.Thus, take the following syllogism in Barbara:

Rule.All men are mortal.Case.Enoch and Elijah were men.\Result.Enoch and Elijah were mortal.

Now, a person who denies this result may admit therule, and, in that case, he must deny the case. Thus:

Denial of Result.Enoch and Elijah were not mortal.Rule. All men are mortal.\Denial of Case.Enoch and Elijah were not men.

354

This kind of syllogism is called Baroco, which is thetypical mood of the second figure. On the other hand,the person who denies the result may admit the case,and in that case he must deny the rule. Thus:

Denial of the Result.Enoch and Elijah were notmortal.Case.Enoch and Elijah were men.\Denial of the Rule.Some men are not mortal.

355

This kind of syllogism is called Bocardo, which is thetypical mood of the third figure.

Baroco and Bocardo are, of course, deductivesyllogisms; but of a very peculiar kind. They are calledby logicians indirect moods, because they need sometransformation to appear as the application of a ruleto a particular case. But if, instead of setting out aswe have here done with a necessary deduction inBarbara, we take a probable deduction of similarform, the indirect moods which we shall obtain will be

Corresponding to Baroco, an hypothesis;and, Corresponding to Bocardo, an induction.

For example, let us begin with this probablededuction in Barbara:

Rule.Most of the beans in this bag are white.Case.This handful of beans are from this bag.\Result.Probably, most of this handful of beansarewhite.

Now, deny the result, but accept the rule:

Denial of Result.Few beans of this handful are white.Rule.Most beans in this bag are white.

356

\Denial of Case.Probably, these beans were takenfrom another bag.

This is an hypothetical inference. Next, deny theresult, but accept the case:

Denial of Result.Few beans of this handful are white.Case.These beans came from this bag.

357

\Denial of Rule.Probably, few beans in the bag arewhite.

This is an induction.

The relation thus exhibited between synthetic anddeductive reasoning is not without its importance.When we adopt a certain hypothesis, it is not alonebecause it will explain the observed facts, but alsobecause the contrary hypothesis would probably leadto results contrary to those observed. So, when wemake an induction, it is drawn not only because itexplains the distribution of characters in the sample,but also because a different rule would probably haveled to the sample being other than it is.

But the advantage of this way of considering thesubject might easily be overrated. An induction isreally the inference of a rule, and to consider it as thedenial of a rule is an artificial conception, onlyadmissible because, when statistical or proportionalpropositions are considered as rules, the denial of arule is itself a rule. So, an hypothesis is really asubsumption of a case under a class and not thedenial of it, except for this, that to deny a

358

subsumption under one class is to admit asubsumption under another.

Bocardo may be considered as an induction, so timidas to lose its amplificative character entirely. Enochand Elijah are specimens of a certan kind of men. Allthat kind of men are shown by these instances to beimmortal. But instead of boldly concluding that allvery pious men, or all men favorites of the Almighty,etc., are immortal, we refrain from specifying thedescription of men, and rest in the merely explicativeinference that some men are im-

359

mortal. So Baroco might be considered as a verytimid hypothesis. Enoch and Elijah are not mortal.Now, we might boldly suppose them to be gods orsomething of that sort, but instead of that we limitourselves to the inference that they are of somenature different from that of man.

But, after all, there is an immense difference betweenthe relation of Baroco and Bocardo to Barbara andthat of Induction and Hypothesis to Deduction.Baroco and Bocardo are based upon the fact that ifthe truth of a conclusion necessarily follows from thetruth of a premise, then the falsity of the premisefollows from the falsity of the conclusion. This isalways true. It is different when the inference is onlyprobable. It by no means follows that, because thetruth of a certain premise would render the truth of aconclusion probable, therefore the falsity of theconclusion renders the falsity of the premiseprobable. At least, this is only true, as we have seenin a former paper, when the word probable is used inone sense in the antecedent and in another in theconsequent.

III

360

A certain anonymous writing is upon a torn piece ofpaper. It is suspected that the author is a certainperson. His desk, to which only he has had access, issearched, and in it is found a piece of paper, the tornedge of which exactly fits, in all its irregularities, thatof the paper in question. It is a fair hypotheticinference that the suspected man was actually theauthor. The ground of this inference evidently is thattwo torn pieces of paper are extremely

361

unlikely to fit together by accident. Therefore, of agreat number of inferences of this sort, but a verysmall proportion would be deceptive. The analogy ofhypothesis with induction is so strong that somelogicians have confounded them. Hypothesis hasbeen called an induction of characters. A number ofcharacters belonging to a certain class are found in acertain object; whence it is inferred that all thecharacters of that class belong to the object inquestion. This certainly involves the same principle asinduction; yet in a modified form. In the first place,characters are not susceptible of simple enumerationlike objects; in the next place, characters run incategories. When we make an hypothesis like thatabout the piece of paper, we only examine a singleline of characters, or perhaps two or three, and wetake no specimen at all of others. If the hypothesiswere nothing but an induction, all that we should bejustified in concluding, in the example above, wouldbe that the two pieces of paper which matched insuch irregularities as have been examined would befound to match in other, say slighter, irregularities.The inference from the shape of the paper to itsownership is precisely what distinguishes hypothesis

362

from induction, and makes it a bolder and moreperilous step.

The same warnings that have been given againstimagining that induction rests upon the uniformity ofNature might be repeated in regard to hypothesis.Here, as there, such a theory not only utterly fails toaccount for the validity of the inference, but it alsogives rise to methods of conducting it which areabsolutely vicious. There are, no doubt, certainuniformities in Nature, the knowledge of

363

which will fortify an hypothesis very much. Forexample, we suppose that iron, titanium, and othermetals exist in the sun, because we find in the solarspectrum many lines coincident in position with thosewhich these metals would produce; and thishypothesis is greatly strengthened by our knowledgeof the remarkable distinctiveness of the particular lineof characters observed. But such a fortification ofhypothesis is of a deductive kind, and hypothesis maystill be probable when such reënforcement iswanting.

There is no greater nor more frequent mistake inpractical logic than to suppose that things whichresemble one another strongly in some respects areany the more likely for that to be alike in others. Thatthis is absolutely false, admits of rigid demonstration;but, inasmuch as the reasoning is somewhat severeand complicated (requiring, like all such reasoning,the use of A, B, C, etc., to set it forth), the readerwould probably find it distasteful, and I omit it. Anexample, however, may illustrate the proposition: Thecomparative mythologists occupy themselves withfinding points of resemblance between solar

364

phenomena and the careers of the heroes of all sortsof traditional stories; and upon the basis of suchresemblances they infer that these heroes areimpersonations of the sun. If there be anything morein their reasonings, it has never been made clear tome. An ingenious logician, to show how futile all thatis, wrote a little book, in which he pretended toprove, in the same manner, that Napoleon Bonaparteis only an impersonation of the sun. It was reallywonderful to see how many points of resemblance hemade out. The truth is, that any two things resembleone another

365

just as strongly as any two others, if reconditeresemblances are admitted. But, in order that theprocess of making an hypothesis should lead to aprobable result, the following rules must be followed:

1. The hypothesis should be distinctly put as aquestion, before making the observations which areto test its truth. In other words, we must try to seewhat the result of predictions from the hypothesis willbe.

2. The respect in regard to which the resemblancesare noted must be taken at random. We must nottake a particular kind of predictions for which thehypothesis is known to be good.

3. The failures as well as the successes of thepredictions must be honestly noted. The wholeproceeding must be fair and unbiased.

Some persons fancy that bias and counter-bias arefavorable to the extraction of truththat hot andpartisan debate is the way to investigate. This is thetheory of our atrocious legal procedure. But Logicputs its heel upon this suggestion. It irrefragablydemonstrates that knowledge can only be furthered

366

by the real desire for it, and that the methods ofobstinacy, of authority, and every mode of trying toreach a foregone conclusion, are absolutely of novalue. These things are proved. The reader is atliberty to think so or not as long as the proof is notset forth, or as long as he refrains from examining it.Just so, he can preserve, if he likes, his freedom ofopinion in regard to the propositions of geometry;only, in that case, if he takes a fancy to read Euclid,he will do well to skip whatever he finds with A, B, C,etc., for, if he reads attentively

367

that disagreeable matter, the freedom of his opinionabout geometry may unhappily be lost forever.

How many people there are who are incapable ofputting to their own consciences this question, '' Do Iwant to know how the fact stands, or not? "

The rules which have thus far been laid down forinduction and hypothesis are such as are absolutelyessential. There are many other maxims expressingparticular contrivances for making syntheticinferences strong, which are extremely valuable andshould not be neglected. Such are, for example, Mr.Mill's four methods. Nevertheless, in the total neglectof these, inductions and hypotheses may andsometimes do attain the greatest force.

IV

Classifications in all cases perfectly satisfactory hardlyexist. Even in regard to the great distinction betweenexplicative and ampliative inferences, examples couldbe found which seem to lie upon the border betweenthe two classes, and to partake in some respects ofthe characters of either. The same thing is true of thedistinction between induction and hypothesis. In the

368

main, it is broad and decided. By induction, weconclude that facts, similar to observed facts, are truein cases not examined. By hypothesis, we concludethe existence of a fact quite different from anythingobserved, from which, according to known laws,something observed would necessarily result. Theformer, is reasoning from particulars to the generallaw; the latter, from effect to cause. The formerclassifies, the latter explains.

369

It is only in some special cases that there can bemore than a momentary doubt to which category agiven inference belongs. One exception is where weobserve, not facts similar under similar circumstances,but facts different under different circumstancesthedifference of the former having, however, a definiterelation to the difference of the latter. Suchinferences, which are really inductions, sometimespresent nevertheless some indubitable resemblancesto hypotheses.

Knowing that water expands by heat, we make anumber of observations of the volume of a constantmass of water at different temperatures. The scrutinyof a few of these suggests a form of algebraicalformula which will approximately express the relationof the volume to the temperature. It may be, forinstance, that v being the relative volume, and t thetemperature, a few observations examined indicate arelation of the form

Upon examining observations at other temperaturestaken at random, this idea is confirmed; and we drawthe inductive conclusion that all observations within

370

the limits of temperature from which we have drawnour observations could equally be so satisfied. Havingonce ascertained that such a formula is possible, it isa mere affair of arithmetic to find the values of a, b,and c, which will make the formula satisfy theobservations best. This is what physicists call anempirical formula, because it rests upon mereinduction, and is not explained by any hypothesis.

Such formulae, though very useful as means ofdescribing

371

in general terms the results of observations, do nottake any high rank among scientific discoveries. Theinduction which they embody, that expansion by heat(or whatever other phenomenon is referred to) takesplace in a perfectly gradual manner without suddenleaps or inummerable fluctuations, although reallyimportant, attracts no attention, because it is whatwe naturally anticipate. But the defects of suchexpressions are very serious. In the first place, aslong as the observations are subject to error, as allobservations are, the formula cannot be expected tosatisfy the observations exactly. But the discrepanciescannot be due solely to the errors of theobservations, but must be partly owing to the error ofthe formula which has been deducted from erroneousobservations. Moreover, we have no right to supposethat the real facts, if they could be had free fromerror, could be expressed by such a formula at all.They might, perhaps, be expressed by a similarformula with an infinite number of terms; but of whatuse would that be to us, since it would require aninfinite number of coefficients to be written down?When one quantity varies with another, if thecorresponding values are exactly known, it is a mere

372

matter of mathematical ingenuity to find some way ofexpressing their relation in a simple manner. If onequantity is of one kindsay, a specific gravityand theother of another kind-say, a temperaturewe do notdesire to find an expression for their relation which iswholly free from numerical constants, since if it werefree from them when, say, specific gravity ascompared with water, and temperature as expressedby the Centigrade thermometer, were in question,numbers would have to be in-

373

troduced when the scales of measurement werechanged. We may, however, and do desire to findformulas expressing the relations of physicalphenomena which shall contain no more arbitrarynumbers than changes in the scales of measurementmight require.

When a formula of this kind is discovered, it is nolonger called an empirical formula, but a law ofNature; and is sooner or later made the basis of anhypothesis which is to explain it. These simpleformulae are not usually, if ever, exactly true, butthey are none the less important for that; and thegreat triumph of the hypothesis comes when itexplains not only the formula, but also the deviationsfrom the formula. In the current language of thephysicists, an hypothesis of this importance is called atheory, while the term hypothesis is restricted tosuggestions which have little evidence in their favor.There is some justice in the contempt which clings tothe word hypothesis. To think that we can strike outof our own minds a true preconception of how Natureacts, in a vain fancy. As Lord Bacon well says: " Thesubtlety of Nature far exceeds the subtlety of sense

374

and intellect: so that these fine meditations, andspeculations, and reasonings of men are a sort ofinsanity, only there is no one at hand to remark it."The successful theories are not pure guesses, but areguided by reasons.

The kinetical theory of gases is a good example ofthis. This theory is intended to explain certain simpleformulae, the chief of which is called the law of Boyle.It is, that if air or any other gas be placed in acylinder with a piston, and if its volume be measuredunder the pressure of the

375

atmosphere, say fifteen pounds on the square inch,and if then another fifteen pounds per square inch beplaced on the piston, the gas will be compressed toone-half its bulk, and in similar inverse ratio for otherpressures. The hypothesis which has been adopted toaccount for this law is that the molecules of a gas aresmall, solid particles at great distances from eachother (relatively to their dimensions), and movingwith great velocity, without sensible attractions orrepulsions, until they happen to approach oneanother very closely. Admit this, and it follows thatwhen a gas is under pressure what prevents it fromcollapsing is not the incompressibility of the separatemolecules, which are under no pressure at all, sincethey do not touch, but the pounding of the moleculesagainst the piston. The more the piston falls, and themore the gas is compressed, the nearer together themolecules will be; the greater number there will be atany moment within a given distance of the piston,the shorter the distance which any one will go beforeits course is changed by the influence of another, thegreater number of new courses of each in a giventime, and the oftener each, within a given distance ofthe piston, will strike it. This explains Boyle's law. The

376

law is not exact; but the hypothesis does not lead usto it exactly. For, in the first place, if the moleculesare large, they will strike each other oftener whentheir mean distances are diminished, and willconsequently strike the piston oftener, and willproduce more pressure upon it. On the other hand, ifthe molecules have an attraction for one another,they will remain for a sensible time within oneanother's influence, and consequently they will notstrike

377

the wall so often as they otherwise would, and thepressure will be less increased by compression.

When the kinetical theory of gases was first proposedby Daniel Bernoulli, in 1738, it rested only on the lawof Boyle, and was therefore pure hypothesis. It wasaccordingly quite naturally and deservedly neglected.But, at present, the theory presents quite anotheraspect; for, not to speak of the considerable numberof observed facts of different kinds with which it hasbeen brought into relation, it is supported by themechanical theory of heat. That bringing togetherbodies which attract one another, or separatingbodies which repel one another, when sensiblemotion is not produced nor destroyed, is alwaysaccompanied by the evolution of heat, is little morethan an induction. Now, it has been shown byexperiment that, when a gas is allowed to expandwithout doing work, a very small amount of heatdisappears. This proves that the particles of the gasattract one another slightly, and but very slightly. Itfollows that, when a gas is under pressure, whatprevents it from collapsing is not any repulsionbetween the particles, since there is none. Now,

378

there are only two modes of force known to us, forceof position or attractions and repulsions, and force ofmotion. Since, therefore, it is not the force of positionwhich gives a gas its expansive force, it must be theforce of motion. In this point of view, the kineticaltheory of gases appears as a deduction from themechanical theory of heat. It is to be observed,however, that it supposes the same law of mechanics(that there are only those two modes of force) whichholds in regard to bodies such as we can see andexamine, to hold also for

379

what are very different, the molecules of bodies. Sucha supposition has but a slender support frominduction. Our belief in it is greatly strengthened byits connection with the law of Boyle, and it is,therefore, to be considered as an hypotheticalinference. Yet it must be admitted that the kineticaltheory of gases would deserve little credence if it hadnot been connected with the principles of mechanics.

The great difference between induction andhypothesis is, that the former infers the existence ofphenomena such as we have observed in cases whichare similar, while hypothesis supposes something of adifferent kind from what we have directly observed,and frequently something which it would beimpossible for us to observe directly. Accordingly,when we stretch an induction quite beyond the limitsof our observation, the inference partakes of thenature of hypothesis. It would be absurd to say thatwe have no inductive warrant for a generalizationextending a little beyond the limits of experience, andthere is no line to be drawn beyond which we cannotpush our inference; only it becomes weaker thefurther it is pushed. Yet, if an induction be pushed

380

very far, we cannot give it much credence unless wefind that such an extension explains some fact whichwe can and do observe. Here, then, we have a kindof mixture of induction and hypothesis supportingone another; and of this kind are most of the theoriesof physics.

381

V

That synthetic inferences may be divided intoinduction and hypothesis in the manner hereproposed,3 admits of no question. The utility andvalue of the distinction are to be tested by theirapplications.

Induction is, plainly, a much stronger kind ofinference than hypothesis; and this is the first reasonfor distinguishing between them. Hypotheses aresometimes regarded as provisional resorts, which inthe progress of science are to be replaced byinductions. But this is a false view of the subject.Hypothetic reasoning infers very frequently a fact notcapable of direct observation. It is an hypothesis thatNapoleon Bonaparte once existed. How is thathypothesis ever to be replaced by an induction? Itmay be said that from the premise that such facts aswe have observed are as they would be if Napoleonexisted, we are to infer by induction that all facts thatare hereafter to be observed will be of the samecharacter. There is no doubt that every hypotheticinference may be distorted into the appearance of aninduction in this way. But the essence of an induction

382

is that it infers from one set of facts another set ofsimilar facts, whereas hypothesis infers from facts ofone kind to facts of another. Now, the facts whichserve as grounds for our belief in the historic reality ofNapoleon are not by any means necessarily the onlykind of facts which are explained by his existence. Itmay be that, at

3 This division was first made in a course of lectures bythe author before the Lowell Institute, Boston, in 1866,and was printed in the Proceedings of the AmericanAcademy of Arts and Sciences, for April 9, 1867.

383

the time of his career, events were being recorded insome way not now dreamed of, that some ingeniouscreature on a neighboring planet was photographingthe earth, and that these pictures on a sufficientlylarge scale may some time come into our possession,or that some mirror upon a distant star will, when thelight reaches it, reflect the whole story back to earth.Never mind how improbable these suppositions are;everything which happens is infinitely improbable. Iam not saying that these things are likely to occur,but that some effect of Napoleon's existence whichnow seems impossible is certain nevertheless to bebrought about. The hypothesis asserts that suchfacts, when they do occur, will be of a nature toconfirm, and not to refute, the existence of the man.We have, in the impossibility of inductively inferringhypothetical conclusions, a second reason fordistinguishing between the two kinds of inference.

A third merit of the distinction is, that it is associatedwith an important psychological or ratherphysiological difference in the mode of apprehendingfacts. Induction infers a rule. Now, the belief of a ruleis a habit. That a habit is a rule active in us, is

384

evident. That every belief is of the nature of a habit,in so far as it is of a general character, has beenshown in the earlier papers of this series. Induction,therefore, is the logical formula which expresses thephysiological process of formation of a habit.Hypothesis substitutes, for a complicated tangle ofpredicates attached to one subject, a singleconception. Now, there is a peculiar sensationbelonging to the act of thinking that each of thesepredicates inheres in the subject. In hypotheticinference this complicated feeling so produced

385

is replaced by a single feeling of greater intensity,that belonging to the act of thinking the hypotheticconclusion. Now, when our nervous system is excitedin a complicated way, there being a relation betweenthe elements of the excitation, the result is a singleharmonious disturbance which I call an emotion.Thus, the various sounds made by the instruments ofan orchestra strike upon the ear, and the result is apeculiar musical emotion, quite distinct from thesounds themselves. This emotion is essentially thesame thing as an hypothetic inference, and everyhypothetic inference involves the formation of suchan emotion. We may say, therefore, that hypothesisproduces the sensuous element of thought, andinduction the habitual element. As for deduction,which adds nothing to the premises, but only out ofthe various facts represented in the premises selectsone and brings the attention down to it, this may beconsidered as the logical formula for paying attention,which is the volitional element of thought, andcorresponds to nervous discharge in the sphere ofphysiology.

Another merit of the distinction between induction

386

and hypothesis is, that it leads to a very naturalclassification of the sciences and of the minds whichprosecute them. What must separate different kindsof scientific men more than anything else are thedifferences of their techniques. We cannot expectmen who work with books chiefly to have much incommon with men whose lives are passed inlaboratories. But, after differences of this kind, thenext most important are differences in the modes ofreasoning. Of the natural sciences, we have, first, theclassificatory sciences, which are purelyinductivesystematic botany

387

and zoölogy, mineralogy, and chemistry. Then, wehave the sciences of theory, as aboveexplainedastronomy, pure physics, etc. Then, wehave sciences of hypothesisgeology, biology, etc.

There are many other advantages of the distinction inquestion which I shall leave the reader to find out byexperience. If he will only take the custom ofconsidering whether a given inference belongs to oneor other of the two forms of synthetic inference givenon page 134, I can promise him that he will find hisadvantage in it, in various ways.

388

PART IILOVE AND CHANCE

389

IThe Architecture of Theories1

Of the fifty or hundred systems of philosophy thathave been advanced at different times of the world'shistory, perhaps the larger number have been, not somuch results of historical evolution, as happythoughts which have accidently occurred to theirauthors. An idea which has been found interestingand fruitful has been adopted, developed, and forcedto yield explanations of all sorts of phenomena. TheEnglish have been particularly given to this way ofphilosophizing; witness, Hobbes, Hartley, Berkeley,James Mill. Nor has it been by any means uselesslabor; it shows us what the true nature and value ofthe ideas developed are, and in that way affordsserviceable materials for philosophy. Just as if a man,being seized with the conviction that paper was agood material to make things of, were to go to workto build a papier mâché house, with roof of roofing-paper, foundations of pasteboard, windows ofparaffined paper, chimneys, bath tubs, locks, etc., all

390

of different forms of paper, his experiment wouldprobably afford valuable lessons to builders, while itwould certainly make a detestable house, so thoseone-idea'd philosophies are exceedingly interestingand instructive, and yet are quite unsound.

The remaining systems of philosophy have been ofthe nature of reforms, sometimes amounting toradical revolutions. suggested by certain difficultieswhich have been found

1 The Monist, January, 1891.

391

to beset systems previously in vogue; and such oughtcertainly to be in large part the motive of any newtheory. This is like partially rebuilding a house. Thefaults that have been committed are, first, that therepairs of the dilapidations have generally not beensufficiently thoroughgoing, and second, that notsufficient pains had been taken to bring the additionsinto deep harmony with the really sound parts of theold structure.

When a man is about to build a house, what a powerof thinking he has to do, before he can safely breakground! With what pains he has to excogitate theprecise wants that are to be supplied! What a studyto ascertain the most available and suitable materials,to determine the mode of construction to which thosematerials are best adapted, and to answer a hundredsuch questions! Now without riding the metaphor toofar, I think we may safely say that the studiespreliminary to the construction of a great theoryshould be at least as deliberate and thorough asthose that are preliminary to the building of adwelling-house.

That systems ought to be constructed

392

architectonically has been preached since Kant, but Ido not think the full import of the maxim has by anymeans been apprehended. What I would recommendis that every person who wishes to form an opinionconcerning fundamental problems, should first of allmake a complete survey of human knowledge, shouldtake note of all the valuable ideas in each branch ofscience, should observe in just what respect each hasbeen successful and where it has failed, in order thatin the light of the thorough acquaintance so attainedof the available

393

materials for a philosophical theory and of the natureand strength of each, he may proceed to the study ofwhat the problem of philosophy consists in, and ofthe proper way of solving it. I must not beunderstood as endeavoring to state fully all that thesepreparatory studies should embrace; on the contrary,I purposely slur over many points, in order to giveemphasis to one special recommendation, namely, tomake a systematic study of the conceptions out ofwhich a philosophical theory may be built, in order toascertain what place each conception may fitlyoccupy in such a theory, and to what uses it isadapted.

The adequate treatment of this single point would filla volume, but I shall endeavor to illustrate mymeaning by glancing at several sciences andindicating conceptions in them serviceable forphilosophy. As to the results to which long studiesthus commenced have led me, I shall just give a hintat their nature.

We may begin with dynamics,field in our day ofperhaps the grandest conquest human science hasever made,I mean the law of the conservation of

394

energy. But let us revert to the first step taken bymodern scientific thought,and a great stride itwas,the inauguration of dynamics by Galileo. Amodern physicist on examining Galileo's works issurprised to find how little experiment had to do withthe establishment of the foundations of mechanics.His principal appeal is to common sense and il lumenaturale. He always assumes that the true theory willbe found to be a simple and natural one. And we cansee why it should indeed be so in dynamics. Forinstance, a body left to its own inertia, moves in astraight line, and

395

a straight line appears to us the simplest of curves. Initself, no curve is simpler than another. A system ofstraight lines has intersections preciselycorresponding to those of a system of like parabolassimilarly placed, or to those of any one of an infinityof systems of curves. But the straight line appears tous simple, because, as Euclid says, it lies evenlybetween its extremities; that is, because viewedendwise it appears as a point. That is, again, becauselight moves in straight lines. Now, light moves instraight lines because of the part which the straightline plays in the laws of dynamics. Thus it is that ourminds having been formed under the influence ofphenomena governed by the laws of mechanics,certain conceptions entering into those laws becomeimplanted in our minds, so that we readily guess atwhat the laws are. Without such a natural prompting,having to search blindfold for a law which would suitthe phenomena, our chance of finding it would be asone to infinity. The further physical studies departfrom phenomena which have directly influenced thegrowth of the mind, the less we can expect to findthe laws which govern them ''simple," that is,composed of a few conceptions natural to our minds.

396

The researches of Galileo, followed up by Huygensand others, led to those modern conceptions of Forceand Law, which have revolutionized the intellectualworld. The great attention given to mechanics in theseventeenth century soon so emphasized theseconceptions as to give rise to the MechanicalPhilosophy, or doctrine that all the phenomena of thephysical universe are to be explained uponmechanical principles. Newton's great discoveryimparted a new

397

impetus to this tendency. The old notion that heatconsists in an agitation of corpuscles was now appliedto the explanation of the chief properties of gases.The first suggestion in this direction was that thepressure of gases is explained by the battering of theparticles against the walls of the containing vessel,which explained Boyle's law of the compressibility ofair. Later, the expansion of gases, Avogadro'schemical law, the diffusion and viscosity of gases, andthe action of Crookes's radiometer were shown to beconsequences of the same kinetical theory; but otherphenomena, such as the ratio of the specific heat atconstant volume to that at constant pressure, requireadditional hypotheses, which we have little reason tosuppose are simple, so that we find ourselves quiteafloat. In like manner with regard to light. That itconsists of vibrations was almost proved by thephenomena of diffraction, while those of polarizationshowed the excursions of the particles to beperpendicular to the line of propagation; but thephenomena of dispersion, etc., require additionalhypotheses which may be very complicated. Thus,the further progress of molecular speculation appearsquite uncertain. If hypotheses are to be tried

398

haphazard, or simply because they will suit certainphenomena, it will occupy the mathematicalphysicists of the world say half a century on theaverage to bring each theory to the test, and sincethe number of possible theories may go up into thetrillions, only one of which can be true, we have littleprospect of making further solid additions to thesubject in our time. When we come to atoms, thepresumption in favor of a simple law seems veryslender. There is room for serious doubt

399

whether the fundamental laws of mechanics holdgood for single atoms, and it seems quite likely thatthey are capable of motion in more than threedimensions.

To find out much more about molecules and atoms,we must search out a natural history of laws ofnature, which may fulfil that function which thepresumption in favor of simple laws fulfilled in theearly days of dynamics, by showing us what kind oflaws we have to expect and by answering suchquestions as this: Can we with reasonable prospect ofnot wasting time, try the supposition that atomsattract one another inversely as the seventh power oftheir distances, or can we not? To suppose universallaws of nature capable of being apprehended by themind and yet having no reason for their special forms,but standing inexplicable and irrational, is hardly ajustifiable position. Uniformities are precisely the sortof facts that need to be accounted for. That a pitchedcoin should sometimes turn up heads and sometimestails calls for no particular explanation; but if it showsheads every time, we wish to know how this resulthas been brought about. Law is par excellence the

400

thing that wants a reason.

Now the only possible way of accounting for the lawsof nature and for uniformity in general is to supposethem results of evolution. This supposes them not tobe absolute, not to be obeyed precisely. It makes anelement of indeterminacy, spontaneity, or absolutechance in nature. Just as, when we attempt to verifyany physical law, we find our observations cannot beprecisely satisfied by it, and rightly attribute thediscrepancy to errors of observation, so we mustsuppose far more minute discrepancies to

401

exist owing to the imperfect cogency of the law itself,to a certain swerving of the facts from any definiteformula.

Mr. Herbert Spencer wishes to explain evolution uponmechanical principles. This is illogical, for fourreasons. First, because the principle of evolutionrequires no extraneous cause; since the tendency togrowth can be supposed itself to have grown from aninfinitesimal germ accidentally started. Second,because law ought more than anything else to besupposed a result of evolution. Third, because exactlaw obviously never can produce heterogeneity out ofhomogeneity; and arbitrary heterogeneity is thefeature of the universe the most manifest andcharacteristic. Fourth, because the law of theconservation of energy is equivalent to theproposition that all operations governed bymechanical laws are reversible; so that an immediatecorollary from it is that growth is not explicable bythose laws, even if they be not violated in the processof growth. In short, Spencer is not a philosophicalevolutionist, but only a half-evolutionist,or, if you will,only a semi-Spencerian. Now philosophy requires

402

thoroughgoing evolutionism or none.

The theory of Darwin was that evolution had beenbrought about by the action of two factors: first,heredity, as a principle making offspring nearlyresemble their parents, while yet giving room for "sporting," or accidental variations,for very slightvariations often, for wider ones rarely; and, second,the destruction of breeds or races that are unable tokeep the birth rate up to the death rate. ThisDarwinian principle is plainly capable of greatgeneralization. Wherever there are large numbers ofobjects,

403

having a tendency to retain certain charactersunaltered, this tendency, however, not beingabsolute but giving room for chance variations, then,if the amount of variation is absolutely limited incertain directions by the destruction of everythingwhich reaches those limits, there will be a gradualtendency to change in directions of departure fromthem. Thus, if a million players sit down to bet at aneven game, since one after another will get ruined,the average wealth of those who remain willperpetually increase. Here is indubitably a genuineformula of possible evolution, whether its operationaccounts for much or little in the development ofanimal and vegetable species.

The Lamarckian theory also supposes that thedevelopment of species has taken place by a longseries of insensible changes, but it supposes thatthose changes have taken place during the lives ofthe individuals, in consequence of effort and exercise,and that reproduction plays no part in the processexcept in preserving these modifications. Thus, theLamarckian theory only explains the development ofcharacters for which individuals strive, while the

404

Darwinian theory only explains the production ofcharacters really beneficial to the race, though thesemay be fatal to individuals.2 But more broadly andphilosophically conceived, Darwinian evolution isevolution by the operation of chance, and thedestruction of bad results, while Lamarckian evolutionis evolution by the effect of habit and effort.

A third theory of evolution is that of Mr. ClarenceKing.

2 The neo-Darwinian, Weismann, has shown thatmortality would almost necessarily result from theaction of the Darwinian principle.

405

The testimony of monuments and of rocks is thatspecies are unmodified or scarcely modified, underordinary circumstances, but are rapidly altered aftercataclysms or rapid geological changes. Under novelcircumstances, we often see animals and plantssporting excessively in reproduction, and sometimeseven undergoing transformations during individuallife, phenomena no doubt due partly to theenfeeblement of vitality from the breaking up ofhabitual modes of life, partly to changed food, partlyto direct specific influence of the element in whichthe organism is immersed. If evolution has beenbrought about in this way, not only have its singlesteps not been insensible, as both Darwinians andLamarckians suppose, but they are furthermoreneither haphazard on the one hand, nor yetdetermined by an inward striving on the other, but onthe contrary are effects of the changed environment,and have a positive general tendency to adapt theorganism to that environment, since variation willparticularly affect organs at once enfeebled andstimulated. This mode of evolution, by external forcesand the breaking up of habits, seems to be called forby some of the broadest and most important facts of

406

biology and paleontology; while it certainly has beenthe chief factor in the historical evolution ofinstitutions as in that of ideas; and cannot possibly berefused a very prominent place in the process ofevolution of the universe in general.

Passing to psychology, we find the elementaryphenomena of mind fall into three categories. First,we have Feelings, comprising all that is immediatelypresent, such as pain, blue, cheerfulness, the feelingthat arises when we contem-

407

plate a consistent theory, etc. A feeling is a state ofmind having its own living quality, independent ofany other state of mind. Or, a feeling is an element ofconsciousness which might conceivably override everyother state until it monopolized the mind, althoughsuch a rudimentary state cannot actually be realized,and would not properly be consciousness. Still, it isconceivable, or supposable, that the quality of blueshould usurp the whole mind, to the exclusion of theideas of shape, extension, contrast, commencementand cessation, and all other ideas, whatsoever. Afeeling is necessarily perfectly simple, in itself, for if ithad parts these would also be in the mind, wheneverthe whole was present, and thus the whole could notmonopolize the mind.3

Besides Feelings, we have Sensations of reaction; aswhen a person blindfold suddenly runs against apost, when we make a muscular effort, or when anyfeeling gives way to a new feeling. Suppose I hadnothing in my mind but a feeling of blue, which weresuddenly to give place to a feeling of red; then, atthe instant of transition there would be a shock, asense of reaction, my blue life being transmuted into

408

red life. If I were further endowed with a memory,that sense would continue for some time, and therewould also be a peculiar feeling or sentimentconnected with it. This last feeling might endure(conceivably I mean) after the memory of theoccurrence and the feelings of blue and red hadpassed away. But the sensation of reaction cannotexist except in the actual presence of the

3 A feeling may certainly be compound, but only invirtue of a perception which is not that feeling nor anyfeeling at all.

409

two feelings blue and red to which it relates.Wherever we have two feelings and pay attention toa relation between them of whatever kind, there isthe sensation of which I am speaking. But the senseof action and reaction has two types: it may either bea perception of relation between two ideas, or it maybe a sense of action and reaction between feelingand something out of feeling. And this sense ofexternal reaction again has two forms; for it is eithera sense of something happening to us, by no act ofours, we being passive in the matter, or it is a senseof resistance, that is, of our expending feeling uponsomething without. The sense of reaction is thus asense of connection or comparison between feelings,either, A, between one feeling and another, or B,between feeling and its absence or lower degree; andunder B we have, First, the sense of the access offeeling, and Second, the sense of remission of feeling.

Very different both from feelings and from reaction-sensations or disturbances of feeling are generalconceptions. When we think, we are conscious that aconnection between feelings is determined by ageneral rule, we are aware of being governed by a

410

habit. Intellectual power is nothing but facility intaking habits and in following them in casesessentially analogous to, but in non-essentials widelyremote from, the normal cases of connections offeelings under which those habits were formed.

The one primary and fundamental law of mentalaction consists in a tendency to generalization.Feeling tends to spread; connections betweenfeelings awaken feelings; neighboring feelingsbecome assimilated; ideas are apt to

411

reproduce themselves. These are so manyformulations of the one law of the growth of mind.When a disturbance of feeling takes place, we have aconsciousness of gain, the gain of experience; and anew disturbance will be apt to assimilate itself to theone that preceded it. , Feelings, by being excited,become more easily excited, especially in the ways inwhich they have previously been excited. Theconsciousness of such a habit constitutes a generalconception.

The cloudiness of psychological notions may becorrected by connecting them with physiologicalconceptions. Feeling may be supposed to exist,wherever a nerve-cell is in an excited condition. Thedisturbance of feeling, or sense of reaction,accompanies the transmission of disturbancebetween nerve-cells or from a nerve-cell to a muscle-cell or the external stimulation of a nerve-cell. Generalconceptions arise upon the formation of habits in thenerve-matter, which are molecular changesconsequent upon its activity and probably connectedwith its nutrition.

The law of habit exhibits a striking contrast to all

412

physical laws in the character of its commands. Aphysical law is absolute. What it requires is an exactrelation. Thus, a physical force introduces into amotion a component motion to be combined with therest by the parallelogram of forces; but thecomponent motion must actually take place exactlyas required by the law of force. On the other hand,no exact conformity is required by the mental law.Nay, exact conformity would be in downright conflictwith the law; since it would instantly crystallizethought and prevent all further formation of habit.The law of mind only makes a given feeling morelikely to arise. It

413

thus resembles the "non-conservative" forces ofphysics, such as viscosity and the like, which are dueto statistical uniformities in the chance encounters oftrillions of molecules.

The old dualistic notion of mind and matter, soprominent in Cartesianism, as two radically differentkinds of substance, will hardly find defenders to-day.Rejecting this, we are driven to some form ofhylopathy, otherwise called monism. Then thequestion arises whether physical laws on the onehand, and the psychical law on the other are to betaken

(A) as independent, a doctrine often called monism,but which I would name neutralism; or,

(B) the psychical law as derived and special, thephysical law alone as primordial, which is materialism;or,

(C) the physical law as derived and special, thepsychical law alone as primordial, which is idealism.

The materialistic doctrine seems to me quite asrepugnant to scientific logic as to common sense;

414

since it requires us to suppose that a certain kind ofmechanism will feel, which would be a hypothesisabsolutely irreducible to reason, an ultimate,inexplicable regularity; while the only possiblejustification of any theory is that it should makethings clear and reasonable.

Neutralism is sufficiently condemned by the logicalmaxim known as Ockham's razor, i.e., that not moreindependent elements are to be supposed thannecessary. By placing the inward and outwardaspects of substance on a par, it seems to renderboth primordial.

The one intelligible theory of the universe is that ofob-

415

jective idealism, that matter is effete mind, inveteratehabits becoming physical laws. But before this can beaccepted it must show itself capable of explaining thetridimensionality of space, the laws of motion, andthe general characteristics of the universe, withmathematical clearness and precision; for no lessshould be demanded of every Philosophy.

Modern mathematics is replete with ideas which maybe applied to philosophy. I can only notice one ortwo. The manner in which mathematicians generalizeis very instructive. Thus, painters are accustomed tothink of a picture

as consisting geometrically of the intersections of itsplane by rays of light from the natural objects to the

416

eye. But geometers use a generalized perspective.4For instance in the figure let O be the eye, let A B CD E be the edge-

4 [The reader will find further light on the followingillustration in any text-book of projective geometry,e.g., Reye, Geometry of Position, I, pp. 1724, or Encyc.Britannca, XI, p. 689.]

417

wise view of any plane, and let a f e D c be theedgewise view of another plane. The geometers drawrays through O cutting both these planes, and treatthe points of intersection of each ray with one planeas representing the point of intersection of the sameray with the other plane. Thus, e represents E, in thepainter's way. D represents itself. C is represented byc, which is further from the eye; and A is representedby a which is on the other side of the eye. Suchgeneralization is not bound down to sensuousimages. Further, according to this mode ofrepresentation every point on one plane represents apoint on the other, and every point on the latter isrepresented by a point on the former. But how aboutthe point f which is in a direction from O parallel tothe represented plane, and how about the point Bwhich is in a direction parallel to the representingplane? Some will say that these are exceptions; butmodern mathematics does not allow exceptions whichcan be annulled by generalization.5 As a point movesfrom C to D and thence to E and off toward infinity,the corresponding point on the other plane movesfrom c to D and thence to e and toward f. But thissecond point can pass through f to a; and when it is

418

there the first point has arrived at A. We thereforesay that the first point has passed through infinity,and that every line joins in to itself somewhat like anoval. Geometers talk of

5 [A more familiar example of this is the introduction ofirrational or surd numbers like . After it was provedthat no ratio of two integers could possibly equal theidea of number was generalized to include the latter.Fractions and the so-called imaginary numbersillustrate the same process of generalization for thesake of making certain operations (i.e. division andfinding the root) continuously applicable.

419

the parts of lines at an infinite distance as points.This is a kind of generalization very efficient inmathematics.

Modern views of measurement have a philosophicalaspect. There is an indefinite number of systems ofmeasuring along a line; thus, a perspectiverepresentation of a scale on one line may be taken tomeasure another, although of course suchmeasurements will not agree with what we call thedistances of points on the latter line. To establish asystem of measurement on a line we must assign adistinct number to each point of it, and for thispurpose we shall plainly have to suppose thenumbers carried out into an infinite number of placesof decimals. These numbers must be ranged alongthe line in unbroken sequence. Further, in order thatsuch a scale of numbers should be of any use, it mustbe capable of being shifted into new positions, eachnumber continuing to be attached to a single distinctpoint. Now it is found that if this is true for''imaginary" as well as for real points (an expressionwhich I cannot stop to elucidate), any such shiftingwill necessarily leave two numbers attached to the

420

same points as before. So that when the scale ismoved over the line by any continuous series ofshiftings of one kind, there are two points which nonumbers on the scale can ever reach, except thenumbers fixed there. This pair of points, thusunattainable in measurement, is called the Absolute.These two points may be distinct and real, or theymay coincide, or they may be both imaginary. As anexample of a linear quantity with a double absolutewe may take probability, which ranges from anunattainable absolute certainty against a propositionto an equally unattainable absolute

421

certainty for it. A line, according to ordinary notions,we have seen is a linear quantity where the twopoints at infinity coincide. A velocity is anotherexample. A train going with infinite velocity fromChicago to New York would be at all the points on theline at the very same instant, and if the time oftransit were reduced to less than nothing it would bemoving in the other direction. An angle is a familiarexample of a mode of magnitude with no realimmeasurable values. One of the questionsphilosophy has to consider is whether thedevelopment of the universe is like the increase of anangle, so that it proceeds forever without tendingtoward anything unattained, which I take to be theEpicurean view, or whether the universe sprang froma chaos in the infinitely distant past to tend towardsomething different in the infinitely distant future, orwhether the universe sprang from nothing in the pastto go on indefinitely toward a point in the infinitelydistant future, which, were it attained, would be themere nothing from which it set out.

The doctrine of the absolute applied to space comesto this, that either

422

First, space is, as Euclid teaches, both unlimited andimmeasurable, so that the infinitely distant parts ofany plane seen in perspective appear as a straightline, in which case the sum of the three angles of atriangle amounts to 180°; or,

Second, space is immeasurable but limited, so thatthe infinitely distant parts of any plane seen inperspective appear as a circle, beyond which all isblackness, and in this case the sum of the threeangles of a triangle is less

423

than 180° by an amount proportional to the area ofthe triangle; or,

Third, space is unlimited but finite, (like the surfaceof a sphere), so that it has no infinitely distant parts;but a finite journey along any straight line wouldbring one back to his original position, and looking offwith an unobstructed view one would see the back ofhis own head enormously magnified, in which casethe sum of the three angles of a triangle exceeds180° by an amount proportional to the area.

Which of these three hypotheses is true we know not.The largest triangles we can measure are such ashave the earth's orbit for base, and the distance of afixed star for altitude. The angular magnituderesulting from subtracting the sum of the two anglesat the base of such a triangle from 180° is called thestar's parallax. The parallaxes of only about forty starshave been measured as yet. Two of them come outnegative, that of Arided (a Cycni), a star ofmagnitude 1 1\2, which is0."082, according to C. A.F. Peters, and that of a star of magnitude 7 3/4,known as Piazzi III 422, which is0."045, according toR. S. Ball. But these negative parallaxes are

424

undoubtedly to be attributed to errors of observation;for the probable error of such a determination isabout 0."075, and it would be strange indeed if wewere to be able to see, as it were, more than halfway round space, without being able to see starswith larger negative parallaxes. Indeed, the very factthat of all the parallaxes measured only two come outnegative would be a strong argument that thesmallest parallaxes really amount to + 0."1, were itnot for the re-

425

flection that the publication of other negativeparallaxes may have been suppressed. I think wemay feel confident that the parallax of the furtheststar lies somewhere between0."05 and + 0."15, andwithin another century our grandchildren will surelyknow whether the three angles of a triangle aregreater or less than 180°,that they are exactly thatamount is what nobody ever can be justified inconcluding. It is true that according to the axioms ofgeometry the sum of the three sides of a triangle areprecisely 180°; but these axioms are now exploded,and geometers confess that they, as geometers,know not the slightest reason for supposing them tobe precisely true. They are expressions of our inbornconception of space, and as such are entitled tocredit, so far as their truth could have influenced theformation of the mind. But that affords not theslightest reason for supposing them exact.

Now, metaphysics has always been the ape ofmathematics. Geometry suggested the idea of ademonstrative system of absolutely certainphilosophical principles; and the ideas of themetaphysicians have at all times been in large part

426

drawn from mathematics. The metaphysical axiomsare imitations of the geometrical axioms; and nowthat the latter have been thrown overboard, withoutdoubt the former will be sent after them. It isevident, for instance, that we can have no reason tothink that every phenomenon in all its minutestdetails is precisely determined by law. That there isan arbitrary element in the universe we see,namely,its variety. This variety must be attributed tospontaneity in some form.

Had I more space, I now ought to show howimportant

427

for philosophy is the mathematical conception ofcontinuity. Most of what is true in Hegel is a darklingglimmer of a conception which the mathematicianshad long before made pretty clear, and which recentresearches have still further illustrated.

Among the many principles of Logic which find theirapplication in Philosophy, I can here only mentionone. Three conceptions are perpetually turning up atevery point in every theory of logic, and in the mostrounded systems they occur in connection with oneanother. They are conceptions so very broad andconsequently indefinite that they are hard to seizeand may be easily overlooked. I call them theconceptions of First, Second, Third. First is theconception of being or existing independent ofanything else. Second is the conception of beingrelative to, the conception of reaction with,something else. Third is the conception of mediation,whereby a first and second are brought into relation.To illustrate these ideas, I will show how they enterinto those we have been considering. The origin ofthings, considered not as leading to anything, but initself, contains the idea of First, the end of things that

428

of Second, the process mediating between them thatof Third. A philosophy which emphasizes the idea ofthe One, is generally a dualistic philosophy in whichthe conception of Second receives exaggeratedattention; for this One (though of course involvingthe idea of First) is always the other of a manifoldwhich is not one. The idea of the Many, becausevariety is arbitrariness and arbitrariness is repudiationof any Secondness, has for its principal componentthe conception of First. In psychology Feeling is

429

First, Sense of reaction Second, General conceptionThird, or mediation. In biology, the idea of arbitrarysporting is First, heredity is Second, the processwhereby the accidental characters become fixed isThird. Chance is First, Law is Second, the tendency totake habits is Third. Mind is First, Matter is Second,Evolution is Third.

Such are the materials out of which chiefly aphilosophical theory ought to be built, in order torepresent the state of knowledge to which thenineteenth century has brought us. Without goinginto other important questions of philosophicalarchitectonic, we can readily foresee what sort of ametaphysics would appropriately be constructed fromthose conceptions. Like some of the most ancient andsome of the most recent speculations it would be aCosmogonic Philosophy. It would suppose that in thebeginning,infinitely remote,there was a chaos ofunpersonalized feeling, which being withoutconnection or regularity would properly be withoutexistence. This feeling, sporting here and there inpure arbitrariness, would have started the germ of ageneralizing tendency. Its other sportings would be

430

evanescent, but this would have a growing virtue.Thus, the tendency to habit would be started; andfrom this with the other principles of evolution all theregularities of the universe would be evolved. At anytime, however, an element of pure chance survivesand will remain until the world becomes an absolutelyperfect, rational, and symmetrical system, in whichmind is at last crystallized in the infinitely distantfuture.

That idea has been worked out by me withelaboration. It accounts for the main features of theuniverse as we

431

know it,-the characters of time, space, matter, force,gravitation, electricity, etc. It predicts many morethings which new observations can alone bring to thetest. May some future student go over this groundagain, and have the leisure to give his results to theworld.

432

IIThe Doctrine of Necessity Examined 1In The Monist for January, 1891, I endeavored toshow what elementary ideas ought to enter into ourview of the universe. I may mention that on thoseconsiderations I had already grounded a cosmicaltheory, and from it had deduced a considerablenumber of consequences capable of being comparedwith experience. This comparison is now in progress,but under existing circumstances must occupy manyyears.

I propose here to examine the common belief thatevery single fact in the universe is preciselydetermined by law. It must not be supposed that thisis a doctrine accepted everywhere and at all times byall rational men. Its first advocate appears to havebeen Democritus, the atomist, who was led to it, aswe are informed, by reflecting upon the"impenetrability, translation, and impact of matter

." That is to say, havingrestricted his attention to a field where no influence

433

other than mechanical constraint could possibly comebefore his notice, he straightway jumped to theconclusion that throughout the universe that was thesole principle of action,a style of reasoning so usual inour day with men not unreflecting as to be more thanexcusable in the infancy of thought. But Epicurus, inrevising the atomic doctrine and repairing itsdefences, found himself obliged

The Monist, April, 1892.

434

to suppose that atoms swerve from their courses byspontaneous chance; and thereby he conferred uponthe theory life and entelechy. For we now see clearlythat the peculiar function of the molecular hypothesisin physics is to open an entry for the calculus ofprobabilities. Already, the prince of philosophers hadrepeatedly and emphatically condemned the dictumof Democritus (especially in the " Physics," Book II,chapters iv, v, vi), holding that events come to passin three ways, namely, (1) by external compulsion, orthe action of efficient causes, (2) by virtue of aninward nature, or the influence of final causes, and(3) irregularly without definite cause, but just byabsolute chance; and this doctrine is of the inmostessence of Aristotelianism. It affords, at any rate, avaluable enumeration of the possible ways in whichanything can be supposed to have come about. Thefreedom of the will, too, was admitted both byAristotle and by Epicurus. But the Stoa, which inevery department seized upon the most tangible,hard, and lifeless element, and blindly denied theexistence of every other, which, for example,impugned the validity of the inductive method andwished to fill its place with the reductio ad absurdum,

435

very naturally became the one school of ancientphilosophy to stand by a strict necessitarianism, thusreturning to a single principle of Democritus thatEpicurus had been unable to swallow.Necessitarianism and materialism with the Stoicswent hand in hand, as by affinity they should. At therevival of learning, Stoicism met with considerablefavor, partly because it departed just enough fromAristotle to give it the spice of novelty, and partlybecause its superficialities well adapted it for

436

acceptance by students of literature and art whowanted their philosophy drawn mild. Afterwards, thegreat discoveries in mechanics inspired the hope thatmechanical principles might suffice to explain theuniverse; and though without logical justification, thishope has since been continually stimulated bysubsequent advances in physics. Nevertheless, thedoctrine was in too evident conflict with the freedomof the will and with miracles to be generallyacceptable, at first. But meantime there arose thatmost widely spread of philosophical blunders, thenotion that associationalism belongs intrinsically tothe materialistic family of doctrines; and thus wasevolved the theory of motives; and libertarianismbecame weakened. At present, historical criticism hasalmost exploded the miracles, great and small; sothat the doctrine of necessity has never been in sogreat vogue as now.

The proposition in question is that the state of thingsexisting at any time, together with certain immutablelaws, completely determine the state of things atevery other time (for a limitation to future time isindefensible). Thus, given the state of the universe in

437

the original nebula, and given the laws of mechanics,a sufficiently powerful mind could deduce from thesedata the precise form of every curlicue of every letterI am now writing.

Whoever holds that every act of the will as well asevery idea of the mind is under the rigid governanceof a necessity co-ordinated with that of the physicalworld, will logically be carried to the proposition thatminds are part of the physical world in such a sensethat the laws of mechanics determine everything thathappens according to

438

immutable attractions and repulsions. In that case,that instantaneous state of things from which everyother state of things is calculable consists in thepositions and velocities of all the particles at anyinstant. This, the usual and most logical form ofnecessitarianism, is called the mechanical philosophy.

When I have asked thinking men what reason theyhad to believe that every fact in the universe isprecisely determined by law, the first answer hasusually been that the proposition is a ''presupposition" or postulate of scientific reasoning. Well, if that isthe best that can be said for it, the belief is doomed.Suppose it be "postulated ": that does not make ittrue, nor so much as afford the slightest rationalmotive for yielding it any credence. It is as if a manshould come to borrow money, and when asked forhis security, should reply he "postulated" the loan. To" postulate " a proposition is no more than to hope itis true. There are, indeed, practical emergencies inwhich we act upon assumptions of certainpropositions as true, because if they are not so, it canmake no difference how we act. But all suchpropositions I take to be hypotheses of individual

439

facts. For it is manifest that no universal principle canin its universality be comprised in a special case orcan be requisite for the validity of any ordinaryinference. To say, for instance, that thedemonstration by Archimedes of the property of thelever would fall to the ground if men were endowedwith free-will, is extravagant; yet this is implied bythose who make a proposition incompatible with thefreedom of the will the postulate of all inference.Considering, too, that the conclusions of

440

science make no pretence to being more thanprobable, and considering that a probable inferencecan at most only suppose something to be mostfrequently, or otherwise approximately, true, butnever that anything is precisely true withoutexception throughout the universe, we see how farthis proposition in truth is from being so postulated.

But the whole notion of a postulate being involved inreasoning appertains to a by-gone and falseconception of logic. Non-deductive, or ampliativeinference, is of three kinds: induction, hypothesis,and analogy. If there be any other modes, they mustbe extremely unusual and highly complicated, andmay be assumed with little doubt to be of the samenature as those enumerated. For induction,hypothesis, and analogy, as far as their ampliativecharacter goes, that is, so far as they concludesomething not implied in the premises, depend uponone principle and involve the same procedure. All areessentially inferences from sampling. Suppose a shiparrives at Liverpool laden with wheat in bulk. Supposethat by some machinery the whole cargo be stirredup with great thoroughness. Suppose that twenty-

441

seven thimblefuls be taken equally from the forward,midships, and aft parts, from the starboard, center,and larboard parts, and from the top, half depth, andlower parts of her hold, and that these being mixedand the grains counted, four-fifths of the latter arefound to be of quality A. Then we infer, experientiallyand provisionally, that approximately four-fifths of allthe grain in the cargo is of the same quality. I say weinfer this experientially and provisionally. By sayingthat we infer it experientially, I mean that ourconclusion makes no pre-

442

tension to knowledge of wheat-in-itself, our , asthe derivation of that word implies, has nothing to dowith latent wheat. We are dealing only with thematter of possible experience,experience in the fullacceptation of the term as something not merelyaffecting the senses but also as the subject ofthought. If there be any wheat hidden on the ship,so that it can neither turn up in the sample nor beheard of subsequently from purchasers, or if it behalf-hidden, so that it may, indeed, turn up, but isless likely to do so than the rest,or if it can affect oursenses and our pockets, but from some strange causeor causelessness cannot be reasoned about,all suchwheat is to be excluded (or have only its proportionalweight) in calculating that true proportion of qualityA, to which our inference seeks to approximate. Bysaying that we draw the inference provisionally, Imean that we do not hold that we have reached anyassigned degree of approximation as yet, but onlyhold that if our experience be indefinitely extended,and if every fact of whatever nature, as fast as itpresents itself, be duly applied, according to theinductive method, in correcting the inferred ratio,then our approximation will become indefinitely close

443

in the long run; that is to say, close to the experienceto come (not merely close by the exhaustion of afinite collection) so that if experience in general is tofluctuate irregularly to and fro, in a manner to deprivethe ratio sought of all definite value, we shall be ableto find out approximately within what limits itfluctuates, and if, after having one definite value, itchanges and assumes another, we shall be able tofind that out, and in short, whatever may be thevariations of this ratio in

444

experience, experience indefinitely extended willenable us to detect them, so as to predict rightly, atlast, what its ultimate value may be, if it have anyultimate value, or what the ultimate law of successionof values may be, if there be any such ultimate law,or that it ultimately fluctuates irregularly withincertain limits, if it do so ultimately fluctuate. Now ourinference, claiming to be no more than thusexperiential and provisional, manifestly involves nopostulate whatever.

For what is a postulate? It is the formulation of amaterial fact which we are not entitled to assume asa premise, but the truth of which is requisite to thevalidity of an inference. Any fact, then, which mightbe supposed postulated, must either be such that itwould ultimately present itself in experience, or not.If it will present itself, we need not postulate it nowin our provisional inference, since we shall ultimatelybe entitled to use it as a premise. But if it neverwould present itself in experience, our conclusion isvalid but for the possibility of this fact beingotherwise than assumed, that is, it is valid as far aspossible experience goes, and that is all that we

445

claim. Thus, every postulate is cut off, either by theprovisionality or by the experientiality of ourinference. For instance, it has been said thatinduction postulates that, if an indefinite successionof samples be drawn, examined, and thrown backeach before the next is drawn, then in the long runevery grain will be drawn as often as any other, thatis to say, postulates that the ratio of the numbers oftimes in which any two are drawn will indefinitelyapproximate to unity. But no such postulate is made;for if, on the one hand, we are to

446

have no other experience of the wheat than fromsuch drawings, it is the ratio that presents itself inthose drawings and not the ratio which belongs tothe wheat in its latent existence that we areendeavoring to determine; while if, on the otherhand, there is some other mode by which the wheatis to come under our knowledge, equivalent toanother kind of sampling, so that after all our care instirring up the wheat, some experiential grains willpresent themselves in the first sampling operationmore often than others in the long run, this verysingular fact will be sure to get discovered by theinductive method, which must avail itself of every sortof experience; and our inference, which was onlyprovisional, corrects itself at last. Again, it has beensaid, that induction postulates that under likecircumstances like events will happen, and that thispostulate is at bottom the same as the principle ofuniversal causation. But this is a blunder, or bevue,due to thinking exclusively of inductions where theconcluded ratio is either 1 or 0. If any suchproposition were postulated, it would be that underlike circumstances (the circumstances of drawing thedifferent samples) different events occur in the same

447

proportions in all the different sets,a propositionwhich is false and even absurd. But in truth no suchthing is postulated, the experiential character of theinference reducing the condition of validity to this,that if a certain result does not occur, the oppositeresult will be manifested, a condition assured by theprovisionality of the inference. But it may be askedwhether it is not conceivable that every instance of acertain class destined to be ever employed as adatum of induction should have one character, whileevery instance

448

destined not to be so employed should have theopposite character. The answer is that in that case,the instances excluded from being subjects ofreasoning would not be experienced in the full senseof the word, but would be among these latentindividuals of which our conclusion does not pretendto speak.

To this account of the rationale of induction I know ofbut one objection worth mention: it is that I thus failto deduce the full degree of force which this mode ofinference in fact possesses; that according to myview, no matter how thorough and elaborate thestirring and mixing process had been, theexamination of a single handful of grain would notgive me any assurance, sufficient to risk money uponthat the next handful would not greatly modify theconcluded value of the ratio under inquiry, while, infact, the assurance would be very high that this ratiowas not greatly in error. If the true ratio of grains ofquality A were 0.80 and the handful contained athousand grains, nine such handfuls out of every tenwould contain from 780 to 820 grains of quality A.The answer to this is that the calculation given is

449

correct when we know that the units of this handfuland the quality inquired into have the normalindependence of one another, if for instance thestirring has been complete and the charactersampled for has been settled upon in advance of theexamination of the sample. But in so far as theseconditions are not known to be complied with, theabove figures cease to be applicable. Randomsampling and predesignation of the charactersampled for should always be striven after ininductive reasoning, but when they cannot beattained, so long as it is conducted

450

honestly, the inference retains some value. When wecannot ascertain how the sampling has been done orthe sample-character selected, induction still has theessential validity which my present account of itshows it to have.

I do not think a man who combines a willingness tobe convinced with a power of appreciating anargument upon a difficult subject can resist thereasons which have been given to show that theprinciple of universal necessity cannot be defended asbeing a postulate of reasoning. But then the questionimmediately arises whether it is not proved to betrue, or at least rendered highly probable, byobservation of nature.

Still, this question ought not long to arrest a personaccustomed to reflect upon the force of scientificreasoning. For the essence of the necessitarianposition is that certain continuous quantities havecertain exact values. Now, how can observationdetermine the value of such a quantity with aprobable error absolutely nil? To one who is behindthe scenes, and knows that the most refinedcomparisons of masses, lengths, and angles, far

451

surpassing in precision all other measurements, yetfall behind the accuracy of bank-accounts, and thatthe ordinary determinations of physical constants,such as appear from month to month in the journals,are about on a par with an upholsterer'smeasurements of carpets and curtains, the idea ofmathematical exactitude being demonstrated in thelaboratory will appear simply ridiculous. There is arecognized method of estimating the probablemagnitudes of errors in physics,the method of leastsquares. It is universally admitted that this methodmakes the errors smaller than they really are;

452

yet even according to that theory an error indefinitelysmall is indefinitely improbable; so that any statementto the effect that a certain continuous quantity has acertain exact value, if well-founded at all, must befounded on something other than observation.

Still, I am obliged to admit that this rule is subject toa certain qualification. Namely, it only applies tocontinuous 2 quantity. Now, certain kinds ofcontinuous quantity are discontinuous at one or attwo limits, and for such limits the rule must bemodified. Thus, the length of a line cannot be lessthan zero. Suppose, then, the question arises howlong a line a certain person had drawn from a markedpoint on a piece of paper. If no line at all can beseen, the observed length is zero; and the onlyconclusion this observation warrants is that thelength of the line is less than the smallest lengthvisible with the optical power employed. But indirectobservations,for example, that the person supposedto have drawn the line was never within fifty feet ofthe paper,may make it probable that no line at allwas made, so that the concluded length will bestrictly zero. In like manner, experience no doubt

453

would warrant the conclusion that there is absolutelyno indigo in a given ear of wheat, and absolutely noattar in a given lichen. But such inferences can onlybe rendered valid by positive experiential evidence,direct or remote, and cannot rest upon a mereinability to detect the quantity in question. We havereason to think there is no indigo in the wheat,because we have remarked that wherever indigo ispro-

2Continuous is not exactly the right word, but I let it goto avoid a long and irrelevant discussion.

454

duced it is produced in considerable quantities, tomention only one argument. We have reason to thinkthere is no attar in the lichen, because essential oilsseem to be in general peculiar to single species. Ifthe question had been whether there was iron in thewheat or the lichen, though chemical analysis shouldfail to detect its presence, we should think some of itprobably was there, since iron is almost everywhere.Without any such information, one way or the other,we could only abstain from any opinion as to thepresence of the substance in question. It cannot, Iconceive, be maintained that we are in any betterposition than this in regard to the presence of theelement of chance or spontaneous departures fromlaw in nature.

Those observations which are generally adduced infavor of mechanical causation simply prove that thereis an element of regularity in nature, and have nobearing whatever upon the question of whether suchregularity is exact and universal, or not. Nay, inregard to this exactitude, all observation is directlyopposed to it; and the most that can be said is that agood deal of this observation can be explained away.

455

Try to verify any law of nature, and you will find thatthe more precise your observations, the more certainthey will be to show irregular departures from thelaw. We are accustomed to ascribe these, and I donot say wrongly, to errors of observation; yet wecannot usually account for such errors in anyantecedently probable way. Trace their causes backfar enough, and you will be forced to admit they arealways due to arbitrary determination, or chance.

But it may be asked whether if there were anelement

456

of real chance in the universe it must not occasionallybe productive of signal effects such as could not passunobserved. In answer to this question, withoutstopping to point out that there is an abundance ofgreat events which one might be tempted to supposewere of that nature, it will be simplest to remark thatphysicists hold that the particles of gases are movingabout irregularly, substantially as if by real chance,and that by the principles of probabilities there mustoccasionally happen to be concentrations of heat inthe gases contrary to the second law ofthermodynamics, and these concentrations, occurringin explosive mixtures, must sometimes havetremendous effects. Here, then, is in substance thevery situation supposed; yet no phenomena everhave resulted which we are forced to attribute tosuch chance concentration of heat, or whichanybody, wise or foolish, has ever dreamed ofaccounting for in that manner.

In view of all these considerations, I do not believethat anybody, not in a state of case-hardenedignorance respecting the logic of science, canmaintain that the precise and universal conformity of

457

facts to law is clearly proved, or even renderedparticularly probable, by any observations hithertomade. In this way, the determined advocate of exactregularity will soon find himself driven to a priorireasons to support his thesis. These received such asocdolager from Stuart Mill in his Examination ofHamilton, that holding to them now seems to me todenote a high degree of imperviousness to reason; sothat I shall pass them by with little notice.

To say that we cannot help believing a givenproposition is no argument, but it is a conclusive factif it be

458

true; and with the substitution of ''I" for "we," it istrue in the mouths of several classes of minds, theblindly passionate, the unreflecting and ignorant, andthe person who has overwhelming evidence beforehis eyes. But that which has been inconceivable to-day has often turned out indisputable on the morrow.Inability to conceive is only a stage through whichevery man must pass in regard to a number ofbeliefs,unless endowed with extraordinary obstinacyand obtuseness. His understanding is enslaved tosome blind compulsion which a vigorous mind ispretty sure soon to cast off.

Some seek to back up the a priori position withempirical arguments. They say that the exactregularity of the world is a natural belief, and thatnatural beliefs have generally been confirmed byexperience. There is some reason in this. Naturalbeliefs, however, if they generally have a foundationof truth, also require correction and purification fromnatural illusions. The principles of mechanics areundoubtedly natural beliefs; but, for all that, the earlyformulations of them were exceedingly erroneous.The general approximation to truth in natural beliefs

459

is, in fact, a case of the general adaptation of geneticproducts to recognizable utilities or ends. Now, theadaptations of nature, beautiful and often marvelousas they verily are, are never found to be quiteperfect; so that the argument is quite against theabsolute exactitude of any natural belief, includingthat of the principle of causation.

Another argument, or convenient commonplace, isthat absolute chance is inconceivable. (This word haseight current significations. The Century Dictionaryenumerates

460

six.) Those who talk like this will hardly be persuadedto say in what sense they mean that chance isinconceivable. Should they do so, it would easily beshown either that they have no sufficient reason forthe statement or that the inconceivability is of a kindwhich does not prove that chance is non-existent.

Another a priori argument is that chance isunintelligible; that is to say, while it may perhaps beconceivable, it does not disclose to the eye of reasonthe how or why of things; and since a hypothesis canonly be justified so far as it renders somephenomenon intelligible, we never can have any rightto suppose absolute chance to enter into theproduction of anything in nature. This argument maybe considered in connection with two others. Namely,instead of going so far as to say that the suppositionof chance can never properly be used to explain anyobserved fact, it may be alleged merely that no factsare known which such a supposition could in any wayhelp in explaining. Or again, the allegation being stillfurther weakened, it may be said that sincedepartures from law are not unmistakably observed,chance is not a vera causa, and ought not

461

unnecessarily to be introduced into a hypothesis.

These are no mean arguments, and require us toexamine the matter a little more closely. Come, mysuperior opponent, let me learn from your wisdom. Itseems to me that every throw of sixes with a pair ofdice is a manifest instance of chance.

"While you would hold a throw of deuce-ace to bebrought about by necessity? " (The opponent'ssupposed remarks are placed in quotation marks.)

462

Clearly one throw is as much chance as another.

"Do you think throws of dice are of a different naturefrom other events? "

I see that I must say that all the diversity andspecificalness of events is attributable to chance.

"Would you, then, deny that there is any regularity inthe world? "

That is clearly undeniable. I must acknowledge thereis an approximate regularity, and that every event isinfluenced by it. But the diversification, specificalness,and irregularity of things I suppose is chance. Athrow of sixes appears to me a case in which thiselement is particularly obtrusive.

"If you reflect more deeply, you will come to see thatchance is only a name for a cause that is unknown tous."

Do you mean that we have no idea whatever whatkind of causes could bring about a throw of sixes?

"On the contrary, each die moves under the influenceof precise mechanical laws."

463

But it appears to me that it is not these laws whichmade the die turn up sixes; for these laws act justthe same when other throws come up. The chancelies in the diversity of throws; and this diversitycannot be due to laws which are immutable.

" The diversity is due to the diverse circumstancesunder which the laws act. The dice lie differently inthe box, and the motion given to the box is different.These are the unknown causes which produce thethrows, and to which we give the name of chance;not the mechanical law which regulates the operationof these causes. You see you are already beginning tothink more clearly about this subject."

464

Does the operation of mechanical law not increasethe diversity?

"Properly not. You must know that the instantaneousstate of a system of particles is defined by six timesas many numbers as there are particles, three for theco-ordinates of each particle's position, and threemore for the components of its velocity. This numberof numbers, which expresses the amount of diversityin the system, remains the same at all times. Theremay be, to be sure, some kind of relation betweenthe co-ordinates and component velocities of thedifferent particles, by means of which the state of thesystem might be expressed by a smaller number ofnumbers. But, if this is the case, a preciselycorresponding relationship must exist between theco-ordinates and component velocities at any othertime, though it may doubtless be a relation lessobvious to us. Thus, the intrinsic complexity of thesystem is the same at all times."

Very well, my obliging opponent, we have nowreached an issue. You think all the arbitraryspecifications of the universe were introduced in onedose, in the beginning, if there was a beginning, and

465

that the variety and complication of nature hasalways been just as much as it is now. But I, for mypart, think that the diversification, the specification,has been continually taking place. Should youcondescend to ask me why I so think, I should givemy reasons as follows:

(1) Question any science which deals with the courseof time. Consider the life of an individual animal orplant, or of a mind. Glance at the history of states, ofinstitutions, of language, of ideas. Examine thesuccessions of

466

forms shown by paleontology, the history of the globeas set forth in geology, of what the astronomer isable to make out concerning the changes of stellarsystems. Everywhere the main fact is growth andincreasing complexity. Death and corruption are mereaccidents or secondary phenomena. Among some ofthe lower organisms, it is a moot point with biologistswhether there be anything which ought to be calleddeath. Races, at any rate, do not die out exceptunder unfavorable circumstances. From these broadand ubiquitous facts we may fairly infer, by the mostunexceptionable logic, that there is probably innature some agency by which the complexity anddiversity of things can be increased; and thatconsequently the rule of mechanical necessity meetsin some way with interference.

(2) By thus admitting pure spontaneity or life as acharacter of the universe, acting always andeverywhere though restrained within narrow boundsby law, producing infinitesimal departures from lawcontinually, and great ones with infinite infrequency,I account for all the variety and diversity of theuniverse, in the only sense in which the really sui

467

generis and new can be said to be accounted for.The ordinary view has to admit the inexhaustiblemultitudinous variety of the world, has to admit thatits mechanical law cannot account for this in theleast, that variety can spring only from spontaneity,and yet denies without any evidence or reason theexistence of this spontaneity, or else shoves it back tothe beginning of time and supposes it dead eversince. The superior logic of my view appears to menot easily controverted.

468

(3) When I ask the necessitarian how he wouldexplain the diversity and irregularity of the universe,he replies to me out of the treasury of his wisdomthat irregularity is something which from the natureof things we must not seek to explain. Abashed atthis, I seek to cover my confusion by asking how hewould explain the uniformity and regularity of theuniverse, whereupon he tells me that the laws ofnature are immutable and ultimate facts, and noaccount is to be given of them. But my hypothesis ofspontaneity does explain irregularity, in a certainsense; that is, it explains the general fact ofirregularity, though not, of course, what each lawlessevent is to be. At the same time, by thus looseningthe bond of necessity, it gives room for the influenceof another kind of causation, such as seems to beoperative in the mind in the formation of associations,and enables us to understand how the uniformity ofnature could have been brought about. That singleevents should be hard and unintelligible, logic willpermit without difficulty: we do not expect to makethe shock of a personally experienced earthquakeappear natural and reasonable by any amount ofcogitation. But logic does expect things general to be

469

understandable. To say that there is a universal law,and that it is a hard, ultimate, unintelligible fact, thewhy and wherefore of which can never be inquiredinto, at this a sound logic will revolt; and will passover at once to a method of philosophizing whichdoes not thus barricade the road of discovery.

(4) Necessitarianism cannot logically stop short ofmaking the whole action of the mind a part of thephysical universe. Our notion that we decide what weare going to

470

do, if as the necessitarian says, it has been calculablesince the earliest times, is reduced to illusion. Indeed,consciousness in general thus becomes a mereillusory aspect of a material system. What we call red,green, and violet are in reality only different rates ofvibration. The sole reality is the distribution ofqualities of matter in space and time. Brain-matter isprotoplasm in a certain degree and kind ofcomplication,a certain arrangement of mechanicalparticles. Its feeling is but an inward aspect, aphantom. For, from the positions and velocities of theparticles at any one instant, and the knowledge ofthe immutable forces, the positions at all other timesare calculable; so that the universe of space, time,and matter is a rounded system uninterfered withfrom elsewhere. But from the state of feeling at anyinstant, there is no reason to suppose the states offeeling at all other instants are thus exactlycalculable; so that feeling is, as I said, a merefragmentary and illusive aspect of the universe. Thisis the way, then, that necessitarianism has to makeup its accounts. It enters consciousness under thehead of sundries, as a forgotten trifle; its scheme ofthe universe would be more satisfactory if this little

471

fact could be dropped out of sight. On the otherhand, by supposing the rigid exactitude of causationto yield, I care not how little,be it but by a strictlyinfinitesimal amount,we gain room to insert mind intoour scheme, and to put it into the place where it isneeded, into the position which, as the sole self-intelligible thing, it is entitled to occupy, that of thefountain of existence; and in so doing we resolve theproblem of the connection of soul and body.

472

(5) But I must leave undeveloped the chief of myreasons, and can only adumbrate it. The hypothesisof chancespontaneity is one whose inevitableconsequences are capable of being traced out withmathematical precision into considerable detail. Muchof this I have done and find the consequences toagree with observed facts to an extent which seemsto me remarkable. But the matter and methods ofreasoning are novel, and I have no right to promisethat other mathematicians shall find my deductionsas satisfactory as I myself do, so that the strongestreason for my belief must for the present remain aprivate reason of my own, and cannot influenceothers. I mention it to explain my own position; andpartly to indicate to future mathematical speculatorsa veritable goldmine, should time and circumstancesand the abridger of all joys prevent my opening it tothe world.

If now I, in my turn, inquire of the necessitarian whyhe prefers to suppose that all specification goes backto the beginning of things, he will answer me withone of those last three arguments which I leftunanswered.

473

First, he may say that chance is a thing absolutelyunintelligible, and, therefore, that we never can beentitled to make such a supposition. But does not thisobjection smack of naive impudence? It is not mine,it is his own conception of the universe which leadsabruptly up to hard, ultimate, inexplicable, immutablelaw, on the one hand, and to inexplicablespecification and diversification of circumstances onthe other. My view, on the contrary, hypothetisesnothing at all, unless it be hypothesis to say that allspecification came about in some sense, and is not tobe

474

accepted as unaccountable. To undertake to accountfor anything by saying boldly that it is due to chancewould, indeed, be futile. But this I do not do. I makeuse of chance chiefly to make room for a principle ofgeneralization, or tendency to form habits, which Ihold has produced all regularities. The mechanicalphilosopher leaves the whole specification of theworld utterly unaccounted for, which is pretty nearlyas bad as to boldly attribute it to chance. I attributeit altogether to chance, it is true, but to chance in theform of a spontaneity which is to some degreeregular. It seems to me clear at any rate that one ofthese two positions must be taken, or elsespecification must be supposed due to a spontaneitywhich develops itself in a certain and not in a chanceway, by an objective logic like that of Hegel. This lastway I leave as an open possibility, for the present; forit is as much opposed to the necessitarian scheme ofexistence as my own theory is.

Secondly, the necessitarian may say there are, at anyrate, no observed phenomena which the hypothesisof chance could aid in explaining. In reply, I pointfirst to the phenomenon of growth and developing

475

complexity, which appears to be universal, and whichthough it may possibly be an affair of mechanismperhaps, certainly presents all the appearance ofincreasing diversification. Then, there is variety itself,beyond comparison the most obtrusive character ofthe universe: no mechanism can account for this.Then, there is the very fact the necessitarian mostinsists upon, the regularity of the universe which forhim serves only to block the road of inquiry. Then,there are the regular relationships between the lawsof nature,simi-

476

larities and comparative characters, which appeal toour intelligence as its cousins, and call upon us for areason. Finally, there is consciousness, feeling, apatent fact enough, but a very inconvenient one tothe mechanical philosopher.

Thirdly, the necessitarian may say that chance is nota vera causa, that we cannot know positively there isany such element in the universe. But the doctrine ofthe vera causa has nothing to do with elementaryconceptions. Pushed to that extreme, it at once cutsoff belief in the existence of a material universe; andwithout that necessitarianism could hardly maintainits ground. Besides, variety is a fact which must beadmitted; and the theory of chance merely consists insupposing this diversification does not antedate alltime. Moreover, the avoidance of hypothesesinvolving causes nowhere positively known to actisonly a recommendation of logic, not a positivecommand. It cannot be formulated in any preciseterms without at once betraying its untenablecharacter,I mean as rigid rule, for as arecommendation it is wholesome enough.

I believe I have thus subjected to fair examination all

477

the important reasons for adhering to the theory ofuniversal necessity, and have shown their nullity. Iearnestly beg that whoever may detect any flaw inmy reasoning will point it out to me, either privatelyor publicly; for if I am wrong, it much concerns me tobe set right speedily. If my argument remainsunrefuted, it will be time, I think, to doubt theabsolute truth of the principle of universal law; andwhen once such a doubt has obtained a living root inany man's mind, my cause with him, I am persuaded,is gained.

478

IIIThe Law of Mind1

In an article published in The Monist for January,1891, I endeavored to show what ideas ought toform the warp of a system of philosophy, andparticularly emphasized that of absolute chance. Inthe number of April, 1892, I argued further in favorof that way of thinking, which it will be convenient tochristen tychism (from , chance). A seriousstudent of philosophy will be in no haste to accept orreject this doctrine; but he will see in it one of thechief attitudes which speculative thought may take,feeling that it is not for an individual, nor for an age,to pronounce upon a fundamental question ofphilosophy. That is a task for a whole era to work out.I have begun by showing that tychism must givebirth to an evolutionary cosmology, in which all theregularities of nature and of mind are regarded asproducts of growth, and to a Schelling-fashionedidealism which holds matter to be mere specializedand partially deadened mind. I may mention, for the

479

benefit of those who are curious in studying mentalbiographies, that I was born and reared in theneighborhood of Concord,I mean in Cambridge,at thetime when Emerson, Hedge, and their friends weredisseminating the ideas that they had caught fromSchelling, and Schelling from Plotinus, from Boehm,or from God knows what minds stricken with themonstrous mysticism of the East. But the atmosphere

1 The Monist, July, 1892.

480

of Cambridge held many an antiseptic againstConcord transcendentalism; and I am not consciousof having contracted any of that virus. Nevertheless,it is probable that some cultured bacilli, somebenignant form of the disease was implanted in mysoul, unawares, and that now, after long incubation,it comes to the surface, modified by mathematicalconceptions and by training in physical investigations.

The next step in the study of cosmology must be toexamine the general law of mental action. In doingthis, I shall for the time drop my tychism out of view,in order to allow a free and independent expansion toanother conception signalized in my first Monist paperas one of the most indispensable to philosophy,though it was not there dwelt upon; I mean the ideaof continuity. The tendency to regard continuity, inthe sense in which I shall define it, as an idea ofprime importance in philosophy may conveniently betermed synechism. The present paper is intendedchiefly to show what synechism is, and what it leadsto. I attempted, a good many years ago, to developthis doctrine in the Journal of Speculative Philosophy(Vol. II.); but I am able now to improve upon that

481

exposition, in which I was a little blinded bynominalistic prepossessions. I refer to it, becausestudents may possibly find that some points notsufficiently explained in the present paper are clearedup in those earlier ones.

What the Law Is

Logical analysis applied to mental phenomena showsthat there is but one law of mind, namely, that ideastend to

482

spread continuously and to affect certain otherswhich stand to them in a peculiar relation ofaffectibility. In this spreading they lose intensity, andespecially the power of affecting others, but gaingenerality and become welded with other ideas.

I set down this formula at the beginning, forconvenience; and now proceed to comment upon it.

Individuality of Ideas

We are accustomed to speak of ideas as reproduced,as passed from mind to mind, as similar or dissimilarto one another, and, in short, as if they weresubstantial things; nor can any reasonable objectionbe raised to such expressions. But taking the word''idea" in the sense of an event in an individualconsciousness, it is clear that an idea once past isgone forever, and any supposed recurrence of it isanother idea. These two ideas are not present in thesame state of consciousness, and therefore cannotpossibly be compared. To say, therefore, that theyare similar can only mean that an occult power fromthe depths of the soul forces us to connect them inour thoughts after they are both no more. We may

483

note, here, in passing, that of the two generallyrecognized principles of association, contiguity andsimilarity, the former is a connection due to a powerwithout, the latter a connection due to a powerwithin.

But what can it mean to say that ideas wholly pastare thought of at all, any longer? They are utterlyunknowable. What distinct meaning can attach tosaying that an idea in the past in any way affects anidea in the future, from which it is completelydetached? A phrase between

484

the assertion and the denial of which there can in nocase be any sensible difference is mere gibberish.

I will not dwell further upon this point, because it is acommonplace of philosophy.

Continuity of Ideas

We have here before us a question of difficulty,analogous to the question of nominalism and realism.But when once it has been clearly formulated, logicleaves room for one answer only. How can a past ideabe present? Can it be present vicariously? To acertain extent, perhaps; but not merely so; for thenthe question would arise how the past idea can berelated to its vicarious representation. The relation,being between ideas, can only exist in someconsciousness: now that past idea was in noconsciousness but that past consciousness that alonecontained it; and that did not embrace the vicariousidea.

Some minds will here jump to the conclusion that apast idea cannot in any sense be present. But that ishasty and illogical. How extravagant, too, topronounce our whole knowledge of the past to be

485

mere delusionl Yet it would seem that the past is ascompletely beyond the bounds of possible experienceas a Kantian thing-in-itself.

How can a past idea be present? Not vicariously.Then, only by direct perception. In other words, to bepresent, it must be ipso facto present. That is, itcannot be wholly past; it can only be going,infinitesimally past, less past than any assignable pastdate. We are thus brought to the conclusion that thepresent is connected with the past by a series of realinfinitesimal steps.

486

It has already been suggested by psychologists thatconsciousness necessarily embraces an interval oftime. But if a finite time be meant, the opinion is nottenable. If the sensation that precedes the presentby half a second were still immediately before me,then, on the same principle the sensation precedingthat would be immediately present, and so on adinfinitum. Now, since there is a time, say a year, atthe end of which an idea is no longer ipso factopresent, it follows that this is true of any finiteinterval, however short.

But yet consciousness must essentially cover aninterval of time; for if it did not, we could gain noknowledge of time, and not merely no veraciouscognition of it, but no conception whatever. We are,therefore, forced to say that we are immediatelyconscious through an infinitesimal interval of time.

This is all that is requisite. For, in this infinitesimalinterval, not only is consciousness continuous in asubjective sense, that is, considered as a subject orsubstance having the attribute of duration; but also,because it is immediate consciousness, its object isipso facto continuous. In fact, this infinitesimally

487

spread-out consciousness is a direct feeling of itscontents as spread out. This will be further elucidatedbelow. In an infinitesimal interval we directly perceivethe temporal sequence of its beginning, middle, andend,not, of course, in the way of recognition, forrecognition is only of the past, but in the way ofimmediate feeling. Now upon this interval followsanother, whose beginning is the middle of the former,and whose middle is the end of the former. Here, wehave an im-

488

mediate perception of the temporal sequence of itsbeginning, middle, and end, or say of the second,third, and fourth instants. From these two immediateperceptions, we gain a mediate, or inferential,perception of the relation of all four instants. Thismediate perception is objectively, or as to the objectrepresented, spread over the four instants; butsubjectively, or as itself the subject of duration, it iscompletely embraced in the second moment. (Thereader will observe that I use the word instant tomean a point of time, and moment to mean aninfinitesimal duration.) If it is objected that, upon thetheory proposed, we must have more than a mediateperception of the succession of the four instants, Igrant it; for the sum of the two infinitesimal intervalsis itself infinitesimal, so that it is immediatelyperceived. It is immediately perceived in the wholeinterval, but only mediately perceived in the last two-thirds of the interval. Now, let there be an indefinitesuccession of these inferential acts of comparativeperception; and it is plain that the last moment willcontain objectively the whole series. Let there be, notmerely an indefinite succession, but a continuous flowof inference through a finite time; and the result will

489

be a mediate objective consciousness of the wholetime in the last moment. In this last moment, thewhole series will be recognized, or known as knownbefore, except only the last moment, which of coursewill be absolutely unrecognizable to itself. Indeed,even this last moment will be recognized like the rest,or, at least, be just beginning to be so. There is alittle elenchus, or appearance of contradiction, here,which the ordinary logic of reflection quite suffices toresolve.

490

Infinity and Continuity, in General

Most of the mathematicians who during the last twogenerations have treated the differential calculushave been of the opinion that an infinitesimalquantity is an absurdity; although, with their habitualcaution, they have often added "or, at any rate, theconception of an infinitesimal is so difficult, that wepractically cannot reason about it with confidenceand security." Accordingly, the doctrine of limits hasbeen invented to evade the difficulty, or, as somesay, to explain the signification of the word "infinitesimal." This doctrine, in one form or another, istaught in all the text-books, though in some of themonly as an alternative view of the matter; it answerswell enough the purposes of calculation, though evenin that application it has its difficulties.

The illumination of the subject by a strict notation forthe logic of relatives had shown me clearly andevidently that the idea of an infinitesimal involves nocontradiction, before I became acquainted with thewritings of Dr. Georg Cantor (though many of thesehad already appeared in the Mathematische Annalenand in Borchardt's Journal, if not yet in the Acta

491

Mathematica, all mathematical journals of the firstdistinction), in which the same view is defended withextraordinary genius and penetrating logic.

The prevalent opinion is that finite numbers are theonly ones that we can reason about, at least, in anyordinary mode of reasoning, or, as some authorsexpress it, they are the only numbers that can bereasoned about mathematically. But this is anirrational prejudice. I long ago

492

showed that finite collections are distinguished frominfinite ones only by one circumstance and itsconsequences, namely, that to them is applicable apeculiar and unusual mode of reasoning called by itsdiscoverer, De Morgan, the "syllogism of transposedquantity."

Balzac, in the introduction of his Physiologie dumariage, remarks that every young Frenchman boastsof having seduced some Frenchwoman. Now, as awoman can only be seduced once, and there are nomore Frenchwomen than Frenchmen, it follows, ifthese boasts are true, that no French women escapeseduction. If their number be finite, the reasoningholds. But since the population is continuallyincreasing, and the seduced are on the averageyounger than the seducers, the conclusion need notbe true. In like manner, De Morgan, as an actuary,might have argued that if an insurance company paysto its insured on an average more than they haveever paid it, including interest, it must lose money.But every modern actuary would see a fallacy in that,since the business is continually on the increase. Butshould war, or other cataclysm, cause the class of

493

insured to be a finite one, the conclusion would turnout painfully correct, after all. The above tworeasonings are examples of the syllogism oftransposed quantity.

The proposition that finite and infinite collections aredistinguished by the applicability to the former of thesyllogism of transposed quantity ought to beregarded as the basal one of scientific arithmetic.

If a person does not know how to reason logically,and I must say that a great many fairly goodmathematicians,yea, distinguished ones,fall underthis category, but

494

simply uses a rule of thumb in blindly drawinginferences like other inferences that have turned outwell, he will, of course, be continually falling into errorabout infinite numbers. The truth is such people donot reason, at all. But for the few who do reason,reasoning about infinite numbers is easier than aboutfinite numbers, because the complicated syllogism oftransposed quantity is not called for. For example,that the whole is greater than its part is not anaxiom, as that eminently bad reasoner, Euclid, madeit to be. It is a theorem readily proved by means of asyllogism of transposed quantity, but not otherwise.Of finite collections it is true, of infinite collectionsfalse. Thus, a part of the whole numbers are evennumbers. Yet the even numbers are no fewer than allthe numbers; an evident proposition since if everynumber in the whole series of whole numbers bedoubled, the result will be the series of evennumbers.

1, 2, 3, 4, 5, 6, etc.2, 4, 6, 8, 10, 12, etc.

So for every number there is a distinct even number.In fact, there are as many distinct doubles of

495

numbers as there are of distinct numbers. But thedoubles of numbers are all even numbers.

In truth, of infinite collections there are but twogrades of magnitude, the endless and theinnumerable. Just as a finite collection isdistinguished from an infinite one by the applicabilityto it of a special mode of reasoning, the syllogism oftransposed quantity, so, as I showed in the paper lastreferred to, a numerable collection is distinguishedfrom an innumerable one by the applicability to it of acertain

496

mode of reasoning, the Fermatian inference, or, as itis sometimes improperly termed, "mathematicalinduction."

As an example of this reasoning, Euler'sdemonstration of the binomial theorem for integralpowers may be given. The theorem is that (x + y)n,where n is a whole number, may be expanded intothe sum of a series of terms of which the first is xn y0and each of the others is derived from the nextpreceding by diminishing the exponent of x by 1 andmultiplying by that exponent and at the same timeincreasing the exponent of y by 1 and dividing bythat increased exponent. Now, suppose thisproposition to be true for a certain exponent, n = M,then it must also be true for n = M + 1. For let one ofthe terms in the expansion of (x + y)M be written Axpyq. Then, this term with the two following will be

Now, when (x + y)M is multiplied by x + y to give (x+ y)M+l, we multiply first by x and then by y insteadof by x and add the two results. When we multiply byx, the second of the above three terms will be the

497

only one giving a term involving xp yq+1 and the thirdwill be the only one giving a term in xp-1yq+2; andwhen we multiply by y the first will be the only termgiving a term in xp yq+1, and the second will be theonly term giving a term in xp-1yq+2. Hence, addinglike terms, we find that the coefficient of xp yq+lin theexpansion of (x + y)m+lwill be the sum of thecoefficients of the first two of the above three terms,and that the coefficient of xp-1yq+2 will be the sum ofthe coefficients of the last two terms. Hence, twosuccessive terms in the expansion of (x + y)m+1 willbe

498

It is, thus, seen that the succession of terms followsthe rule. Thus if any integral power follows the rule,so also does the next higher power. But the firstpower obviously follows the rule. Hence, all powersdo so.

Such reasoning holds good of any collection ofobjects capable of being ranged in a series whichthough it may be endless, can be numbered so thateach member of it receives a definite integralnumber. For instance, all the whole numbersconstitute such a numerable collection. Again, allnumbers resulting from operating according to anydefinite rule with any finite number of whole numbersform such a collection. For they may be arranged in aseries thus. Let F be the symbol of operation. Firstoperate on 1, giving F (1). Then, operate on a second1, giving F (1,1). Next, introduce 2, giving 3rd, F(2);4th F(2,1); 5th, F(1,2); 6th, F(2,2). Next use a thirdvariable giving 7th, F(1,1,1); 8th, F(2,1,1); 9th,F(1,2,1); 10th, F(2,2,1); 11th, F(1,1,2); 12th,

499

F(2,1,2); 13th, F(1,2,2); 14th, F(2,2,2). Nextintroduce 3, and so on, alternately introducing newvariables and new figures; and in this way it is plainthat every arrangement of integral values of thevariables will receive a numbered place in the series.2

The class of endless but numerable collections (socalled because they can be so ranged that to eachone corresponds

2 This proposition is substantially the same as atheorem of Cantor, though it is enunciated in a muchmore general form.

500

a distinct whole number) is very large. But there arecollections which are certainly innumerable. Such isthe collection of all numbers to which endless seriesof decimals are capable of approximating. It has beenrecognized since the time of Euclid that certainnumbers are surd or incommensurable, and are notexactly expressible by any finite series of decimals,nor by a circulating decimal. Such is the ratio of thecircumference of a circle to its diameter, which weknow is nearly 3.1415926. The calculation of thisnumber has been carried to over 700 figures withoutthe slightest appearance of regularity in theirsequence. The demonstrations that this and manyother numbers are incommensurable are perfect.That the entire collection of incommensurablenumbers is innumerable has been clearly proved byCantor. I omit the demonstration; but it is easy to seethat to discriminate one from some other would, ingeneral, require the use of an endless series ofnumbers. Now if they cannot be exactly expressedand discriminated, clearly they cannot be ranged in alinear series.

It is evident that there are as many points on a line

501

or in an interval of time as there are of real numbersin all. These are, therefore, innumerable collections.Many mathematicians have incautiously assumed thatthe points on a surface or in a solid are more thanthose on a line. But this has been refuted by Cantor.Indeed, it is obvious that for every set of values ofcoördinates there is a single distinct number.Suppose, for instance, the values of the coordinatesall lie between 0 and + 1. Then if we compose anumber by putting in the first decimal place the firstfigure of the first coördinate, in the second the firstfigure of the

502

second coördinate, and so on, and when the firstfigures are all dealt out go on to the second figures inlike manner, it is plain that the values of thecoördinates can be read off from the single resultingnumber, so that a triad or tetrad of numbers, eachhaving innumerable values, has no more values thana single incommensurable number.

Were the number of dimensions infinite, this wouldfail; and the collection of infinite sets of numbershaving each innumerable variations, might, therefore,be greater than the simple innumerable collection,and might be called endlessly infinite. The singleindividuals of such a collection could not, however, bedesignated, even approximately, so that this is indeeda magnitude concerning which it would be possible toreason only in the most general way, if at all.

Although there are but two grades of magnitudes ofinfinite collections, yet when certain conditions areimposed upon the order in which individuals aretaken, distinctions of magnitude arise from thatcause. Thus, if a simply endless series be doubled byseparating each unit into two parts, the successivefirst parts and also the second parts being taken in

503

the same order as the units from which they arederived, this double endless series will, so long as it istaken in that order, appear as twice as large as theoriginal series. In like manner the product of twoinnumerable collections, that is, the collection ofpossible pairs composed of one individual of each, ifthe order of continuity is to be maintained, is, byvirtue of that order, infinitely greater than either ofthe component collections.

We now come to the difficult, question. What iscontinuity? Kant confounds it with infinite divisibility,saying

504

that the essential character of a continuous series isthat between any two members of it a third canalways be found. This is an analysis beautifully clearand definite; but unfortunately, it breaks down underthe first test. For according to this, the entire seriesof rational fractions arranged in the order of theirmagnitude, would be an infinite series, although therational fractions are numerable, while the points of aline are innumerable. Nay, worse yet, if from thatseries of fractions any two with all that lie betweenthem be excised, and any number of such finite gapsbe made, Kant's definition is still true of the series,though it has lost all appearance of continuity.

Cantor defines a continuous series as one which isconcatenated and perfect. By a concatenated series,he means such a one that if any two points are givenin it, and any finite distance, however small, it ispossible to proceed from the first point to the secondthrough a succession of points of the series each at adistance from the preceding one less than the givendistance. This is true of the series of rational fractionsranged in the order of their magnitude. By a perfectseries, he means one which contains every point such

505

that there is no distance so small that this point hasnot an infinity of points of the series within thatdistance of it. This is true of the series of numbersbetween 0 and 1 capable of being expressed bydecimals in which only the digits o and 1 occur.

It must be granted that Cantor's definition includesevery series that is continuous; nor can it be objectedthat it includes any important or indubitable case of aseries not continuous. Nevertheless, it has someserious defects. In

506

the first place, it turns upon metrical considerations;while the distinction between a continuous and adiscontinuous series is manifestly non-metrical. In thenext place, a perfect series is defined as onecontaining '' every point" of a certain description. Butno positive idea is conveyed of what all the pointsare: that is definition by negation, and cannot beadmitted. If that sort of thing were allowed, it wouldbe very easy to say, at once, that the continuouslinear series of points is one which contains everypoint of the line between its extremities. Finally,Cantor's definition does not convey a distinct notionof what the components of the conception ofcontinuity are. It ingeniously wraps up its propertiesin two separate parcels, but does not display them toour intelligence.

Kant's definition expresses one simple property of acontinuum; but it allows of gaps in the series. Tomend the definition, it is only necessary to notice howthese gaps can occur. Let us suppose, then, a linearseries of points extending from a point, A, to a point,B, having a gap from B to a third point, C, andthence extending to a final limit, D; and let us

507

suppose this series conforms to Kant's definition.Then, of the two points, B and C, one or both mustbe excluded from the series; for otherwise, by thedefinition, there would be points between them. Thatis, if the series contains C, though it contains all thepoints up to B, it cannot contain B. What is required,therefore, is to state in non-metrical terms that if aseries of points up to a limit is included in acontinuum the limit is included. It may be remarkedthat this is the property of a continuum to whichAristotle's attention seems to have been directed

508

when he defines a continuum as something whoseparts have a common limit. The property may beexactly stated as follows: If a linear series of points iscontinuous between two points, A and D, and if anendless series of points be taken, the first of thembetween A and D and each of the others betweenthe last preceding one and D, then there is a point ofthe continuous series between all that endless seriesof points and D, and such that every other point ofwhich this is true lies between this point and D. Forexample, take any number between 0 and 1, as 0.1;then, any number between 0.1 and 1, as 0.11; thenany number between 0.11 and 1, as 0.111; and soon, without end. Then, because the series of realnumbers between 1 and is continuous, there must bea least real number, greater than every number ofthat endless series. This property, which may becalled the Aristotelicity of the series, together withKant's property, or its Kanticity, completes thedefinition of a continuous series.

The property of Aristotelicity may be roughly statedthus: a continuum contains the end point belongingto every endless series of points which it contains. An

509

obvious corollary is that every continuum contains itslimits. But in using this principle it is necessary toobserve that a series may be continuous except inthis, that it omits one or both of the limits.

Our ideas will find expression more conveniently if,instead of points upon a line, we speak of realnumbers. Every real number is, in one sense, the limitof a series, for it can be indefinitely approximated to.Whether every real number is a limit of a regularseries may perhaps be

510

open to doubt. But the series referred to in thedefinition of Aristotelicity must be understood asincluding all series whether regular or not.Consequently, it is implied that between any twopoints an innumerable series of points can be taken.

Every number whose expression in decimals requiresbut a finite number of places of decimals iscommensurable. Therefore, incommensurablenumbers suppose an infinitieth place of decimals. Theword infinitesimal is simply the Latin form ofinfinitieth; that is, it is an ordinal formed frominfinitum, as centesimal from centum. Thus,continuity supposes infinitesimal quantities. There isnothing contradictory about the idea of suchquantities. In adding and multiplying them thecontinuity must not be broken up, and consequentlythey are precisely like any other quantities, exceptthat neither the syllogism of transposed quantity, northe Fermatian inference applies to them.

If A is a finite quantity and i an infinitesimal, then in acertain sense we may write A + i = A. That is to say,this is so for all purposes of measurement. But thisprinciple must not be applied except to get rid of all

511

the terms in the highest order of infinitesimalspresent. As a mathematician, I prefer the method ofinfinitesimals to that of limits, as far easier and lessinfested with snares. Indeed, the latter, as stated insome books, involves propositions that are false; butthis is not the case with the forms of the methodused by Cauchy, Duhamel, and others. As theyunderstand the doctrine of limits, it involves thenotion of continuity, and, therefore, contains inanother shape the very same ideas as the doctrine ofinfinitesimals.

512

Let us now consider an aspect of the Aristotelicalprinciple which is particularly important in philosophy.Suppose a surface to be part red and part blue; sothat every point on it is either red or blue, and, ofcourse, no part can be both red and blue. What,then, is the color of the boundary line between thered and the blue? The answer is that red or blue, toexist at all, must be spread over a surface; and thecolor of the surface is the color of the surface in theimmediate neighborhood of the point. I purposely usea vague form of expression. Now, as the parts of thesurface in the immediate neighborhood of anyordinary point upon a curved boundary are half ofthem red and half blue, it follows that the boundary ishalf red and half blue. In like manner, we find itnecessary to hold that consciousness essentiallyoccupies time; and what is present to the mind atany ordinary instant, is what is present during amoment in which that instant occurs. Thus, thepresent is half past and half to come. Again, the colorof the parts of a surface at any finite distance from apoint, has nothing to do with its color just at thatpoint; and, in the parallel, the feeling at any finiteinterval from the present has nothing to do with the

513

present feeling, except vicariously. Take anothercase: the velocity of a particle at any instant of timeis its mean velocity during an infinitesimal instant inwhich that time is contained. Just so my immediatefeeling is my feeling through an infinitesimal durationcontaining the present instant.

514

Analysis of Time

One of the most marked features about the law ofmind is that it makes time to have a definite directionof flow from past to future. The relation of past tofuture is, in reference to the law of mind, differentfrom the relation of future to past. This makes one ofthe great contrasts between the law of mind and thelaw of physical force, where there is no moredistinction between the two opposite directions intime than between moving northward and movingsouthward.

In order, therefore, to analyze the law of mind, wemust begin by asking what the flow of time consistsin. Now, we find that in reference to any individualstate of feeling, all others are of two classes, thosewhich affect this one (or have a tendency to affect it,and what this means we shall inquire shortly), andthose which do not. The present is affectible by thepast but not by the future.

Moreover, if state A is affected by state B, and stateB by state C, then A is affected by state C, thoughnot so much so. It follows, that if A is affectible by B,

515

B is not affectible by A.

If, of two states, each is absolutely unaffectible bythe other, they are to be regarded as parts of thesame state. They are contemporaneous.

To say that a state is between two states means thatit affects one and is affected by the other. Betweenany two states in this sense lies an innumerableseries of states affecting one another; and if a statelies between a given state and any other state whichcan be reached by inserting

516

states between this state and any third state, theseinserted states not immediately affecting or beingaffected by either, then the second rate mentioned,immediately affects or is affected by the first, in thesense that in the one the other is ipso facto presentin a reduced degree.

These propositions involve a definition of time and ofits flow. Over and above this definition they involve adoctrine, namely, that every state of feeling isaffectible by every earlier state.

That Feelings Have Intensive Continuity

Time with its continuity logically involves some otherkind of continuity than its own. Time, as the universalform of change, cannot exist unless there issomething to undergo change, and to undergo achange continuous in time, there must be acontinuity of changeable qualities. Of the continuityof intrinsic qualities of feeling we can now form but afeeble conception. The development of the humanmind has practically extinguished all feelings, excepta few sporadic kinds, sound, colors, smells, warmth,etc., which now appear to be disconnected and

517

disparate. In the case of colors, there is atridimensional spread of feelings. Originally, allfeelings may have been connected in the same way,and the presumption is that the number ofdimensions was endless. For development essentiallyinvolves a limitation of possibilities. But given anumber of dimensions of feeling, all possible varietiesare obtainable by varying the intensities of thedifferent elements. Accordingly, time logicallysupposes a continuous range of intensity in feeling. Itfollows, then, from the definition of

518

continuity, that when any particular kind of feeling ispresent, an infinitesimal continuum of all feelingsdiffering infinitesimally from that is present.

That Feelings Have Spatial Extension

Consider a gob of protoplasm, say an amoeba or aslime-mould. It does not differ in any radical wayfrom the contents of a nerve-cell, though its functionsmay be less specialized. There is no doubt that thisslime-mould, or this amoeba, or at any rate somesimilar mass of protoplasm feels. That is to say, itfeels when it is in its excited condition. But note howit behaves. When the whole is quiescent and rigid, aplace upon it is irritated. Just at this point, an activemotion is set up, and this gradually spreads to otherparts. In this action, no unity nor relation to anucleus, or other unitary organ can be discerned. It isa mere amorphous continuum of protoplasm, withfeeling passing from one part to another. Nor is thereanything like a wave-motion. The activity does notadvance to new parts, just as fast as it leaves oldparts. Rather, in the beginning, it dies out at a slowerrate than that at which it spreads. And while theprocess is going on, by exciting the mass at another

519

point, a second quite independent state of excitationwill be set up. In some places, neither excitation willexist, in others each separately, in still other places,both effects will be added together. Whatever thereis in the whole phenomenon to make us think there isfeeling in such a mass of protoplasm,feeling, butplainly no personality,goes logically to show that thatfeeling has a subjective, or substantial, spatialextension, as the excited

520

state has. This is, no doubt, a difficult idea to seize,for the reason that it is a subjective, not an objective,extension. It is not that we have a feeling of bigness;though Professor James, perhaps rightly, teachesthat we have. It is that the feeling, as a subject ofinhesion, is big. Moreover, our own feelings arefocused in attention to such a degree that we are notaware that ideas are not brought to an absoluteunity; just as nobody not instructed by specialexperiment has any idea how very, very little of thefield of vision is distinct. Still, we all know how theattention wanders about among our feelings; and thisfact shows that those feelings that are not co-ordinated in attention have a reciprocal externality,although they are present at the same time. But wemust not tax introspection to make a phenomenonmanifest which essentially involves externality.

Since space is continuous, it follows that there mustbe an immediate community of feeling between partsof mind infinitesimally near together. Without this, Ibelieve it would have been impossible for mindsexternal to one another, ever to become co-ordinated, and equally impossible for any coördination

521

to be established in the action of the nerve-matter ofone brain.

Affections of Ideas

But we are met by the question what is meant bysaying that one idea affects another. Theunravelment of this problem requires us to trace outphenomena a little further.

Three elements go to make up an idea. The first is itsintrinsic quality as a feeling. The second is the energy

522

with which it affects other ideas, an energy which isinfinite in the here-and-nowness of immediatesensation, finite and relative in the recency of thepast. The third element is the tendency of an idea tobring along other ideas with it.

As an idea spreads, its power of affecting other ideasgets rapidly reduced; but its intrinsic quality remainsnearly unchanged. It is long years now since I lastsaw a cardinal in his robes; and my memory of theircolor has become much dimmed. The color itself,however, is not remembered as dim. I have noinclination to call it a dull red. Thus, the intrinsicquality remains little changed; yet more accurateobservation will show a slight reduction of it. Thethird element, on the other hand, has increased. Aswell as I can recollect, it seems to me the cardinals Iused to see wore robes more scarlet than vermillionis, and highly luminous. Still, I know the colorcommonly called cardinal is on the crimson side ofvermillion and of quite moderate luminosity, and theoriginal idea calls up so many other hues with it, andasserts itself so feebly, that I am unable any longer toisolate it.

523

A finite interval of time generally contains aninnumerable series of feelings; and when thesebecome welded together in association, the result is ageneral idea. For we have just seen how bycontinuous spreading an idea becomes generalised.

The first character of a general idea so resulting isthat it is living feeling. A continuum of this feeling,infinitesimal in duration, but still embracinginnumerable parts, and also, though infinitesimal,entirely unlimited, is immediately present. And in itsabsence of boundedness a

524

vague possibility of more than is present is directlyfelt.

Second, in the presence of this continuity of feeling,nominalistic maxims appear futile. There is no doubtabout one idea affecting another, when we candirectly perceive the one gradually modified andshaping itself into the other. Nor can there any longerbe any difficulty about one idea resembling another,when we can pass along the continuous field ofquality from one to the other and back again to thepoint which we had marked.

Third, consider the insistency of an idea. The

525

insistency of a past idea with reference to the presentis a quantity which is less the further back that pastidea is, and rises to infinity as the past idea isbrought up into coincidence with the present. Herewe must make one of those inductive applications ofthe law of continuity which have produced

526

such great results in all the positive sciences. Wemust extend the law of insistency into the future.Plainly, the insistency of a future idea with referenceto the present is a quantity affected by the minussign; for it is the present that affects the future, ifthere be any effect, not the future that affects thepresent. Accordingly, the curve of insistency is a sortof equilateral hyperbola. (See the figure.) Such aconception is none the less mathematical, that itsquantification cannot now be exactly specified.

Now consider the induction which we have here beenled into. This curve says that feeling which has notyet emerged into immediate consciousness is alreadyaffectible and already affected. In fact, this is habit,by virtue of which an idea is brought up into presentconsciousness by a bond that had already beenestablished between it and another idea while it wasstill in futuro.

We can now see what the affection of one idea byanother consists in. It is that the affected idea isattached as a logical predicate to the affecting ideaas subject. So when a feeling emerges intoimmediate consciousness, it always appears as a

527

modification of a more or less general object alreadyin the mind. The word suggestion is well adapted toexpressing this relation. The future is suggested by,or rather is influenced by the suggestions of, thepast.

Ideas Cannot Be Connected Except by Continuity

That ideas can nowise be connected withoutcontinuity is sufficiently evident to one who reflectsupon the matter. But still the opinion may beentertained that after continuity has once made theconnection of ideas possible,

528

then they may get to be connected in other modesthan through continuity. Certainly, I cannot see howanyone can deny that the infinite diversity of theuniverse, which we call chance, may bring ideas intoproximity which are not associated in one generalidea. It may do this many times. But then the law ofcontinuous spreading will produce a mentalassociation; and this I suppose is an abridgedstatement of the way the universe has been evolved.But if I am asked whether a blind àvágkh I cannotbring ideas together, first I point out that it would notremain blind. There being a continuous connectionbetween the ideas, they would infallibly becomeassociated in a living, feeling, and perceiving generalidea. Next, I cannot see what the mustness ornecessity of this àvágkh would consist in. In theabsolute uniformity of the phenomenon, says thenominalist. Absolute is well put in; for if it merelyhappened so three times in succession, or threemillion times in succession, in the absence of anyreason, the coincidence could only be attributed tochance. But absolute uniformity must extend over thewhole infinite future; and it is idle to talk of thatexcept as an idea. No; I think we can only hold that

529

wherever ideas come together they tend to weld intogeneral ideas; and wherever they are generallyconnected, general ideas govern the connection; andthese general ideas are living feelings spread out.

Mental Law Follows the Forms of Logic

The three main classes of logical inference areDeduction, Induction, and Hypothesis. Thesecorrespond to three chief modes of action of thehuman soul. In deduction the

530

mind is under the dominion of a habit or associationby virtue of which a general idea suggests in eachcase a corresponding reaction. But a certainsensation is seen to involve that idea. Consequently,that sensation is followed by that reaction. That is theway the hind legs of a frog, separated from the restof the body, reason, when you pinch them. It is thelowest form of psychical manifestation.

By induction, a habit becomes established. Certainsensations, all involving one general idea, arefollowed each by the same reaction; and anassociation becomes established, whereby thatgeneral idea gets to be followed uniformly by thatreaction.

Habit is that specialization of the law of mindwhereby a general idea gains the power of excitingreactions. But in order that the general idea shouldattain all its functionality, it is necessary, also, that itshould become suggestible by sensations. That isaccomplished by a psychical process having the formof hypothetic inference. By hypothetic inference, Imean, as I have explained in other writings, aninduction from qualities. For example, I know that the

531

kind of man known and classed as a '' mugwump "has certain characteristics. He has a high self-respectand places great value upon social distinction. Helaments the great part that rowdyism and unrefinedgood-fellowship play in the dealings of Americanpoliticians with their constituency. He thinks that thereform which would follow from the abandonment ofthe system by which the distribution of offices ismade to strengthen party organizations and a returnto the original and essential conception of

532

office-filling would be found an unmixed good. Heholds that monetary considerations should usually bethe decisive ones in questions of public policy. Herespects the principle of individualism and of laissez-faire as the greatest agency of civilization. Theseviews, among others, I know to be obtrusive marks ofa "mugwump." Now, suppose I casually meet a manin a railway-train, and falling into conversation findthat he holds opinions of this sort; I am naturally ledto suppose that he is a "mugwump." That ishypothetic inference. That is to say, a number ofreadily verifiable marks of a mugwump beingselected, I find this man has these, and infer that hehas all the other characters which go to make athinker of that stripe. Or let us suppose that I meet aman of a semi-clerical appearance and a sub-pharisaical sniff, who appears to look at things fromthe point of view of a rather wooden dualism. Hecites several texts of scripture and always withparticular attention to their logical implications; andhe exhibits a sternness, almost amounting tovindictiveness, toward evil-doers, in general. I readilyconclude that he is a minister of a certaindenomination. Now the mind acts in a way similar to

533

this, every time we acquire a power of co-ordinatingreactions in a peculiar way, as in performing any actrequiring skill. Thus, most persons have a difficulty inmoving the two hands simultaneously and in oppositedirections through two parallel circles nearly in themedial plane of the body. To learn to do this, it isnecessary to attend, first, to the different actions indifferent parts of the motion, when suddenly ageneral conception of the action springs up and itbecomes perfectly easy. We think the motion

534

we are trying to do involves this action, and this, andthis. Then, the general idea comes which unites allthose actions, and thereupon the desire to performthe motion calls up the general idea. The samemental process is many times employed whenever weare learning to speak a language or are acquiring anysort of skill.

Thus, by induction, a number of sensations followedby one reaction become united under one generalidea followed by the same reaction; while by thehypothetic process, a number of reactions called forby one occasion get united in a general idea which iscalled out by the same occasion. By deduction, thehabit fulfils its function of calling out certain reactionson certain occasions.

Uncertainty of Mental Action

The inductive and hypothetic forms of inference areessentially probable inferences, not necessary; whilededuction may be either necessary or probable.

But no mental action seems to be necessary orinvariable in its character. In whatever manner themind has reacted under a given sensation, in that

535

manner it is the more likely to react again; were this,however, an absolute necessity, habits would becomewooden and ineradicable, and no room being left forthe formation of new habits, intellectual life wouldcome to a speedy close. Thus, the uncertainty of themental law is no mere defect of it, but is on thecontrary of its essence. The truth is, the mind is notsubject to "law," in the same rigid sense that matteris. It only experiences gentle forces which merelyrender it more likely to act in a given way than itotherwise would be. There

536

always remains a certain amount of arbitraryspontaneity in its action, without which it would bedead.

Some psychologists think to reconcile the uncertaintyof reactions with the principle of necessary causationby means of the law of fatigue. Truly for a law, thislaw of fatigue is a little lawless. I think it is merely acase of the general principle that an idea in spreadingloses its insistency. Put me tarragon into my salad,when I have not tasted it for years, and I exclaim "What nectar is this! " But add it to every dish I tastefor week after week, and a habit of expectation hasbeen created; and in thus spreading into habit, thesensation makes hardly any more impression uponme; or, if it be noticed, it is on a new side from whichit appears as rather a bore. The doctrine that fatigueis one of the primordial phenomena of mind I ammuch disposed to doubt. It seems a somewhat littlething to be allowed as an exception to the greatprinciple of mental uniformization. For this reason, Iprefer to explain it in the manner here indicated, as aspecial case of that great principle. To consider it assomething distinct in its nature, certainly somewhat

537

strengthens the necessitarian position; but even if itbe distinct, the hypothesis that all the variety andapparent arbitrariness of mental action ought to beexplained away in favor of absolute determinism doesnot seem to me to recommend itself to a sober andsound judgment, which seeks the guidance ofobserved facts and not that of prepossessions.

538

Restatement of the Law

Let me now try to gather up all these odds and endsof commentary and restate the law of mind, in aunitary way.

First, then, we find that when we regard ideas from anominalistic, individualistic, sensualistic way, thesimplest facts of mind become utterly meaningless.That one idea should resemble another or influenceanother, or that one state of mind should so much asbe thought of in another is, from that standpoint,sheer nonsense.

Second, by this and other means we are driven toperceive, what is quite evident of itself, thatinstantaneous feelings flow together into a continuumof feeling, which has in a modified degree thepeculiar vivacity of feeling and has gained generality.And in reference to such general ideas, or continua offeeling, the difficulties about resemblance andsuggestion and reference to the external, cease tohave any force.

Third, these general ideas are not mere words, nor dothey consist in this, that certain concrete facts will

539

every time happen under certain descriptions ofconditions; but they are just as much, or rather farmore, living realities than the feelings themselves outof which they are concreted. And to say that mentalphenomena are governed by law does not meanmerely that they are describable by a generalformula; but that there is a living idea, a consciouscontinuum of feeling, which pervades them, and towhich they are docile.

Fourth, this supreme law, which is the celestial andliving harmony, does not so much as demand thatthe special

540

ideas shall surrender their peculiar arbitrariness andcaprice entirely; for that would be self-destructive. Itonly requires that they shall influence and beinfluenced by one another.

Fifth, in what measure this unification acts, seems tobe regulated only by special rules; or, at least, wecannot in our present knowledge say how far it goes.But it may be said that, judging by appearances, theamount of arbitrariness in the phenomena of humanminds is neither altogether trifling nor veryprominent.

Personality

Having thus endeavored to state the law of mind, ingeneral, I descend to the consideration of a particularphenomenon which is remarkably prominent in ourown consciousnesses, that of personality. A stronglight is thrown upon this subject by recentobservations of double and multiple personality. Thetheory which at one time seemed plausible that twopersons in one body corresponded to the two halvesof the brain will, I take it, now be universallyacknowledged to be insufficient. But that which these

541

cases make quite manifest is that personality is somekind of co-ordination or connection of ideas. Notmuch to say, this, perhaps. Yet when we considerthat, according to the principle which we are tracingout, a connection between ideas is itself a generalidea, and that a general idea is a living feeling, it isplain that we have at least taken an appreciable steptoward the understanding of personality. Thispersonality, like any general idea, is not a thing to beapprehended in an instant. It has to be lived in time;

542

nor can any finite time embrace it in all its fullness.Yet in each infinitesimal interval it is present andliving, though specially colored by the immediatefeelings of that moment. Personality, so far as it isapprehended in a moment, is immediate self-consciousness.

But the word co-ordination implies somewhat morethan this; it implies a teleological harmony in ideas,and in the case of personality this teleology is morethan a mere purposive pursuit of a predeterminateend; it is a developmental teleology. This is personalcharacter. A general idea, living and conscious now, itis already determinative of acts in the future to anextent to which it is not now conscious.

This reference to the future is an essential element ofpersonality. Were the ends of a person alreadyexplicit, there would be no room for development, forgrowth, for life; and consequently there would be nopersonality. The mere carrying out of predeterminedpurposes is mechanical. This remark has anapplication to the philosophy of religion. It is that agenuine evolutionary philosophy, that is, one thatmakes the principle of growth a primordial element of

543

the universe, is so far from being antagonistic to theidea of a personal creator, that it is really inseparablefrom that idea; while a necessitarian religion is in analtogether false position and is destined to becomedisintegrated. But a pseudo-evolutionism whichenthrones mechanical law above the principle ofgrowth, is at once scientifically unsatisfactory, asgiving no possible hint of how the universe has comeabout, and hostile to all hopes of personal relations toGod.

544

Communication

Consistently with the doctrine laid down in thebeginning of this paper, I am bound to maintain thatan idea can only be affected by an idea in continuousconnection with it. By anything but an idea, it cannotbe affected at all. This obliges me to say, as I do say,on other grounds, that what we call matter is notcompletely dead, but is merely mind hide-bound withhabits. It still retains the element of diversification;and in that diversification there is life. When an ideais conveyed from one mind to another, it is by formsof combination of the diverse elements of nature, sayby some curious symmetry, or by some union of atender color with a refined odor. To such forms thelaw of mechanical energy has no application. If theyare eternal, it is in the spirit they embody; and theirorigin cannot be accounted for by any mechanicalnecessity. They are embodied ideas; and so only canthey convey ideas. Precisely how primary sensations,as colors and tones, are excited, we cannot tell, inthe present state of psychology. But in our ignorance,I think that we are at liberty to suppose that theyarise in essentially the same manner as the other

545

feelings, called secondary. As far as sight and hearingare in question, we know that they are only excitedby vibrations of inconceivable complexity; and thechemical senses are probably not more simple. Eventhe least psychical of peripheral sensations, that ofpressure, has in its excitation conditions which,though apparently simple, are seen to be complicatedenough when we consider the molecules and theirattractions. The principle with which I

546

set out requires me to maintain that these feelingsare communicated to the nerves by continuity, sothat there must be something like them in theexcitants themselves. If this seems extravagant, it isto be remembered that it is the sole possible way ofreaching any explanation of sensation, whichotherwise must be pronounced a general fact,absolutely inexplicable and ultimate. Now absoluteinexplicability is a hypothesis which sound logicrefuses under any circumstances to justify.

I may be asked whether my theory would befavorable or otherwise to telepathy. I have nodecided answer to give to this. At first sight, it seemsunfavorable. Yet there may be other modes ofcontinuous connection between minds other thanthose of time and space.

The recognition by one person of another'spersonality takes place by means to some extentidentical with the means by which he is conscious ofhis own personality. The idea of the secondpersonality, which is as much as to say that secondpersonality itself, enters within the field of directconsciousness of the first person, and is as

547

immediately perceived as his ego, though lessstrongly. At the same time, the opposition betweenthe two persons is perceived, so that the externalityof the second is recognized.

The psychological phenomena of intercommunicationbetween two minds have been unfortunately littlestudied. So that it is impossible to say, for certain,whether they are favorable to this theory or not. Butthe very extraordinary insight which some personsare able to gain of others from indications so slightthat it is difficult to ascertain what they are, iscertainly rendered more comprehensible by the viewhere taken.

548

A difficulty which confronts the synechistic philosophyis this. In considering personality, that philosophy isforced to accept the doctrine of a personal God; butin considering communication, it cannot but admitthat if there is a personal God, we must have a directperception of that person and indeed be in personalcommunication with him. Now, if that be the case,the question arises how it is possible that theexistence of this being should ever have beendoubted by anybody. The only answer that I can atpresent make is that facts that stand before our faceand eyes and stare us in the face are far from being,in all cases, the ones most easily discerned. That hasbeen remarked from time immemorial.

Conclusion

I have thus developed as well as I could in a littlespace the synechistic philosophy, as applied to mind.I think that I have succeeded in making it clear thatthis doctrine gives room for explanations of manyfacts which without it are absolutely and hopelesslyinexplicable; and further that it carries along with itthe following doctrines: 1st, a logical realism of themost pronounced type; 2nd, objective idealism; 3rd,

549

tychism, with its consequent thoroughgoingevolutionism. We also notice that the doctrinepresents no hindrances to spiritual influences, suchas some philosophies are felt to do.

550

IVMan's Glassy Essence1

In The Monist for January, 1891, I tried to show whatconceptions ought to form the brick and mortar of aphilosophical system. Chief among these was that ofabsolute chance for which I argued again in lastApril's number.2 In July, I applied anotherfundamental idea, that of continuity, to the law ofmind. Next in order, I have to elucidate, from thepoint of view chosen, the relation between thepsychical and physical aspects of a substance.

The first step towards this ought, I think, to be theframing of a molecular theory of protoplasm. Butbefore doing that, it seems indispensable to glance atthe constitution of matter, in general. We shall, thus,unavoidably make a long detour; but, after all, ourpains will not be wasted, for the problems of thepapers that are to follow in the series will call for theconsideration of the same question.

All physicists are rightly agreed the evidence isoverwhelming which shows all sensible matter is

551

composed of molecules in swift motion and exertingenormous mutual attractions, and perhaps repulsions,too. Even Sir William Thomson, Lord Kelvin, whowishes to explode action at a distance and return tothe doctrine of a plenum, not only speaks ofmolecules, but undertakes to assign definite mag-

1The Monist, October, 1892.2 I am rejoiced to find, since my last paper was printed,that a philosopher as subtle and profound as Dr. EdmundMontgomery has long been arguing for the same elementin the universe. Other world-renowned thinkers, as M.Renouvier and M. Delboeuf, appear to share this opinion.

552

nitudes to them. The brilliant Judge Stallo, a manwho did not always rightly estimate his own qualitiesin accepting tasks for himself, declared war upon theatomic theory in a book well worth careful perusal. Tothe old arguments in favor of atoms which he foundin Fechner's monograph, he was able to make repliesof considerable force, though they were not sufficientto destroy those arguments. But against modernproofs he made no headway at all. These set outfrom the mechanical theory of heat. Rumford'sexperiments showed that heat is not a substance.Joule demonstrated that it was a form of energy. Theheating of gases under constant volume, and otherfacts instanced by Rankine, proved that it could notbe an energy of strain. This drove physicists to theconclusion that it was a mode of motion. Then it wasremembered that John Bernoulli had shown that thepressure of gases could be accounted for byassuming their molecules to be moving uniformly inrectilinear paths. The same hypothesis was now seento account for Avogadro's law, that in equal volumesof different kinds of gases exposed to the samepressure and temperature are contained equalnumbers of molecules. Shortly after, it was found to

553

account for the laws of diffusion and viscosity ofgases, and for the numerical relation between theseproperties. Finally, Crookes's radiometer furnished thelast link in the strongest chain of evidence whichsupports any physical hypothesis.

Such being the constitution of gases, liquids mustclearly be bodies in which the molecules wander incurvilinear paths, while in solids they move in orbitsor quasi-orbits. (See my definition solid II, I, in theCentury Dictionary.)

554

We see that the resistance to compression and tointerpenetration between sensible bodies is, by one ofthe prime propositions of the molecular theory, due inlarge measure to the kinetical energy of the particles,which must be supposed to be quite remote from oneanother, on the average, even in solids. Thisresistance is no doubt influenced by finite attractionsand repulsions between the molecules. All theimpenetrability of bodies which we can observe is,therefore, a limited impenetrability due to kinetic andpositional energy. This being the case, we have nological right to suppose that absolute impenetrability,or the exclusive occupancy of space, belongs tomolecules or to atoms. It is an unwarrantedhypothesis, not a vera causa.3 Unless we are to giveup the theory of energy, finite positional attractionsand repulsions between molecules must be admitted.Absolute impenetrability would amount to an infiniterepulsion at a certain distance. No analogy of knownphenomena exists to excuse such a wanton violationof the principle of continuity as such a hypothesis is.In short, we are logically bound to adopt theBoscovichian idea that an atom is simply adistribution of component potential energy

555

throughout space (this distribution being absolutelyrigid), combined with inertia. The potential energybelongs to two molecules, and is to be conceived asdifferent between molecules A and B from what it isbetween molecules A and C. The distribution ofenergy is not necessarily spherical. Nay, a moleculemay conceivably have more than one center; it mayeven have a central curve,

3 By a vera causa, in the logic of science, is meant astate of things known to exist in some cases andsupposed to exist in other cases because it wouldaccount for observed phenomena.

556

returning into itself. But I do not think there are anyobserved facts pointing to such multiple or linearcenters. On the other hand, many facts relating tocrystals, especially those observed by Voigt,4 go toshow that the distribution of energy is harmonical butnot concentric. We can easily calculate the forceswhich such atoms must exert upon one another byconsidering 5 that they are equivalent toaggregations of pairs of electrically positive andnegative points infinitely near to one another. Aboutsuch an atom there would be regions of positive andof negative potential, and the number anddistribution of such regions would determine thevalency of the atom, a number which it is easy to seewould in many cases be somewhat indeterminate. Imust not dwell further upon this hypothesis, atpresent. In another paper, its consequences will befurther considered.

I cannot assume that the students of philosophy whoread this magazine are thoroughly versed in modernmolecular physics, and, therefore, it is proper tomention that the governing principle in this branch ofscience is Clausius's law of the virial. I will first state

557

the law, and then explain the peculiar terms of thestatement. This statement is that the total kineticenergy of the particles of a system in stationarymotion is equal to the total virial. By a system is heremeant a number of particles acting upon oneanother.6 Stationary motion is a quasi-orbital motionamong

4 Wiedemann, Annalen, 18871889.5 See Maxwell on Spherical Harmonics, in his Electricityand Magnetism.6 The word system has three peculiar meanings inmathematics. (A.) It means an orderly exposition of thetruths of astronomy, and hence(footnote continued on next page)

558

a system of particles so that none of them areremoved to indefinitely great distances nor acquireindefinitely great velocities. The kinetic energy of aparticle is the work which would be required to bringit to rest, independently of any forces which may beacting upon it. The virial of a pair of particles is halfthe work which the force which actually operatesbetween them would do if, being independent of thedistance, it were to bring them together. Theequation of the virial is

Here m is the mass of a particle, v its velocity, R isthe attraction between two particles, and r is thedistance between them. The sign S on the left handside signifies that the values of mv2 are to besummed for all the particles, and SS on the righthand side signifies that the values of Rr are to besummed for all the pairs of particles. If there is anexternal pressure P (as from the atmosphere) uponthe system, and the volume of vacant space withinthe boundary of that pressure is V, then the virialmust be understood as including 3/2PV, so that theequation is

559

There is strong (if not demonstrative) reason forthinking that the temperature of any body above theabsolute zero (273° C.), is proportional to theaverage kinetic energy

a theory of the motions of the stars; as the Ptolemaicsystem, the Copernican system. This is much like thesense in which we speak of the Calvinistic system oftheology, the Kantian system of philosophy, etc. (B.) Itmeans the aggregate of the planets considered as allmoving in somewhat the same way, as the solarsystem; and hence any aggregate of particles movingunder mutual forces. (C.) It means a number of forcesacting simultaneously upon a number of particles

560

of its molecules, or say aq where a is a constant andq is the absolute temperature. Hence, we may writethe equation

where the heavy lines above the different expressionssignify that the average values for single moleculesare to be taken. In 1872, a student in the Universityof Leyden, Van der Waals, propounded in his thesisfor the doctorate a specialization of the equation ofthe virial which has since attracted great attention.Namely, he writes it

The quantity b is the volume of a molecule, which hesupposes to be an impenetrable body, and all thevirtue of the equation lies in this term which makesthe equation a cubic in V, which is required toaccount for the shape of certain isothermal curves.7But if the idea of an impenetrable atom is illogical,that of an impenetrable molecule is almost absurd.For the kinetical theory of matter teaches us that amolecule is like a solar system or star-cluster inminiature. Unless we suppose that in all heating of

561

gases and vapors internal work is performed upon themolecules, implying that their atoms are atconsiderable distances, the whole kinetical theory ofgases falls to the ground. As for the term added to P,there is no more than a partial and roughlyapproximative justification for it. Namely, let usimagine

7 But, in fact, an inspection of these curves is sufficientto show that they are of a higher degree than the third.For they have the line V= o, or some line V a constantfor an asymptote, while for small values of P, thevalues of d2p/(dV)2 are positive.

562

two spheres described round a particle as theircenter, the radius of the larger being so great as toinclude all the particles whose action upon the centeris sensible, while the radius of the smaller is so largethat a good many molecules are included within it.The possibility of describing such a sphere as theouter one implies that the attraction of the particlesvaries at some distances inversely as some higherpower of the distance than the cube, or, to speakmore clearly, that the attraction multiplied by thecube of the distance diminishes as the distanceincreases; for the number of particles at a givendistance from any one particle is proportionate to thesquare of that distance and each of these gives aterm of the virial which is the product of theattraction into the distance. Consequently, unless theattraction multiplied by the cube of the distancediminished so rapidly with the distance as soon tobecome insensible, no such outer sphere as issupposed could be described. However, ordinaryexperience shows that such a sphere is possible; andconsequently there must be distances at which theattraction does thus rapidly diminish as the distanceincreases. The two spheres, then, being so drawn,

563

consider the virial of the central particle due to theparticles between them. Let the density of thesubstance be increased, say, N times. Then, for everyturn, Rr, of the virial before the condensation, therewill be N terms of the same magnitude after thecondensation. Hence, the virial of each particle will beproportional to the density, and the equation of thevirial becomes

564

This omits the virial within the inner sphere, theradius of which is so taken that within that distancethe number of particles is not proportional to thenumber in a large sphere. For Van der Waals thisradius is the diameter of his hard molecules, whichassumption gives his equation. But it is plain that theattraction between the molecules must to a certainextent modify their distribution, unless some peculiarconditions are fulfilled. The equation of Van derWaals can be approximately true, therefore, only for agas. In a solid or liquid condition, in which theremoval of a small amount of pressure has little effecton the volume, and where consequently the virialmust be much greater than , the virial mustincrease with the volume. For suppose we had asubstance in a critical condition in which an increaseof the volume would diminish the virial more than itwould increase 3/2 . If we were forcibly to diminishthe volume of such a substance, when thetemperature became equalized, the pressure which itcould withstand would be less than before, and itwould be still further condensed, and this would goon indefinitely until a condition were reached in whichan increase of volume would increase 3/2 . more

565

than it would decrease the virial. In the case ofsolids, at least, P may be zero; so that the statereached would be one in which the virial increaseswith the volume, or the attraction between theparticles does not increase so fast with a diminutionof their distance as it would if the attraction wereinversely as the distance.

Almost contemporaneously with Van der Waals'spaper, another remarkable thesis for the doctoratewas presented at Paris by Amagat. It related to theelasticity and ex-

566

pansion of gases, and to this subject the superbexperimenter, its author, has devoted his wholesubsequent life. Especially interesting are hisobservations of the volumes of ethylene and ofcarbonic acid at temperatures from 20° to 100° andat pressures ranging from an ounce to 5000 poundsto the square inch. As soon as Amagat had obtainedthese results, he remarked that the ''coefficient ofexpansion at constant volume," as it is absurdlycalled, that is, the rate of variation of the pressurewith the temperature, was very nearly constant foreach volume. This accords with the equation of thevirial, which gives

Now, the virial must be nearly independent of thetemperature, and, therefore, the last term almostdisappears. The virial would not be quite independentof the temperature, because if the temperature (i.e.,the square of the velocity of the molecules) islowered, and the pressure correspondingly lowered,so as to make the volume the same, the attractions ofthe molecules will have more time to produce their

567

effects, and consequently, the pairs of molecules theclosest together will be held together longer andcloser; so that the virial will generally be increased bya decrease of temperature. Now, Amagat'sexperiments do show an excessively minute effect ofthis sort, at least, when the volumes are not toosmall. However, the observations are well enoughsatisfied by assuming the "coefficient of expansion atconstant volume " to consist wholly of the first term,

. Thus, Amagat's experiments enable us to de-

568

termine the values of a and thence to calculate thevirial; and this we find varies for carbonic acid gasnearly inversely to . There is, thus, a roughapproximation to satisfying Van der Waals's equation.But the most interesting result of Amagat'sexperiments, for our purpose at any rate, is that thequantity a, though nearly constant for any onevolume, differs considerably with the volume, nearlydoubling when the volume is reduced fivefold. Thiscan only indicate that the mean kinetic energy of agiven mass of the gas for a given temperature isgreater the more the gas is compressed. But the lawsof mechanics appear to enjoin that the mean kineticenergy of a moving particle shall be constant at anygiven temperature. The only escape fromcontradiction, then, is to suppose that the meanmass of a moving particle diminishes upon thecondensation of the gas. In other words, many of themolecules are dissociated, or broken up into atoms orsub-molecules. The idea that dissociation should befavored by diminishing the volume will be pronouncedby physicists, at first blush, as contrary to all ourexperience. But it must be remembered that thecircumstances we are speaking of, that of a gas

569

under fifty or more atmospheres pressure, are alsounusual. That the " coefficient of expansion underconstant volume " when multiplied by the volumesshould increase with a decrement of the volume isalso quite contrary to ordinary experience; yet itundoubtedly takes place in all gases under greatpressure. Again, the doctrine of Arrhenius 8 is nowgenerally accepted, that the molecular

8 Anticipated by Clausius as long ago as 1857; and byWilliamson in 1851.

570

conductivity of an electrolyte is proportional to thedissociation of ions. Now the molecular conductivity ofa fused electrolyte is usually superior to that of asolution. Here is a case, then, in which diminution ofvolume is accompanied by increased dissociation.

The truth is that several different kinds of dissociationhave to be distinguished. In the first place, there isthe dissociation of a chemical molecule to formchemical molecules under the regular action ofchemical laws. This may be a double decomposition,as when iodhydric acid is dissociated, according tothe formula

or, it may be a simple decomposition, as whenpentachloride of phosphorus is dissociated accordingto the formula

All these dissociations require, according to the lawsof thermo-chemistry, an elevated temperature. In thesecond place, there is the dissociation of a physicallypolymerous molecule, that is, of several chemicalmolecules joined by physical attractions. This I am

571

inclined to suppose is a common concomitant of theheating of solids and liquids; for in these bodies thereis no increase of compressibility with the temperatureat all comparable with the increase of theexpansibility. But, in the third place, there is thedissociation with which we are now concerned, whichmust be supposed to be a throwing off ofunsaturated sub-molecules or atoms from themolecule. The molecule may, as I have said, beroughly likened to a solar system. As such,

572

molecules are able to produce perturbations of oneanother's internal motions; and in this way a planet,i.e., a sub-molecule, will occasionally get thrown offand wander about by itself, till it finds anotherunsaturated sub-molecule with which it can unite.Such dissociation by perturbation will naturally befavored by the proximity of the molecules to oneanother.

Let us now pass to the consideration of that specialsubstance, or rather class of substances, whoseproperties form the chief subject of botany and ofzoölogy, as truly as those of the silicates form thechief subject of mineralogy: I mean the life-slimes, orprotoplasm. Let us begin by cataloguing the generalcharacters of these slimes. They one and all exist intwo states of aggregation, a solid or nearly solid stateand a liquid or nearly liquid state; but they do notpass from the former to the latter by ordinary fusion.They are readily decomposed by heat, especially inthe liquid state; nor will they bear any considerabledegree of cold. All their vital actions take place attemperatures very little below the point ofdecomposition. This extreme instability is one of

573

numerous facts which demonstrate the chemicalcomplexity of protoplasm. Every chemist will agreethat they are far more complicated than thealbumens. Now, albumen is estimated to contain ineach molecule about a thousand atoms; so that it isnatural to suppose that the protoplasms containseveral thousands. We know that while they arechiefly composed of oxygen, hydrogen, carbon, andnitrogen, a large number of other elements enter intoliving bodies in small proportions; and it is likely thatmost of these enter into the composition ofprotoplasms.

574

Now, since the numbers of chemical varieties increaseat an enormous rate with the number of atoms permolecule, so that there are certainly hundreds ofthousands of substances whose molecules containtwenty atoms or fewer, we may well suppose that thenumber of protoplasmic substances runs into thebillions or trillions. Professor Cayley has given amathematical theory of "trees," with a view ofthrowing a light upon such questions; and in thatlight the estimate of trillions (in the English sense)seems immoderately moderate. It is true that anopinion has been emitted, and defended amongbiologists, that there is but one kind of protoplasm;but the observations of biologists, themselves, havealmost exploded that hypothesis, which from achemical standpoint appears utterly incredible. Theanticipation of the chemist would decidedly be thatenough different chemical substances havingprotoplasmic characters might be formed to account,not only for the differences between nerve-slime andmuscle-slime, between whale-slime and lion-slime,but also for those minuter pervasive variations whichcharacterize different breeds and single individuals.

575

Protoplasm, when quiescent, is, broadly speaking,solid; but when it is disturbed in an appropriate way,or sometimes even spontaneously without externaldisturbance, it becomes, broadly speaking, liquid. Amoner in this state is seen under the microscope tohave streams within its matter; a slime-mould slowlyflows by force of gravity. The liquefaction starts fromthe point of disturbance and spreads through themass. This spreading, however, is not uniform in alldirections; on the contrary, it takes at one

576

time one course, at another another, through thehomogeneous mass, in a manner that seems a littlemysterious. The cause of disturbance being removed,these motions gradually (with higher kinds ofprotoplasm, quickly) cease, and the slime returns toits solid condition.

The liquefaction of protoplasm is accompanied by amechanical phenomenon. Namely, some kinds exhibita tendency to draw themselves up into a globularform. This happens particularly with the contents ofmuscle-cells. The prevalent opinion, founded on someof the most exquisite experimental investigations thatthe history of science can show, is undoubtedly thatthe contraction of muscle-cells is due to osmoticpressure; and it must be allowed that that is a factorin producing the effect. But it does not seem to methat it satisfactorily accounts even for the phenomenaof muscular contraction; and besides, even nakedslimes often draw up in the same way. In this case,we seem to recognize an increase of the surface-tension. In some cases, too, the reverse action takesplace, extraordinary pseudopodia being put forth, asif the surface-tension were diminished in spots.

577

Indeed, such a slime always has a sort of skin, dueno doubt to surface-tension, and this seems to giveway at the point where a pseudopodium is put forth.

Long-continued or frequently repeated liquefaction ofthe protoplasm results in an obstinate retention ofthe solid state, which we call fatigue. On the otherhand, repose in this state, if not too much prolonged,restores the liquefiability. These are both importantfunctions.

The life-slimes have, further, the peculiar property ofgrowing. Crystals also grow; their growth, however,con-

578

sists merely in attracting matter like their own fromthe circumambient fluid. To suppose the growth ofprotoplasm of the same nature, would be to supposethis substance to be spontaneously generated incopious supplies wherever food is in solution.Certainly, it must be granted that protoplasm is but achemical substance, and that there is no reason whyit should not be formed synthetically like any otherchemical substance. Indeed, Clifford has clearlyshown that we have overwhelming evidence that it isso formed. But to say that such formation is asregular and frequent as the assimilation of food isquite another matter. It is more consonant with thefacts of observation to suppose that assimilatedprotoplasm is formed at the instant of assimilation,under the influence of the protoplasm alreadypresent. For each slime in its growth preserves itsdistinctive characters with wonderful truth, nerve-slime growing nerve-slime and muscle-slime muscle-slime, lion-slime growing lion-slime, and all thevarieties of breeds and even individual charactersbeing preserved in the growth. Now it is too much tosuppose there are billions of different kinds ofprotoplasm floating about wherever there is food.

579

The frequent liquefaction of protoplasm increases itspower of assimilating food; so much so, indeed, thatit is questionable whether in the solid form itpossesses this power.

The life-slime wastes as well as grows; and this tootakes place chiefly if not exclusively in its liquidphases.

Closely connected with growth is reproduction; andthough in higher forms this is a specialized function,it is universally true that wherever there isprotoplasm, there is,

580

will be, or has been a power of reproducing thatsame kind of protoplasm in a separated organism.Reproduction seems to involve the union of twosexes; though it is not demonstrable that this isalways requisite.

Another physical property of protoplasm is that oftaking habits. The course which the spread ofliquefaction has taken in the past is rendered therebymore likely to be taken in the future; although thereis no absolute certainly that the same path will befollowed again.

Very extraordinary, certainly, are all these propertiesof protoplasm; as extraordinary as indubitable. Butthe one which has next to be mentioned, whileequally undeniable, is infinitely more wonderful. It isthat protoplasm feels. We have no direct evidencethat this is true of protoplasm universally, andcertainly some kinds feel far more than others. Butthere is a fair analogical inference that all protoplasmfeels. It not only feels but exercises all the functionsof mind.

Such are the properties of protoplasm. The problem is

581

to find a hypothesis of the molecular constitution ofthis compound which will account for theseproperties, one and all.

Some of them are obvious results of the excessivelycomplicated constitution of the protoplasm molecule.All very complicated substances are unstable; andplainly a molecule of several thousand atoms may beseparated in many ways into two parts in each ofwhich the polar chemical forces are very nearlysaturated. In the solid protoplasm, as in other solids,the molecules must be supposed to be moving as itwere in orbits, or, at least, so as not to wander

582

indefinitely. But this solid cannot be melted, for thesame reason that starch cannot be melted; becausean amount of heat insufficient to make the entiremolecules wander is sufficient to break them upcompletely and cause them to form new and simplermolecules. But when one of the molecules isdisturbed, even if it be not quite thrown out of itsorbit at first, sub-molecules of perhaps severalhundred atoms each are thrown off from it. These willsoon acquire the same mean kinetic energy as theothers, and, therefore, velocities several times asgreat. They will naturally begin to wander, and inwandering will perturb a great many other moleculesand cause them in their turn to behave like the oneoriginally deranged. So many molecules will thus bebroken up, that even those that are intact will nolonger be restrained within orbits, but will wanderabout freely. This is the usual condition of a liquid, asmodern chemists understand it; for in all electrolyticliquids there is considerable dissociation.

But this process necessarily chills the substance, notmerely on account of the heat of chemicalcombination, but still more because the number of

583

separate particles being greatly increased, the meankinetic energy must be less. The substance being abad conductor, this heat is not at once restored. Nowthe particles moving more slowly, the attractionsbetween them have time to take effect, and theyapproach the condition of equilibrium. But theirdynamic equilibrium is found in the restoration of thesolid condition, which, therefore, takes place, if thedisturbance is not kept up.

When a body is in the solid condition, most of itsmole-

584

cules must be moving at the same rate, or, at least,at certain regular sets of rates; otherwise the orbitalmotion would not be preserved. The distances ofneighboring molecules must always be kept betweena certain maximum and a certain minimum value. Butif, without absorption of heat, the body be throwninto a liquid condition, the distances of neighboringmolecules will be far more unequally distributed, andan effect upon the virial will result. The chilling ofprotoplasm upon its liquefaction must also be takeninto account. The ordinary effect will no doubt be toincrease the cohesion and with that the surface-tension, so that the mass will tend to draw itself up.But in special cases, the virial will be increased somuch that the surface-tension will be diminished atpoints where the temperature is first restored. In thatcase, the outer film will give way and the tension atother places will aid in causing the general fluid to bepoured out at those points, forming pseudopodia.

When the protoplasm is in a liquid state, and thenonly, a solution of food is able to penetrate its massby diffusion. The protoplasm is then considerablydissociated; and so is the food, like all dissolved

585

matter. If then the separated and unsaturated sub-molecules of the food happen to be of the samechemical species as sub-molecules of the protoplasm,they may unite with other sub-molecules of theprotoplasm to form new molecules, in such a fashionthat when the solid state is resumed, there may bemore molecules of protoplasm than there were at thebeginning. It is like the jackknife whose blade andhandle, after having been severally lost and replaced,were found and put together to make a new knife.

586

We have seen that protoplasm is chilled byliquefaction, and that this brings it back to the solidstate, when the heat is recovered. This series ofoperations must be very rapid in the case of nerve-slime and even of muscle-slime, and may account forthe unsteady or vibratory character of their action. Ofcourse, if assimilation takes place, the heat ofcombination, which is probably trifling, is gained. Onthe other hand, if work is done, whether by nerve orby muscle, loss of energy must take place. In thecase of the muscle, the mode by which theinstantaneous part of the fatigue is brought about iseasily traced out. If when the muscle contracts it beunder stress, it will contract less than it otherwisewould do, and there will be a loss of heat. It is like anengine which should work by dissolving salt in waterand using the contraction during the solution to lift aweight, the salt being recovered afterwards bydistillation. But the major part of fatigue has nothingto do with the correlation of forces. A man must laborhard to do in a quarter of an hour the work whichdraws from him enough heat to cool his body by asingle degree. Meantime, he will be getting heated,he will be pouring out extra products of combustion,

587

perspiration, etc., and he will be driving the blood atan accelerated rate through minute tubes at greatexpense. Yet all this will have little to do with hisfatigue. He may sit quietly at his table writing, doingpractically no physical work at all, and yet in a fewhours be terribly fagged. This seems to be owing tothe deranged sub-molecules of the nerve-slime nothaving had time to settle back into their propercombinations. When such sub-molecules are thrownout, as they must be from time to time, there is somuch waste of material.

588

In order that a sub-molecule of food may bethoroughly and firmly assimilated into a brokenmolecule of protoplasm, it is necessary not only that itshould have precisely the right chemical composition,but also that it should be at precisely the right spot atthe right time and should be moving in precisely theright direction with precisely the right velocity. If allthese conditions are not fulfilled, it will be moreloosely retained than the other parts of the molecule;and every time it comes round into the situation inwhich it was drawn in, relatively to the other parts ofthat molecule and to such others as were nearenough to be factors in the action, it will be in specialdanger of being thrown out again. Thus, when apartial liquefaction of the protoplasm takes placemany times to about the same extent, it will, eachtime, be pretty nearly the same molecules that werelast drawn in that are now thrown out. They will bethrown out, too, in about the same way, as toposition, direction of motion, and velocity, in whichthey were drawn in; and this will be in about thesame course that the ones last before them werethrown out. Not exactly, however; for the very causeof their being thrown off so easily is their not having

589

fulfilled precisely the conditions of stable retention.Thus, the law of habit is accounted for, and with it itspeculiar characteristic of not acting with exactitude.

It seems to me that this explanation of habit, asidefrom the question of its truth or falsity, has a certainvalue as an addition to our little store of mechanicalexamples of actions analogous to habit. All theothers, so far as I know, are either statical or elseinvolve forces which, taking only the

590

sensible motions into account, violate the law ofenergy. It is so with the stream that wears its ownbed. Here, the sand is carried to its most stablesituation and left there. The law of energy forbidsthis; for when anything reaches a position of stableequilibrium, its momentum will be at a maximum, sothat it can according to this law only be left at rest inan unstable situation. In all the statical illustrations,too, things are brought into certain states and leftthere. A garment receives folds and keeps them; thatis, its limit of elasticity is exceeded. This failure tospring back is again an apparent violation of the lawof energy; for the substance will not only not springback of itself (which might be due to an unstableequilibrium being reached) but will not even do sowhen an impulse that way is applied to it.Accordingly, Professor James says, ''the phenomenaof habit . . . are due to the plasticity of the . . .materials." Now, plasticity of materials means thehaving of a low limit of elasticity. (See the CenturyDictionary, under solid.) But the hypotheticalconstitution of protoplasm here proposed involves noforces but attractions and repulsions strictly followingthe law of energy. The action here, that is, the

591

throwing of an atom out of its orbit in a molecule,and the entering of a new atom into nearly, but notquite the same orbit, is somewhat similar to themolecular actions which may be supposed to takeplace in a solid strained beyond its limit of elasticity.Namely, in that case certain molecules must bethrown out of their orbits, to settle down againshortly after into new orbits. In short, the plastic solidresembles protoplasm in being partially andtemporarily liquefied by a slight me-

592

chanical force. But the taking of a set by a solid bodyhas but a moderate resemblance to the taking of ahabit, inasmuch as the characteristic feature of thelatter, its inexactitude and want of completedeterminacy, is not so marked in the former, if it canbe said to be present there, at all.

The truth is that though the molecular explanation ofhabit is pretty vague on the mathematical side, therecan be no doubt that systems of atoms having polarforces would act substantially in that manner, andthe explanation is even too satisfactory to suit theconvenience of an advocate of tychism. For it mayfairly be urged that since the phenomena of habitmay thus result from a purely mechanicalarrangement, it is unnecessary to suppose that habit-taking is a primordial principle of the universe. Butone fact remains unexplained mechanically, whichconcerns not only the facts of habit, but all cases ofactions apparently violating the law of energy; it isthat all these phenomena depend upon aggregationsof trillions of molecules in one and the same conditionand neighborhood; and it is by no means clear howthey could have all been brought and left in the same

593

place and state by any conservative forces. But letthe mechanical explanation be as perfect as it may,the state of things which it supposes presentsevidence of a primordial habit-taking tendency. For itshows us like things acting in like ways because theyare alike. Now, those who insist on the doctrine ofnecessity will for the most part insist that the physicalworld is entirely individual. Yet law involves anelement of generality. Now to say that generality isprimordial, but gen-

594

eralization not, is like saying that diversity isprimordial but diversification not. It turns logic upsidedown. At any rate, it is clear that nothing but aprinciple of habit, itself due to the growth by habit ofan infinitesimal chance tendency toward habit-taking,is the only bridge that can span the chasm betweenthe chance-medley of chaos and the cosmos of orderand law.

I shall not attempt a molecular explanation of thephenomena of reproduction, because that wouldrequire a subsidiary hypothesis, and carry me awayfrom my main object. Such phenomena, universallydiffused though they be, appear to depend uponspecial conditions; and we do not find that allprotoplasm has reproductive powers.

But what is to be said of the property of feeling? Ifconsciousness belongs to all protoplasm, by whatmechanical constitution is this to be accounted for?The slime is nothing but a chemical compound. Thereis no inherent impossibility in its being formedsynthetically in the laboratory, out of its chemicalelements; and if it were so made, it would present allthe characters of natural protoplasm. No doubt, then,

595

it would feel. To hesitate to admit this would bepuerile and ultra-puerile. By what element of themolecular arrangement, then, would that feeling becaused? This question cannot be evaded or pooh-poohed. Protoplasm certainly does feel; and unlesswe are to accept a weak dualism, the property mustbe shown to arise from some peculiarity of themechanical system. Yet the attempt to deduce it fromthe three laws of mechanics, applied to never soingenious a mechanical contrivance, would obviouslybe futile. It can never be explained, unless we

596

admit that physical events are but degraded orundeveloped forms of psychical events. But oncegrant that the phenomena of matter are but theresult of the sensibly complete sway of habits uponmind, and it only remains to explain why in theprotoplasm these habits are to some slight extentbroken up, so that according to the law of mind, inthat special clause of it sometimes called the principleof accommodation,9 feeling becomes intensified. Nowthe manner in which habits generally get broken up isthis. Reactions usually terminate in the removal of astimulus; for the excitation continues as long as thestimulus is present. Accordingly, habits are generalways of behavior which are associated with theremoval of stimuli. But when the expected removal ofthe stimulus fails to occur, the excitation continuesand increases, and non-habitual reactions take place;and these tend to weaken the habit. If, then, wesuppose that matter never does obey its ideal lawswith absolute precision, but that there are almostinsensible fortuitous departures from regularity, thesewill produce, in general, equally minute effects. Butprotoplasm is in an excessively unstable condition;and it is the characteristic of unstable equilibrium,

597

that near that point excessively minute causes mayproduce startlingly large effects. Here, then, theusual departures from regularity will be followed byothers that are very great; and the large fortuitousdepartures from law so produced, will tend stillfurther to break up the laws, supposing that theseare of

9 " Physiologically, . . . accommodation means thebreaking up of a habit . . . Psychologically, it meansreviving consciousness." Baldwin, Psychology, Part III,ch. i., § 5.

598

the nature of habits. Now, this breaking up of habitand renewed fortuitous spontaneity will, according tothe law of mind, be accompanied by an intensificationof feeling. The nerve-protoplasm is, without doubt, inthe most unstable condition of any kind of matter;and consequently, there the resulting feeling is themost manifest.

Thus we see that the idealist has no need to dread amechanical theory of life. On the contrary, such atheory, fully developed, is bound to call in a tychisticidealism as its indispensable adjunct. Whereverchance-spontaneity is found, there, in the sameproportion, feeling exists. In fact, chance is but theoutward aspect of that which within itself is feeling. Ilong ago showed that real existence, or thing-ness,consists in regularities. So, that primeval chaos inwhich there was no regularity was mere nothing,from a physical aspect. Yet it was not a blank zero;for there was an intensity of consciousness there incomparison with which all that we ever feel is but asthe struggling of a molecule or two to throw off alittle of the force of law to an endless andinnumerable diversity of chance utterly unlimited.

599

But after some atoms of the protoplasm have thusbecome partially emancipated from law, whathappens next to them? To understand this, we haveto remember that no mental tendency is so easilystrengthened by the action of habit as is thetendency to take habits. Now, in the higher kinds ofprotoplasm, especially, the atoms in question havenot only long belonged to one molecule or another ofthe particular mass of slime of which they are parts;but before that, they were constituents of food of aprotoplasmic con-

600

stitution. During all this time, they have been liable tolose habits and to recover them again; so that now,when the stimulus is removed, and the foregonehabits tend to reassert themselves, they do so in thecase of such atoms with great promptness. Indeed,the return is so prompt that there is nothing but thefeeling to show conclusively that the bonds of lawhave ever been relaxed.

In short, diversification is the vestige of chance-spontaneity; and wherever diversity is increasing,there chance must be operative. On the other hand,wherever uniformity is increasing, habit must beoperative. But wherever actions take place under anestablished uniformity, there so much feeling as theremay be takes the mode of a sense of reaction. That isthe manner in which I am led to define the relationbetween the fundamental elements of consciousnessand their physical equivalents.

It remains to consider the physical relations ofgeneral ideas. It may be well here to reflect that ifmatter has no existence except as a specialization ofmind, it follows that whatever affects matteraccording to regular laws is itself matter. But all mind

601

is directly or indirectly connected with all matter, andacts in a more or less regular way; so that all mindmore or less partakes of the nature of matter. Hence,it would be a mistake to conceive of the psychical andthe physical aspects of matter as two aspectsabsolutely distinct. Viewing a thing from the outside,considering its relations of action and reaction withother things, it appears as matter. Viewing it from theinside, looking at its immediate character as feeling, itappears as consciousness. These two views arecombined when we

602

remember that mechanical laws are nothing butacquired habits, like all the regularities of mind,including the tendency to take habits, itself; and thatthis action of habit is nothing but generalization, andgeneralization is nothing but the spreading offeelings. But the question is, how do general ideasappear in the molecular theory of protoplasm?

The consciousness of a habit involves a general idea.In each action of that habit certain atoms get thrownout of their orbit, and replaced by others. Upon allthe different occasions it is different atoms that arethrown off, but they are analogous from a physicalpoint of view, and there is an inward sense of theirbeing analogous. Every time one of the associatedfeelings recurs, there is a more or less vague sensethat there are others, that it has a general character,and of about what this general character is. Weought not, I think, to hold that in protoplasm habitnever acts in any other than the particular waysuggested above. On the contrary, if habit be aprimary property of mind, it must be equally so ofmatter, as a kind of mind. We can hardly refuse toadmit that wherever chance motions have general

603

characters, there is a tendency for this generality tospread and to perfect itself. In that case, a generalidea is a certain modification of consciousness whichaccompanies any regularity or general relationbetween chance actions.

The consciousness of a general idea has a certain "unity of the ego," in it, which is identical when itpasses from one mind to another. It is, therefore,quite analogous to a person; and, indeed, a person isonly a particular kind of general idea. Long age, inthe Journal of Speculative

604

Philosophy (Vol. II, p. 156), I pointed out that aperson is nothing but a symbol involving a generalidea; but my views were, then, too nominalistic toenable me to see that every general idea has theunified living feeling of a person.

All that is necessary, upon this theory, to theexistence of a person is that the feelings out of whichhe is constructed should be in close enoughconnection to influence one another. Here we candraw a consequence which it may be possible tosubmit to experimental test. Namely, if this be thecase, there should be something like personalconsciousness in bodies of men who are in intimateand intensely sympathetic communion. It is true thatwhen the generalization of feeling has been carriedso far as to include all within a person, a stopping-place, in a certain sense, has been attained; andfurther generalization will have a less lively character.But we must not think it will cease. Esprit de corps,national sentiment, sympathy, are no meremetaphors. None of us can fully realize what theminds of corporations are, any more than one of mybrain-cells can know what the whole brain is thinking.

605

But the law of mind clearly points to the existence ofsuch personalities, and there are many ordinaryobservations which, if they were critically examinedand supplemented by special experiments, might, asfirst appearances promise, give evidence of theinfluence of such greater persons upon individuals. Itis often remarked that on one day half a dozenpeople, strangers to one another, will take it into theirheads to do one and the same strange deed, whetherit be a physical experiment, a crime, or an act ofvirtue. When the thirty thousand young people of thesociety for Christian

606

Endeavor were in New York, there seemed to me tobe some mysterious diffusion of sweetness and light.If such a fact is capable of being made out anywhere,it should be in the church. The Christians have alwaysbeen ready to risk their lives for the sake of havingprayers in common, of getting together and prayingsimultaneously with great energy, and especially fortheir common body, for "the whole state of Christ'schurch militant here in earth," as one of the missalshas it. This practice they have been keeping upeverywhere, weekly, for many centuries. Surely, apersonality ought to have developed in that church,in that " bride of Christ," as they call it, or else thereis a strange break in the action of mind, and I shallhave to acknowledge my views are much mistaken.Would not the societies for psychical research bemore likely to break through the clouds, in seekingevidences of such corporate personality, than inseeking evidences of telepathy, which, upon thesame theory, should be a far weaker phenomenon?

607

VEvolutionary Love1

At First Blush:Counter-Gospels

Philosophy, when just escaping from its golden pupa-skin, mythology, proclaimed the great evolutionaryagency of the universe to be Love. Or, since thispirate-lingo, English, is poor in such-like words, let ussay Eros, the exuberance-love. Afterwards,Empedocles set up passionate-love and hate as thetwo co-ordinate powers of the universe. In somepassages, kindness is the word. But certainly, in anysense in which it has an opposite, to be seniorpartner of that opposite, is the highest position thatlove can attain. Nevertheless, the ontologicalgospeller, in whose days those views were familiartopics, made the One Supreme Being, by whom allthings have been made out of nothing, to becherishing-love. What, then, can he say to hate?Never mind, at this time, what the scribe of theapocalypse, if he were John, stung at length by

608

persecution into a rage unable to distinguishsuggestions of evil from visions of heaven, and sobecome the Slanderer of God to men, may havedreamed. The question is rather what the sane Johnthought, or ought to have thought, in order to carryout his idea consistently. His statement that God islove seems aimed at that saying of Ecclesiastes thatwe cannot tell whether God bears us love or hatred."Nay," says John, "we can tell, and very simply! Weknow and have

1The Monist, January, 1893.

609

trusted the love which God hath in us. God is love.''There is no logic in this, unless it means that Godloves all men. In the preceding paragraph, he hadsaid, "God is light and in him is no darkness at all."We are to understand, then, that as darkness ismerely the defect of light, so hatred and evil are mereimperfect stages of àgáph and, àgaqón love andloveliness. This concords with that utterance reportedin John's Gospel: " God sent not the Son into theworld to judge the world; but that the world shouldthrough him be saved. He that believeth on him isnot judged: he that believeth not hath been judgedalready. . . . And this is the judgment, that the lightis come into the world, and that men loved darknessrather than the light." That is to say, God visits nopunishment on them; they punish themselves, bytheir natural affinity for the defective. Thus, the lovethat God is, is not a love of which hatred is thecontrary; otherwise Satan would be a co-ordinatepower; but it is a love which embraces hatred as animperfect stage of it, an Anterosyea, even needshatred and hatefulness as its object. For self-love isno love; so if God's self is love, that which he lovesmust be defect of love; just as a luminary can light up

610

only that which otherwise would be dark. HenryJames, the Swedenborgian, says: "It is no doubt verytolerable finite or creaturely love to love one's own inanother, to love another for his conformity to one'sself: but nothing can be in more flagrant contrastwith the creative Love, all whose tenderness ex vitermini must be reserved only for what intrinsically ismost bitterly hostile and negative to itself." This isfrom Substance and Shadow: an Essay on the

611

Physics of Creation. It is a pity he had not filled hispages with things like this, as he was able easily todo, instead of scolding at his reader and at peoplegenerally, until the physics of creation was well-nighforgot. I must deduct, however, from what I justwrote: obviously no genius could make his everysentence as sublime as one which discloses for theproblem of evil its everlasting solution.

The movement of love is circular, at one and thesame impulse projecting creations into independencyand drawing them into harmony. This seemscomplicated when stated so; but it is fully summedup in the simple formula we call the Golden Rule. Thisdoes not, of course, say, Do everything possible togratify the egoistic impulses of others, but it says,Sacrifice your own perfection to the perfectionment ofyour neighbor. Nor must it for a moment beconfounded with the Benthamite, or Helvetian, orBeccarian motto, Act for the greatest good of thegreatest number. Love is not directed to abstractionsbut to persons; not to persons we do not know, norto numbers of people, but to our own dear ones, ourfamily and neighbors. " Our neighbor," we remember,

612

is one whom we live near, not locally perhaps, but inlife and feeling.

Everybody can see that the statement of St. John isthe formula of an evolutionary philosophy, whichteaches that growth comes only from love, fromI willnot say self-sacrifice, but from the ardent impulse tofulfil another's highest impulse. Suppose, forexample, that I have an idea that interests me. It ismy creation. It is my creature; for as shown in lastJuly's Monist, it is a little person. I love it; and I willsink myself in perfecting it. It is not

613

by dealing out cold justice to the circle of my ideasthat I can make them grow, but by cherishing andtending them as I would the flowers in my garden.The philosophy we draw from John's gospel is thatthis is the way mind develops; and as for the cosmos,only so far as it yet is mind, and so has life, is itcapable of further evolution. Love, recognizing germsof loveliness in the hateful, gradually warms it intolife, and makes it lovely. That is the sort of evolutionwhich every careful student of my essay The Law ofMind, must see that synechism calls for.

The nineteenth century is now fast sinking into thegrave, and we all begin to review its doings and tothink what character it is destined to bear ascompared with other centuries in the minds of futurehistorians. It will be called, I guess, the EconomicalCentury; for political economy has more directrelations with all the branches of its activity than hasany other science. Well, political economy has itsformula of redemption, too. It is this: Intelligence inthe service of greed ensures the justest prices, thefairest contracts, the most enlightened conduct of allthe dealings between men, and leads to the

614

summum bonum, food in plenty and perfect comfort.Food for whom? Why, for the greedy master ofintelligence. I do not mean to say that this is one ofthe legitimate conclusions of political economy, thescientific character of which I fully acknowledge. Butthe study of doctrines, themselves true, will oftentemporarily encourage generalizations extremelyfalse, as the study of physics has encouragednecessitarianism. What I say, then, is that the greatattention paid to economical questions during ourcentury

615

has induced an exaggeration of the beneficial effectsof greed and of the unfortunate results of sentiment,until there has resulted a philosophy which comesunwittingly to this, that greed is the great agent inthe elevation of the human race and in the evolutionof the universe.

I open a handbook of political economy,the mosttypical and middling one I have at hand,and therefind some remarks of which I will here make a briefanalysis. I omit qualifications, sops thrown toCerberus, phrases to placate Christian prejudice,trappings which serve to hide from author and readeralike the ugly nakedness of the greed-god. But I havesurveyed my position. The author enumerates "threemotives to human action:

The love of self;

The love of a limited class having common interestsand feelings with one's self;

The love of mankind at large."

Remark, at the outset, what obsequious title isbestowed on greed,"the love of self." Love! The

616

second motive is love. In place of "a limited class "put "certain persons,'' and you have a fairdescription. Taking "class " in the old-fashionedsense, a weak kind of love is described. In the sequel,there seems to be some haziness as to thedelimitation of this motive. By the love of mankind atlarge, the author does not mean that deep,subconscious passion that is properly so called; butmerely public-spirit, perhaps little more than a fidgetabout pushing ideas. The author proceeds to acomparative estimate of the worth of these motives.Greed, says he, but using, of course, another word, "is not so great an evil as is commonly sup-

617

posed. . . . Every man can promote his own interestsa great deal more effectively than he can promoteany one else's, or than any one else can promotehis." Besides, as he remarks on another page, themore miserly a man is, the more good he does. Thesecond motive "is the most dangerous one to whichsociety is exposed." Love is all very pretty: " no higheror purer source of human happiness exists." (Ahem!)But it is a "source of enduring injury," and, in short,should be overruled by something wiser. What is thiswiser motive? We shall see.

As for public spirit, it is rendered nugatory by the "difficulties in the way of its effective operation." Forexample, it might suggest putting checks upon thefecundity of the poor and the vicious; and " nomeasure of repression would be too severe," in thecase of criminals. The hint is broad. Butunfortunately, you cannot induce legislatures to takesuch measures, owing to the pestiferous" tendersentiments of man towards man." It thus appears,that public-spirit, or Benthamism, is not strongenough to be the effective tutor of love, (I amskipping to another page), which must, therefore, be

618

handed over to " the motives which animate men inthe pursuit of wealth," in which alone we can confide,and which '' are in the highest degree beneficent."2Yes, in the "highest degree" without exception arethey beneficent to the being upon whom all theirblessings are poured out, namely, the Self, whose"sole object," says the writer in accumulating wealthis his in-

2 How can a writer have any respect for science, assuch, who is capable of confounding with the scientificpropositions of political economy, which have nothingto say concerning what is "beneficent," suchbrummagem generalisations as this?

619

dividual " sustenance and enjoyment." Plainly, theauthor holds the notion that some other motive mightbe in a higher degree beneficent even for the man'sself to be a paradox wanting in good sense. He seeksto gloze and modify his doctrine; but he lets theperspicacious reader see what his animating principleis; and when, holding the opinions I have repeated,he at the same time acknowledges that society couldnot exist upon a basis of intelligent greed alone, hesimply pigeon-holes himself as one of the eclectics ofinharmonious opinions. He wants his mammonflavored with a soupçon of god.

The economists accuse those to whom theenunciation of their atrocious villainies communicatesa thrill of horror of being sentimentalists. It may beso: I willingly confess to having some tincture ofsentimentalism in me, God be thanked! Ever sincethe French Revolution brought this leaning of thoughtinto ill-repute,and not altogether undeservedly, Imust admit, true, beautiful, and good as that greatmovement was,it has been the tradition to picturesentimentalists as persons incapable of logicalthought and unwilling to look facts in the eyes. This

620

tradition may be classed with the French traditionthat an Englishman says godam at every secondsentence, the English tradition that an American talksabout "Britishers," and the American tradition that aFrenchman carries forms of etiquette to aninconvenient extreme, in short with all thosetraditions which survive simply because the men whouse their eyes and ears are few and far between.Doubtless some excuse there was for all thoseopinions in days gone by; and sentimentalism, whenit

621

was the fashionable amusement to spend one'sevenings in a flood of tears over a woefulperformance on a candle-litten stage, sometimesmade itself a little ridiculous. But what after all issentimentalism? It is an ism, a doctrine, namely, thedoctrine that great respect should be paid to thenatural judgments of the sensible heart. This is whatsentimentalism precisely is; and I entreat the readerto consider whether to contemn it is not of allblasphemies the most degrading. Yet the nineteenthcentury has steadily contemned it, because it broughtabout the Reign of Terror. That it did so is true. Still,the whole question is one of how much. The Reign ofTerror was very bad; but now the Gradgrind bannerhas been this century long flaunting in the face ofheaven, with an insolence to provoke the very skiesto scowl and rumble. Soon a flash and quick peal willshake economists quite out of their complacency, toolate. The twentieth century, in its latter half, shallsurely see the deluge-tempest burst upon the socialorder,to clear upon a world as deep in ruin as thatgreed-philosophy has long plunged it into guilt. Nopost-thermidorian high jinks then!

622

So a miser is a beneficent power in a community, ishe? With the same reason precisely, only in a muchhigher degree, you might pronounce the Wall Streetsharp to be a good angel, who takes money fromheedless persons not likely to guard it properly, whowrecks feeble enterprises better stopped, and whoadministers wholesome lessons to unwary scientificmen, by passing worthless checks upon them,as youdid, the other day, to me, my millionaire Master inglomery, when you thought you saw your way

623

to using my process without paying for it, and of sobequeathing to your children something to boast oftheir father about,and who by a thousand wiles putsmoney at the service of intelligent greed, in his ownperson. Bernard Mandeville, in his Fable of the Bees,maintains that private vices of all descriptions arepublic benefits, and proves it, too, quite as cogentlyas the economist proves his point concerning themiser. He even argues, with no slight force, that butfor vice civilization would never have existed. In thesame spirit, it has been strongly maintained and is to-day widely believed that all acts of charity andbenevolence, private and public, go seriously todegrade the human race.

The Origin of Species of Darwin merely extendspolitico-economical views of progress to the entirerealm of animal and vegetable life. The vast majorityof our contemporary naturalists hold the opinion thatthe true cause of those exquisite and marvellousadaptations of nature for which, when I was a boy,men used to extol the divine wisdom is that creaturesare so crowded together that those of them thathappen to have the slightest advantage force those

624

less pushing into situations unfavorable tomultiplication or even kill them before they reach theage of reproduction. Among animals, the meremechanical individualism is vastly reënforced as apower making for good by the animal's ruthlessgreed. As Darwin puts it on his title-page, it is thestruggle for existence; and he should have added forhis motto: Every individual for himself, and the Deviltake the hindmost! Jesus, in his sermon on theMount, expressed a different opinion.

625

Here, then, is the issue. The gospel of Christ saysthat progress comes from every individual merginghis individuality in sympathy with his neighbors. Onthe other side, the conviction of the nineteenthcentury is that progress takes place by virtue of everyindividual's striving for himself with all his might andtrampling his neighbor under foot whenever he gets achance to do so. This may accurately be called theGospel of Greed.

Much is to be said on both sides. I have notconcealed, I could not conceal, my own passionatepredilection. Such a confession will probably shockmy scientific brethren. Yet the strong feeling is initself, I think, an argument of some weight in favor ofthe agapastic theory of evolution,so far as it may bepresumed to bespeak the normal judgment of theSensible Heart. Certainly, if it were possible to believein agapasm without believing it warmly, that factwould be an argument against the truth of thedoctrine. At any rate, since the warmth of feelingexists, it should on every account be candidlyconfessed; especially since it creates a liability to one-sidedness on my part against which it behooves my

626

readers and me to be severally on our guard.

Second Thoughts:Irenica.

Let us try to define the logical affinities of thedifferent theories of evolution. Natural selection, asconceived by Darwin, is a mode of evolution in whichthe only positive agent of change in the wholepassage from moner to man is fortuitous variation. Tosecure advance in a definite direction chance has tobe seconded by some action that

627

shall hinder the propagation of some varieties orstimulate that of others. In natural selection, strictlyso called, it is the crowding out of the weak. Insexual selection, it is the attraction of beauty, mainly.

The Origin of Species was published toward the endof the year 1859. The preceding years since 1846had been one of the most productive seasons,or ifextended so as to cover the great book we areconsidering, the most productive period of equallength in the entire history of science from itsbeginnings until now. The idea that chance begetsorder, which is one of the corner-stones of modernphysics (although Dr. Carus considers it "the weakestpoint in Mr. Peirce's system,") was at that time putinto its clearest light. Quetelet had opened thediscussion by his Letters on the Application ofProbabilities to the Moral and Political Sciences, awork which deeply impressed the best minds of thatday, and to which Sir John Herschel had drawngeneral attention in Great Britain. In 1857, the firstvolume of Buckle's History of Civilisation had createda tremendous sensation, owing to the use he made ofthis same idea. Meantime, the "statistical method"

628

had, under that very name, been applied withbrilliant success to molecular physics. Dr. JohnHerapath, an English chemist, had in 1847 outlinedthe kinetical theory of gases in his MathematicalPhysics; and the interest the theory excited had beenrefreshed in 1856 by notable memoirs by Clausiusand Krönig. In the very summer preceding Darwin'spublication, Maxwell had read before the BritishAssociation the first and most important of hisresearches on this subject. The consequence wasthat the idea that

629

fortuitous events may result in a physical law, andfurther that this is the way in which those laws whichappear to conflict with the principle of theconservation of energy are to be explained, had takena strong hold upon the minds of all who were abreastof the leaders of thought. By such minds, it wasinevitable that the Origin of Species, whose teachingwas simply the application of the same principle tothe explanation of another " non-conservative "action, that of organic development, should be hailedand welcomed. The sublime discovery of theconservation of energy by Helmholtz in 1847, andthat of the mechanical theory of heat by Clausius andby Rankine, independently, in 1850, had decidedlyoverawed all those who might have been inclined tosneer at physical science. Thereafter a belated poetstill harping upon " science peddling with the namesof things" would fail of his effect. Mechanism wasnow known to be all, or very nearly so. All this time,utilitarianism,that improved substitute for theGospel,was in its fullest feather; and was a naturalally of an individualistic theory. Dean Mansell'sinjudicious advocacy had led to mutiny among thebondsmen of Sir William Hamilton, and the

630

nominalism of Mill had profited accordingly; andalthough the real science that Darwin was leadingmen to was sure some day to give a death-blow tothe sham-science of Mill, yet there were severalelements of the Darwinian theory which were sure tocharm the followers of Mill. Another thing:anaesthetics had been in use for thirteen years.Already, people's acquaintance with suffering haddropped off very much; and as a consequence, thatunlovely hardness by which our times are socontrasted

631

with those that immediately preceded them, hadalready set in, and inclined people to relish a ruthlesstheory. The reader would quite mistake the drift ofwhat I am saying if he were to understand me aswishing to suggest that any of those things (exceptperhaps Malthus) influenced Darwin himself. What Imean is that his hypothesis, while without disputeone of the most ingenious and pretty ever devised,and while argued with a wealth of knowledge, astrength of logic, a charm of rhetoric, and above allwith a certain magnetic genuineness that was almostirresistible, did not appear, at first, at all near tobeing proved; and to a sober mind its case looks lesshopeful now than it did twenty years ago; but theextraordinarily favorable reception it met with wasplainly owing, in large measure, to its ideas beingthose toward which the age was favorably disposed,especially, because of the encouragement it gave tothe greed-philosophy.

Diametrically opposed to evolution by chance, arethose theories which attribute all progress to aninward necessary principle, or other form of necessity.Many naturalists have thought that if an egg is

632

destined to go through a certain series ofembryological transformations, from which it isperfectly certain not to deviate, and if in geologicaltime almost exactly the same forms appearsuccessively, one replacing another in the sameorder, the strong presumption is that this lattersuccession was as predeterminate and certain to takeplace as the former. So, Nägeli, for instance,conceives that it somehow follows from the first lawof motion and the peculiar, but unknown, molecularconstitution of protoplasm, that forms mustcomplicate

633

themselves more and more. Kölliker makes one formgenerate another after a certain maturation has beenaccomplished. Weismann, too, though he callshimself a Darwinian, holds that nothing is due tochance, but that all forms are simple mechanicalresultants of the heredity from two parents.3 It isvery noticeable that all these different sectaries seekto import into their science a mechanical necessity towhich the facts that come under their observation donot point. Those geologists who think that thevariation of species is due to cataclysmic alterationsof climate or of the chemical constitution of the airand water are also making mechanical necessity chieffactor of evolution.

Evolution by sporting and evolution by mechanicalnecessity are conceptions warring against oneanother. A third method, which supersedes theirstrife, lies enwrapped in the theory of Lamarck.According to his view, all that distinguishes thehighest organic forms from the most rudimentary hasbeen brought about by little hypertrophies oratrophies which have affected individuals early intheir lives, and have been transmitted to their

634

offspring. Such a transmission of acquired charactersis of the general nature of habit-taking, and this isthe representative and derivative within thephysiological domain of the law of mind. Its action isessentially dissimilar to that of a physical force; andthat is the secret of the repugnance of suchnecessitarians as Weismann to admitting itsexistence. The Lamarckians further suppose thatalthough some of the

3 I am happy to find that Dr. Carus, too, ranksWeismann among the opponents of Darwin,notwithstanding his flying that flag.

635

modifications of form so transmitted were originallydue to mechanical causes, yet the chief factors oftheir first production were the straining of endeavorand the overgrowth superinduced by exercise,together with the opposite actions. Now, endeavor,since it is directed toward an end, is essentiallypsychical, even though it be sometimes unconscious;and the growth due to exercise, as I argued in mylast paper, follows a law of a character quite contraryto that of mechanics.

Lamarckian evolution is thus evolution by the force ofhabit.That sentence slipped off my pen while one ofthose neighbors whose function in the social cosmosseems to be that of an Interrupter, was asking me aquestion. Of course, it is nonsense. Habit is mereinertia, a resting on one's oars, not a propulsion. Nowit is energetic projaculation (lucky there is such aword, or this untried hand might have been put toinventing one) by which in the typical instances ofLamarckian evolution the new elements of form arefirst created. Habit, however, forces them to takepractical shapes, compatible with the structures theyaffect, and in the form of heredity and otherwise,

636

gradually replaces the spontaneous energy thatsustains them. Thus, habit plays a double part; itserves to establish the new features, and also tobring them into harmony with the generalmorphology and function of the animals and plants towhich they belong. But if the reader will now kindlygive himself the trouble of turning back a page ortwo, he will see that this account of Lamarckianevolution coincides with the general description of theaction of love, to which, I suppose, he yielded hisassent.

637

Remembering that all matter is really mind,remembering, too, the continuity of mind, let us askwhat aspect Lamarckian evolution takes on within thedomain of consciousness. Direct endeavor canachieve almost nothing. It is as easy by takingthought to add a cubit to one's stature, as it is toproduce an idea acceptable to any of the Muses bymerely straining for it, before it is ready to come. Wehaunt in vain the sacred well and throne ofMnemosyne; the deeper workings of the spirit takeplace in their own slow way, without our connivance.Let but their bugle sound, and we may then makeour effort, sure of an oblation for the altar ofwhatsoever divinity its savor gratifies. Besides thisinward process, there is the operation of theenvironment, which goes to break up habits destinedto be broken up and so to render the mind lively.Everybody knows that the long continuance of aroutine of habit makes us lethargic, while asuccession of surprises wonderfully brightens theideas. Where there is a motion, where history is a-making, there is the focus of mental activity, and ithas been said that the arts and sciences reside withinthe temple of Janus, waking when that is open, but

638

slumbering when it is closed. Few psychologists haveperceived how fundamental a fact this is. A portion ofmind abundantly commissured to other portionsworks almost mechanically. It sinks to a condition of arailway junction. But a portion of mind almostisolated, a spiritual peninsula, or cul-de-sac, is like arailway terminus. Now mental commissures arehabits. Where they abound, originality is not neededand is not found; but where they are in defect,spontaneity is set free. Thus, the first

639

step in the Lamarckian evolution of mind is theputting of sundry thoughts into situations in whichthey are free to play. As to growth by exercise, I havealready shown, in discussing Man's Glassy Essence, inlast October's Monist, what its modus operandi mustbe conceived to be, at least, until a second equallydefinite hypothesis shall have been offered. Namely,it consists of the flying asunder of molecules, and thereparation of the parts by new matter. It is, thus, asort of reproduction. It takes place only duringexercise, because the activity of protoplasm consistsin the molecular disturbance which is its necessarycondition. Growth by exercise takes place also in themind. Indeed, that is what it is to learn. But the mostperfect illustration is the development of aphilosophical idea by being put into practice. Theconception which appeared, at first, as unitary, splitsup into special cases; and into each of these newthought must enter to make a practicable idea. Thisnew thought, however, follows pretty closely themodel of the parent conception; and thus ahomogeneous development takes place. The parallelbetween this and the course of molecularoccurrences is apparent. Patient attention will be able

640

to trace all these elements in the transaction calledlearning.

Three modes of evolution have thus been broughtbefore us; evolution by fortuitous variation, evolutionby mechanical necessity, and evolution by creativelove. We may term them tychastic evolution, ortychasm, anancastic evolution, or anancasm, andagapastic evolution, or agapasm. The doctrines whichrepresent these as severally of principal importance,we may term tychasticism, anancas-

641

ticism, and agapasticism. On the other hand themere propositions that absolute chance, mechanicalnecessity, and the law of love, are severally operativein the cosmos, may receive the names of tychism,anancism, and agapism.

All three modes of evolution are composed of thesame general elements. Agapasm exhibits them themost clearly. The good result is here brought to pass,first, by the bestowal of spontaneous energy by theparent upon the offspring, and, second, by thedisposition of the latter to catch the general idea ofthose about it and thus to subserve the generalpurpose. In order to express the relation thattychasm and anancasm bear to agapasm, let meborrow a word from geometry. An ellipse crossed by astraight line is a sort of cubic curve; for a cubic is acurve which is cut thrice by a straight line; now astraight line might cut the ellipse twice and itsassociated straight line a third time. Still the ellipsewith the straight line across it would not have thecharacteristics of a cubic. It would have, for instance,no contrary flexure, which no true cubic wants; and itwould have two nodes, which no true cubic has. The

642

geometers say that it is a degenerate cubic. Just so,tychasm and anancasm are degenerate forms ofagapasm.

Men who seek to reconcile the Darwinian idea withChristianity will remark that tychastic evolution, likethe agapastic, depends upon a reproductive creation,the forms preserved being those that use thespontaneity conferred upon them in such wise as tobe drawn into harmony with their original, quite afterthe Christian scheme. Very good! This only showsthat just as love cannot have a

643

contrary, but must embrace what is most opposed toit, as a degenerate case of it, so tychasm is a kind ofagapasm. Only, in the tychastic evolution progress issolely owing to the distribution of the napkin-hiddentalent of the rejected servant among those notrejected, just as ruined gamesters leave their moneyon the table to make those not yet ruined so muchthe richer. It makes the felicity of the lambs just thedamnation of the goats, transposed to the other sideof the equation. In genuine agapasm, on the otherhand, advance takes place by virtue of a positivesympathy among the created springing fromcontinuity of mind. This is the idea which tychasticismknows not how to manage.

The anancasticist might here interpose, claiming thatthe mode of evolution for which he contends agreeswith agapasm at the point at which tychasm departsfrom it. For it makes development go through certainphases, having its inevitable ebbs and flows, yettending on the whole to a foreordained perfection.Bare existence by this its destiny betrays an intrinsicaffinity for the good. Herein, it must be admitted,anancasm shows itself to be in a broad acception a

644

species of agapasm. Some forms of it might easily bemistaken for the genuine agapasm. The Hegelianphilosophy is such an anancasticism. With itsrevelatory religion, with its synechism (howeverimperfectly set forth), with its '' reflection," the wholeidea of the theory is superb, almost sublime. Yet,after all, living freedom is practically omitted from itsmethod. The whole movement is that of a vastengine, impelled by a vis a tergo, with a blind andmysterious fate of arriving at a lofty goal. I mean that

645

such an engine it would be, if it really worked; but inpoint of fact, it is a Keely motor. Grant that it reallyacts as it professes to act, and there is nothing to dobut accept the philosophy. But never was there seensuch an example of a long chain of reasoning,shall Isay with a flaw in every link?no, with every link ahandful of sand, squeezed into shape in a dream. Orsay, it is a pasteboard model of a philosophy that inreality does not exist. If we use the one preciousthing it contains, the idea of it, introducing thetychism which the arbitrariness of its every stepsuggests, and make that the support of a vitalfreedom which is the breath of the spirit of love, wemay be able to produce that genuine agapasticism,at which Hegel was aiming.

A Third Aspect:Discrimination

In the very nature of things, the line of demarcationbetween the three modes of evolution is not perfectlysharp. That does not prevent its being quite real;perhaps it is rather a mark of its reality. There is inthe nature of things no sharp line of demarcationbetween the three fundamental colors, red, green,

646

and violet. But for all that they are really different.The main question is whether three radically differentevolutionary elements have been operative; and thesecond question is what are the most strikingcharacteristics of whatever elements have beenoperative.

I propose to devote a few pages to a very slightexamination of these questions in their relation to thehistorical development of human thought. I firstformulate for the reader's convenience the briefestpossible definitions of the

647

three conceivable modes of development of thought,distinguishing also two varieties of anancasm andthree of agapasm. The tychastic development ofthought, then, will consist in slight departures fromhabitual ideas in different directions indifferently,quite purposeless and quite unconstrained whetherby outward circumstances or by force of logic, thesenew departures being followed by unforeseen resultswhich tend to fix some of them as habits more thanothers. The anancastic development of thought willconsist of new ideas adopted without foreseeingwhither they tend, but having a character determinedby causes either external to the mind, such aschanged circumstances of life, or internal to the mindas logical developments of ideas already accepted,such as generalizations. The agapastic developmentof thought is the adoption of certain mentaltendencies, not altogether heedlessly, as in tychasm,nor quite blindly by the mere force of circumstancesor of logic, as in anancasm, but by an immediateattraction for the idea itself, whose nature is divinedbefore the mind possesses it, by the power ofsympathy, that is, by virtue of the continuity of mind;and this mental tendency may be of three varieties,

648

as follows: First, it may affect a whole people orcommunity in its collective personality, and be thencecommunicated to such individuals as are in powerfullysympathetic connection with the collective people,although they may be intellectually incapable ofattaining the idea by their private understandings oreven perhaps of consciously apprehending it. Second,it may affect a private person directly, yet so that heis only enabled to apprehend the idea, or toappreciate its attractiveness,

649

by virtue of his sympathy with his neighbors, under theinfluence of a striking experience or development of thought.The conversion of St. Paul may be taken as an example of whatis meant. Third, it may affect an individual, independently of hishuman affections, by virtue of an attraction it exercises upon hismind, even before he has comprehended it. This is thephenomenon which has been well called the divination genius; for it is due to the continuity between the man's mindand the Most High.

Let us next consider by means of what tests we can dis-criminate between these different categories of evolution. Noabsolute criterion is possible in the nature of things, since in thenature of things there is no sharp line of demarcation betweenthe different classes. Nevertheless, quantitative symptoms maybe found by which a sagacious and sympathetic judge of humannature may be able to estimate the approximate proportions inwhich the different kinds of influence are commingled.

So far as the historical evolution of human thought has beentychastic, it should have proceeded by insensible or minutesteps; for such is the nature of chances when so multiplied as toshow phenomena of regularity. For example, assume that of thenative-born white adult males of the United States in 1880, one-fourth part were below 5 feet 4 inches in stature and one-fourth

650

part above 5 feet 8 inches. Then by the principles of probability,among the whole population, we should expect

216under 4feet 6inches, 216above 6feet48 " 4 " 5 " 48 " 69 " 4 " 4 " 9 " 6

less than 2 " 4 " 3 " less than 2 " 6

651

I set down these figures to show how insignificantlyfew are the cases in which anything very far out ofthe common run presents itself by chance. Thoughthe stature of only every second man is includedwithin the four inches between 5 feet 4 inches and 5feet 8 inches, yet if this interval be extended bythrice four inches above and below, it will embrace allour 8 millions odd of native-born adult white males(of 1880), except only 9 taller and 9 shorter.

The test of minute variation, if not satisfied,absolutely negatives tychasm. If it is satisfied, weshall find that it negatives anancasm but notagapasm. We want a positive test, satisfied bytychasm, only. Now wherever we find men's thoughttaking by imperceptible degrees a turn contrary tothe purposes which animate them, in spite of theirhighest impulses, there, we may safely conclude,there has been a tychastic action.

Students of the history of mind there be of anerudition to fill an imperfect scholar like me with envyedulcorated by joyous admiration, who maintain thatideas when just started are and can be little morethan freaks, since they cannot yet have been critically

652

examined, and further that everywhere and at alltimes progress has been so gradual that it is difficultto make out distinctly what original step any givenman has taken. It would follow that tychasm hasbeen the sole method of intellectual development. Ihave to confess I cannot read history so; I cannothelp thinking that while tychasm has sometimes beenoperative, at others great steps covering nearly thesame ground and made by different menindependently, have been mistaken for a succcssionof small steps, and further that students

653

have been reluctant to admit a real entitative "spirit"of an age or of a people, under the mistaken andunscrutinized impression that they should thus beopening the door to wild and unnatural hypotheses. Ifind, on the contrary, that, however it may be withthe education of individual minds, the historicaldevelopment of thought has seldom been of atychastic nature, and exclusively in backward andbarbarizing movements. I desire to speak with theextreme modesty which befits a student of logic whois required to survey so very wide a field of humanthought that he can cover it only by areconnaissance, to which only the greatest skill andmost adroit methods can impart any value at all; but,after all, I can only express my own opinions and notthose of anybody else; and in my humble judgment,the largest example of tychasm is afforded by thehistory of Christianity, from about its establishment byConstantine, to, say, the time of the Irishmonasteries, an era or eon of about 500 years.Undoubtedly the external circumstance which morethan all others at first inclined men to acceptChristianity in its loveliness and tenderness, was thefearful extent to which society was broken up into

654

units by the unmitigated greed and hard-heartednessinto which the Romans had seduced the world. Andyet it was that very same fact, more than any otherexternal circumstance, that fostered that bitternessagainst the wicked world of which the primitivegospel of Mark contains not a single trace. At least, Ido not detect it in the remark about the blasphemyagainst the Holy Ghost, where nothing is said aboutvengeance, nor even in that speech where theclosing lines of Isaiah are quoted, about the wormand the fire that feed

655

upon the "carcasses of the men that havetransgressed against me." But little by little thebitterness increases until in the last book of the NewTestament, its poor distracted author represents thatall the time Christ was talking about having come tosave the world, the secret design was to catch theentire human race, with the exception of a paltry144,000, and souse them all in a brimstone lake, andas the smoke of their torment went up forever andever, to turn and remark, " There is no curse anymore." Would it be an insensible smirk or a fiendishgrin that should accompany such an utterance? Iwish I could believe St. John did not write it; but it ishis gospel which tells about the " resurrection untocondemnation,"that is of men's being resuscitatedjust for the sake of torturing them;and, at any rate,the Revelation is a very ancient composition. One canunderstand that the early Christians were like mentrying with all their might to climb a steep declivity ofsmooth wet clay; the deepest and truest element oftheir life, animating both heart and head, wasuniversal love; but they were continually, and againsttheir wills, slipping into a party spirit, every slipserving as a precedent, in a fashion but too familiar

656

to every man. This party feeling insensibily grew untilby about A.D. 330 the luster of the pristine integritythat in St. Mark reflects the white spirit of light wasso far tarnished that Eusebius, (the Jared Sparks ofthat day), in the preface to his History, couldannounce his intention of exaggerating everythingthat tended to the glory of the church and ofsuppressing whatever might disgrace it. His Latincontemporary Lactantius is worse, still; and so thedarkling went on increasing until

657

before the end of the century the great library ofAlexandria was destroyed by Theophilus,4 untilGregory the Great, two centuries later, burnt thegreat library of Rome, proclaiming that "Ignorance isthe mother of devotion," (which is true, just asoppression and injustice is the mother of spirituality),until a sober description of the state of the churchwould be a thing our not too nice newspapers wouldtreat as "unfit for publication." All this movement isshown by the application of the test given above tohave been tychastic. Another very much like it on asmall scale, only a hundred times swifter, for thestudy of which there are documents by the library-full, is to be found in the history of the FrenchRevolution.

Anancastic evolution advances by successive strideswith pauses between. The reason is that in thisprocess a habit of thought having been overthrown issupplanted by the next strongest. Now this nextstrongest is sure to be widely disparate from the first,and as often as not is its direct contrary. It remindsone of our old rule of making the second candidatevice-president. This character, therefore, clearly

658

distinguishes anancasm from tychasm. The characterwhich distinguishes it from agapasm is itspurposelessness. But external and internal anancasmhave to be examined separately. Development underthe pressure of external circumstances, orcataclysmine evolution, is in most cases unmistakableenough. It has numberless degrees of intensity, fromthe brute force, the plain war, which has more thanonce turned the current of the world's thought, downto the hard fact of evidence, or what has been

4 See Draper's History of Intellectual Development,chap. x.

659

taken for it, which has been known to convince menby hordes. The only hesitation than can subsist in thepresence of such a history is a quantitative one.Never are external influences the only ones whichaffect the mind, and therefore it must be a matter ofjudgment for which it would scarcely be worth whileto attempt to set rules, whether a given movement isto be regarded as principally governed from withoutor not. In the rise of medieval thought, I meanscholasticism and the synchronistic art developments,undoubtedly the crusades and the discovery of thewritings of Aristotle were powerful influences. Thedevelopment of scholasticism from Roscellin toAlbertus Magnus closely follows the successive stepsin the knowledge of Aristotle. Prantl thinks that thatis the whole story, and few men have thumbed morebooks than Carl Prantl. He has done good solid work,notwithstanding his slap-dash judgments. But weshall never make so much as a good beginning ofcomprehending scholasticism until the whole hasbeen systematically explored and digested by acompany of students regularly organized and heldunder rule for that purpose. But as for the period weare now specially considering, that which

660

synchronised the Romanesque architecture, theliterature is easily mastered. It does not quite justifyPrantl's dicta as to the slavish dependence of theseauthors upon their authorities. Moreover, they kept adefinite purpose steadily before their minds,throughout all their studies. I am, therefore, unableto offer this period of scholasticism as an example ofpure external anancasm, which seems to be thefluorine of the intellectual elements. Perhaps therecent Japanese reception of western ideas is

661

the purest instance of it in history. Yet in combinationwith other elements, nothing is commoner. If thedevelopment of ideas under the influence of thestudy of external facts be considered as externalanancasm,it is on the border between the externaland the internal forms,it is, of course, the principalthing in modern learning. But Whewell, whosemasterly comprehension of the history of sciencecritics have been too ignorant properly to appreciate,clearly shows that it is far from being theoverwhelmingly preponderant influence, even there.

Internal anancasm, or logical groping, whichadvances upon a predestined line without being ableto foresee whither it is to be carried nor to steer itscourse, this is the rule of development of philosophy.Hegel first made the world understand this; and heseeks to make logic not merely the subjective guideand monitor of thought, which was all it had beenambitioning before, but to be the very mainspring ofthinking, and not merely of individual thinking but ofdiscussion, of the history of the development ofthought, of all history, of all development. Thisinvolves a positive, clearly demonstrable error. Let the

662

logic in question be of whatever kind it may, a logic ofnecessary inference or a logic of probable inference(the theory might perhaps be shaped to fit either), inany case it supposes that logic is sufficient of itself todetermine what conclusion follows from givenpremises; for unless it will do so much, it will notsuffice to explain why an individual train of reasoningshould take just the course it does take, to saynothing of other kinds of development. It thussupposes that from given premises, only oneconclusion can logically be drawn,

663

and that there is no scope at all for free choice. Thatfrom given premises only one conclusion can logicallybe drawn, is one of the false notions which havecome from logicians' confining their attention to thatNantucket of thought, the logic of non-relative terms.In the logic of relatives, it does not hold good.

One remark occurs to me. If the evolution of history isin considerable part of the nature of internalanancasm, it resembles the development of individualmen; and just as 33 years is a rough but natural unitof time for individuals, being the average age atwhich man has issue, so there should be anapproximate period at the end of which one greathistorical movement ought to be likely to besupplanted by another. Let us see if we can make outanything of the kind. Take the governmentaldevelopment of Rome as being sufficiently long andset down the principal dates.

B.C. 753,Foundation of Rome.

B.C. 510,Expulsion of theTarquins.

664

B.C. 27,Octavius assumes titleAugustus.

A.D. 476,End of WesternEmpire.

A.D. 962,Holy Roman Empire.

A.D.1453,Fall of Constantinople.

The last event was one of the most significant inhistory, especially for Italy. The intervals are 243,483, 502, 486, 491 years. All are rather curiouslynear equal, except the first which is half the others.Successive reigns of kings would not commonly be sonear equal. Let us set down a few dates in the historyof thought.

665

B.C.585, Eclipse of Thales. Beginning of Greekphilosophy.

A.D.30, The crucifixion.

AD. 529, Closing of Athenian schools. End ofGreek philosophy.

A.D.1125,(Approximate) Rise of the Universitiesof Bologna and Paris.

A.D.1543,Publication of the ''De Revolutionibus"of Copernicus. Beginning of ModernScience.

The intervals are 615, 499, 596, 418, years. In thehistory of metaphysics, we may take the following:

B.C. 322, Death of Aristotle.

A.D. 1274, Death of Aquinas.

A.D. 1804, Death of Kant.

The intervals are 1595 and 530 years. The former isabout thrice the latter.

666

From these figures, no conclusion can fairly bedrawn. At the same time, they suggest that perhapsthere may be a rough natural era of about 500 years.Should there be any independent evidence of this,the intervals noticed may gain some significance.

The agapastic development of thought should, if itexists, be distinguished by its purposive character,this purpose being the development of an idea. Weshould have a direct agapic or sympatheticcomprehension and recognition of it, by virtue of thecontinuity of thought. I here take it for granted thatsuch continuity of thought has been sufficientlyproved by the arguments used in my paper on the"Law of Mind " in The Monist of last July. Even ifthose arguments are not quite convincing inthemselves, yet if they

667

are reënforced by an apparent agapasm in the historyof thought, the two propositions will lend one anothermutual aid. The reader will, I trust, be too wellgrounded in logic to mistake such mutual support fora vicious circle in reasoning. If it could be showndirectly that there is such an entity as the " spirit ofan age" or of a people, and that mere individualintelligence will not account for all the phenomena,this would be proof enough at once of agapasticismand of synechism. I must acknowledge that I amunable to produce a cogent demonstration of this;but I am, I believe, able to adduce such argumentsas will serve to confirm those which have been drawnfrom other facts. I believe that all the greatestachievements of mind have been beyond the powersof unaided individuals; and I find, apart from thesupport this opinion receives from synechisticconsiderations, and from the purposive character ofmany great movements, direct reason for so thinkingin the sublimity of the ideas and in their occurringsimultaneously and independently to a number ofindividuals of no extraordinary general powers. Thepointed Gothic architecture in several of itsdevelopments appears to me to be of such a

668

character. All attempts to imitate it by modernarchitects of the greatest learning and genius appearflat and tame, and are felt by their authors to be so.Yet at the time the style was living, there was quitean abundance of men capable of producing works ofthis kind of gigantic sublimity and power. In morethan one case, extant documents show that thecathedral chapters, in the selection of architects,treated high artistic genius as a secondaryconsideration, as if there were no lack of persons ableto supply

669

that; and the results justify their confidence. Wereindividuals in general, then, in those ages possessedof such lofty natures and high intellect? Such anopinion would break down under the firstexamination.

How many times have men now in middle life seengreat discoveries made independently and almostsimultaneously! The first instance I remember wasthe prediction of a planet exterior to Uranus byLeverrier and Adams. One hardly knows to whom theprinciple of the conservation of energy ought to beattributed, although it may reasonably be consideredas the greatest discovery science has ever made. Themechanical theory of heat was set forth by Rankineand by Clausius during the same month of February,1850; and there are eminent men who attribute thisgreat step to Thomson. 5 The kinetical theory ofgases, after being started by John Bernoulli and longburied in oblivion, was reinvented and applied to theexplanation not merely of the laws of Boyle, Charles,and Avogadro, but also of diffusion and viscosity, byat least three modern physicists separately. It is wellknown that the doctrine of natural selection was

670

presented by Wallace and by Darwin at the samemeeting of the British Association; and Darwin in his"Historical Sketch" prefixed to the later editions of hisbook shows that both were anticipated by obscureforerunners. The method of spectrum analysis wasclaimed for Swan as well as for Kirchhoff, and therewere others who perhaps had still better claims. Theauthorship of the Periodical Law of the ChemicalElements is disputed between a Russian,

5 Thomson, himself, in his article Heat in theEncyclopedia Britannica, never once mentions thename of Clausius.

671

a German, and an Englishman; although there is noroom for doubt that the principal merit belongs to thefirst. These are nearly all the greatest discoveries ofour times. It is the same with the inventions. It maynot be surprising that the telegraph should havebeen independently made by several inventors,because it was an easy corollary from scientific factswell made out before. But it was not so with thetelephone and other inventions. Ether, the firstanaesthetic, was introduced independently by threedifferent New England physicians. Now ether hadbeen a common article for a century. It had been inone of the pharmacopoeias three centuries before. Itis quite incredible that its anaesthetic property shouldnot have been known; it was known. It had probablypassed from mouth to ear as a secret from the daysof Basil Valentine; but for long it had been a secret ofthe Punchinello kind. In New England, for manyyears, boys had used it tor amusement. Why thenhad it not been put to its serious use? No reason canbe given, except that the motive to do so was notstrong enough. The motives to doing so could onlyhave been desire for gain and philanthropy. About1846, the date of the introduction, philanthropy was

672

undoubtedly in an unusually active condition. Thatsensibility, or sentimentalism, which had beenintroduced in the previous century, had undergone aripening process, in consequence of which, thoughnow less intense than it had previously been, it wasmore likely to influence unreflecting people than ithad ever been. All three of the ether-claimants hadprobably been influenced by the desire for gain; butnevertheless they were certainly not insensible to theagapic influences.

673

I doubt if any of the great discoveries ought,properly, to be considered as altogether individualachievements; and I think many will share this doubt.Yet, if not, what an argument for the continuity ofmind, and for agapasticism is here! I do not wish tobe very strenuous. If thinkers will only be persuadedto lay aside their prejudices and apply themselves tostudying the evidences of this doctrine, I shall be fullycontent to await the final decision.

674

SUPPLEMENTARY ESSAY:THE PRAGMATISM OF PEIRCEBy John Dewey

The term pragmatism was introduced into literaturein the opening sentences of Professor James'sCalifornia Union address in 1898. The sentences runas follows: "The principle of pragmatism, as we maycall it, may be expressed in a variety of ways, all ofthem very simple. In the Popular Science Monthly forJanuary, 1878, Mr. Charles S. Peirce introduces it asfollows:" etc. The readers who have turned to thevolume referred to have not, however, found theword there. From other sources we know that thename as well as the idea was furnished by Mr. Peirce.The latter has told us that both the word and theidea were suggested to him by a reading of Kant, theidea by the Critique of Pure Reason, the term by the"Critique of Practical Reason." 1 The article in theMonist gives such a good statement of both the ideaand the reason for selecting the term that it may bequoted in extenso. Peirce sets out by saying that with

675

men who work in laboratories, the habit of mind ismolded by experimental work much more than theyare themselves aware. "Whatever statement you maymake to him, he [the experimentalist] will eitherunderstand as meaning that if a given prescription foran experiment ever can be and ever is carried out inact, an experience of a given description will result, orelse he will see no sense at all in what you say."Having himself the experimental mind and beinginterested in methods of thinking, '' he framed thetheory that a conception, that is, the rational purportof a word or other expression, lies

1 See article on "Pragmatism," in Baldwin's Dictionary,Vol. 2., p 322, and the Monist, Vol. 15, p. 162.

676

exclusively in its bearing upon the conduct of life; sothat, since obviously nothing that might not resultfrom experiment can have any direct bearing uponconduct, if one can define accurately all theconceivable experimental phenomena which theaffirmation or denial of a concept could imply, one willhave therein a complete definition of the concept,and there is absolutely nothing more in it. For thisdoctrine, he invented the name pragmatism."

After saying that some of his friends wished him tocall the doctrine practicism or practicalism, he saysthat he had learned philosophy from Kant, and thatto one "who still thought in Kantian terms mostreadily, praktisch and pragmatisch were as far apartas the two poles, the former belonging to a region ofthought where no mind of the experimentalist typecan ever make sure of solid ground under his feet,the latter expressing relation to some definite humanpurpose. Now quite the most striking feature of thenew theory was its recognition of an inseparableconnection between rational cognition and humanpurpose." 2

From this brief statement, it will be noted that Peirce

677

confined the significance of the term to thedetermination of the meaning of terms, or better,propositions; the theory was not, of itself, a theory ofthe test, or the truth, of propositions. Hence the titleof his original article: How to Make Ideas Clear. In hislater writing, after the term had been used as atheory of truth,he proposed the more limited"pragmaticism" to designate his original specificmeaning.3 But even with respect to the meaning ofpropositions, there is a marked difference betweenhis pragmaticism and the pragmatism of, say, James.Some of the critics (especially continental) of thelatter would have saved themselves some futilebeating of the air, if they had reacted to James'sstatements instead of to their own as-

2 Kant discriminates the laws of morality, which are apriori, from rules of skill, having to do with technique orart, and counsels of prudence, having to do withwelfare. The latter he calls pragmatic; the a priori lawspractical. See Metaphysics of Morals, Abbott's trans.,pp. 33 and 34.3 See the article in the Monist already mentioned, andanother one in the same volume, p. 481, "The Issues ofPragmaticism."

678

sociations with the word " pragmatic." Thus Jamessays in his California address: "The effective meaningof any philosophic proposition can always be broughtdown to some particular consequence, in our futurepractical experience, whether active or passive; thepoint lying rather in the fact that the experience mustbe particular, than in the fact that it must be active."(Italics mine.)

Now the curious fact is that Peirce puts moreemphasis upon practise (or conduct) and less uponthe particular; in fact, he transfers the emphasis tothe general. The following passage is worth quotationbecause of the definiteness with which it identifiesmeaning with both the future and with the general."The rational meaning of every proposition lies in thefuture. How so? The meaning of a proposition is itselfa proposition. Indeed, it is no other than the veryproposition of which it is the meaning: it is atranslation of it. But of the myriads of forms intowhich a proposition may be translated, which is thatone which is to be called its very meaning? It is,according to the pragmaticist, that form in which theproposition becomes applicable to human conduct,

679

not in these or those special circumstances nor whenone entertains this or that special design, but thatform which is most applicable to self-control underevery situation and to every purpose." Hence, "itmust be simply the general description of all theexperimental phenomena which the assertion of theproposition virtually predicts." Or, paraphrasing,pragmatism identifies meaning with formation of ahabit, or way of acting having the greatest generalitypossible, or the widest range of application toparticulars. Since habits or ways of acting are just asreal as particulars, it is committed to a belief in thereality of "universals.'' Hence it is not a doctrine ofphenomenalism, for while the richness of phenomenalies in their sensuous quality, pragmatism does notintend to define these (leaving them, as it were, tospeak for themselves), but "eliminates their sentialelement, and endeavors to define the rationalpurport, and this it finds in the purposive bearing ofthe word or proposition in question." Moreover, notonly are generals real, but they are physically

680

efficient. The meanings " the air is stuffy " and "stuffy air is unwholesome" may determine, forexample, the opening of the window. Accordingly onthe ethical side, " the pragmaticist does not make thesummum bonum to consist in action, but makes it toconsist in that process of evolution whereby theexistent comes more and more to embody thosegenerals . . . ; in other words, becomes, throughaction an embodiment of rational purports or habitsgeneralized as widely as possible." 4

The passages quoted should be compared with whatPeirce has to say in the Baldwin Dictionary article.There he says that James's doctrine seems to commitus to the belief "that the end of man is actiona stoicalmaxim which does not commend itself as forcibly tothe present writer at the age of sixty as it did atthirty. If it be admitted, on the contrary, that actionwants an end, and that the end must be somethingof a general description, then the spirit of the maximitself . . . would direct us toward something differentfrom practical facts, namely, to generalideas . . . .The only ultimate good which the practicalfacts to which the maxim directs attention can

681

subserve is to further the development of concretereasonableness . . . .Almost everybody will now agreethat the ultimate good lies in the evolutionary processin some way. If so, it is not in individual reactions intheir segregation, but in something general orcontinuous. Synechism is founded on the notion thatthe coalescence, the becoming continuous, thebecoming governed by laws, the becoming instinctwith general ideas, are but phases of one and thesame process of the growth of reasonableness. This isfirst shown to be true with mathematical exactitudein the field of logic, and is thence inferred to holdgood metaphysically. It is not opposed topragmaticism . . . but includes that procedure as astep."

Here again we have the doctrine of pragmaticism asa doctrine that meaning or rational purport resides inthe setting up of habits or generalized methods, adoctrine passing over into

4 It is probably fair to see here an empirical renderingof the Kantian generality of moral action, while thedistinction and connection of "rational purport" and"sensible particular" have also obvious Kantianassociations.

682

the metaphysics of synechism. It will be well now torecur explicitly to Peirce's earlier doctrine which heseems to qualifyalthough, as he notes, he upheld thedoctrine of the reality of generals even at the earlierperiod. Peirce sets out, in his article on the " Fixationof Belief," with the empirical difference of doubt andbelief expressed in the facts that belief determines ahabit while doubt does not, and that belief is calmand satisfactory while doubt is an uneasy anddissatisfied state from which we struggle to emerge;to attain, that is, a state of belief, a struggle whichmay be called inquiry. The sole object of inquiry is thefixation of belief. The scientific method of fixation has,however, certain rivals: one is that of " tenacity"constant reiteration, dwelling upon everythingconducive to the belief, avoidance of everythingwhich might unsettle itthe will to believe. The methodbreaks down in practice because of man's socialnature; we have to take account of contrary beliefs inothers, so that the real problem is to fix the belief ofthe community; for otherwise our own belief isprecariously exposed to attack and doubt. Hence theresort to the method of authority. This method breaksdown in time by the fact that authority can not fix all

684

beliefs in all their details, and because of the conflictwhich arises between organized traditions. There maythen be recourse to what is " agreeable to reason"amethod potent in formation of taste and in estheticproductions and in the history of philosophy,but amethod which again fails to secure permanentagreements in society, and so leaves individual beliefat the mercy of attack. Hence, finally, recourse toscience, whose fundamental hypothesis is this:"There are real things, whose characters are entirelyindependent of our opinions about them; thoserealities affect our senses according to regular laws,and . . . by taking advantage of the laws ofperception, we can ascertain by reasoning how thingsreally are, and any man if he have sufficientexperience and reason enough about it, will be led tothe one true conclusion." 5

It will be noted that the quotation employs the terms" reality " and " truth," while it makes them a part ofthe state-

5 P. 26.

685

ment of the hypothesis entertained in scientificprocedure. Upon such a basis, what meanings attachto the terms " reality " and " truth " ? Since they aregeneral terms, their meanings must be determinedon the basis of the effects, having practical bearings,which the object of our conception has. Now theeffect which real things have is to cause beliefs;beliefs are then the consequences which give thegeneral term reality a " rational purport." And on theassumption of the scientific method, thedistinguishing character of the real object must bethat it tends to produce a single universally acceptedbelief. "All the followers of science are fully persuadedthat the processes of investigation, if only pushed farenough, will give one certain solution to everyquestion to which they can be applied." "This activityof thought by which we are carried, not where wewish, but to a foreordained goal, is like the operationof destiny . . . . This great law is embodied in theconception of truth and reality. The opinion which isfated to be ultimately agreed to by all whoinvestigate, is what we mean by the truth, and theobject represented in this opinion is the real.''6 In asubsequent essay (on the "Probability of Induction ")

686

Peirce expressly draws the conclusion which followsfrom this statement; viz., that this conception of truthand reality makes everything depend upon thecharacter of the methods of inquiry and inference bywhich conclusions are reached. "In the case ofsynthetic inferences we know only the degree oftrustworthiness of our proceeding. As all knowledgecomes from synthetic inference, we must also inferthat all human certainty consists merely in ourknowing that the processes by which our knowledgehas been derived are such as must generally have ledto true conclusions "7true conclusions, once more,being those which command the agreement ofcompetent inquiries.

Summing up, we may say that Peirce's pragmaticismis a doctrine concerning the meaning, conception, orrational purport of objects, namely, that these consistin the " effects, which might conceivably havepractical bearings, we conceive the ob-

6 P. 5657.7 P. 105.

687

ject of our conception to have. Then, our conceptionof these effects is the whole of our conception of theobject." 8 "Our idea of anything is our idea of itssensible effects," and if we have any doubt as towhether we really believe the effects to be sensible orno, we have only to ask ourselves whether or no weshould act any differently in their presence. In short,our own responses to sensory stimuli are theultimate, or testing, ingredients in our conception ofan object. In the literal sense of the word pragmatist,therefore, Peirce is more of a pragmatist than James.

He is also less of a nominalist. That is to say, heemphasizes much less the particular sensibleconsequence, and much more the habit, the genericattitude of response, set up in consequence ofexperiences with a thing. In the passage in theDictionary already quoted he speaks as if in his laterlife he attached less importance to action, and moreto " concrete reasonableness" than in his earlierwriting. It may well be that the relative emphasis hadshifted. But there is at most but a difference ofemphasis. For in his later doctrine, concreterationality means a change in existence brought

688

about through action, and through action whichembodies conceptions whose own specific existenceconsists in habitual attitudes of response. In hisearlier writing, the emphasis upon habits, assomething generic, is explicit. "What a thing means issimply what habits it involves."9 More elaborately,"Induction infers a rule. Now the belief of a rule is ahabit. That a habit is a rule, active in us, is evident.That every belief is of the nature of a habit, in so faras it is of a general character, has been shown in theearlier papers of this series." 10

The difference between Peirce and James which nextstrikes us is the greater emphasis placed by theformer upon the method of procedure. As thequotations already made show, everything ultimatelyturned, for Peirce, upon the trustworthiness of theprocedures of inquiry. Hence his high estimate oflogic, as compared with Jamesat least James in hislater days. Hence also

8 P. 45.9P. 43.10 P. 151

689

his definite rejection of the appeal to the Will toBelieveunder the form of what he calls the method oftenacity. Closely associated with this is the fact thatPeirce has a more explicit dependence upon thesocial factor than has James. The appeal in Peirce isessentially to the consensus of those who haveinvestigated, using methods which are capable ofemployment by all. It is the need for socialagreement, and the fact that in its absence "themethod of tenacity" will be exposed to disintegrationfrom without, which finally forces upon mankind thewider and wider utilization of the scientific method.

Finally, both Peirce and James are realists. Thereasonings of both depend upon the assumption ofreal things which really have effects or consequences.Of the two, Peirce makes clearer the fact that inphilosophy at least we are dealing with theconception of reality, with reality as a term havingrational purport, and hence with something whosemeaning is itself to be determined in terms ofconsequences. That " reality" means the object ofthose beliefs which have, after prolonged andcoöperative inquiry, becomes stable, and " truth " the

690

quality of these beliefs is a logical consequence of thisposition. Thus while "we may define the real as thatwhose characters are independent of what anybodymay think them to be . . . it would be a great mistaketo suppose that this definition makes the idea ofreality perfectly clear." 11 For it is only the outcome ofpersistent and conjoint inquiry which enables us togive intelligible meaning in the concrete to theexpression "characters independent of what anybodymay think them to be.'' (This is the pragmatic wayout of the egocentric predicament.) And while mypurpose is wholly expository I can not close withoutinquiring whether recourse to Peirce would not havea most beneficial influence in contemporarydiscussion. Do not a large part of our epistemologicaldifficulties arise from an attempt to define the " real "as something given prior to reflective inquiry insteadof as that which reflective inquiry is forced to reachand to which when it is reached belief can stablycling?

11 P. 53.

691

BIBLIOGRAPHY OF PEIRCE'S PUBLISHEDWRITINGSI. Writings of General Interest.1

A. Three papers in the Journal of SpeculativePhilosophy, Vol. 2 (1868).

1. "Questions Concerning Certain FacultiesClaimed for Man," pp. 103114.

2. "Some Consequences of Four Incapacities,"pp. 140157.

3. "Ground of Validity of the Laws of Logic," pp.193208.

These three papers, somewhat loosely connected,deal mainly with the philosophy of discursive thought.The first deals with our power of intuition, and holdsthat "every thought is a sign." The second, one of themost remarkable of Peirce's writings, contains anacute criticism of the Cartesian tradition and anoteworthy argument against the traditionalemphasis on "images" in thinking. The third contains,

692

inter alia, a refutation of Mill's indictment of thesyllogism. The same volume of the Journal containstwo unsigned communications on Nominalism and onthe Meaning of Determined.

B. Review of Fraser's "Berkeley," in the NorthAmerican Review, Vol. 113 (1871), pp. 449472.

This paper contains an important analysis onmedieval realism, and of Berkeley's nominalism. (AScotist realism continues to distinguish Peirce's workafter this.)

C. "Illustrations of the Logic of Science," in PopularScience Monthly, Vols. 1213 (18771878).Reprinted in Pt. I of this volume. The first andsecond papers were also published in the RevuePhilosophique, Vols. 67 (1879).

D. Ten papers in the Monist, Vols. 13 (18911893),and 1516 (19051906). The first five are reprintedin Pt. II of this volume.

The sixth paper, "Reply to the Necessitarians," Vol. 3,pp. 526570, is an answer to the criticism of theforegoing by the editor of the Monist, Vol. 2, pp.560ff.; cf. Vol. 3, pp. 68ff. and 571ff., and McCrie,"The Issues of Synechism," Vol. 3, pp. 380ff.

693

1 The following classification is arbitrary, as some ofPeirce's most significant reflections occur in papersunder headings II. and III. It may, however, be useful.

694

7. "What Pragmatism Is?" Vol. 15, pp. 161181.

8. "The Issues of Pragmaticism," Vol. 15, pp.481499.

9. "Mr. Peterson's Proposed Discussion," Vol. 16,pp. 147ff.

10. "Prolegomena to an Apology forPragmaticism," Vol. 16, PP. 492546.

The last four papers develop Peirce's thought byshowing its agreement and disagreement with thepragmatism of James and Schiller. The last papercontains his Method of Existential Graphs.

E. "The Reality of God," in the Hibbert Journal, Vol.7 (1908), pp. 96112. (This article contains briefindications of many of Peirce's leading ideas.)

F. Six Papers in the Open Court, Vols. 67 (1893).

1. "Pythagorics" (on the Pythagoreanbrotherhood), pp. 33753377.

2. "Dmesis" (on charity towards criminals), pp.33993402.

695

3. "The Critic of Arguments (I.), Exact Thinking,"pp. 33913394.

4. "The Critic of Arguments (II.), The Reader isIntroduced to Relatives," pp. 34153419. (Thelast two contain a very clear succinct account ofthe general character of Peirce's logic.)

5. "What is Christian Faith?" pp. 37433745.

6. "The Marriage of Religion and Science," pp.35593560.

G. Articles in Baldwin's "Dictionary of Philosophy ":Individual, kind, matter and form, possibility,pragmatism, priority, reasoning, sign, scientificmethod, sufficient reason, synechism, anduniformity.

H. "Pearson's Grammar of Science," in PopularScience Monthly, Vol. 58 (1901), pp. 296306. (Acritique of Pearson's conceptualism and of hisutilitarian view as to the aim of science.)

II. Writings of Predominantly Logical Interest.

A. Five Papers on Logic, read before the AmericanAcademy of Arts and Sciences. Published in theProceedings of the Academy, Vol. 7 (1867).

696

1. "On an Improvement in Boole's Calculus ofLogic," pp. 250261. (Suggests improvements inBoole's logic, especially in the representation ofparticular propositions. The association ofprobability with the notion of relative frequencybecame a leading idea of Peirce's thought.)

2. "On the Natural Classification of Arguments,"pp. 261- 287. (A suggestive distinction betweenthe leading principle and the premise of anargument. Contains also an interesting note (pp.283284) denying the posi-

697

tivistic maxim that, "no hypothesis is admissiblewhich is not capable of verification by directobservation.")

3. "On a New List of Categories," pp. 287298.The categories are: Being, Quality (Referenceto a Ground), Relation (Reference to aCorrelate), Representation (Reference to anInterpretant), Substance. "Logic has for itssubject-genus all symbols and not merelyconcepts." Symbols include terms, propositions,and arguments.

4. "Upon the Logic of Mathematics," pp. 402412."There are certain general propositions fromwhich the truths of mathematics followsyllogistically."

5. "Upon Logical Comprehension and Extension,"pp. 416432. (Interesting historical references tothe use of these terms and an attack on thesupposed rule as to their inverse proportionality.)

B. "Description of a Notation for the Logic ofRelations," in Memoires of the American Academy,Vol. 9 (1870), pp. 317378. (Shows the relation of

698

inclusion between classes to be more fundamentalthan Boole's use of equality. Extends the Booleiancalculus to DeMorgan's logic of relative terms.)

C. "On the Algebra of Logic," American Journal ofMathematics, Vol. 3 (1880), pp. 1557. (Referred toby Schroeder as Peirce's Hauptwerk in"Vorlesungen über die Algebra der Logik," Vol. 1.,p. 107.)

D. "On the Logic of Number," American Journal ofMathematics, Vol. 4 (1881), pp. 8595.

E. "Brief Description of the Algebra of Relatives,"Reprinted from ??, pp. 16.

F. "On the Algebra of Logic: A Contribution to thePhilosophy of Notation," American Journal ofMathematics, Vol 7 (1884), pp. 180202.

G. "A Theory of Probable Inference" and notes "Ona Limited Universe of Marks" and on the "Logic ofRelatives" in "Studies in Logic by members of theJohns Hopkins University," Boston, 1883, pp.126203.

H. "The Regenerated Logic," Monist, Vol. 7, pp.1940. "The Logic of Relatives," Monist, Vol. 7, pp.

699

161217. (An elaborate development of his ownlogic of relatives, by way of review of Schroeder'sbook.)

I. Miscellaneous Notes, etc.

1. Review of Venn's "Logic of Chance," NorthAmerican Review, July, 1867.

2. "On the Application of Logical Analysis toMultiple Al-

700

gebra," Proceedings of the American Academy,Vol. 10 (1875), pp. 392394.

3. "Note on Grassman's 'Calculus of Extension,' "Proceedings of the American Academy, Vol. 13(1878), pp. 115116.

4. "Note on Conversion," Mind, Vol. 1, p. 424.

5. Notes and Additions to Benjamin Peirce's"Linear Associative Algebra," American Journal ofMathematics, Vol. 4 (1881), pp. 92ff., especiallypp. 221229.

6. "Logical Machines," American Journal ofPsychology, Vol. 1 (1881).

7. "infinitesimals," Science, Vol. 11 (1900), p.430.

8. "Some Amazing Mazes," Monist, Vol. 18 (Apriland July, 1908), and Vol. 19 (Jan.,1909).

9. "On Non0Aristotelian Logic" (Letter), Monist,Vol. 20.

J. A Syllabus of Certain Topics of Logic. 1903.Boston. Alfred Mudge & Sons (A four page

701

brochure).

K. Articles in Baldwin's "Dictionary of Philosophy"on: laws of thought, leading principle, logic (Exactand symbolic), modality, negation, predicate andpredication, probable inference, quality, quantity,relatives, significant, simple, subject, syllogism,theory, truth and falsity universal, universe,validity, verification, whole and parts.

III. Researches in the Theory and Methods ofMeasurement.

A. General and Astronomic.

1. "On the Theory of Errors and Observation, "Report of the Superintendnt of the U.S. CoastSurvey for 1870, pp. 22022.

2. "Note on the Theory of Economy of Research,"Report of the U.S. Coast Survey for 1876, pp.197201. (This paper deals with the relationbetween the utility and the cost of diminishingthe probable error.)

3. "Apparatus for Recording a Mean of ObservedTimes," U.S. Coast Survey, 1877. Appendix No.15 to Report of 1875.

702

4. "Ferrero's Metodo dei Minimi Quadrati,"American Journal of Mathematics, Vol. 1 (1878),pp. 5563.

5. "Photometric Researches," Annals of theAstronomical Observatory of Harvard College,Vol. 9 (1878), pp 1181.

6. "Methods and Results. measurement ofGravity. Washington. 1879.

7. "Methods and Results. A catalogue of Stars forObservations of Lattitude. Washington. 1879.

703

8. "On the Ghosts in Rutherford's 'DiffractionSpectra,"' American Journal of Mathematics, Vol.2 (1879), pp. 330347.

9. "Note on a Comparison of a Wave-Length witha Meter," American Journal of Science, Vol. 18(1879), P. 51.

10. "A Quincuncial Projection of the Sphere,"American Journal of Mathematics, Vol. 2 (1879),pp. 394, 396.

11. "Numerical Measure of Success ofPredictions," Science, Vol. 4 (1884), p. 453.

12. "Proceedings Assay Commission"Washington, 1888. (Joint Reports on Weighing.)

B. Geodetic Researches. The Pendulum.

1. "Measurement of Gravity at Initial Stations inAmerica and Europe," Report of the U. S. CoastSurvey, 1876, pp. 202237 and 410416.

2. "De l'influence de la flexibilité du trépied surl'oscillation du pendule a réversion," ConférenceGeodesique Internationale (1877) Comptes

704

Rendus, Berlin, 1878, pp. 171 187. (This paperwas introduced by Plantamour and was followedby the notes of Appolzer.)

3. "On the Influence of Internal Friction uponthe Correction of the Length of the Second'sPendulum," Proceedings of the AmericanAcademy, Vol. 13 (1878), pp. 396401.

4. "On a Method of Swinging Pendulums for theDetermina- tion of Gravity proposed by M. Faye,"American Journal of Science, Vol. 18 (1879), pp.112119.

5. "Results of Pendulum Experiments," AmericanJournal of Science, Vol. 20 (1880).

6. "Flexure of Pendulum Supports," Report of theU. S. Coast Survey, 1881, pp. 359441.

7. "On the Deduction of the Ellipticity of theEarth from the Pendulum Experiment," Report ofthe U. S. Coast Survey, 1881, pp. 442456.

8. "Determinations of Gravity at Stations inPennsylvania," Report of U. S. Coast Survey,1883, Appendix 19 and PP. 473486.

9. "On the Use of the Noddy," Report of the U.

705

S. Coast Survey, 1884, PP. 475482.

10. "Effect of the Flexure of a Pendulum uponthe Period of Oscillation," Report of the U. S.Coast Survey, 1884, pp. 483485.

11. "On the Influence of a Noddy, and ofUnequal Temperature upon the Periods of aPendulum," Report of the U. S. Coast andGeodetic Survey for 1885, pp. 509512.

C. Psychologic. "On Small Differences in Sensation"(in co-

706

operation with J. Jastrow), National Academy ofSciences, Vol. 3 (1884), pp. 111.

IV. Philologic. "Shakespearian Pronunciation" (incoöperation with J. B. Noyes), North AmericanReview, Vol. 98 (April, 1864), pp. 342369.

V. Contributions to the Nation.

Lazelle, Capt. H. M., One Law in Nature. Nation, Vol.17, No. 419.

Newcomb, S., Popular Astronomy. Vol. 27, No. 683.

Read, C., Theory of Logic, 1878. Vol. 28, No. 718.

Rood, 0. N., Modern Chromatics, 1879. Vol. 29, No.746.

Note on the American Journal of Mathematics. Vol.29, No. 756.

Jevons, W. S., Studies in Deductive Logic, 1880. Vol.32, No. 822.

Ribot, Th., The Psychology of Attention, 1890. Vol.50, No. 1303.

James, W., The Principles of Psychology, 1890. Vol.

707

53, Nos. 1357 and 1358.

Comte, A. (F. Harrison, editor), The New Calendar ofGreat Men, 1892. Vol. 54, No. 1386.

Lobatchewsky, N. (Translator: G. B. Halsted),Geometrical Researches on the Theory of Parallels,1891. Vol. 54, No. 1389.

Lombroso, C., The Man of Genius, 1891. Vol. 54, No.1391.

Note on William James' abridgment of his Psychology,1892. Vol. 54, No. 1394.

McClelland, W. J., A Treatise on the Geometry of theCircle, 1891. Vol. 54, No. 1395.

Buckley, Arabella B., Moral Teachings of Science,1892. Vol. 54, No. 1405.

Hale, E. E., A New England Boyhood, 1893. Vol. 57,No. 1468.

Mach, E. (Translator: T. J. McCormack), The Scienceof Mechanics, 1893. Vol. 57, No. 1475.

Ritchie, D. G., Darwin and Hegel, 1893. Vol. 57, No.1482.

708

Huxley, T. H., Method and Results, 1893. Vol. 58,No. 1489.

Scott, Sir Walter, Familiar Letters of Sir Walter Scott.Vol. 58, No. 1493.

Gilbert, W. (Translator: P. F. Mottelay), MagneticBodies. Vol. 58, No. 1494 and No. 1495.

Forsyth, A. R., Theory of Functions of a ComplexVariable, 1893; and Harkness, J., A Treatise on theTheory of Functions, 1893; and Picard, E., Traitéd'analyse, 1893. Vol. 58, No. 1498.

A Short Sketch of Helmholtz, Sept. 13, 1894. Vol. 59,No. 1524.

Windelband, W. (Translator: J. H. Tufts), A History ofPhilosophy; and Falkenberg, R. (Translator: A. C.Armstrong), History of Modern Philosophy; andBascom, J., An Historical Interpretation ofPhilosophy; and Burt, B. C., A History of ModernPhilosophy. Vol. 59, Nos. 1526 and 1527.

709

Spinoza (Translators: W. H. White and Amelia H.Stirling), Ethics, 1894. Vol. 59, No. 1532.

Watson, J., Comte, Mill, and Spencer, 1895. Vol. 60,No. 1554.

Jones, H., A Critical Account of the Philosophy ofLotze, 1895; and Eberhard, V., Die Grundbegriffe derebenen Geometrie, 1895; and Klein, F. (Translator:A. Ziwet), Riemann and his Significance for theDevelopment of Modern Mathematics, 1895; andDavis, N. K., Elements of Inductive Logic, 1895. Vol.61, No. 1566.

Benjamin, P., The Intellectual Rise in Electricity,1895. Vol. 62, No. 1592.

Baldwin, J. M., The Story of the Mind, 1898. Vol. 67,No. 1737.

Darwin, G. H., The Tides and Kindred Phenomena inthe Solar System, 1898. Vol. 67, No. 1747.

Marshall, H. R., Instinct and Reason, 1898. Vol. 68,No. 1774.

Britten, F. J., Old Clocks and Watches and their

710

Makers, 1899. Vol. 69, No. 1778.

Renouvier, Ch., et Prat, L. La Nouvelle Monadologie,1899. Vol. 69, No. 1779.

Mackintosh, R., From Comte to Benjamin Kidd, 1899;and Moore, J. H., Better-World Philosophy, 1899. Vol.69, No. 1784.

Ford, P. L., The Many-sided Franklin, 1899. Vol. 69,No. 1793.

Avenel, G. d', Le Mécanisme de la vie moderne, 1900.Vol. 70, No. 1805.

Reid, W., Memoirs and Correspondence of LyonPlayfair, 1899. Vol. 70, No. 1806.

Stevenson, F. S., Robert Grosseteste, 1899. Vol. 70,No. 1816.

Thilly, F., Introduction to Ethics, 1900. Vol. 70, No.1825.

Wallace, A. R., Studies, Scientific and Social, 1900.Vol. 72, No. 1854.

Sime, J., William Herschel and His Work, 1900. Vol.72, No. 1856.

711

Rand, B. (Editor), The Life, Unpublished Letters, andPhilosophical Regimen of Anthony, Earl ofShaftesbury, 1900; and Robertson, J. M. (Editor),Characteristics of Men, etc., by Shaftesbury, 1900.Vol. 72, No. 1857.

Bacon, Rev. J. M., By Land and Sea, 1901. Vol. 72,No. 1865.

Jordan, W. L., Essays in Illustration of the Action ofAstral Gravitation in Natural Phenomena, 1900. Vol.72, No. 1876.

Goblot, E., Le Vocabulaire Philosophique, 1901. Vol.72, No. 1877.

Fraser, A. C. (Editor), The Works of George Berkeley,1901. Vol. 73, No. 1883.

Frazer, P., Bibliotics, 1901. Vol. 73, No. 1883.

Caldecott, A., The Philosophy of Religion in Englandand America, 1901. Vol. 73, No. 1885.

Review of four physical books. Vol. 73, No. 1887.

Maher, M., Psychology: Empirical and Rational, 1901.Vol. 73, No. 1892.

Mezes, S. E., Ethics, 1901. Vol. 73, No. 1895.

712

Report of the Meeting of the National Academy ofSciences, Philadelphia, 1901. Vol. 73, No. 1899.

713

Crozier, J. B., History of Intellectual Developments onthe Lines of Modern Evolution. Vol. III., 1901, Vol.74, No. 1908.

Richardson, E. C., Classification, Theoretical andPractical, 1901. Vol. 74, No. 1913.

Vallery-Radot, R. (Translator: Mrs. R. L. Devonshire),The Life of Pasteur. Vol. 74, No. 1914.

Giddings, F. H., Inductive Sociology, 1902. Vol. 74,No. 1918.

Report on the Meeting of the National Academy ofSciences, Washington, D. C., 1902. Vol. 74, No.1921.

Emerson, E. R., The Story of the Vine, 1902. Vol. 74,No. 1926.

Joachim, H. H., A Study of the Ethics of Spinoza,1901. Vol. 75, No. 1932.

Review of four chemistry text-books, 1902. Vol. 75,No. 1934.

Royce, J., The World and the Individual, Vol. II.,1901. Vol. 75, No. 1935. (For a review of Vol. 1.,

714

probably by Peirce, see 1900, Vol. 70, No. 1814.)

Thorpe, T. E., Essays in Historical Chemistry, 1902.Vol. 75, No. 1938.

Paulsen, F., Immanuel Kant: His Life and Doctrine,1902. Vol. 75, No. 1941.

Aikens, H. A., The Principles of Logic, 1902. Vol. 75,No. 1942.

Drude, P., The Theory of Optics, 1902. Vol. 75, No.1944.

Valentine, E. S., Travels in Space, 1902; and Walker,F., Aerial Navigation, 1902. Vol. 75, No. 1947.

Baillie, J. B., The Origin and Significance of Hegel'sLogic, 1901. Vol. 75, No. 1950.

Forsyth, A. R., Theory of Differential Equations, Vol.IV., 1902. Vol. 75, No. 1952.

Ellwanger, G. W., The Pleasures of the Table, 1902.Vol. 75, No. 1955.

Earle, Alice M., Sundials and Roses of Yesterday,1902. Vol. 75, No. 1956.

Smith, Rev. T., Euclid: His Life and System, 1902.

715

Vol. 76, No. 1961.


Hibben, J. G., Hegel's Logic, 1902. Vol. 76, No. 1977.

Mellor, J. W., Higher Mathematics for Students ofChemistry and Physics, 1903. Vol. 76, No. 1977.

Sturt, H. C. (Editor), Personal Idealism, 1902. Vol.76, No. 1979.

Baldwin, J. M., Dictionary of Philosophy andPsychology, Vol. II., 1902. Vol. 76, No. 1980.

Note on Kant's Prolegomene edited in English by Dr.P. Carus, 1903. Vol. 76, No. 1981.

Smith, N., Studies in the Cartesian Philosophy, 1902.Vol. 77, No. 1985.

Hinds, J. I. D., Inorganic Chemistry, 1902. Vol. 77,No. 1986.

Clerke, Agnes M., Problems in Astrophysics, 1903.Vol. 77, No. 1987.

Michelson, A. A., Light Waves and their Uses, 1903;

716

and Fleming, J. A, Waves and Ripples in Water,1902. Vol. 77, No. 1989.

717

Note on Sir Norman Lockyer. Vol. 77, No. 1794.

Note on British and American Science, 1903. Vol. 77,No. 1996.

Welby, Lady Victoria, What is Meaning? 1903; andRussell B, The Principles of Mathematics, 1903. Vol.77, No. 1998.

Note on the Practical Application of the Theory ofFunctions, 1903. Vol. 77, No. 1999.

Fahie, J. J., Galileo. Vol. 78, No. 2015.

Halsey, F. A., The Metric Fallacy, and Dale, S. S., TheMetric Failure in the Textile Industry. Vol. 78, No.2020.

Newcomb, S., The Reminiscences of an Astronomer,1903. Vol. 78, No. 2021.

Boole, Mrs. M. E., Lectures on the Logic of Arithmetic,1903; and Bowden, J., Elements of the Theory ofIntegers, 1903. Vol. 78, No. 2024.


718

Lévy-Bruhl, L. (Translator: Kathleen de Beaumont-Klein), The Philoso- phy of Auguste Comte, 1903.Vol. 78, No. 2026.

Turner, W., History of Philosophy, 1903. Vol. 79, No.2036.

Duff, R. A., Spinoza's Political and Ethical Philosophy.Vol. 79, No. 2038.

Allbutt, T. C., Notes on the Composition of ScientificPapers, 1904. Vol. 79, No. 2039.

Sylvester, J. J., The Collected Mathematical Papersof, Vol. I. Vol. 79, No. 2045.

Renouvier, Ch., Les Derniers Entretiens, 1904, andDewey, J., Studies in Logical Theory, 1903. Vol. 79,No. 2046.

Royce, J., Outlines of Psychology. Vol. 79, No. 2048.

Straton, G. M., Experimental Psychology and itsBearing upon Culture. Vol. 79, No. 2055.

Report on the Meeting of the National Academy ofSciences, New York, 1904. Vol. 79, No. 2057.

Boole, Mrs. M. E., The Preparation of the Child forScience, 1904. Vol. 80, No. 2062.

719

Royce, J., Herbert Spencer, 1904. Vol. 80, No. 2065.

Strutt, R. J., The Becquerel Rays and the Propertiesof Radium, 1904. Vol. 80, No. 2066.

Schuster, A., An Introduction to the Theory of Optics,1904. Vol. 80, No. 2071.

Findlay, A., The Phase Rule and its Application, 1904.Vol. 80, No. 2074.


Flint, R., Philosophy as Scientia Scientiarum, 1904;and Peirce, C. S., A Syllabus of Certain Topics ofLogic, 1903. Vol. 80, No. 2079.

Arnold, R. B., Scientific Fact and MetaphysicalReality, 1904, also a Note on Mendeleeff's Principlesof Chemistry. Vol. 80, No. 2083.

720

chance, love, and logic : philosophical essays - fels

Documents