Zimmermann - Criteria of Identity

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DEAN W. ZIMMERMAN

CRITERIA OF IDENTITY AND THE IDENTITY MYSTICS

1. INTRODUCTION

The centerpiece of this paper is the construction of a framework in which

to state theses of mereological supervenience assertions about the de-

pendence of wholes upon their parts. The project is given its point by

the light it sheds upon two controversies over criteria of synchronic anddiachronic unity. Some philosophers (the Identity Mystics, as I shall call

them) claim that, at least in the case of human beings, there is no reason to

look for informative criteria of identity over time. I shall argue that, given

certain highly plausible theses of mereological supervenience, if human

beings are wholly material if, that is, they have no immaterial soul then

this view is untenable. In the final section, I consider a problem that arises

for those who suppose that criteria of synchronic and diachronic unity are,

in a certain sense, intrinsic.

2. THE ROLE OF CRITERIA OF IDENTITY

I begin, however, with a brief description of the philosophical disputes that

have given rise to the technical terminology of criteria of synchronic and

diachronic unity or identity.

It is relatively easy to say what a principle of synchronic unity is sup-

posed to do: it tells us under what conditions a group of things go together

to compose a whole in the case of spatially located objects, under what

conditions a group of smaller things go to make up a spatially larger whole.

Such principles will look something like this: a set of things S constitutes

a whole of kind K if and only if . . . , where the ellipsis is to be filled in by

some condition on the members ofS.

Principles of diachronic unity tell us under what conditions a successionof things existing at different moments go together to compose a tempo-

rally extended whole. But this way of putting things may already seem

to presuppose what it should not: the doctrine of temporal parts, which

Erkenntnis 48: 281301, 1998.

1998 Kluwer Academic Publishers. Printed in the Netherlands.


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282 DEAN W. ZIMMERMAN

Figure 1. The ship of Theseus.

says that just as spatially extended objects have different parts at different

places, temporally extended objects have different parts at different times.

Philosophers friendly to this doctrine will no doubt regard principles of

diachronic and synchronic unity as precisely parallel in form; the rest of uswill disagree. But are there any successions of things existing at different

moments that can be accepted by both the friends and enemies of temporal

parts, and so used to state criteria of diachronic unity that are neutral with

respect to the doctrine of temporal parts?

After a thorough survey of alternative frameworks for giving criteria of

diachronic identity, Harold Noonan concludes that such criteria are best

taken as stating conditions necessary and sufficient for a series of events

to constitute the history of a persisting thing. His idea can be applied to

the Ship of Theseus, a ship kept continuously functioning over many years

by gradual replacement of all the original boards. In situation (1) (see Fig-

ure 1), the discarded boards become flotsam, never recovered; in situation

(2), they are saved by an antiquarian and then finally reassembled to form

the ship occupying the spatiotemporal path c; in (3), the boards are never

replaced, so that Theseus ship becomes gradually unseaworthy, ceasing to

be a ship long before the antiquarian puts his boards together.

Noonan shows that the position of best candidate or closest contin-

uer theorists comes to something like this: Consider all the events that oc-

cur within the boundaries of some ship or other in situation (3) including

those rather uneventful occurrences Cardinal Mercier dubbed unchanges,

such as a certain boards retaining its location relative to the contours of the

ship. If we think of events as exemplifications of properties or as property

instances, then an event happening within some ships boundaries can be

construed as the exemplification of an intrinsic property (of which morelater) by any aggregate of boards, and the holding of a relation of distance

between any parts. All the events (that are instances of these event-types)

going on within the boundaries of Theseus ship in situation (3) also occur


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CRITERIA OF IDENTITY AND THE IDENTITY MYSTICS 283

Figure 2. The fissioning simple.

in situation (2). In the former, they constitute the history of a single ship; in

the latter, they do not. The best candidate theorist can interpret the namesin the diagram as referring to series of events of this sort. Her thesis can

then be put in this way: c and c are the same events; in situation (3) they

go together with the events a to constitute the history of a single ship; in

situation (2) they do not, but constitute instead the history of a ship that

came into being for the first time when the antiquarian put his collection of

planks together. The opponent of best candidate theories of identity holds

that, given the precise similarity of the series of events a + c and a + c,

the one constitutes the history of a single ship only if the other does.

As Noonan realizes, controversies will sometimes arise over whether

one has the same or different events in counterfactual situations. Con-

sider the two circumstances depicted in Figure 2: situation (4) involves

the fissioning of a simple particle; in situation (5), a process goes on that is

intrinsically just like a + c in (4). The best candidate theorist would likely

judge that c and c are distinct though qualitatively identical. The sub-

strate of the c events is identical with the substrate of the a events; but the

substrate of the c events is not identical with the substrate of the a events.

On the assumption that no event could have had a different substrate than

it actually had,1 the c and c events cannot be the same.2

I assume that every event is the exemplification of a property; so contro-

versies over event identity across possible worlds can be avoided altogether

simply by stating criteria of unity in terms of the properties exemplified by

objects at different times. Competing criteria of diachronic unity can then

be given in terms of potential histories of objects, where the histories inquestion consist of collections of parts and potential parts taken at differ-

ent times and paired with the properties and relations they exemplify or

might have exemplified at those times. If fixing the intrinsic properties of


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and spatial relations among the parts in these collections is all it takes to

settle whether such a series constitutes the history of a single persisting

thing, then the criteria of diachronic unity are intrinsic; otherwise, not. It

is this approach to criteria that will fall out of the theory of mereologicalsupervenience developed in the next section.

But what exactly are intrinsic properties? Intrinsic properties are those

that do not differ between qualitative duplicates; no matter how different

the environments of qualitative duplicates, their intrinsic properties remain

the same. As David Lewis points out, this is a pretty tight definitional

circle. One can, it may be hoped, do better. Lewis, in discussions of the

intrinsic and extrinsic, introduces the notions of loneliness and accom-

paniment where an item is lonely just in case nothing exists beside

itself and any proper parts it might have, and something is accompanied

if and only if not lonely.3 Elsewhere, I have proposed this account of

the intrinsic:4 First, define provisionally spatially and temporally intrinsic

properties as those that do not imply either spatial or temporal accom-paniment, or spatial or temporal loneliness. Then introduce a notion of

parthood for properties, and say that a property is completely intrinsic

if and only if every part that is also a property is intrinsic by the pro-

visional criterion. Intrinsic properties are those necessarily equivalent to

completely intrinsic properties.

3. MEREOLOGICAL SUPERVENIENCE AND CRITERIA OF UNITY

It should now be more or less clear what criteria of synchronic and di-

achronic unity look like, and what such things are supposed to do. I turn

then to the notion of mereological supervenience the thesis that wholes

are dependent upon their parts. For I think it is the conviction that mere-

ological supervenience must be true that fuels the search for criteria of

identity.

Jaegwon Kim has suggested that mereological dependence the de-

pendence of wholes on their parts is a species of supervenience: super-

venience with multiple domains.5 I suggest that criteria of synchronic

and diachronic unity are themselves supervenience theses. Principles of

synchronic unity state that wholes of a certain sort supervene upon parts

arranged in a certain way; principles of diachronic unity state that a per-

sisting whole of a certain sort supervenes upon a series of collections of

parts arranged in certain ways. I set up a schematic framework for mul-tiple domain supervenience, in which mereological dependence and its

implications with respect to criteria of synchronic and diachronic unity

will become clear.


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Before diving into the details, Ill introduce a simple analogy to mo-

tivate the theory on offer. The analogy comes from flip books: books

with pictures in the lower or upper right-hand corner of each page, which

produce a moving image when one riffles through the pages from front toback. Each little picture is, often enough, made out of a bunch of dots. The

arrangement of dots on a given page determines what object or group of

objects is depicted on that page; the series of all the arrangements of dots

that appear on the pages determines what the object or objects depicted

do over time whether one disappears or disintegrates, whether new ones

appear, and so on. Given the same arrangements of dots appearing in the

same order, the same objects must appear doing the same things.

The thesis of mereological supervenience I shall articulate affirms that

something analogous is true of wholes and their parts. The parts are the

dots; if a class of wholes are made entirely of a given sort of part, then

fixing how things are at a time on the level of the parts will determine

how things are at that time on the level of wholes. Furthermore, fixing howthings are over time on the level of parts determines how things are during

that time on the level of persisting wholes. The analogy with flip books

will prove helpful both where it holds and where it fails.

Let (D1) be the subvenient domain the collection of parts and po-

tential parts in terms of which principles of synchronic and diachronic

unity will be stated, the things that will have the subvenient properties

upon which wholes will supervene. And let (D2) be the domain of wholes

that can be made out of the members of (D1). Generally, (D1) and (D2)

will be disjoint. The B-properties and relations or subvenient properties

and relations constitute the supervenience base. The A-properties should

include all properties of wholes which are thought to be determined by theproperties and arrangement of their parts. In order for there to be princi-

ples of synchronic and diachronic unity, these will have to include sortal

properties, like being an organism or being a cat.6

If principles of synchronic and diachronic unity are intrinsic, then the

supervenience base (the B-properties) need only include the intrinsic prop-

erties of parts (including their causal dispositions, both active and passive)

and the spatial relations holding among them. If, on the other hand, such

principles are notintrinsic, more will be needed in the supervenience base:

what Kim has called generalized relations will have to be added in

particular, generalized spatial and spatiotemporal relations. For every spa-

tial relation that holds between myself and something else of a certain

kind (for instance, being two feet from, which holds between me and oneof my bookshelves), there is a generalized spatial relation I have, which

is really the property of standing in that relation to something or other


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of that kind (in this case, being two feet from a bookshelf). The extrinsic

determiners of identity that I shall consider countenancing are general-

ized spatial relations to things having intrinsic properties appropriate to

items in the domain of parts, or to events involving the exemplificationof such properties. So if the intrinsic property having positive charge is

in the supervenience base, then the generalized relation being two feet

from something having positive charge would also be in the supervenience

base. Well call this way of enriching the supervenience base, admitting

extrinsic determiners.

First, I define a notion meant to capture something like the complete

state of a collection of objects at a time complete, that is, with respect to

subvenient properties and relations.

F is a synchronic complete specification with respect to B =dfF is a property of sets which is such that, necessarily, for any

sets S and S, S and S both have F iff there is a one-onefunction f from S (and its subsets) to S (and its subsets) such

that, for any x and {y, z} in S, and any B-property P and B-

relation R, x has P ifff x has P, and {y, z} is in the extension

ofR ifff{y, z} is in the extension ofR.

(D1)

In a domain of flip-book dots, which vary only in color and location on

the page, the notion of a synchronic complete specification for dots comes

to this: a property of a set of dots on a single page that fixes their spatial

relations and colors. Any two groups of dots with the same synchronic

complete specification will include dots of the same colors arranged in the

same way. Synchronic complete specifications F and F

are structure-specific indiscernible just in case, necessarily, a set exemplifies the one if

and only if it exemplifies the other.

The pursuit of principles of synchronic unity for complex objects is

justified by the conviction that wholes are dependent upon their parts: Fix

how things are at the level of parts, and youve fixed how things are on the

level of wholes. This conviction can be turned into a more precise principle

of synchronic supervenience:

For every set S and S of members of (D1), and all worlds w1

and w2, if S in w1 and S in w2 exemplify structure-specific

indiscernible synchronic complete specifications, then Sconsti-

tutes an object in w1 if and only ifS does in w2; and if eitherconstitutes an object, then there is an object constituted by S in

w1 that is indiscernible with respect to A-properties from one

constituted by S in w2.7

(SS)


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There are two ways of reading (SS): the B-properties that go into the

complete specifications of the sets of parts may be restricted to intrinsic

determiners, or expanded to include extrinsic ones as well. One might have

doubts about the truth of (SS) on the intrinsic reading: In the domain ofdots, there are groups that wouldconstitute a picture of a cat without a tail,

but for the presence of nearby dots that make them just part of a picture

of a cat with a tail. Similarly, suppose the subvenient domain consists of

living cells and the supervenient domain of mammals, like poor Tibbles

the cat, who has just lost her tail in a very sudden accident.8 Couldnt there

be sets of cells constituting just a part of a cat that are intrinsically just like

the set of cells now constituting all of Tibbles? If so, cells arranged just like

Tibbless could have failed to constitute a cat. Someone who accepts this

reasoning must throw extrinsic determiners into the supervenience base as

well. Then the difference between the external situations of the two sets of

cells will make a difference in the generalized spatial relations exemplified

by the cells.But whether (SS) be construed weakly (by including extrinsic determin-

ers in the supervenience base) or strongly (by excluding them), it implies

that there are principles of synchronic unity.9 For any particular kind K

of object made of the parts in (D1), there will be a set G of synchronic

complete specifications such that a set S from (D1) constitutes a whole of

kind K if and only if it exemplifies one of the members of G. Granted, this

set G will consist of infinitely many different complete specifications of

arrangements of parts, at least in the case of complex objects made of more

than just a few parts that can be arranged in more than just a few ways. But

that doesnt prove that there is no hope of our seeing what the members

ofG have in common; the difference between those types of arrangementswhich yield wholes and those that dont may be quite simple. In any case,

if synchronic supervenience is true with respect to some domains of parts

and wholes, then there are necessary connections between what goes on

at the level of parts and what goes on at the level of wholes. Even if it

should prove too hard for us to formulate precise necessary and sufficient

conditions for the emergence of a whole out of parts, we should still hope

to be able to find some sufficient conditions, and to see that some others

are necessary. To deny that principles of synchronic unity exist for some

domain of complex things is, by my lights, nearly incoherent. To deny such

supervenience is to say that, although the complex things are made entirely

out of things of some other kind, nonetheless everything could have been

the same at the level of these parts and yet some of the complex things havefailed to exist. On this view, making a complex thing out of parts takes

more than just putting the parts together in the right way; it even takes


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more (assuming the supervenience base to include extrinsic determiners)

than making sure the parts are in the right sort of environment. What more

could be asked for is beyond me.10

Principles ofdiachronic unity follow from the supervenience of persist-ing wholes upon the histories of the parts that make them up at different

times. Formulating a thesis of diachronic supervenience requires the no-

tions of a B-micro-history, and of the B-micro-history exemplified by a

particular object.

T is a B-micro-history =df Tis an ordered series of ordered pairs

B, t such that: (1) B is a synchronic complete specification,

(2) t is a real number, and (3) one member of T is earlier than

another iff its second member is lower than that of the other.

(D2)

The numerical member of these pairs will be used to measure, in minutes,

the temporal distances between the parts of the micro-history. If the differ-

ence between the numbers in two members of a micro-history is three, this

signifies that, if the micro-history were exemplified, then the one with the

lower number would occur three minutes before the one with the higher

number where (D3), below, gives the relevant meaning of exemplifi-

cation. In the realm of flip-book pictures, a micro-history is a series of

possible ways for dots to be arranged on a page, with a page number

attached to each arrangement. A series of sets of actual dots exemplifies

such a micro-history only if each group of dots in the series exemplifies

one of the arrangements, and the pages on which they appear come in

the order specified. In the general case, exemplification of a micro-history

comes to this:

A series U of sets of members of (D1) exemplifies B-micro-

history T =df . There is a one-one function f from U onto T

such that: (1) for every pair Sand S of members U, S exempli-

fies the first member off S, and S exemplifies the first member

of f S; and (2) Ss exemplification of the first member of f S

occurs n minutes earlier than Ss if and only if the second

member off Ssubtracted from the second member off S = n.

(D3)

Diachronic supervenience is a matter of the exemplification of indis-

cernible micro-histories having the same macro-results. Now in the case

of dots, theres no need to ask questions about whether the dot on page

three that is part of the cats tail is the same as some dot on page four. Eachdot is confined to its own page. But in the case of real wholes made out

of real parts, this is a question that does matter. If God were to annihilate

all the atoms in my body at noon, while an evil demon simultaneously


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replaced them with duplicates arranged exactly as mine would have been,

many would be inclined to say that I failed to survive the mishap. We

want to be able to recognize the difference between the exemplification

of my micro-history in this way (with the instantaneous replacement ofall the cells by new ones at some point) and an exemplification of the

same micro-history in which the annihilation and creation doesnt occur.

I shall say that exemplifications of micro-histories are structure-specific

indiscernible only if parts that play a certain role in one exemplification

of a micro-history have counterparts playing the same role in the other

exemplification of the micro-history.

Us exemplification of B-micro-history T is structure-specific

indiscernible from Us exemplification of B-micro-history

T =df (1) U exemplifies T and U exemplifies T; and (2)

there is a one-one function f from members ofU onto members

ofU which is such that, for every pair of members S1 and S2 ofU, S1 and S2 exemplify synchronic complete specifications P1

and P2 in T if and only if: (a) f S1 and f S2 exemplify a Q1 and

Q2 in T that are structure-specific indiscernible from P1 and

P2; (b) ift1 and t2 are the numbers paired with P1 and P2 in T,

and t3 and t4 are the numbers paired with Q1 and Q2 in T, then

t1 > t2 if and only ift3 > t4, and t1 t2 = t3 t4; and (c) if an

individual x or pair y and z in S1 and S2 exemplify properties

or relations in the supervenience base when S1 exemplifies P1

and when S2 exemplifies P2, then there must be an individual

t, or pair u and v, in both f S1 and f S2 exemplifying the same

properties or relations when Q

1

and Q

2

are exemplified.

(D4)

Clause (2a) insures that each exemplification of a synchronic complete

specification by a member of U gets matched up with a corresponding

exemplification of an indiscernible synchronic complete specification by

a member of U. Clause (2b) insures that these exemplifications of syn-

chronic complete specifications come in the same temporal order, sepa-

rated by the same temporal distances. Clause (2c) insures that parts in

the subvenient domain that persist from one part of the micro-history to

another are paired with corresponding persisting parts in the other micro-

history.

Now it is obvious that when two series of dots are arranged in the

same ways on pages that are bound together in the same order, flippingone of the resulting books will reveal a cat chasing a mouse if and only if

flipping the other book would do the same. Something analogous is true

for any domain of wholes made out of parts. When there are indiscernible


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exemplifications of micro-histories, the one can be the history of a single

supervening object if and only if the other is; and the supervening ob-

jects must be indiscernible with respect to kind and other A-properties. So

some micro-histories will be paired with supervening objects. The relevantpairing relation and notion of indiscernibility of A-histories are these:

Us exemplification of B-micro-history T constitutes the his-

tory of a single object x =df U exemplifies T; and, for all

times t during Us exemplification of T, x exists at t iff x is

constituted at t by some member of U which then exemplifies

some element of T.

(D5)

x and y have the same A-history during t and t =df there is

a series of A-properties S such that: (a) x exemplifies every

member of S during t, and y exemplifies every member of S

during t; (2) a property is in Sif it is an A-property exemplified

by x during t or by y during t; (3) for every pair P and Q in S,x exemplifies P n minutes before Q during t iffy exemplifies

P n minutes before Q during t.

(D6)

The diachronic supervenience of wholes on parts can now be stated:

For all series U and U consisting of sets of the members of

(D1), and all worlds w1 and w2, if Us exemplification of B-

micro-history T is structure-specific indiscernible from Us

exemplification of B-micro-history T, then (1) Us exempli-

fication of T un w1 constitutes the history of a single object

iffUs exemplification ofT does in w2; and (2) if either ex-

emplification constitutes the history of a single object, then, forevery object x constituted by Us exemplification of T,11 x has

the same A-history during the time of this exemplification as

some object y constituted by Us exemplification ofT during

the time of the latter exemplification.

(DS)

The existence of diachronic criteria of unity follows from (DS). For

any kind of supervenient whole K that can be made out of the parts in the

subvenient domain, there is a set L ofB-micro-histories which includes all

and only the B-micro-histories that are the histories of a K. By (DS), none

of these could have been exemplified without being the history of a K. So

it is a necessary and sufficient condition for a given B-micro-history to be

the history of a K that it belong to the set L. This, I shall argue, constitutesan informative criterion of diachronic unity for Ks.

In what sense, and under what conditions will the set L of micro-

histories serve as an informative criterion of diachronic unity for Ks? For


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one thing, there should be no Ks in the subvenient domain. But even in

some cases where there are no Ks in the realm of parts, the resulting

criterion may be less informative than one would like. Suppose, for in-

stance, that there were infinitely divisible Aristotelian matter, every chunkcomposed of smaller bits of the same stuff. And suppose the domain of

supervening wholes contains all and only the hunks of this stuff that weigh

more than one kilogram, and the subvenient domain all and only the hunks

that weigh one kilogram or less. Now I suppose there will be something

informative about the criterion implied by the version of (DS) resulting in

this case. For instance, a kind of mereological essentialism would probably

be true of this stuff: a more-than-one-kilogram mass of it cannot survive

the gain or loss of any smaller-than-one-kilogram parts; and as long as

you have all the same smaller-than-one-kilogram parts, you have the same

larger-than-one-kilogram whole. But the supervenient and subvenient do-

mains in this case are such obviously trivial restrictions on a single broader,

naturally occurring kind, that the information gleaned from the criteriondoes not seem worth much.

More is learned if the subvenient kind is very different from the super-

venient kind, with associated persistence conditions different from those

of the supervening wholes. If criteria for ships can be given in terms of

the histories of planks, criteria for cells in terms of the histories of organic

molecules, criteria for organisms in terms of the histories of cells, and so

on, then there will be, it seems to me, importantly informative criteria of

diachronic unity. In general, the more dissimilar the subvenient and su-

pervenient domains, the more informative the criteria that follow from the

thesis of mereological supervenience.

If properties like being a part ofthis

ship and relations like being partof the same persisting ship as were allowed into the supervenience base of

a thesis of mereological supervenience for ships, there would be no assur-

ance whatsoever that informative criteria of diachronic unity would follow.

But since the supervenience base is restricted to just intrinsic properties of

parts and their relations to other such parts, there should be no danger of

uninformativeness resulting from the impurity of the ideology employed

in the statement of mereological supervenience.

Here is the most serious objection to the whole enterprise of deriving

criteria of diachronic unity from mereological supervenience: What has

been proven to follow from (DS) is just the existence of a set of micro-

histories that coincides with all the possible careers of supervening objects.

But, for any even mildly complex domain of wholes, there will be infinitelymany such micro-histories. The condition, having a micro-history that

is a member of L might be, for all we know, impossibly complicated


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for human beings to grasp in its details. So we have no assurance that a

criterion that follows from mereological supervenience could in any sense

inform us of anything.

The contention here is that the members ofL might be such a heteroge-neous bunch, with so little in common, that there is nothing more we can

say about them than that they happen to be just the set of micro-histories

upon which the wholes in question supervene. I maintain that, at least in

the case of the sorts of familiar, complex material objects that most interest

us, a defeatist attitude towards our ability to grasp what these histories have

in common is highly suspect. Consider, for example, what this would mean

in the case of the supervenience of cats upon the histories of smallish bits

of cat-hair, cat-flesh, and cat-bone. What if these histories had too little in

common for us to make useful generalizations about them? Then wouldnt

they also have too little in common for us to be able to have reasonable

convictions concerning when we have or do not have the same cat?

I take it that our evidence for sameness of cat comes from observingcats observing how cat-hair changes color only gradually, how cats grow

only gradually, how changes in look or behavior tend to be retained, etc.

And indiscernible histories of feline flesh and hair will be indiscernible

with respect to the observations of these sorts that they make possible; so

there couldnt be indiscernible micro-histories the one of which provided

more evidence for the persistence of a cat than the other. Furthermore, our

sensitivity to the observations that justify belief in cat persistence is not

a wholly subrational process we dont have bare intuitions about cat

identities that bypass the evidence of our senses, that are not grounded in

the awareness of similarities and differences with respect to hair-coloring,

behavior, size, shape, and arrangements of feline bodily parts. These sim-ilarities and differences are not only completely determined by the micro-

histories of feline flesh and hair; knowing about them is simply a matter of

knowing about the micro-history, knowing that there are bits of cat flesh

and hair arranged thus and so, and that these bits at one time are suitably

related to similar collections of bits at later times.

Could there be a merely contingent connection, perhaps in the form of

a brute but non-necessary law of nature, connecting micro-histories of cat

parts with facts about persisting cats? I doubt it. For one thing, there would

be no way to tell the difference between a world in which the law holds and

one in which it does not. The micro-histories determine all the observable

facts, so no observable differences between such worlds could appear. And

just try imagining what would be involved in the failure of cat-persistenceto supervene upon micro-histories of feline flesh, blood, and bone. Tibbles

survives the routine loss of a single hair, say, in our world; none the worse


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for wear, she wanders on, and grows a new one. But, in some other world

a world in which there are no changes in the laws governing the behavior

of feline cells, for weve included causal powers of parts in the superve-

nience base, she loses the hair, and poof, shes gone. Of course, nothingelse happens differently; a cat (a different one) wanders on, growing its

new hair, digesting the same mouse that Tibbles ate moments before, etc.

Unless removal of the hair had resulted in something substantially different

in the nonactual world such as the loss of something like a kitty-soul

this is too wild to countenance as a possibility. If a cat, or any other thing,

is just a whole made out of suitably arranged cells, then the micro-histories

of these cells determine the histories of wholes with a force stronger than

mere nomic necessity.

4. OBJECTIONS FROM THE IDENTITY MYSTICS

There are important new voices being raised against criteria of diachronic

unity for human beings.12 One wonders how they would respond to all this.

The old guard objectors to criteria, such as Chisholm and Swinburne,13

reason as follows: there are no informative criteria of identity for persons;

there would be if persons were large material objects the size of living

human bodies; therefore a person is not a living human body. But the new

opponents of criteria for persons, including Trenton Merricks and E. J.

Lowe, do not accept this reasoning. They ask: Why could there not be

large-scale physical objects six-foot-tall, 150 pound objects, for instance

that lack informative criteria of identity? Their answer: No reason at all.

How might Lowe and Merricks try to resist my argument? I say com-

plex objects made out of parts supervene upon them, are dependent upon

them. And this requires criteria of unity that can be given in terms of those

parts. Lowe might respond by simply denying that persons need supervene

on, say, molecules or cells, since on his view14 persons have neither

molecules nor cells nor anything else as parts. A person like myself is a

material object, in that I have material properties like being six feet tall and

weighing 150 pounds. But I am unlike the human organism here, and the

mass of stuff that makes it up, in that I have no parts.

Theres a familiar objection to views according to which one material

object can constitute a distinct one: Since each is just like the other with

respect to locally manifest properties, each is 150 pounds if either is. But

then lifting both should be like lifting 300 pounds. But it isnt.15This objection is not as devastating as I once thought.16 Heres the

problem with it. Take anything with parts that add up to 150 pounds; when

you lift it, you lift something that weighs 150 pounds (the object itself) and


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something that weighs 100 pounds (its bottom two-thirds) and something

that weighs 50 pounds (its top one-third); so why doesnt that take 300-

pounds-worth of effort? Answer: because the extra things lifted were

just parts of the whole. So in figuring how much work it will take to lifta given collection of objects, one must never add the weight of one to the

weight of another if the one is part of the other. There are a number of

principles that will insure this doesnt happen. For instance, if all the parts

in a set are constituted, ultimately, of atomic parts, one can simply say:

Add the weights of all the smallest parts of anything in the set. Or, if

theres one member that has every other member as a part, say: Weigh

only the biggest member. Now, in the normal case of coincident objects

say, a 150-pound hunk of clay and the 150-pound statue made from it

following such principles gives the right results. Since every part of the

clay is a part of the statue (or at least is constituted entirely of parts of the

statue), you shouldnt add the weight of any hunk of clay to the reading of

150 pounds that results from weighing the statue alone.Notice, however, what happens when we accuse Lowe of countenanc-

ing distinct objects with weights that dont add up. Applying the dont

count common parts principle for figuring weights doesnt help. Since the

150-pound person doesnt have any proper parts, a fortiori it has no part

(proper or improper) of the coincident hunk of matter or human organism

as a proper part. Could it have the organism as a whole as an improperpart?

Then the organism would be its sole part. But the organism is not simple; so

this seems ruled out, by the transitivity of part. Could the simple person

be a part (proper or improper) of the organism? Not an improper part, for

the reasons just mentioned. And suppose you insist that it is a proper part of

the organism. Well, the organism then consists of all the cells, molecules,and so on, plus this extra part, the person. Ignore that extra part for a

moment, and whats left of the organism still weighs 150 pounds. So the

remainder reached by subtracting the person from the whole (a remainder

which sure looks like a living human organism so far as I can see, there is

no independent motivation for saying that the organism has a simple person

as a part), plus the person (which has no part in common with it), should

still weigh 300 pounds. It follows from Lowes view, then, that there really

are two wholly distinct objects here, a person and a living human organism,

each weighing 150 pounds but sharing no parts in common. The fact that

both can be lifted so easily constitutes an empirical refutation of his theory.

If, then, persons are to be material objects coincident with these gross

physical bodies, they had better have some physical parts. And this takesus to Trenton Merrickss view: although human persons are wholes made

entirely of living cells, nonetheless there are no informative criteria of


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diachronic unity for persons. This implies that (DS) is false for the do-

mains of persons and living cells that is, human beings do not supervene

mereologically upon their cells.

But recall what this would mean: there are indiscernible micro-historiestelling precisely the same stories about cells, one of which is the history

of a single human being, the other not. Now if extrinsic determiners were

excluded from the supervenience base, one could imagine cases that might

fit this bill. Remember Tibbles and her tail: there might be indiscernible

micro-histories involving feline cells, the one of which is the history of a

cat that loses her tail, the other of which is not a history of a whole cat

at all rather, it is partly the history of a whole cat, but also partly the

history of a proper part of a cat (all of Tibbles but her tail). Supposing

we buy this possibility, we should allow generalized spatial relations in

the supervenience base. But once extrinsic determiners are let in, denying

diachronic supervenience of persons on their cells becomes truly heroic. It

amounts to the claim that everything could have been the same with respectto all the histories of human cells everywhere (recall that there is now no

limit to the range of spatial relations to other cells that can be generalized

and included in the supervenience base), and yet there be some persons

missing from the world, or some extra ones appearing. How could human

beings be made completely out of cells, yet float free in this way from

their parts? If certain kinds of wholes are made entirely out of certain kinds

of parts, then worlds that are globally indiscernible with respect to what

goes on at the level of these parts had better be globally indiscernible with

respect to what goes on at the level of wholes. To claim that its possible for

there to have been differences in when and where persons are constituted

by cells even if everything had been the same at the level of cells is topromulgate a kind of identity mysticism. Persons are material objects,

but they can come loose from their parts, can pass from one set of parts to

another like shadows.

5. INTRINSIC CRITERIA OF UNITY?

Accepting the moral drawn from the case of Tibbles, above, leads one

very naturally to conclude that no interesting kind of whole supervenes

synchronically upon just the intrinsic properties of and spatial relations

among objects in the domain of parts. Sortal properties for complex objects

appear to be extrinsically sensitive in the following sense:


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Being a C is extrinsically sensitive =df being a C is possibly

such that there is an object x which: (1) is a C, and (2) has a

proper part y that is not a C but is constituted by some set S of

members of (D1) that is possibly such that: (a) it will constitutex, (b) x will be a C, and (c) S will exemplify a set-theoretic

complete specification (extrinsic determiners excluded) that is

indiscernible from the one it exemplifies while constituting the

proper part y.

(D7)

An extrinsically sensitive C is one that a thing can lack just in virtue of

being a proper part of a C; and a set could constitute a part of some x that

is a C at t, and then come to constitute x itself at t, and be intrinsically

just the same at t and t.

If causation does not propagate instantaneously, then any criterion of

synchronic unity that appeals in an essential way to causal relations is in

danger of being extrinsically sensitive. Let x be Tibbles with a tail, andS be the set of all Tibbless cells except for those in her tail. Consider

the synchronic complete specification S exemplifies now (absent extrinsic

determiners). Given that causal influence takes a finite time to be felt,

couldnt the cells in the tail have been annihilated or have jumped away by

some freak of quantum mechanics, leaving S, for the moment, intrinsically

just as it is? If so, then, unless we want to say that S constitutes a cat even

now (with the tail still attached), we must admit that being a cat does not

supervene upon intrinsic determiners alone the criterion of synchronic

unity for cats must include extrinsic determiners as well.

A natural response to this argument is to balk at the alleged possibility

described: it is impossible for there to be a set of cells intrinsically just like

S is now, but without a tail (or at least a part of a tail) attached. But arent

all of the particles that make up the tail-cells at some distance from the

particles that make up the cells in S? If so, it would seem that there must

be a time-lag, however small, during which the particles in the tail-cells

could be gone but before which their absence would not be registered by

any intrinsic changes in S.

Are there ways in which this conclusion could be avoided? One could

insist that the instant the cells in question cease to be parts of the cat,

something changes somewhere in the cells that remain. This will require

either instantaneous causation at a distance, or that some parts of the tail

cells are coincident with some parts of some members ofS. I take it that the

latter is preferable. But can there really be parts of one cell coincident withparts of another? If they share some parts in common, this is possible as

two homes may share a common wall. The members of the supervenience

base can, however, be chosen in such a way that none shares parts with


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any other. This may require arbitrary stipulation about where one cell ends

and another begins, but that shouldnt effect the truth of the supervenience

thesis.

I am inclined to accept all this, but to insist that criteria of synchronicunity are intrinsic nonetheless. But then what sorts of complex wholes

could there be what kinds of complex things are not extrinsically sensi-

tive? In order that a kind C not be extrinsically sensitive, no C can contain

smaller parts that could come to constitute it without changing intrinsically.

So ifx is a C, then any set of parts of x that either does constitute or could

constitute a Cmust be such that the C they do or would constitute would be

distinct from x. In other words, something very much like mereological es-

sentialism must be true for things of kind C. This does not bother me, since

I think there are independent reasons to be a mereological essentialist. Let

me briefly recount them:

Whenever there is a question concerning whether a certain collection

of objects composes a whole, there is also a question concerning whethera certain mass of mattercomposes a whole the mass of matter composed

of all the bits of stuff that constitute the members of the collection. This

mass of matter is itself physical, and (according to me) itself a whole not

a collection or plurality. By my lights, then, whenever one asks, Do the

members of S compose a whole?, the answer is always Yes because

theres bound to be a mass of matter that is identical with the sum of the

members of S. Whats more, masses of matter arent like cats and ships;

theyre not sensitive to extrinsic factors; they dont cease to be when scat-

tered, or when other things are attached to them or detached from them. So

whether or not the members ofS compose something does not depend on

relations to things outside the group; in fact, it doesnt even depend uponrelations (other than mere coexistence) to things inside the group.

Now if the members of S compose a whole distinct from the mass of

matter, then there would be two physical objects, of different kinds but

otherwise exactly alike, in the same place at the same time. But thats

impossible. So the only object thats really there, or even could be there,

is just the mass of matter. Collections of objects only compose masses of

matter; so, naturally, all principles of synchronic unity are intrinsic.

There are at least two spots where this train slows down enough for

almost everyone but me to jump off. The first is at the point where I say

that, for every collection of objects, there is a mass of matter that is the

sum of those objects. I have defended this thesis at great length elsewhere,

and with such relentlessness of detail as to put off almost everyone whohas tried to work out my argument (always a good defensive strategy). 17

But heres the bare bones of my reasoning:


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A mass of matter is simply the kind of thing that we refer to by mass

terms preceded by the or an unstressed some as in, He gave me some

water, which I mixed with the water from Heraclitus tub. A leading fea-

ture of masses is their mereological rigidity: we are unwilling to allow thatI still have precisely the same water he gave me if Ive spilled even a few

drops; although I may still have mostof the water he gave me. Now some

philosophers want to say were picking out pluralities, not wholes, when

we talk in this way of some water or the copper in the statue; but I say this

couldnt be so, at least not in general. Heres why: Aristotelian theories of

matter are, if false, only contingently false; there could have been, perhaps

even are, what Aristotle called homeomerous substances homogeneous

stuffs that dont break down into simple atoms, but are instead of the same

kind through and through. An artifact or organism made out of some such

stuff-kind K would be constituted by a mass of matter that could not be

identified with a plurality of smallest K-parts. Nor would it be safe to pick

a set of parts of some arbitrary size and use those as ersatz-atoms. Afterall, these ersatz-atoms, to do duty for the mass of K, cannot survive the

gain or loss of any parts. But, since the grid used to select the ersatz-atoms

was chosen arbitrarily, it turns out that any portion of K you pick is in fact

a whole that cannot gain or lose parts.

Solving metaphysical problems of constitution requires that one take

into account the possibility of Aristotelian stuff-kinds. It would be absurdly

parochial to rest content with the reflection that the heaps of matter of

which we are constituted do not appear to be homeomerous, and so can

be treated as sets of atoms. Couldnt things have turned out differently

for us? Or, if not precisely for us (perhaps we are necessarily constituted

by electrons and quarks, themselves necessarily indivisible), at least forbeings just like us in every way that matters? And so I plump for a theory of

masses that treats all the most fundamental material stuff-kinds as physical

wholes, not collections of atoms.

The second point at which many philosophers would jump off is at the

rejection of coincident entities. I say there cant be, in the same place at

the same time, both a human being that can gain or lose parts and a mass

of matter that cannot. The friends of temporal parts say both can be there

because, really, theres just one thing filling that place a single temporal

part shared between four-dimensional objects that diverge before and after

the time in question. The human being and the stuff she is now made of

overlap for a tiny stretch of space-time, like intersecting roads with a single

square of pavement in common. Others who, like me, reject temporal partsare nonetheless friends of coincident objects; there can be two physical

wholes here with differing persistence conditions, but weighing the same


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amount and sharing, at some level, all the same parts. This sort of brute

difference between intrinsically indiscernible physical things is, I fear, be-

yond my comprehension. So I see no choice but to stay on the train until the

last stop: The only true principles of synchronic unity are ones that yieldmasses of matter. Garden variety objects that ostensibly gain and lose parts

over time must be logical constructions out of masses, or processes passing

through various parcels of stuff in something like the way a hurricane is

a process that passes through many different tracts of air and water.

There are many who would reject this argument for mereological es-

sentialism but insist that criteria of synchronic unity are intrinsic. 18 What

motivates their commitment? One factor is probably this: Once extrinsic

determiners are allowed to play a role in criteria of synchronic unity, there

would seem to be no way to exclude them from criteria of diachronic

unity, and thus no principled way to resist best candidate theories of

identity. I suspect that anyone who rejects both the doctrine of temporal

parts and best candidate theories of identity will be forced inexorablytowards mereological essentialism. But I do not pretend to have shown

this here.

NOTES

I have benefited from the criticisms and questions of my commentator and members

of the audience in Innsbruck, and also from very detailed comments on an early draft

from Trenton Merricks and Loretta Torrago. The paper was also read at Purdue University,

where Franklin Mason, Martin Curd, and others provided some very helpful criticisms and

suggestions.1

I defend this assumption in Zimmerman (1997b).2 Compare Noonan (1989, 161162).3 Lewis (1983).4 See Appendix 1 of Zimmerman (1997a) and Langton et al. (1997).5 Cf. Kim (1993b). The scheme developed in this section is foreshadowed in Zimmerman

(1997a).6 Would any animal physically indiscernible from an ordinary cat still be a cat, even if

it were not generated from ordinary cat DNA? Some say no its not a cat unless its

a descendent of ordinary earthly cats. But it could mate with ordinary cats, and produce

cat-like offspring. Surely the animal would have the same persistence conditions as ordi-

nary cats. So, I would argue, there must be some persistence-condition-determining sortal

property that such a creature would share with ordinary cats.7 I do not say if either constitutes an object, then the object constituted by S in w1 is

indiscernible with respect to A-properties from the one constituted by S

in w2, since Ido not want to alienate the friends of coincident objects at least not at this point. A similar

complication appears in (DS).

I am indebted to Franklin Mason for pointing out that earlier versions of (SS) and (DS)

presupposed that there are no coincident objects differing in sortal and other properties.


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8 Poor Tibbles wandered into a philosophical laboratory by accident back in the sixties.

Peter Geach was chief investigator. For an account of the incident, cf. Wiggins (1968).9 My strategy here should be compared with Kims (1993c) for proving, in the case of

single-domain supervenience, that supervening properties are equivalent to disjunctions of

maximal B-properties (the strongest consistent properties constructible from propertiesin the supervenience base).10 Artifacts might be thought to represent a counterexample to this claim; couldnt there

be a block of marble just like the David, related in the same ways to other bits of marble

as the David, but not a statue? I take this failure of supervenience as just another reason to

think that artifacts and artworks are fictions, logical constructions out of objects and times.

Consider the ease with which a piece of driftwood or a urinal may be turned into a piece

of art. How could such a change really represent a difference in the number of objects

there are? And arent all artworks and artifacts on a continuum with such frivolous cases

of creation?11 I leave open the possibility that more than one object be constituted by Us exemplifi-

cation of T; there is no need, at this point, to presuppose the falsity of a metaphysics of

coincident objects.12

Cf. Merricks (1998), Lowe (1996, ch. 2), Lowe (1989, 121137), Oderberg (1993), andMackenzie (1983) 161174). There is considerable skepticism about the availability of

informative criteria of identity in Mavrodes (1977) and Quinn (1978).13 Swinburne concludes that the only live possibility, then, is that persons are (or at least

have) an immaterial part; while Chisholm, in some moods at least, wants to leave open the

more bizarre possibility that persons are tiny physical particles. See Swinburne (1997) and

Chisholm (1989).14 See Lowe (1996, ch. 2).15 Cf. Zimmerman (1995a, 8593) and (1995b).16 Thanks to Peter van Inwagen and Peter Simons for making me see this.17 Cf. Zimmerman (1995a).18 Compare, e.g., van Inwagen (1990, 1213).

REFERENCES

Chisholm, R. M.: 1989, On Metaphysics, University of Minnesota Press, Minneapolis, pp.

2541 and 11928.

Kim, J.: 1993a, Supervenience and Mind: Selected Philosophical Essays, Cambridge

University Press, Cambridge.

Kim, J.: 1993b, Supervenience for Multiple Domains, reprinted in Kim (1993a), pp. 109

30.

Kim, J.: 1993c, Concepts of Supervenience, reprinted in Kim (1993a), pp. 5378.

Langton, R. and Lewis, D.: 1998, Defining Intrinsic , Philosophy and Phenomenolog-

ical Research 58, 33345.

Lowe, E. J.: 1996, Subjects of Experience, Cambridge University Press, Cambridge.

Lowe, E. J.: 1989, Kinds of Being, Basil Blackwell, Oxford.Mackenzie, P. T.: 1983, Personal Identity and the Imagination, Philosophy 58, 16174.

Mavrodes, G. I.: 1977, The Life Everlasting and the Bodily Criterion of Identity, Nos

11, 2739.

Merricks, T.: 1998, There are no Criteria of Identity Over Time, Nos 32, 10624.


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Noonan, H.: 1989, Personal Identity, Routledge, London.

Oderberg, D. S.: 1993, The Metaphysics of Identity Over Time, St. Martins Press, New

York.

Quinn, P. L.: 1978, Personal Identity, Bodily Continuity and Resurrection, International

Journal for Philosophy of Religion 9, 10113.Swinburne, R.: 1997, The Evolution of the Soul, revised ed., Clarendon Press, Oxford, pp.

14560.

Van Inwagen, P.: 1990, Material Beings, Cornell University Press, Ithaca, New York.

Wiggins, D.: 1968, On Being in the Same Place at the Same Time, Philosophical Review

77, 905.

Zimmerman, D. W.: 1995a, Theories of Masses and Problems of Constitution, The

Philosophical Review 104, 53110.

Zimmerman, D. W.: 1995b, Ist ein Krper-Austausch mglich? Kommentar zu Peter van

Inwagen, in J. Brandl, A. Hieke, and P. Simons (eds.) Metaphysik Neue Zugnge zu

alten Fragen, Academia Verlag, St. Augustin, pp. 26568.

Zimmerman, D. W.: 1997a, Immanent Causation, Nos supplementary volume (Philo-

sophical Perspectives, Vol. 11: Mind, Causation, and World), pp. 43371.

Zimmerman, D. W.: 1997b, Chisholm and the Essences of Events, in L. E. Hahn (ed.),

The Philosophy of Roderick M. Chisholm, Open Court, La Salle, Illinois, pp. 73100.

Department of Philosophy

University of Notre Dame

Notre Dame, IN 46556

USA

E-mail: [email protected]


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