wartofsky memorial lecture

8/8/2019 Wartofsky Memorial Lecture

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External vs Internal Relations, States

vs Processes: Some Old PhilosophicalProblems in New Physical Clothes

John StachelDepartment of Physics &Center for Einstein Studies

Boston University

Wartofsky Memorial Lecture, 28 September 2005

Graduate School CUNY


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Sunny Auyang


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How is Quantum Field Theory Possible?--

Sonny Auyang (1995)

We must mark the logical distinction between substantiveand general concepts, or the substantive content andthe categorial frameworkof a theory. Electron,electrically charged, a dozen and in between aresubstantive concepts, which characterize the subject

matter of the empirical sciences. Object, property,quantity, and relation are general concepts thatconstitute the categorial frameworkwithin which thesubstantive contents are acknowledged as a descriptionof the world. ... Modern physical theories introduce

radically new substantive concepts but maintain thecontinuity of the categorial framework. They do notoverthrow general common concepts but rethink themand make them their own, effectively clarifying andreinforcing them.


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Conceptual Foundations of Scientific Thought/An

Introduction to the Philosophy of Science

The concept ofexternal and internal relations has

a long history in philosophy and science, and is

not self-evident distinction, to say the least. Butit means that certain relations among parts

cannot be characterized by enumeration or by

simple analysis of part by part. Rather, such

internal relations are characteristic of thesystem as a whole, and are exhibited only in the

systemic unity of a whole (p. 354).


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Conceptual Foundations (contd)

[A] thing, insofar as it is more than an

instantaneous occurrence and has duration

through time, is aprocess. This introduces some

odd results in our ways of talking. For example,talking would be a process but we would hardly

talk of it as a thing; similarly, it is not usual

to talk of a rock or a human being as a process

(p. 332).


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Some Notes on Internal and External

Relations and Representation--Mark H.

Bickhard

Internal relations are

those relations that are

intrinsic to the natureof one or more of the

relata. They are a kind

of essential relation,

rather than an essentialproperty. ...


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Note On My Terminology-JSI shall use property (often confined, as in

the quotation here, to a 1-place relation)

without prejudice, as synonymous with a

relation R, which may have any number

of places:

R(1, 2, ,N),

whereN= 1 is not excluded.


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Some Notes Bickhard (contd)

The Idealists of the 19th century made massiveuse of internal relations. The universe was

supposed to be a whole united by internalrelations among everything. Russell reactedstrongly against internal relations (althoughsome of his reasons were based more on thefact that the Idealists Green and Bradleysupposed all internal relations to be symmetricthan on internal relations per se), but wasunable to do away with all of them.


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T. H.Green and F. H. Bradley


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Bertrand Russell


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The Classification of Relations,

Bertrand RussellMr. Bradley has argued much and hotly

against the view that relations are ever

purely external. I am not certain

whether I understand what he means by

the expression but I think I should be

retaining his phraseology if I describedmy view as the view that all relations are

external


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Some Notes Bickhard (concluded)

Quine has ushered in a period in which all thingsintensional or modal or normative are under

grave suspicion, and to be rejected if at allpossible. Internal relations have mostlydisappeared from the scene because of theiressentialism. All relations are assumed to beexternal, except that most people, including

most philosophers, today dont know what aninternal relation is, and, therefore, dont knowwhat an external relation is either.


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Richard Rorty


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Relations, Internal and

ExternalRichard Rorty (1967)Two extreme positions have been put forward by

philosophers who regard the internal-externaldistinction as unclear or incoherent. The first is that all

of a things properties are essential to its being what itis (and a fortiori) that all its relations are internal to it.This position is associated with idealism and monism The second extreme position holds that none of athings properties are essential to it (and a fortiori that

no relations are internal to it). Both positions holdthat the traditional essence-accident distinction, whichwas drawn by common sense and was first formulatedexplicitly by Aristotle, must be abandoned.


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Metaphysics--

Aristotle

... it is clear that each

individual thing is one

and the same with its

essence, and not

accidentally so, but

because to understandanything is to

understand its

essence.


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Relations, Internal and

ExternalRorty (contd)It may be useful to put the contrast between the

roughly Aristotelian common-sense view and

the two extreme views yet another way. If wesay that common sense holds that there are

both particulars and properties of particulars,

then we may say that common sense holds that

each particular stands in a necessary relation tosome of its properties and a contingent relation

to others.


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Roy Bhaskar


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The Possibility of Naturalism

Roy Bhaskar (1979)The doctrine that all relations are external is implicit in

the Humean theory of causality [and] has beenaccepted by virtually the whole orthodox (empiricist

and neo-Kantian) tradition in the philosophy of science.Conversely, rationalists, absolute idealists andmistresses of the art of Hegelian and Bergsoniandialectics have usually subscribed to the equallyerroneous view that all relations are internal Now it

is essential to recognize that some relations areinternal, and some are not [I]t is an epistemologicallycontingent question whether or not some given relationis internal


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Moore vs McTaggartAlthough he had studied with Bradley and McTaggartat Cambridge, Moore was an early leader in therevolt against absolute idealism. Amazed by thepeculiar character of philosophical controversy,

Moore supposed that common-sense beliefs aboutthe world are correct as they are. The purpose ofphilosophy is not to debate their truth, but rather toseek an appropriate analysis of their significance.

Moore's departure from idealistic philosophy began

with a criticism of internal relations in the carefulanalysis of truth and falsity in "The Nature ofJudgment" (1899).


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McTaggart andMoore


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Katherine Hawley


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Why Temporary Properties are not

Relations between Physical Objects

and Times --Katherine Hawley

Take this banana. It is now yellow, and

when I bought it yesterday it was green.

How can a single object be both green allover and yellow all over without

contradiction? It is, of course, the passage

of time which dissolves the contradiction,

but how is this possible? How can abanana ripen? These questions raise the

problem of change.


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Temporal Parts- Katherine

Hawley (2004)The two most popular accounts of persistence areperdurance theory (perdurantism) and endurancetheory (endurantism). Perdurantists believe that

ordinary things like animals, boats and planets havetemporal parts (things persist by perduring).Endurantists believe that ordinary things do not havetemporal parts; instead they are wholly presentwhenever they exist (things persist by enduring). This

looks like a straightforward ontological disagreement, adispute about what exists. Perdurantists think thatobjects have both spatial and temporal parts, whileendurantists think they have only spatial parts.


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Temporal Parts- Hawley

(contd)Other non-standard views take the basic

perdurantist idea that persistence is

much like spatial extension, then theydevelop the idea in different ways. For

example, perhaps persisting things

stretch out four-dimensionally throughtime, but without being subdivided into

temporal parts.


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David Finkelstein


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A Process Conception of Nature--

David Finkelstein (1973)

The powerful conceptions of nature surveyed

incorporate two recent revolutions [relativity and

quantum-JS] and yet may still be upside-down Theyemploy spacetime to describe matter and process as

though spacetime were primary and process secondary

.. I believe the way has been prepared to turn over the

structure of present physics, to take process as

fundamental at the microscopic level and spacetime

and matter as semimacroscopic statistical constructs

akin to temperature and entropy.


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My Account of :Structural RealismRelations, Internal and External

Things between Relations

Relations between Things

Quiddity and Haecceity

Processes and Events

Dynamic Structural RealismSocial Relations

Background-Dependent and Background-Independent Physical Theories


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What is Structural Realism?

The term structural realism can be (and has been)interpreted in a number of different ways. I assume that, insuch discussions, the concept of structure refers to someset ofrelations between the things or entities that they relate,called the relata.

Here I interpret things in the broadest possible sense: theymay be material objects, physical fields, mathematicalconcepts, social relations, processes, etc. So, in this section,thing is used in a sense that includes processes.

Later thing is used in a more restricted sense, in which it iscontrasted with process.


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The Relation Between Things

and Relations

People have used the term structural

realism to describe different approachesto the nature of the relation betweenthings and relations. These differencesall seem to be variants ofthree basic

possibilities:


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I. There are only relations

without relata.

( Krause 2004)


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Relations Without Relata?As applied to a particular relation, this assertion

seems incoherent. It only makes sense if it is

interpreted as the metaphysical claim thatultimately there are only relations; that is, in

any given relation, all of its relata can in turn

be interpreted as relations. Thus, the totality of

structural relations reduces to relationsbetween relations between relations ...


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Simon Saunders (2003).

I believe that objects arestructures; I see noreason to suppose that

there are ultimateconstituents of theworld, which are notthemselves to beunderstood in structural

terms. So far as I amconcerned, it is turtles allthe way down.


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Jean ToussaintDesanti


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La philosophie silencieuse ou critique des

philosophies de la science (1975)

There no longer exists a fixed point, from which one could

hope to recapture, even in its simple form, the

configuration ofknowledge and thereby propose its

closure. It is not the temptation that is lacking but the

instrument that would allow one to give into it in a

convincing manner. Neither from the side of the

Subject, nor that of the Concept, nor that of Nature do

we find something today to nourish and complete atotalizing discourse. It is better to take note of this and,

on this score, to renounce an anachronistic rear-guard

battle.


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More Attractive PossibilitiesIt is undoubtedly true that, in certain cases, the

relata can in turn be interpreted as relations;but I would not want to be bound by the claim

that this is always the case.

I find rather more attractive the following twopossibilities:


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II. There are relations, inwhich the things are primary

and their relation is

secondary (often calledexternal relations)


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III. There are relations, in

which the relation is primary

while the things aresecondary.

(often called internal

relations)


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Essential vs AccidentalIn order to make sense of either of these possibilities, and

hence of the distinction between them, one must assumethat there is always a distinction between the essential

and non-essential or accidental properties of any thing(remember the earlier discussion).

For example, in quantum mechanics, electrons arecharacterized by their essential properties ofmass, spinand charge. All other properties that they may exhibitin various processes - such as positions, momenta, or

energies - are non-essential and relational.As this example suggests, the distinction between essential

and non-essential properties - and indeed thedistinction between elementary and composite entities -may be theory-dependent (see Dosch 2004).


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Essential vs Accidental (contd)One could convert either possibility into a

metaphysical doctrine: All relations are

external or All relations are internal; andsome philosophers have done so (remember the

earlier discussion).

But, in contradistinction to I, there is no need

to do so to make sense of II and III. If one

does not, then the two are quite compatible.


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Essential vs Accidental

(concluded)For II to hold (i.e. things are primary and their

relation is secondary), no essential property of

the relata can depend on the particular relationunder consideration.

While for III to hold( i.e. the relation is primary

and the relata are secondary ), at least one

essential property of each of the relata must

depend on the relation.


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Fourth logical possibility:

IV. There are things, such

that any relation betweenthem is only apparent


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Example: two dolls pre-programmed to each

move separately, but as if each were dancing

with the other (the apparent relation - I assume

that dancing together'' is a real relationbetween two people).


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GottfriedWilhelm von Leibniz


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Leibniz Monadology

Again, one might convert this possibility into a universalclaim: All relations are only apparent.

Leibniz monadology, for example, might be interpretedas asserting that all relations between monads are onlyapparent. God set up a pre-established harmonyamong them, so that they are pre-programmed tobehave as if they were related to each other.

As a metaphysical doctrine, I find IV even less attractivethan I. And if adopted, it could hardly qualify as avariant of structural realism, so I shall not mention IV

any further.


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Dynamic Structural Realism

While several eminent philosophers of science (e.g.French and Ladyman) have opted for version I ofstructural realism, to me versions II and III (each

interpreted non-metaphysically) are the mostattractive. They do not require commitment to anymetaphysical doctrine, but allow for a decision on thecharacter of the relations constituting a particularstructure on a case-by-case basis. And the decision may

change on the basis ofadditional knowledge or theproblem being considered.

For further discussion of cases II and III, see Stachel 2002, whichrefers to case II as relations between things, and to case III asthings between relations.


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Dynamic SR (contd)

My approach leads to a picture of the world, in which

there are entities of many different natural kinds, and

it is inherent in the nature of each kind to be structured

in various ways. These structures themselves are

organized into various structural hierarchies, which do

not all form a linear sequence (chain); rather, the result

is something like a partially-ordered set of structures.

This picture is dynamic in two senses; there are:1) changes in the world,

2) changes in our knowledge of the world.


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Dynamic SR (contd)

1) As well as a synchronic aspect, the entities andstructures making up our current picture of the worldhave a diachronic aspect: they arise, evolve, and

ultimately disappear-- they constitute processes thatcan be analyzed synchronically and diachronically.

2) Our current picture is itselfsubject to change. Whatparticular entities and structures are posited, andwhether a given entity is to be regarded as a thing or a

relation, are not decisions that are forever fixed andunalterable; they may change with changes in ourempirical knowledge and/or our theoreticalunderstanding of the world. So I might best describethis viewpoint as dynamic structural realism.


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Dynamic SR (conclusion)

Two Footnotes:

For further discussion of the structural

hierarchy, see Stachel 2004. For manyexamples of such hierarchies in physics, biologyand cosmology, see Ellis 2002.

Although my concepts of entity and structure are

meant to be ontological, the term onticstructural realism has been preempted andgiven a different significance (seeLadyman1998).


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Excursus into Social Relations

I choose to cite Karl Marx here because:

Both Marx Wartofsky and I chose this Marxearly on as our guide to thought and action.

He is too often treated today, like Spinoza andHegel as a dead dog.

[I]t was the good pleasure of the peevish, arrogant, mediocreEpigonoi who now talk large in cultured Germany, to treat Hegelin same way as the brave Moses Mendelssohn in Lessing's timetreated Spinoza, i.e., as a "dead dog." I therefore openly avowedmyself the pupil of that mighty thinker (Marx,Afterwordto Vol.One ofCapital).


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KarlMarx1839


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Example of Internal Relations

in Social Science

Marxs concept of social relations, in general,

relations of production in particularValue and Capital are relations between people

expressed through relations between things:

As biological individuals, human beings are the

bearers (Trger) of these social relations

As physical goods, commodities are the bearers


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Wage Labor andCapitalKarl

Marx (1849)Capital consists of raw materials, instruments of

labor and means of subsistence Embodied

labor that serves as the means of newproduction is capital.

So say the economists

What is a Negro slave? A human being of the

black race. The one explanation is worth asmuch as the other


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Wage Labor andCapitalMarx

(contd) A Negro is a Negro. Only in certain

definite [social] relations is he

transformed into a slave. A cotton-spinning machine is a machine forspinning cotton. Only in certain [social]relations is it transformed into capital.

Sundered from these relations, it is aslittle capital as gold in and for itself ismoney, or sugar is theprice of sugar.


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Critique of Hegels Philosophy

ofLaw- Marx (1843)Hegel thinks he has proven that the subjectivity of the state,

sovereignty, the monarch, is essentially characterised as thisindividual, in abstraction from all his other characteristics, andthis individual is raised to the dignity of monarch in an immediate,

natural fashion, i.e., through his birth in the course of nature.Sovereignty, monarchial dignity, would thus be born. The body ofthe monarch determines his dignity. Thus at the highest point ofthe state, barePhysis rather than reason would be the determiningfactor. Birth would determine the quality of the monarch as itdetermines the quality of cattle.

Hegel has demonstrated that the monarch must be born, which noone questions, but not that birth makes one a monarch.

That man becomes monarch by birth can as little be made into ametaphysical truth as can the Immaculate Conception of Mary.


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GeorgWilhelm Friedrich Hegel


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Critique of Hegels Philosophy

ofLaw- Marx (contd)The prince's hereditary character results from his

concept. He is to be the person who is specified from

the entire race of men, who is distinguished from all

other persons. But then what is the ultimate fixed

difference of one person from all others? The body.

And the highest function of the body is sexual activity.

Hence the highest constitutional act of the king is his

sexual activity, because through this he makes a kingand carries on his body. The body of his son is the

reproduction of his own body, the creation of a royal

body.


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Capital, Vol. OneKarl Marx

(1867)Reflexive relations of this kind arealtogether very curious. For instance, one

man is king only because other men standin the relation ofsubjects to him. They,on the other hand, imagine that they aresubjects because he is king.

Marx calls internal relations reflexive


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Structure and Individuality

In Marxs examples, the social relations

supervene on an already-existent

biological individuality.

As a woman, Elizabeth Windsor has

biologically distinctive features.

She is Queen of England only becauseher subjects acknowledge her to be queen


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Alienation: Marxs Conception

ofMan in Capitalist Society Bertell Ollmann has claimed that Marxs

viewpoint requires allrelations to be

internal. But I think this is wrong. Therelation ofuse value between people and

goods is based on the inherent properties

of each good. Its wood burns at a certaintemperature, whether or not a tree is

ever cut down for fuel.


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Confusion of biological and

social relations

By quoting Shakespeare, Marx humorously

reminds us how often people confuse the

biological with the social:


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Much Ado About Nothing

Dogberry: Come hither, neighbor Seacoal:

God hath blessed you with a good name:

to be a well favored man is a gift offortune; but to read and write comes by

nature.

[well favored = good looking]


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Loss of Individuality

It seems that, as deeper and deeper levels of these

structural hierarchies are probed, the property

ofinherent individuality that characterizesmore complex, higher-level entities- such as a

particular crystal in physics, or a particular cell

in biology is lost. Using some old philosophical

terminology, I say that a level at has beenreached, which the entities characterizing this

level possess quiddity but not haecceity.


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Quiddity and Haecceity

Quiddity refers to the essential nature of an entity, its natural kind;and-- at least at the deepest level which we have reached so far -entities of different natural kinds exist, e.g., electrons, quarks,gluons, photons, etc.

Believers in a unified `Theory of Everything'' will hope thatultimately only entities of one natural kind will be needed, and thatall apparently different kinds will emerge from the relationalproperties of the one fundamental quiddity. String theory might beregarded as an example of such a theory; but, aside from otherproblems, its current framework is based on a fixed a background

space-time (see Stachel 2005).

What distinguishes entities of the same natural kind (quiddity)from each other, their unique individuality or primitive thisness,''is called their haecceity.


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John Duns Scotus

Dictionary of Philosophy Dagobert D


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Dictionary of PhilosophyDagobert D.

Runes, ed. (1962)

Quiddity (Lat. quidditas, whatness) Essence, that which is describedin a definition- Vernon J. Bourke

Haecceity (Lat. haecceitas, literally thisness) A term employed byDuns Scotus to express that by which a quiddity, or generalessence, becomes an individual, particular nature, or being. That

incommunicable nature which constitutes the individualdifference, or individualizes singular beings belonging to a class;hence his principle ofindividuation.J. J. Rolbieck

Teller (1995) following Adams (1979), noted the utility of the termhaecceity,and his suggestion has been followed by manyphilosophers of physics


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Quiddity withoutHaecceity

Traditionally, it was always assumed that every

entity has a unique individuality: a haecceity as

well as a quiddity.However, modern physics has reached a point,

at which we are led to postulate entities that

have quiddity but no inherent haecceity, i.e.,

individuality that is independent of therelational structures in which they may occur.

Elementary particles are such entities


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Quiddity withoutHaecceity (contd)

Electrons,for example, have quiddity: mass,

spin, charge; but no inherent haecceity.

In so far as they have any haecceity (and degrees of haecceity mustbe distinguished) it is inherited from the structure of relations in

which they are enmeshed. In this sense, they are indeed examples

of the case III, things between relations.

For example, three electrons confined to a particular

box'' (i.e., infinite potential well) may be distinguishedfrom all other electrons, but not from each other.


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Three Roads to Quantum Gravity--


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Three Roads to Quantum Gravity--

Smolin (2002).

An event may bethought of as the

smallest part of aprocess .... But do notthink ofan event as achange happening toan otherwise static

object. It isjust achange, no more thanthat.


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General Relativity Without

PointsIt is probably better to avoid attributing physical

significance to point events, and accordingly tomathematically reformulate general relativity

in terms ofsheaves

For one such reformulation of differentialgeometry, see Mallios (1998), and forapplications to general relativity, see Mallios(2004) and Mallios (2003)


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Principle of Individuation:

Space-time (contd)Individuation by means of position in space-time

works at the level of theories with a fixed space-time structure, notably special-relativistictheories of matter and/or fields.*

*Actually, the story is more complicated than this. The points of Minkowski space-time, for example, are themselves homogeneous, and some physical frameworkmust be introduced in order to physically individuate them. Only after this hasbeen done, can these points be used to individuate other events or processes. Thephysical framework may be fixed non-dynamically (e.g., by using rods and clocksintroduced a priori); or if fixed by dynamical process (e.g., light rays and massiveparticles obeying dynamical equations), the resulting individuation must be thesame for all possible dynamical processes. This is better said in the language offiber bundles, in which particular dynamical physical fields are represented bycross-sections of the appropriate bundle: If the metric of the base space is given apriori, the individuation of the points of the base space is either also so given, or isthe same for all cross-sections of the bundle (see Stachel and Iftime 2005).


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General Relativity

But, according to general relativity, because ofthe dynamical nature of all space-time

structures, the points of space-time lackinherent haecceity; thus they cannot be usedfor individuation of other physical events in ageneral-relativistic theory of matter and/ornon-gravitational fields. This is the purport of

the hole argument (see Stachel 1993 andearlier references therein).


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General Relativity (contd)

The points of space-time have quiddity as such,but only gain haecceity (to the extent that theydo) from the properties they inherit from the

metrical or other physical relations imposed onthem.In particular, the points can obtain haecceity from the inertio-gravitational fieldassociated with the metric tensor: For example, the four non-vanishing invariantsof the Riemann tensor in an empty space-time can be used to individuate thesepoints in the generic case (see ibid., pp. 142-143)

Again this is better said in the language of fibered manifolds, in which particulardynamical physical fields are represented by cross-sections of the manifold: Onecan now define the base space as the quotient of the total space by the fibration.Thus, even the points of the base space (let alone its metric) are not defined apriori, and their individuation depends on the choice of a cross-section of thefibered manifold, which will include specification of a particular inertio-gravitational field. For a detailed discussion, see Stachel and Iftime 2005.


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Individuation by Physical Events

Indeed, as a consequence of thiscircumstance, in general relativity theconverse attempt has been made: toindividuate the points of space-time bymeans of the individuation of the physical(matter or field) events or processesoccurring at them; i.e., by the relation

between these points and someindividuating properties of matter and/ornon-gravitational fields.


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I di id ti b Ph i l E t ( td)


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Individuation by Physical Events (contd)

Like the points of space-time, insofar as they

have any individuality, it is inherited from the

structure of relations in which these particles

or quanta are embedded. For example, in a

process involving a beam of electrons, a

particular electron may be individuated by the

click of a particle counter.The macroscopic counter is assumed to be inherently individuated. It seems that,

for such individuation of an object, a level of structural complexity must be

reached, at which the object can be uniquely and irreversibly marked in a way

that distinguishes it from other objects of the same nature (quiddity).


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Quantum MechanicsMy argument is based on an approach to quantummechanics that does not deal with quantum systems inisolation, but only with processes that such a systemcan undergo. (For further discussion of this approach,see Stachel 1986, 1997).A process (Feynman uses process, but Bohr uses phenomenon todescribe the same thing) starts with the preparation of the system, whichthen undergoes some interaction(s), and ends with the registration of someresult (a ``measurement''). In this approach, a quantum system is definedby certain essential properties (its quiddity); but manifests other, non-essential properties (its haecceity) only at the beginning (preparation) andend (registration) of some process. (Note that the initially-prepared

properties need not be the same as the finally-registered ones.) The basictask of quantum mechanics is to calculate a probability amplitude for theprocess leading from the initially prepared-values to the finally-registeredones.


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Niels Bohr


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Richard Feynman


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Quantum MechanicsAs Bohr emphasized, the existence of the quantum of

action h prevents such a complete separation between aquantum-mechanical system and its macroscopicsurroundings: Quantum mechanics can only treat opensystems.

Two major consequences are:

1) A full description of a quantum-mechanicalphenomenon (Bohr) or process (Feynman)-- the wordprocess will be used hereafter-- must include a

specification of the result of an initial preparation ofthe system, an account of the type ofinteractions itundergoes subsequently, and of the result of some actofregistration (measurement) to which the system isfinally subjected.


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Quantum Mechanics (contd)

2) A maximal quantum-mechanical preparationor registration only specifies half the dataabout a system that would be specifiable

classically. For example, while one could inprinciple prepare or register a classical-mechanical system with a determinate positionand momentum, one can only prepare or

register a quantum-mechanical system witheither a determinate position or momentum.(Such quantum-mechanical quantities are oftenreferred to, in a somewhat misleading fashion,as observables.).


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Quantum Mechanics (contd)

As a consequence, a typical proposition about aprocess involving an electron might read:

At time t1 the electron was prepared withmomentum p0, subsequently passed through acertain electric field E, and at (a later) time t2was registered at position q0, .

Quantum mechanics assigns a probability tosuch a proposition as explained next.


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Probability Amplitudes and

Feynman Paths.Because of point 2), rather than being analogous

to preparation of an individual classical system,

a quantum mechanical preparation isanalogous to the preparation of a classical

ensemble. Given such an ensemble, only the

probability for a definite value of that half of

the data chosen for final registration(measurement) can be calculated.


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Feynman Paths (contd)In quantum mechanics too, only the probability

of a quantum-mechanical process leading froman initial preparation to a final measurement

can be defined (in limiting cases, thisprobability may be 1--certainty, or 0--impossibility). The central difference inquantum mechanics is that, rather than a

probability (or probability density in thecontinuous case) as in the classical case, onecomputes a probability amplitude a complexnumber of amplitude e 1 for each process.


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Feynman Paths (contd)This amplitude must then be squared to getthe corresponding probability. Using Diracsbra-ket notation, one may write as thetotal amplitude for some process connecting aninitially prepared value a and a finallyregistered reading b (note that a and b may bethe values of different observables). The

probability of this process is then equal to thesquare of the absolute value of the amplitude: .

P ( apb ) = 2.


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Haecceity via Inernal Relations

In all three of these cases - space-time points orregions in general relativity, elementaryparticles in quantum mechanics, and field

quanta in quantum field theory - insofar as thefundamental entities have haecceity, theyinherit it from the structure of relations inwhich they are enmeshed. But there is animportant distinction here between general

relativity one the one hand and quantummechanics and quantum field theory on theother: the former is background-independentwhile the latter two are not.


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A Quantum Theory of Gravity

This suggests an approach to the search for a theory ofquantum gravity. The theory that we are looking for mustunderlie both classical general relativity and quantumtheory, in the sense that each of these two theory shouldemerge from quantum gravity by some appropriatelimiting process. Whatever the ultimate nature(s)(quiddities) of the fundamental entities of a quantum gravitytheory turn out to be, it is hard to believe that they willpossess an inherent individuality (haecceity) alreadyabsent at the levels of both general relativity and quantumtheory.

So I was led to propose that, whatever the nature(s) of thefundamental entities of quantum gravity, they will lackinherent haecceity, and that such individuality as theymanifest will be the result of the structure of dynamicalinternal relations in which they are enmeshed.

The Principle of Maximal


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Given some physical theory, how can oneimplement this requirement of no inherenthaecceity? Generalizing from the previous

examples, I maintain that the way to assurethe inherent indistinguishability in of thefundamental entities of the theory is torequire the theory to be formulated in such

a way that physical results are invariantunder all possible permutations of the basicentities of the same kind (same quiddity).

The Principle of Maximal

Permutability


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The Principle of Maximal Permutability (contd)

The exact content of the principle depends on thenature of the fundamental entities. For theories , suchas non-relativistic quantum mechanics, that are basedon a finite number of discrete fundamental entities, thepermutations will also be finite in number, andmaximal permutability becomes invariance under thefull symmetric group. For theories, such as generalrelativity, that are based on fundamental entities thatare continuously, and even differentiably related toeach other, so that they form a differentiable manifold,permutations become diffeomorphisms. For a

diffeomorphism of a manifold is nothing but acontinuous and differentiable permutation of the pointsof that manifold.


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The Principle of Maximal Permutability (contd)

Here, diffeomorphisms are to be understood in the active sense, as

point transformations acting on the points of the manifold, as

opposed to the passive sense, in which they act upon the

coordinates of the points, leading to coordinate re-descriptions of

the same point. See Stachel and Iftime (2005) for a more detailed

discussion, based on the use of fibered manifolds and local

diffeomorphisms

So, maximal permutability becomes invariance under the full

diffeomorphism group. Further extensions to an infinite number

of discrete entities or mixed cases of discrete-continuous entities, if

needed, are obviously possible.

Dynamical Individuation


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Dynamical Individuation

In both the case of non-relativistic quantum mechanics and of generalrelativity, it is only through dynamical considerations that individuation iseffected.

In the first case, it is through specification of a possible quantum-mechanical process that the otherwise indistinguishable particles areindividuated.

Example: The electron that was emitted by this source at 11:00 a.m. andproduced a click of that Geiger counter at 11:01 a.m..

In the second case, it is through specification of a particular solution tothe gravitational field equations that the points of the space-time manifoldare individuated

Example The point in the source free solution at which the four non-vanishing invariants of the Riemann tensor have the following values: ...


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So one would expect the principle of

maximal permutability of thefundamental entities to be part of atheory in which these entities are onlyindividuated dynamically.

And one would expect it to apply to anytheory of quantum gravity

Th Thi


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Thomas Thiemann

Thomas Thiemann (2001) has pointed out that in the


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Thomas Thiemann (2001) has pointed out that, in thepassage from classical to quantum gravity, there isgood reason to expect diffeomorphism invariance to be

replaced by some discrete combinatorial principle:

The concept of a smooth space-time should not haveany meaning in a quantum theory of the gravitationalfield where probing distances beyond the Planck length

must result in black hole creation which then evaporatein Planck time, that is, spacetime should befundamentally discrete. But clearly smoothdiffeomorphisms have no room in such a discretespacetime. The fundamental symmetry is probably

something else, maybe a combinatorial one, that lookslike a diffeomorphism group at large scales.


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States or Processes: Which is

primary ?There has been a long-standing debate betweenadherents of covariant and canonicalapproaches to quantum gravity. The former

attempt to develop a four-dimensionally-invariant theory of quantum gravity from theoutset; the latter start from a (3+1)-breakup ofspace-time, emphasizing three-dimensionalspatial invariance, developing quantum

kinematics before quantum dynamics.

Christian Wthrich


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Christian Wthrich


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Wthrich (2003)

Christian Wthrich has related this debate to the philosophicaldebate between proponents of the endurance view of time andthose of the perdurance view , which reflects a disagreementconcerning whether, and to what degree, time is on a par withspatial dimensions.

According to the former view, ''an object is said to endure just in caseit exists at more than one time.'

According to the latter view, objects perdure by having differenttemporal parts at different times with no part being present atmore than one time. Perdurance implies that two [space-like]hypersurfaces ... do not share enduring objects but rather harbour

different parts of the same four-dimensional object.

Things vs Processes


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g

I use a different terminology to make this important distinction.

One approach to the quantum gravity problems places primaryemphasis on the three-dimensional state of some thing; from thispoint of view, a process is just a succession of different states ofthis thing. (The relation of this succession of states to someconcept of ``time'' is a contentious issue).

The other approach places primary emphasis on four-dimensionalprocesses; from this point of view, a state is just a particularspatial cross-section of a process and of secondary importance: allsuch cross-sections are equal, and each sequence of statesrepresents a different ``perspective'' on the same process.


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Classical Physics

In pre-relativistic physics, the absolute time provided a

natural foliation of space-time into spatial cross-

sections. So, even if one favored the process''

viewpoint for philosophical reasons, there was little

harm done to physics - if not to philosophy - in using

the alternate state viewpoint. While the split into

spaces was not unique (one inertial frame is as good as

another), each inertial frame corresponding to a

different preferred fibration of space-time,they allshared a unique time (absolute simultaneity). In short,

there was a unique breakup of 4-dimensions into (3+1).


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Special Relativity

In special-relativistic physics, this is no longer the case:there are an infinite number of such preferred cross-sections (one for each family of parallel space-likehyperplanes in Minkowski space). Not only is the split

into spaces not unique (one inertial frame is still asgood as another), but now they do not even agree on aunique time slicing (the relativity of simultaneity):there is a different foliation for each preferredfibration. In short, there is a three-parameter family of``natural'' breakups of 4-dimensions into (3+1). So, inspecial-relativistic physics, and quite apart fromphilosophical considerations, the process approachhas much to recommend it over the ``state'' approach.


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General Relativity

General relativity is an inherently four-dimensional theory of space-time-- evenmore so than special relativity. There is

no ``natural'' breakup of space-time intospaces and times, such as the inertialframes provide in special relativity.There are no preferred timelike

fibrations or spacelike foliations.


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Three Roads to Quantum Gravity--Lee Smolin


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Q y

(2002)

[R]elativity theory and quantum theory each... tell us--no, better, they scream at us-- that our world is a

history of processes. Motion and change are primary.

Nothing is, except in a very approximate and

temporary sense. How something is, or what its state is,

is an illusion. It may be a useful illusion for some

purposes, but if we want to think fundamentally we

must not lose sight of the essential fact that it is an

illusion. So to speak the language of the new physics we

must learn a vocabulary in which process is moreimportant than, and prior to, stasis.


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Bryce DeWitt

Gl b l Q t Fi ld Th


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Global Quantum Field Theory-

Bryce DeWitt (2003)Bryce DeWitt, in his final book, has put the case in thecontext of quantum field theory:

When expounding the fundamentals of quantum fieldtheory physicists almost universally fail to apply thelessons that relativity theory taught them early in thetwentieth century. Although they carry out theircalculations in a covariant way, in deriving theircalculational rules they seem unable to wean

themselves from canonical methods and Hamiltonians,which are holdovers from the nineteenth century, andare tied to the cumbersome (3+1)-dimensional baggageof conjugate momenta, bigger-than-physical Hilbertspaces and constraints.

Quanta of Space or of Space Time?


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Quanta of Space or of Space-Time?

Whether one should be looking forquanta of space or quanta of space-timeseems to be one essential point ofdifference between the canonical loop

quantum gravity approach and thecovariant causal set approach.


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Rafael Sorkin


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Causal Set Theory

Causal set theory, a process approach to quantumgravity, does not attempt a quantization of the classicaltheory. Rather, its aim is to construct a quantum

theory of causal sets based on two features of classicalgeneral relativity that it takes as fundamental:

1) the causal structure, which is replaced by a discretecausal set; and

2) The four-volume element, which is replaced by thequantum of process.


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Fay Dowker


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Most physicists believe that in any final

theory of quantum gravity, space-timeitself will be quantized and grainy in

nature. .... So the smallest possible

volume in four-dimensional space-time,the Planck volume, is 10-42 cubic

centimetre seconds. If we assume that

each of these volumes counts a single

space-time quantum, this provides adirect quantification of the bulk.


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Conclusion (Whew!)

I hope to have convinced you by force (!!!) ofexample that:

1) modern physics can transform oldphilosophical debates into current physicalissues;

2) not only does physics seem to force certainchoices on us in these debates, but

3) these choices in turn can play a role indetermining the direction of current research


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wartofsky memorial lecture

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