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The Problem of Material Constitution Author(s): Michael C. Rea Source: The Philosophical Review, Vol. 104, No. 4 (Oct., 1995), pp. 525-552 Published by: Duke University Press on behalf of Philosophical Review Stable URL: https://www.jstor.org/stable/2185816 Accessed: 16-09-2019 03:26 UTC

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The Philosophical Review, Vol. 104, No. 4 (October 1995)

The Problem of Material Constitution

Michael C. Rea

There are various puzzles that set our intuitions about composition

and identity against one another. Four that are particularly well

known are the Growing Argument (also known as the Paradox of

Increase), the Ship of Theseus Puzzle, the Body-minus Argument

(usually presented by way of Peter Geach's story about Tibbles the

cat), and Allan Gibbard's puzzle about Lumpl and Goliath (a piece

of clay and a statue, respectively). Such puzzles have received a

great deal of attention in the literature over the past thirty years,

and there is an impressive and growing variety of solutions available

for each of them. Surprisingly, however, no one has really discussed

how all of the different puzzles, and their solutions, are interrelat-

ed. On the surface, they seem to raise different problems; but

clearly the puzzles are related somehow. They raise similar ques-

tions and generate similar sets of possible solutions. But, as yet,

nothing has been said about how far the similarities extend.

What I intend to show is that there is one problem underlying

these four familiar puzzles (and their many variants). This problem

I will call "the problem of material constitution." I say it underlies

the four puzzles for the following reason: every solution to the

problem of material constitution is equally a solution to each of

these four puzzles, though not vice versa. One might therefore view

each of the four puzzles as a more or less imperfect statement of

the problem of material constitution. I have chosen these puzzles

in particular because they are the most widely discussed' and be-

cause they are typically treated in isolation from one another. They

have been used as points of departure in discussing a variety of

different topics (for example, contingent identity, arbitrary unde-

tached parts, temporal parts, indeterminate identity, mereological

essentialism, and so on); but it is not always obvious how or wheth-

er these different discussions are related to one another. Thus my

aim in showing that one problem underlies these puzzles is to re-

veal the common thread that unifies this group of otherwise ap-

'Though the Growing Argument is not nearly as widely discussed as the other three.

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MICHAEL C. REA

parently disparate discussions. Moreover, once it is clear what the

common problem is, it will be possible to provide an exhaustive

taxonomy of solutions-something which thus far has not been

available.2

In what follows, I will show that there are five individually plau-

sible and jointly incompatible assumptions underlying each of the

puzzles under consideration. The problem of material constitution

just is the fact that these five assumptions are both plausible and

incompatible.3 I will begin by providing a very general statement

of the problem. I will present the five assumptions and provide a

short argument showing how they conflict with one another. Then,

in subsequent sections, I will go on to show how these assumptions

underlie each of the four puzzles. I will conclude by providing an

exhaustive taxonomy of possible solutions to the problem.

1. The Problem Stated

First, some terminology. Following Peter van Inwagen, let us take

'the ps' as a plural variable-a term of collective reference that

refers neither to the set containing the ps, nor to any object whose

parts are the ps. (For example, 'the present citizens of the United

States' refers collectively to everyone who is presently a citizen of

the United States; it does not refer to the set that contains all of

the present citizens of the United States, nor does it refer to the

scattered object, if such there be, that is composed of them.) 'The

ps', in the expression 'the ps compose x', will thus refer collectively

to all of the ps, whatever they are, that together compose the object

x, and let us say that 'the ps compose x' is an abbreviation for 'the

ps are all parts of x and no two of the ps overlap and every part of

x overlaps at least one of the p'.4 Further, let us say that if the ps

20f course, there are many lists of possible solutions for particular puz- zles available. (See, for example, Burke 1994a; Doepke 1982; Heller 1990, 3-4; and Simons 1987, 119-120.) But no one has provided the kind of exhaustive taxonomy of solutions to the problem of material constitution that I will offer at the end of this paper. On the distinction between a list and a taxonomy, see note 32.

3A11 four puzzles raise the problem within the context of an ontology of three-dimensional enduring objects; but only the fourth raises the proW lem within the context of an ontology of four-dimensional perduring ob- jects. I defer detailed discussion of this point to the end of section 4.

4See van Inwagen 1990, 23ff. It will be convenient to think of the rele- vant ps in the puzzles discussed in this paper as particles (the one exception

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THE PROBLEM OF MATERIAL CONSTITUTION

compose x and the ps compose y, then x constitutes y.5 Finally, in

the following assumptions let F be a schematic letter that takes as

substitution instances nouns such as 'human being', 'ship', 'cat',

'statue', and so on, and let R be a schematic letter that takes as

substitution instances relations such as 'is at all times composed

by', 'is at all times composed by some proportion of', and so on.

Now for the problem. Intuitively, the problem of material consti-

tution arises whenever it appears that an object a and an object b

constitute one another and yet are essentially related to their parts

in different ways. The puzzles under consideration in this paper are

all stories in which something like this is the case; and they are

troubling because it seems we can account for the relevant appear-

ance only by somehow denying that it is veridical or by sacrificing

some intuition about composition or identity-for example, by giv-

ing up our natural assumption that distinct objects cannot share all

of the same parts at the same time, or that identity is necessary.

At the core of each of the puzzles are five assumptions. Infor-

mally, they are: (i) there is an F and there are ps that compose it,

(ii) if the ps compose an F, then they compose an object that is

essentially such that it bears a certain relation R to its parts, (iii)

if the ps compose an F, then they compose an object that can exist

and not bear R to its parts, (iv) if the ps compose both a and b,

then a is identical with b, and (v) if a is identical with b then a is

necessarily identical with b. Let us call these assumptions, respec-

tively, the Existence Assumption, the Essentialist Assumption, (with

apologies to Frankfurt) the Principle of Alternative Compositional

Possibilities (or PACP for short), the Identity Assumption, and the

Necessity Assumption. We can state them more formally as follows:

Existence Assm.:

(3x) (3ps) (]t) (x is an F & the ps compose x at t) Essentialist Assm.:

(Vx) (Vps) (Vt) [x is an F & the ps compose x at t D (3zl) (the ps compose z1 at t & D (Vqs) (Vt) (the qs compose z1 at t D z1 bears R to the qs)) ]

being the Ship of Theseus puzzle, where for purely heuristic reasons it is more convenient to think of the relevant ps as planks of wood).

5Note that constitution, as I define it, is a symmetric relation. This is nonstandard, but it is convenient in the present context and I see no com- pelling reason for understanding constitution as antisymmetric.

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MICHAEL C. REA

PACP.

(Vx) (Vps) (Vt) [x is an F & the ps compose x at t D (3z2) (the

ps compose z2 at t & O (3qs) (it) (the qs compose z2 at t and z2 does not bear R to the qs))]

Identity Assm.:

(Vx) (Vy) (Vps) (Vt) (the ps compose x at t & the ps compose y

at t D x = y)6 Necessity Assm.:

(Vx) (Vy) [x = y D D((x exists V y exists) D x = y)]

As I said earlier, the problem of material constitution just is the

fact that these five assumptions are both individually plausible and

jointly incompatible. The following argument shows that they are

incompatible with one another:

(1) S is an F and the ps compose S at t. (Instantiation of Ex-

istence Assm.)

(2) There is a z1 such that the ps compose z1 at t and, neces-

sarily, for all qs and t, the qs compose z1 at t only if z1 bears R to the qs. (From 1, Essentialist Assm.)

(3) There is a z2 such that the ps compose z2 at t and, possibly,

there are qs and t such that the qs compose z2 at t and z2 does not bear R to the qs. (From 1, PACP)

(4) The ps compose Z1 at t and, necessarily, for all qs and t, the qs compose Z1 at t only if Z1 bears R to the qs. (Instantiation of 2)

(5) The ps compose Z2 at t and, possibly, there are qs and t

such that the qs compose Z2 at t and Z2 does not bear R to the qs. (Instantiation of 3)

(6) Z1 = Z2 (From Identity Assm., 4, 5)

(7) Possibly, Z1 exists or Z2 exists and Z1 $A Z2. (From 4, 5) (8) Z1 $A Z2. (From 7, Necessity Assm.) ** Contradiction (6, 8)

I have now stated the problem of material constitution in its most

general form, and I have claimed that the above five assumptions

underlie each of the four puzzles under consideration. In the fol-

lowing four sections, I will justify this claim.

6This thesis is alternatively referred to as "mereological extensionality" (see Simons 1987, 28) and it is commonly expressed by the claim "consti- tution is identity."

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THE PROBLEM OF MATERIAL CONSTITUTION

2. The Growing Argument

The Growing Argument has its origin in the fifth century B.C. in

the writings of the comic playwright Epicharmus. The scene in

which it appears depicts a person who, hoping to collect a debt

from a friend, receives instead a philosophical argument. The up-

shot of the debtor's argument is that since a person is identical

with the aggregate of particles that constitutes him or her, any

addition of particles will result in a new person (since it will result

in a new aggregate); but, of course, he (the debtor) has undergone

many such additions since the debt was contracted, so he cannot

now be considered the same person as the one who contracted the

debt. Consequently, he does not owe any money.7 Slightly different

versions of this argument have been discussed by many philoso-

phers throughout history.8 The basic line of reasoning, however, is

just this: Just as adding to a given quantity of objects yields a new

quantity, adding parts to a human being yields a new human being;

hence, growth is impossible. Let us now identify the assumptions

of the Growing Argument.

In order to even get started, the argument must make an Exis-

tence Assumption: it must assume that there are such things as

human beings and things that compose human beings. (Above, it

is particles that are said to compose human beings; but, of course,

the paradox arises no matter what we take the ps to be.)

The argument also makes an Essentialist Assumption. As I have

presented the argument, it assumes that where there is a human

being composed of particles, there is an aggregate of particles (an

7My summary is based on David Sedley's reconstruction of the scene in question (1982, 255-75; see 271 n. 1 for the list of sources on which his reconstruction is based). I am grateful to Brad Inwood for drawing my attention to this article.

8For instance: Aristotle (De Generatione et Corruptione, 321a), the Academ- ics and the Stoics (Long and Sedley 1987, 166-75), Abelard (Henry 1972, 118ff.), John Locke (1975, 328ff.), G. W. Leibniz (1981, 237-38), David Hume (1978, 255ff.), Thomas Hobbes (1839, 135-38), and more recently Roderick Chisholm (1976, 157-58). According to Sedley (1982), the first systematic treatment of this argument came in the writings of the Stoics as they sought to combat various paradoxes raised by the Academics. It was in the course of these discussions that the Ship of Theseus paradox and the Body-minus Argument were introduced. For more on the history of this argument in ancient philosophy, I strongly recommend Sedley 1982 and Long and Sedley 1987.

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MICHAEL C. REA

object such that, necessarily, it exists and has its constituent parti-

cles as parts just in case those particles exist) that constitutes him

or her. This entails (though it is not entailed by) the claim that

there is an object composed of those particles that cannot gain or

lose material parts-in other words, there is an object such that,

necessarily, for all qs and t, the qs compose z at t only if z bears RI to the qs, where R1 is defined as follows:

z bears R1 to the qs =DF there is no time t such that z exists

and the qs do not compose z at t.

And since this latter claim is all that is required to show that growth

is paradoxical, we can, for convenience, let R1 stand as our substi-

tution instance for R.

It is worth pointing out here that no particular definition of R

is crucial to the problem of material constitution; any definition

will do so long as one can tell a plausible story that makes it seem

that there are (or can be) objects a and b that constitute one an-

other, one of which essentially bears R to its parts while the other

doesn't. In the context of the Growing Argument, we assume that

one of the objects in question is an aggregate because that is the

easiest way to show the force of the analogy with quantities. There

seems to be no reason to think that the fact that quantities do not

grow has any relevance to the question of whether human beings

grow, unless we think that there is a sense in which a human being

is a quantity; and there is such a sense if we think that a human

being is (that is, is identical with) an aggregate of particles. But

denying that there are aggregates will not solve the problem of

material constitution; it will only reduce the plausibility of one

story that expresses it.9

The Identity Assumption justifies the claim that a human being

is identical with the object that cannot gain or lose material parts.

And the Necessity Assumption is needed because, if we deny it,

there is no reason to think that because a human being is at one

91n general, denying the Existence Assumption, the Essentialist Assump- tion, or the PACP for particular substitution instances of F and R will not solve the problem of material constitution. As we will see in section 6, to solve the problem without rejecting the Identity Assumption or the Neces- sity Assumption, one must deny the conjunction of the other three as- sumptions for all substitution instances of F and R. To do less is to provide, at best, an incomplete solution to the problem.

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THE PROBLEM OF MATERIAL CONSTITUTION

time identical with one object that satisfies the Essentialist Assump-

tion, he or she cannot at some other time be identical with a dif-

ferent object satisfying the Essentialist Assumption. But, of course,

the argument must reason this way in order to reach its conclusion.

These four assumptions the proponent of the Growing Argu-

ment endorses. The point of the argument is to show that they are

incompatible with a fifth, a Principle of Alternative Compositional

Possibilities. In the above formulation, the fifth assumption is that

human beings grow in size; but it is worth pointing out here that

in light of what we have chosen as our Essentialist Assumption, we

could just as easily assume that human beings diminish or undergo

replacement of their parts.'0 Any of these will do, because they all

entail that where there is a human being, the ps that compose it

compose something that can exist and fail to bear R1 to its parts.

And once this assumption is in place, we have our complete set of

five individually plausible and jointly incompatible assumptions. To

escape the conclusion of the Growing Argument, it is necessary

and sufficient to reject any one of them.

3. The Ship of Theseus

The ship on which he [Theseus] sailed with the youths and was kept

safe [coming] back, the thirty-oared vessel, the Athenians preserved

until the time of Demetrius of Phalerus, removing the old pieces of

wood and putting in strong ones, and putting them together so that

the ship was a model for the philosophers with respect to the disputed

argument about growing, some of them saying it remained the same,

some of them saying it did not remain the same."

The ship of Theseus puzzle is a near relative of the puzzle pre-

sented by the Growing Argument.'2 Whether or not the Ship of

Theseus itself survived its many repairs, its memory at least has

survived in the history of philosophy due to the ship's standard

role as an illustration in discussions of identity through mereolog-

ical change. As Plutarch tells us, the ship was often discussed in

connection with the Growing Argument; it is mentioned in the

10Perhaps this is why the Ship of Theseus came to be discussed in con- nection with the Growing Argument (see Sedley 1982, 257-59).

"Plutarch, Life of Theseus, 23 (my own translation). 12See Sedley 1982, 257-59.

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MICHAEL C. REA

writings of Leibniz, Hume, and Hobbes;'3 and it has been the sub- ject of much discussion in the contemporary literature. Hobbes is

responsible for the Ship of Theseus puzzle as it is discussed today. Briefly, the puzzle is as follows.

Consider the Ship of Theseus: a wooden ship that, over the

course of time, gradually undergoes the replacement of each of its

constituent planks. Clearly, it seems, the ship survives each individ-

ual replacement; hence, there is good reason to think that the ship

that exists once the series of replacements is complete is the ship

we originally started out with. But now suppose someone takes the

discarded planks and puts them back together in their original

form as a ship:'4 it seems that there is also good reason to think

that this ship is the ship we started out with. But, of course, both

ships cannot be the Ship of Theseus; so the question is, Which of

the final two ships is identical with the original?

The answer to this question is often seen to depend upon wheth-

er "continuity of matter" or "continuity of form" is more impor-

tant as a criterion for reidentifying objects; and the puzzle is typi-

cally seen to arise from the fact that we have intuitions that pull us in both directions.'5 But, to my mind, treating the problem this way-as a problem about "identity criteria"-does not really cut

to the heart of the issue. Rather, it seems that the central question

here really is, How is the Ship of Theseus related to its parts? For the

importance of a criterion of reidentification for a given object de-

pends largely upon how that object is related to its parts. For ex-

ample, if the Ship of Theseus cannot undergo part replacement

(for example, if it is a mere aggregate of planks) then perhaps the

"continuity of matter" criterion will be more important. On the

other hand, if it is the kind of object that can survive complete

replacement of its parts, then perhaps the "continuity of form"

criterion will be more important.'6

13Leibniz 1981, 231-32; Hume 1978, 255ff.; Hobbes 1839, 135-38. IThis is Hobbes's contribution. See Hobbes 1839, 135-38. 15See, for example, Dauer 1973; Davis 1973; Hirsch 1982, 68-71; Lowe

1983; Scaltsas 1980 and 1981; and Smart 1972 and 1974. 16This oversimplifies a bit because it does not account for positions ac-

cording to which neither criterion is more important. For instance, one might hold that at the beginning of the story, 'the Ship of Theseus' refers ambiguously to two co-located objects, one of which has some proportion of its parts essentially and the other of which does not. On this view, neither criterion would be more important.

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THE PROBLEM OF MATERIAL CONSTITUTION

In this way, the Ship of Theseus puzzle is just like the Growing

Argument. We might well have said that the central question in

the Growing Argument is, How is a human being related to its parts? For the argument reaches its conclusion only because we have in-

tuitions that suggest that a human being is a mere aggregate of

particles and intuitions that suggest that a human being can survive

various kinds of mereological change; and once we have deter-

mined how a human being is related to its parts, we will have taken

the first crucial step toward solving the problem.'7 Likewise, the

Ship of Theseus puzzle is puzzling precisely because it appeals to

similarly conflicting intuitions. Of course, the Ship of Theseus puz-

zle does not explicitly assume that wherever we find a ship com-

posed of planks, we find an aggregate that is essentially composed

of those planks; but obviously we must have some intuition that

suggests that the ship cannot undergo full replacement of its

parts-otherwise the plank-hoarder's ship'8 would no longer be a

viable candidate for the name 'Ship of Theseus'.19

Thus it seems that the best way to solve the Ship of Theseus

puzzle is to treat it as an instance of the problem of material con-

stitution rather than as a puzzle about identity criteria. To confirm

this, I will show that underlying the puzzle are the five assumptions

outlined in section 1 and that rejecting any one of them will suffice

to provide an answer to the question, Which of the final two ships

is the Ship of Theseus?20

17It is only the first step because (unless we just deny that there are human beings) we must still account for the relation between a human being and the aggregate of particles that constitutes him or her (for ex- ample, by denying that there are aggregates, by saying that a human being is co-located or contingently identical with an aggregate, etc.).

18The plank-hoarder's ship is the ship that (at the end of the story) is composed of all of the planks that originally composed the Ship of The- seus. The other ship is the continuously repaired ship.

19Earlier I said that each of the puzzles under consideration in this paper presents us with a scenario in which it appears that an object a and an object b share all of the same parts and yet are essentially related to those parts in different ways. In the other puzzles, it is obvious what the relevant a and b are. Here it is not so obvious, but in light of what has just been said it should be clear that my view is that the plank-hoarder's ship and the original Ship of Theseus are the a and b in this puzzle. I see it this way because the parts that compose the plank-hoarder's ship are the same parts that composed the original vessel, and I take it that the point of the story is to evoke our intuitions that these objects bear different relations to those parts.

20A caveat: It should be noted that a four-dimensionalist's response to

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MICHAEL C. REA

The Existence Assumption is that there are ships and ps that

compose ships (the Ship of Theseus is our instance). If this as-

sumption is false, then it will be because there are no ships, or

because ships are not composite entities. In either case, the appro-

priate response to the question is to say that it is unanswerable: the

puzzle needs to be restated in terms that do not presuppose the

existence of ships that have proper parts.

To identify the Essentialist Assumption, it will be helpful first to

identify the PACP. It seems that the Ship of Theseus story is puz-

zling in part because we assume that ships can undergo complete

part replacement. Indeed, if we deny this, then we know immedi-

ately that the continuously repaired ship is not the Ship of Theseus.

Hence, if we deny the PACP then we will identify the plank-hoar-

der's ship as the Ship of Theseus. In contrast, then, it seems that

what leads us to think that the plank-hoarder's ship is a viable

contender for the name 'Ship of Theseus' is the intuition that

where we have a ship, we have something that cannot undergo com-

plete part replacement-something that is necessarily such that if

the ps compose it at a certain time, then, at all times, some pro-

portion of the ps are among the objects that compose it. Thus, it

seems that the Essentialist Assumption here is that if the ps com-

pose a ship at time t, then there is a z such that the ps compose z

at t and, necessarily, for all qs and t, the qs compose z at t only if z bears R2 to the qs, where R2 is defined as follows:

z bears R2 to the qs =DF for some n ? 1, at every time t', at least 1/n of the qs compose z.

And if we deny this assumption, then it seems that (short of re-

placing R2 with some different relation) the correct response is to

identify the continuously repaired ship with the Ship of Theseus.

For suppose that the ps compose the Ship of Theseus and that they

compose nothing that cannot survive complete part replacement.

Then, by the PACP, it is possible for the Ship of Theseus to survive

complete part replacement; thus there is no reason not to identify

the continuously repaired ship with the Ship of Theseus (both at

the end of the story and at every step throughout).21

the Ship of Theseus puzzle will not be determined by her decision to reject one of the above assumptions, since (as I mentioned earlier, and as I will discuss more fully at the end of section 4) the Ship of Theseus puzzle does not raise the problem of material constitution for a four-dimensionalist.

210ne might object here as follows: Since the plank-hoarder's ship would

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THE PROBLEM OF MATERIAL CONSTITUTION

That the Identity Assumption underlies this puzzle is clear from

the fact that we (initially, anyway) assume that there is just one ship

composed of the original planks at the beginning of the puzzle.

To reject the Identity Assumption is to admit that there might have

been two (or more) co-located ships, one of which came to be

dismantled and rebuilt, the other (or another) of which survived

a replacement of all of its parts. But, of course, if this were the

case, then neither ship at the end of the story would be the Ship

of Theseus, for there would be no such thing as the ship that was

composed of the original planks. Hence, the question is simply

defective.

Finally, the Necessity Assumption is needed in the context of the

puzzle to rule out the possibility that the Ship of Theseus was iden-

tical with something that could not survive complete part replace-

ment, but is no longer identical with it. To reject the Necessity

Assumption (and no other) is, in the present context, to embrace

temporary identity (the thesis that possibly, there is an object a

and an object b such that a is identical with b at one time and

distinct from b at another). Of course, denying the Necessity As-

sumption is not equivalent to accepting the temporary identity the-

sis; but given how we have defined R in the Essentialist Assumption

(i.e., as R2), one who denies the Necessity Assumption and endorses

all four other assumptions is committed to temporary identity.22

For suppose one holds that at the beginning of the story, the Ship

of Theseus is identical (but not necessarily so) with something (call

it Z1) that cannot survive complete part replacement. Then at the

end of the story either the Ship of Theseus is distinct from Z1, or

have been the Ship of Theseus had the ship merely been disassembled and then reassembled (that is, had none of its parts been replaced), in the actual case the plank-hoarder's ship should be identified with the Ship of Theseus as well. My reply is that this presupposes that part replacement never really occurs. The Ship of Theseus is gradually disassembled as planks are removed from it, and the continuously repaired ship is an object one portion of which is the partially disassembled Ship of Theseus and another portion of which is a partially constructed new ship. Thus, to raise this objection is in fact to endorse the Essentialist Assumption and deny the PACP. I am grateful to a referee for this journal for bringing this oW jection to my attention.

22Note that those (like Allan Gibbard) who endorse contingent identity and four-dimensionalism are not committed to temporary identity because four-dimensionalism entails that the PACP as it is here defined is false (see page 542 and note 38).

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MICHAEL C. REA

it is identical with Z1 (though it might not have been) and there-

fore has not undergone complete part replacement. In the former

case, the temporary identity thesis is true; thus one who wants to

embrace contingent identity but avoid temporary identity must say

that the latter case obtains. But why should we think that this case

obtains? That is, why should we think that the ship has not under-

gone complete part replacement? Is it because it cannot? Then the

PACP is false.23 On the other hand, if the PACP is true, then pre-

sumably we could construct a puzzle just like the Ship of Theseus

(call it "the Ship of Odysseus puzzle") in which the relevant ship

does undergo part replacement; then the proponent of contingent

identity will be forced to embrace temporary identity or else deny

that the ship and the object that cannot survive complete part

replacement were ever identical in the first place (thus rejecting

the Identity Assumption). So, in the present context, to reject the

Necessity Assumption (and to endorse the other four) commits

one to temporary identity; and once one is committed to tempo-

rary identity, there seems to be no reason to identify the plank-

hoarder's ship as the Ship of Theseus. For if the temporary identity

thesis is true, then why think that just because Z1 is identical with

the Ship of Theseus at the beginning of the story, it is identical

with the Ship of Theseus at the end of the story as well? Indeed,

because we have not rejected the Identity Assumption or the PACP,

there is good reason not to think this: it is possible for the Ship of

Theseus to undergo complete part replacement. But, of course, Z1

cannot undergo complete replacement of its parts; hence, though

Z, was identical with the Ship of Theseus at the beginning of the story, it is no longer, since presumably the ship has survived its

many repairs and is in fact the continuously repaired ship.24

230r else co-located with the original Ship of Theseus was another ship that could undergo complete part replacement, in which case the Identity Assumption is false.

241t is unacceptable to say here that perhaps Z1 was identical to the Ship of Theseus at the beginning of the story, was distinct from the Ship of Theseus so long as the original planks lay unassembled, but then became identical with the Ship of Theseus again once the planks were reassembled. For we would then have the bizarre consequence that at the precise mo- ment the planks were reassembled, the Ship of Theseus somehow instan- taneously moved from wherever the continuously repaired ship was to wher- ever the plank-hoarder's ship was; but this view seems too bizarre and ad hoc to be considered as a serious option for solving the puzzle.

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THE PROBLEM OF MA TERIAL CONSTITUTION

I have now shown that rejecting any of the above five conflicting

assumptions will suffice to tell us which (if either) of the final two

ships is the Ship of Theseus. In concluding this section, I would

like to emphasize the fact that the fundamental problem here will

arise whether or not we suppose the original planks are reassembled

in their original form. Indeed, if the argument of this section is

correct, the problem arises just as soon as we suppose the Ship of

Theseus can undergo complete replacement of its parts. Thus, it

turns out that the function of Hobbes's twist on the puzzle is purely

rhetorical: it highlights the fact that we have intuitions that conflict

with the PACP, intuitions that we might otherwise suppress if the

puzzle merely asked us to decide whether the continuously re-

paired ship was the Ship of Theseus or whether Theseus's ship lay

disassembled in the plank-hoarder's yard.

4. The Body-minus Argument

The Body-minus Argument is another puzzle with a long history.

Its origin is in Chrysippus, where it appears as the paradox of Dion

and Theon.25 More recently, the puzzle has been reintroduced by

Wiggins, who casts it in terms of the now familiar story about Tib-

bles the cat.26 The story runs roughly as follows.27

Consider Tibbles-a cat who, at a certain time t, is endowed with

a tail, but who unfortunately finds herself separated from that tail

at some later time t'. (Let us suppose that Tibbles's tail is annihilated

sometime after t and shortly before t'.) The body that Tibbles has

when her tail is intact we shall call 'Body'; we will use the name

'Body-minus' to refer to Body minus the tail. Thus Body and Body-

minus coexist, and indeed overlap, prior to the annihilation of

Tibbles's tail; but clearly Body is not identical with Body-minus-

Body-minus is just a proper part of Body. Now, the problem arises

as follows.

25David Sedley speculates that Chrysippus raised the paradox as a re- joinder to the Growing Argument. For details, see Sedley 1982, 270.

26A story that Wiggins (1968) borrowed from Geach (see 1980, sec. 110) who, in turn, developed it from a (unfortunately unnamed) passage in William of Sherwood. Other recent versions and/or discussions of the puz- zle are to be found in Heller 1990, Noonan 1976, Simons 1987, Thomson 1983, and van Inwagen 1981.

27The version I present here is loosely based on versions by van Inwagen and Simons.

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MICHAEL C. REA

At t, it seems that Tibbles is identical with Body. Thus

(1) At t Tibbles = Body.

At t', however, after Tibbles has suffered the annihilation of her

tail, it seems that Tibbles is identical with Body-minus. Hence

(2) At t': Tibbles = Body-minus.

But, of course, since identity is not merely temporary, it follows

from (1) and (2) that

(3) (Tibbles = Body) & (Tibbles = Body-minus).

And since identity is transitive, (3) entails

(4) Body = Body-minus.

But (4) is false. Hence something must have gone wrong.

Typically, the problem is said to reside in one of eight assump-

tions made by the argument:28

(a) Material objects such as Tibbles exist.

(b) Material objects such as Tibbles and her parts are three-

dimensional enduring objects.29

(c) Material objects such as Tibbles can survive gain and loss

of material parts.

(d) Proper parts of material objects, such as Body-minus, exist

even while undetached from the objects of which they are

proper parts.

(e) Identity is transitive.

(f) Identity is not relative to a sortal concept.

28The following list comes (with some alterations) from Simons 1987, 119.

29As opposed to four-dimensional perduring objects. (Following estab- lished convention, I say that an object "endures" if it persists through time by being wholly present at every time at which it exists and I say that an object "perdures" if it persists by being partially present (i.e., by having spatiotemporal parts) at every time at which it exists. Hence perduring objects are four-dimensional since they are extended in time just as they are extended in space.) The assumption is made in setting up the problem. 'Tibbles = Body' and 'Tibbles = Body-minus' can be true only if the names refer to three-dimensional objects (or three-dimensional stages of objects). For, in the above scenario, if the names refer to four-dimensional objects, then Tibbles, Body, and Body-minus turn out to be different objects by virtue of the fact that each has parts that the others don't have.

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THE PROBLEM OF MATERIAL CONSTITUTION

(g) Identity is not temporary, or relative to a time.

(h) Distinct material objects cannot fully occupy the same place

at the same time or share all their proper parts at the same

time.

By rejecting any one of these assumptions, it is possible to avoid

the unwelcome conclusion that Body = Body-minus.

It will be useful to digress here briefly and note that insofar as

rejecting any one of these assumptions solves the problem of ma-

terial constitution, it will also solve the other puzzles under consid-

eration in this paper; hence, this list, when prefaced by the words

'Reject one of the following:', constitutes what is perhaps the most

comprehensive list of possible solutions to the problem of material

constitution currently available. But the list is not exhaustive. There

are solutions to the problem (indeed, to the Body-minus argument

itself) available that do not reject any of the assumptions listed

above.30 Moreover, as a list of solutions to the problem of material

constitution, the list is not accurate: there are solutions listed above

that solve only some of the puzzles that express the problem.31

And, finally, it is not at all clear why rejecting any one of these

assumptions will provide a solution to the other puzzles under con-

sideration in this paper-or at least it is not immediately clear.

What we need is a general statement of the problem underlying

each of these different puzzles, together with a taxonomy of pos-

sible solutions that shows how the different available solutions are

related to one another and provides a relatively easy means of clas-

sifying newly discovered solutions.32

30See, for example, Burke 1994a and 1994b. 31Rejecting (b), (d), or (e) will solve the Body-Minus puzzle as it is

usually presented, but rejecting these will not solve the problem of material constitution. More on this below.

321 say it would be good to have a taxonomy of possible solutions rather than a list because it would be much harder (perhaps impossible) to pro- vide the latter. The reason for this is that there is no end to the variety of possible solutions to a problem: one can solve the Ship of Theseus puzzle, for example, by denying that there are boats, by denying that there are artifacts, by denying that there are any material objects other than wooden planks and Leprechauns, and so on. Each of these alternatives might be

seen as a different solution, but they can all be categorized as solutions that deny the Existence Assumption by denying that there are ships. For this reason, it seems that the prospects for providing an exhaustive tax- onomy of solutions-a list of such categories-are much better than the prospects for providing an exhaustive list of solutions.

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MICHAEL C. REA

And so we return to the Body-minus argument, with the goal of

recasting it in such a way as to show that it expresses essentially

the same problem expressed by the Growing Argument and the

Ship of Theseus puzzle. This is a relatively easy matter, for once we

realize that the upshot of the story is that there is something par-

adoxical about a cat's losing its tail, it becomes clear that the as-

sumptions underlying the Growing Argument will be necessary and

sufficient to show this. The Existence Assumption is that there are

cats and ps that compose them (Tibbles is our instance here); the

Essentialist Assumption is that for any cat, the ps that compose it

compose an object that cannot survive the loss of a part (in the

story, Body satisfies this assumption, and we can again take R1 as

our substitution instance for R); the PACP is that for any cat, the

ps that compose it compose an object that can survive the loss of

a part (hence our intuition that Tibbles, unlike Body, can survive

the annihilation of Tibbles's tail); the Identity Assumption entails

that Tibbles is identical with Body; and the Necessity Assumption

entails that Tibbles is necessarily identical with Body. Making the relevant substitutions, we can recast the Body-minus argument as

an argument of the sort outlined in section 1 (I leave this to the

reader), and we of course find that the scenario is paradoxical.

Note that this formulation of the argument does not assume that

Body-minus exists-hence it assumes nothing with respect to the

"doctrine of arbitrary undetached parts" (hereafter, "DAUP")33-

nor does it assume that identity is transitive. The reason for this is

that neither of those assumptions are essential to the puzzle.34 On

33The doctrine of arbitrary undetached parts is (roughly) the doctrine that in every occupiable subregion of the region of space occupied by an object 0 at a certain time t, there is an object that exists at t and is a part of 0 (see van Inwagen 1981, 123). It is generally assumed that assumption (d) is true only if DAUP is true.

341t may be helpful to point out here that DAUP is not essential to the puzzle because it is stronger than necessary. That is, it entails but is not entailed by the puzzle's Essentialist Assumption. In "The Doctrine of Ar- bitrary Undetached Parts," Peter van Inwagen argues that DAUP entails what he calls "mereological near-essentialism." Mereological near-essen- tialism is

the thesis that it is impossible for an object to lose any of its parts; that is ... if a part is removed from an object, and no new part is added to the "remain- der," then that object must therewith cease to exist. (1981, 124)

But clearly if mereological near-essentialism is true, then the above Essen-

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THE PROBLEM OF MATERIAL CONSTITUTION

an intuitive level, all one really needs in order to show that there

is something paradoxical about Tibbles losing her tail are the

premises that Tibbles and Body exist, that Tibbles = Body, and that

Tibbles can but Body cannot survive the loss of Tibbles's tail. On

a more rigorous level, all one needs are the five assumptions out-

lined in section 1. Consequently, one cannot solve the problem of

material constitution simply by taking a particular stand on DAUP

or the transitivity of identity.

Moreover, one cannot solve the problem of material constitution

by rejecting (b) either. One can solve the Body-minus puzzle by

rejecting (b); but the reason for this is that once we have rejected

(b), we can admit that Tibbles exists and Body exists without ad-

mitting that one constitutes the other. Thus the Body-minus puzzle

does not even raise the problem of material constitution for the

four-dimensionalist, because once we have accepted four-dimen-

sionalism we no longer have an instance of material constitution.

To see why this is so, we must first clear up an ambiguity that arises

when our assumptions are read from a four-dimensionalist per-

spective.

The locus of ambiguity is in expressions of the form 'the ps

compose 0 at t'.35 Such an expression might mean that, at t, the

ps compose the object 0, or it might mean that the ps compose

the object O-at-t. From a three-dimensionalist perspective, these amount to the same thing: if the ps compose 0 then they also

compose O-at-t, since 'O-at-t' is just another name for 0.36 But from a four-dimensionalist perspective, 'O-at-t' names a temporal stage

of O, hence if the ps compose 0, then they do not compose O-at-t and vice versa. This ambiguity infects all of the assumptions except

the Necessity Assumption and it also makes a difference as to what

object we take to be the referent of the name 'Body'. I will not

tialist Assumption must be true. Hence, insofar as DAUP entails mereolog- ical near-essentialism, it entails the above Essentialist Assumption. (And in fact van Inwagen would reject this assumption, for he thinks that, for any ps, the ps compose something only if their activity constitutes a life; but a living being is just a being that is capable of changing its parts over time (see van Inwagen 1990, chap. 9).).

350f course, other expressions are ambiguous from a four-dimension- alist perspective: for example, 'O exists at t' might mean 'it is true at t that 0 exists' or 'O has a temporal stage at f. But in these cases, the ambiguity does not make much difference in how one reads the argument.

360n this issue, see Merricks 1994.

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MICHAEL C. REA

belabor this issue by explicitly considering all of the possible ways

of disambiguating these premises; it will suffice simply to say that

every expression of the form 'the ps compose 0 at t' should be

understood to mean that, at t, the ps compose the object 0.37 In-

deed, the four-dimensionalist will do best simply to drop the 'at t'

qualifiers altogether since, on her view, if it is true at one time that

the ps compose 0, then it is true at all times.

But if this is right, then according to the four-dimensionalist it

is false that, at t, the ps that compose Tibbles also compose Body.38

For, in the context of the story, the name 'Tibbles' clearly refers

to the whole cat (that is, the object that, according to the four-

dimensionalist, fills the region of spacetime that constitutes the

entire life of the cat). But Body occupies only part of that region,

since its career is terminated whenever Tibbles's tail is annihilated.

Thus, according to the four-dimensionalist, Body is at best a proper

spatiotemporal part of Tibbles. But then Body does not constitute

Tibbles and so there is reason to think that Body might be identical

with Tibbles; thus there is no paradox.

So the Body-minus Argument does not raise the problem of ma-

terial constitution for the four-dimensionalist. And neither do the

other two puzzles we have considered so far. The problem of ma-

terial constitution arises whenever it appears that there is an object

a and an object b that constitute one another and are essentially

related to their parts in different ways. But in each of the puzzles

37The reason we must disambiguate these premises in this way is that if we disambiguate them the other way, it turns out that (for the four-dimen- sionalist) the Identity Assumption claims that if x and y share a temporal stage, then x = y. But this is as ludicrous as saying that if x and y overlap spatially then x = y. But it doesn't have to be read this way, and so we may just stipulate that it is to be read by the four-dimensionalist with the 'at t' qualifiers dropped. And if we disambiguate the Identity Assumption this way, then, to preserve the validity of our inferences, the other premises must be disambiguated this way as well.

381t is also false that objects undergo mereological change; hence, ac- cording to the four-dimensionalist, the PACP as it is defined above is false. But I take it that, though the four-dimensionalist in fact denies the PACP here, she does not solve the puzzle by denying it. For the point of the PACP is to bring out the fact that Tibbles and Body are essentially related to their parts in different ways; but the four-dimensionalist does not need to deny this in order to solve the puzzle. For if Body does not constitute Tibbles, then the puzzle is already solved: there is no reason to think Tibbles and Body are identical, and hence no reason to think that they shouldn't be related to their parts in different ways.

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THE PROBLEM OF MAT ERIAL CONSTITUTION

we have considered so far (and, generally, in any puzzle that pur-

ports to show that actual mereological change is paradoxical), our

putative a and b do not appear to the four-dimensionalist to con-

stitute one another; in each case she will simply say that one is a

proper spatiotemporal part of the other.

But this does not mean that the problem of material constitution

does not arise at all for the four-dimensionalist; it just means that

we have not yet found the right story to raise it. What we need is

a story in which even the four-dimensionalist will grant that there

appear to be objects a and b that constitute one another and are

essentially related to their parts in different ways. Allan Gibbard's

puzzle about Lumpl and Goliath is just such a story.

5. Lumpl and Goliath

The Lumpl/Goliath story is original to Gibbard (1975), and it is

designed to show that there are some contingent identities. It runs

as follows.

A sculptor sets out to create a statue of the infant Goliath, but

he does so in the following way: he sculpts Goliath's upper body

from one piece of clay, his lower body from another, and then

finishes the statue by sticking the two pieces of clay together. Thus,

in joining the two pieces of clay he simultaneously brings into ex-

istence a new piece of clay and a completed statue of the infant

Goliath. He allows the clay to harden, but then a day later (perhaps

dissatisfied with his work) he smashes the statue, thereby termi-

nating the careers of both the statue and the piece of clay.

The question is whether the statue in this story (Goliath) is iden-

tical with the piece of clay (Lumpl). Gibbard answers affirmatively

since Lumpl and Goliath come into existence at the same time and

pass out of existence at the same time and share all of the same

spatiotemporal parts at all times during which they both exist. But,

he says, Lumpl is not necessarily identical with Goliath since it is

possible that Lumpl exist and Goliath not and vice versa. (For ex-

ample, such a possibility might have been realized if, while the sculpture was still wet, the sculptor had squeezed Lumpl into a ball

and reshaped it into a statue of David, or if, after the statue had

hardened, Goliath's finger had been annihilated.) Thus, Gibbard

concludes, there are some contingent identities.

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MICHAEL C. REA

As I have said, Gibbard constructed this story with a particular

aim in mind-to show that identity is sometimes contingent. How-

ever it should be obvious by now that granting Gibbard's conclu-

sion is but one of many possible solutions to the problem raised

by the Lumpl/Goliath story. This is because it is just another ex-

pression of the problem of material constitution. It turns out,

though, that when we try to identify the assumptions of the

Lumpl/Goliath story, we find that, unlike the other stories we have

considered, this one presents us with two distinct puzzles. One

shows that there is something paradoxical about the fact that an

object could have had material parts other than those it in fact has;

the other shows that there is something paradoxical about the fact

that an object could have had a different shape (or, more generally,

a different arrangement of parts) than it in fact has. Still, we can

identify in each puzzle five assumptions of the sort presented in

section 1.

In the first puzzle, paradox seems to arise from the fact that

Goliath can but Lumpl cannot survive the loss of small parts; and

initially it looks as if this might be just another puzzle about mer-

eological change. However, we must recall that this is a four-di-

mensionalist's puzzle; hence, saying (for example) that Goliath los-

es a finger is just a loose way of saying that one "temporal stage"

of Goliath has a finger whereas a later one does not. Thus it is not

mereological change that poses the problem; rather, the puzzle aris-

es from the fact that Lumpl and Goliath actually share all of the

same spatiotemporal parts (and hence seem to be identical), but

Goliath could have been composed of different parts whereas

Lumpl could not. Thus the Existence Assumption is that there are

statues and ps that compose them (and Goliath is the instance);

the Essentialist Assumption is that if the ps compose a statue, then

the ps compose something (Lumpl is our instance) such that it

cannot exist and fail to be composed of the ps; the Identity As-

sumption, as always, remains the same and justifies our intuition

that Lumpl = Goliath; the Necessity Assumption, which Gibbard

rejects, is reflected in our intuition that if Lumpl = Goliath then

Lumpl could not have been distinct from Goliath; and the PACP

is that if the ps compose a statue, they compose something that

could have existed and failed to be composed of them (Goliath

satisfies this assumption). To generate these assumptions, we sub-

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THE PROBLEM OF MATERIAL CONSTITUTION

stitute 'statue' for F and R3 for R, where R3 is defined as follows:

Suppose the ps actually compose z. Then

z bears R3 to the qs =DF the qs = the ps.

In the second puzzle, paradox arises from the fact that Lumpl

can whereas Goliath cannot survive certain changes in the arrange-

ment of its parts. In particular, Lumpl can but Goliath cannot be-

come a non-statue.39 We can accommodate this simply by modify-

ing the Essentialist Assumption and the PACP by replacing R3 with

R4, where R4 is defined as follows:

z bears R4 to the ps =DF the ps compose a statue.

Gibbard's story is the only one of the puzzles we have seen that

explicitly acknowledges a possibility of this sort; but clearly it is

possible for, say, the aggregate of particles that constitutes a human

being to exist when the human being does not, and likewise for

cats and other composite objects. Thus Gibbard's puzzle is superior

to the other three as an instance of the problem of material con-

stitution in that (i) it is puzzling for three-dimensionalists and four-

dimensionalists alike, and (ii) it highlights the fact that "formal"

change is just as paradoxical as material change.

6. Solutions

We have now seen that one problem underlies four familiar philo-

sophical puzzles. The problem, again, is that for any composite

object a, we can (generally) identify an object b that constitutes it

and is essentially related to its parts in a way that a is not. The

Identity Assumption tells us that a is identical with b (constitution

is identity); the Necessity Assumption tells us that a and b could

not have been distinct; hence a and b are not essentially' related to their parts in different ways. To solve the problem, we must (i)

reject the Identity Assumption, (ii) reject the Necessity Assump-

tion, or (iii) reject some feature of the story that introduces the

problem (that is, claim that a does not exist or that b does not

391ndeed, Goliath cannot even become a non-Goliath-shaped statue; but for convenience let us ignore this. To take account of this fact, we would simply have to replace 'statue' in the relevant places with 'Goliath-shaped statue'.

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MICHAEL C. REA

exist or that one or the other is not related to its parts in the way

we think it is).40 To do (iii) we must reject the Existence Assump-

tion, the Essentialist Assumption, or the PACP for whatever F and

R are presupposed in the case at hand. (In other words, to give a

complete solution to the problem without rejecting the Identity As-

sumption or the Necessity Assumption, we must reject the con-

junction of the other three assumptions for all substitution in-

stances of F and R.) The puzzles we have considered in this paper

differ only insofar as they supply different substitution instances

for F and R and different stories to engage our intuitions about

the five conflicting assumptions.

We are now in a position to categorize the solutions to the prob-

lem of material constitution. One natural way to do it would be to

identify three categories corresponding to (i), (ii), and (iii) above, and, for any given puzzle, three different ways for a solution to fall

into the third category. However, since one may reject a proposi-

tion either by claiming that it is false or by claiming that it is neither

true nor false, and since there are few philosophers who do the

latter for any of the assumptions we are considering, I will group

the "indeterminacy solutions" in a separate category of their own,

leaving in the remaining three categories only solutions that deny

the relevant assumption. Let us now look at these four categories

in a bit more detail.

6.1 Solutions that deny the Identity Assumption

As I have already noted, the Identity Assumption corresponds

(roughly) to the view that is sometimes expressed by the phrase

"constitution is identity."'41 To deny it, one must hold that, some-

times, distinct objects have all of the same parts at the same time.

Among the philosophers who explicitly defend this sort of view are

Fred Doepke (1982), MarkJohnston (1992), Peter Simons (1987),

401 take it that if, in a particular story, it turns out that a and b exist but do not constitute one another, then we simply do not have a story that raises the problem. Thus "deny that a and b constitute one another" will not count as a general strategy for solving the problem.

41We would have a more precise correspondence if the assumption con- tained a biconditional.

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THE PROBLEM OF MATERIAL CONSTITUTION

199-204), and David Wiggins (1968 and 1980). Furthermore, it

seems that those who adopt "relative-identity" solutions should

also be seen as falling into this camp. A relative-identity solution is

any solution that maintains that all expressions of the form 'x = y' in the assumptions and the argument of section 1 should be re-

placed by claims of the form 'x is the same F as y', where F is a

schematic letter taking sortal terms as substitution instances. (One

might hold such a view if, for example, one followed Geach (1980)

in holding that all true identity statements are relativized to a sor-

tal; but one need not go this far in order to endorse a relative-

identity solution.) Presumably, the relative-identity theorist could

endorse appropriately modified versions of the Identity Assump-

tion and the Necessity Assumption, but she would reject them as

they stand since they contain unqualified expressions of the form

'x = y'. But this alone will not suffice to solve the problem of

material constitution. To see this, consider the Lumpl/Goliath puz-

zle from the point of view of a relative-identity theorist. Either

Lumpl is the same statue as Goliath, or it is not. If it is, then the

problem of material constitution (or a relative-identity version of

it) arises with a vengeance; for, according to the story, it is possible

that Lumpl not be the same statue as Goliath. If, however, Lumpl

is not the same statue as Goliath, then the Identity Assumption is

false; for according to the story Lumpl and Goliath in fact share

all of the same spatiotemporal parts throughout both of their ca-

reers-and this despite the fact that, on the present view, one is a

statue and the other is either a different statue or not a statue at

all. Thus, it seems, either an appeal to relative identity does not

solve the problem of material constitution at all, or else it entails

a rejection even of a "relativized" version of the Identity Assump-

tion. Hence, it seems reasonable to categorize relative-identity so-

lutions as solutions that deny the Identity Assumption.42 Among

those who defend relative identity solutions are Hugh Chandler

(1971), Peter Geach (1980, 215-18), and Nicholas Griffin (1977,

177-85).

421 must emphasize, though, that it is possible to hold that identity is sortal relative, endorse (a relativized version of) the Identity Assumption, and solve the problem of material constitution by denying one of the other assumptions that generate the problem. However, one who does this will not be solving the problem simply by appeal to relative identity.

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MICHAEL C. REA

6.2 Solutions that deny the Necessity Assumption

These solutions will hold that there are cases where 'a = b' is true

and it is possible that a exists or b exists and 'a = b' is false. As we

have seen, this is the solution that Gibbard adopts. Moreover, the

views of Gallois (1990) and Myro (1986)43 also fall under this cat-

egory since they maintain that some identity statements are just

temporarily true.

6.3 Solutions that deny the conjunction of the remaining

assumptions for all substitution instances of F and R

In this category I group the views of philosophers who accept the

other two assumptions and thus solve every puzzle that raises the

problem of material constitution by rejecting some feature or other

of the story that raises it. Also, it is worth pointing out that most

philosophers whose views fall into this category do not solve every

puzzle the same way: they deny the conjunction of the three sche- matic assumptions for all substitution instances for F and R, but

they deny different conjuncts for different instances. Following are

some examples.

6.3.1 Denying the Existence Assumption

The Existence Assumption states that (for a given I) (i) there are

Es and (ii) there are things that compose Fs.44 Hence falling within

this category will be all of the various solutions (to particular puz-

zles) that deny either or both of these claims for the relevant sub- stitution instances of F. For example, van Inwagen denies (i) for

all substitution instances of F except those where F is a simple or

a living organism, and he denies (ii) for all substitution instances

of F except those where F is a living organism (since simples are

not composite). And Unger (1980) denies (i) for all substitution

43Myro gives credit for the view to Paul Grice. 441t also states that there are times; but denying that there are times

does not seem to constitute a solution to the problem. This is because the problem could, with some work, be recast to do away with the assumption that there are times.

45See van Inwagen 1990, chap. 9. However, van Inwagen notes that 'the

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THE PROBLEM OF MATERIAL CONSTITUTION

instances of F except those where F is a simple, and so he denies (ii) for all substitution instances of F whatsoever.

6.3.2 Denying the Essentialist Assumption

The Essentialist Assumption says that if the ps compose an object

O (which is an I), then they compose an object such that (for some specified R), necessarily, that object exists only if it bears R to its

parts. This is consistent with saying that 0 is the only object the ps

compose; it is also consistent with saying that, in addition to com-

posing 0, the ps compose exactly one other object-perhaps an

aggregate-or, indeed, many such objects that are distinct from 0

but co-located with it for some period of time. To deny the Essen-

tialist Assumption for some F and R is to say that there is at least

one case where there are ps that compose an Fbut do not compose

something such that, necessarily, it exists only if it bears R to its

parts. Van Inwagen, for example, denies the Essentialist Assump-

tion in all cases where it implies that the ps that compose a living

organism compose something that cannot undergo complete re-

placement of its parts (1990, chap. 9), though he might accept it

in cases where it implies that an F (where F is a natural-kind term)

cannot become a non-F. Likewise, Burke also accepts it in some

cases where it implies that an F cannot become a non-F, and he

seems to deny it in cases where it implies that the ps that compose

an Aristotelian substance compose something that cannot undergo mereological change.46

ps' might refer to just one object (ibid., 24), and that one might want to say that, in a sort of degenerate sense, simples are self-composing (ibid., 98). Viewing things this way, van Inwagen accepts the Existence Assumption for simples.

46See Burke 1994a and 1994b. In discussing the Body-minus argument, for example, Burke claims that the right solution is to say that Body-minus passes away as soon as its parts come to compose a cat, since cats are cats essentially and non-cats are non-cats essentially. In saying this, I take it that he means that the ps that compose Body-minus compose an object of the sort described in its Essentialist Assumption (that is, such that, necessarily, it exists only if it bears RI to its parts) only until the ps come to compose a cat. Once the ps compose a cat, however, they no longer compose an object of the sort described in the Essentialist Assumption; but then the Essentialist Assumption is false.

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MICHAEL C. REA

6.3.3 Denying the PACP

The PACP maintains that if the ps compose an object 0 that is an

F and an object Z that satisfies the Essentialist Assumption for some R, it is possible that 0 exist and fail to bear R to its parts. Mereo- logical essentialists-Chisholm (1976), for example -deny this principle for substitution instances of R that imply that objects do

not have their parts essentially. The Academics (apparently) denied

this principle for substitution instances of R that imply that mer- eological change is possible.

6.4 Indeterminacy Solutions

These will be any solutions that attempt to solve the problem by

saying that the Identity Assumption, the Necessity Assumption, or the conjunction of the other three is neither true nor false. The

only indeterminacy solutions (that I am aware of) that have been

discussed in any detail as such are solutions that maintain that the

Identity Assumption is indeterminate because it is sometimes in- determinate whether 'x = y' is true.47

This completes our taxonomy of solutions to the problem of

material constitution. All of the available solutions to the problem

fall under one of the above categories, and it seems that any possible

solutions to the problem must also fall under one of these cate- gories.48

University of Notre Dame

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Alvin Plantinga, Philip Quinn, Dean Zimmerman, and two anonymous ref- erees for the Philosophical Review for helpful comments on earlier drafts of this paper.

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