Composition as Identity Doesn't Settle the Special Composition Question

Composition as Identity Doesn’tSettle the Special CompositionQuestion1

ross p. cameron

University of Leeds

Orthodoxy says that the thesis that composition is identity (CAI) entails universal-

ism: the claim that any collection of entities has a sum. If this is true it counts in

favour of CAI, since a thesis about the nature of composition that settles the

otherwise intractable special composition question (SCQ) is desirable. But I argue

that it is false: CAI is compatible with the many forms of restricted composition,

and SCQ is no easier to answer given CAI than otherwise. Furthermore, in seeing

why this is the case we reveal an objection to CAI: that it allows for the facts con-

cerning what there is to be settled whilst leaving open the question about what is

identical to what.

1. Composition as Identity and SCQ

The thesis that composition is identity (CAI) is the thesis that the Xs

compose A iff the Xs is identical to A.2 If this thesis is to be compati-

ble with any mereological view other than mereological nihilism, we

must allow that many-one identity statements make sense: that is, that

it makes sense to say of a plurality of things that they are (collec-

tively) identical to some one thing. Identity, on this view, holds

between every thing and itself, but can also hold between a thing and

some things. When there is a complex A composed of parts x1, x2, . . .

xn, while each of A=x1, A=x2, . . . A=xn is false, as is, of course,

1 Thanks to Elizabeth Barnes, Karen Bennett, Daniel Elstein, Kris McDaniel, Ned

Markosian, Jeff Russell, Ted Sider, Jason Turner, Meg Wallace, Robbie Williams,

Richard Woodward, and an anonymous referee for PPR for helpful discussion.2 Discussing the thesis forces us to be ungrammatical or misleading. I will choose

the former, and say things like ‘The Xs is identical to A’ rather than ‘The Xs are

identical to A’ which could easily be confused with meaning that each of the Xs is

identical to A, which is obviously not what the believer in CAI intends.

COMPOSITION AS IDENTITY DOESN’T SETTLE THE SPECIAL COMPOSITION QUESTION 531

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A={ x1, x2, . . . xn }, what is true is simply A= x1, x2, . . . xn. And, of

course, we must also countenance many-many identities: if A is the

sum of the Xs and B the sum of the Ys, then A,B= x1, x2, . . . xn, y1,

y2, . . . yn.3

CAI is conceptually revisionary, then: it forces one to either accept

the coherence of many-one and many-many identity or to reject the

coherence of complex objects. But conceptual revision can be rational

if the resulting theory is beneficial,4 just as ontological posits can be

justified by the utility of the resulting ontology. So we should ask: what

benefits might acceptance of CAI bring?

Amongst the potential advantages of CAI are that certain mere-

ological claims get settled by the logic of identity.5 If parthood is a

primitive relation, it’s an open question, e.g., whether the Xs can

compose two distinct things. But if to be a part of Y is to be

amongst some things that is identical to Y, as CAI says, then the

uniqueness of composition is entailed by the fact that identity is

Euclidean: if the Xs compose A and B then, since Xs=A and Xs=B,

A=B.

Relatedly, one might think that an important benefit of CAI is that

it settles the special composition question (SCQ): under what condi-

tions do a collection of objects compose some further object?6 Nihilists

say: never. Universalists say: always. And then, of course, there are

many forms of restricted composition that specify conditions for com-

position that are sometimes, but not always, met.

The multiplicity of answers to SCQ, without any clear way of set-

tling on the correct one, might appear worrying. It would be desirable

to have a thesis about the nature of composition that settled the issue.

CAI promises to do that by settling it in favour of universalism.7 The

thought is this: of course whenever you’ve got some things, the Xs,

you’ve got their sum, for their sum just is the Xs! Whenever you’ve

3 Note then that many-many identity can’t be understood as follows: Xs=Ys iff the

Xs are amongst the Ys and the Ys are amongst the Xs. For in the above example,

assuming there’s more than one of the Xs, and that A and B do not overlap, then

A is not amongst x1, x2, . . . xn, y1, y2, . . . yn nor is x1, e.g., amongst A,B.4 Assuming we can understand the resulting theory, of course. If you think you just

don’t understand the required notions of many-many and many-one identity . . .

well, I sympathise; and perhaps it’s appropriate to simply reject CAI on the

grounds that this doesn’t make sense. But it’s more interesting if we can respond

to the proponents of CAI in a way that should be acceptable by their own lights;

that’s what I’m trying to do here.5 See Sider (2007) for discussion. Cf. Lewis (1991).6 SCQ was asked by van Inwagen (1990).7 See Sider (2007) for discussion. See also Merricks (2005).

532 ROSS P. CAMERON

got some things, you’ve got those things; so if a sum just is its parts,

whenever you’ve got some things you’ve got their sum, which is

universalism.

I am going to argue against this. I claim that CAI does not settle

things in favour of universalism. If I am right, what looked like a

potential benefit of CAI is not one after all. That is not to say that we

shouldn’t accept CAI, of course: there may be other motivations for

CAI that make it worth adopting. But in fact I’ll argue that once we

see why CAI doesn’t entail universalism, this raises a potential objec-

tion to CAI.

Here’s where the thought that CAI entails universalism goes wrong.

CAI, as stated, entails simply that there is a complex object in all and

only those cases when there is a case of many-one identity. So CAI tells

us that when there is a complex object, it is identical to its parts, and

that when the many is identical to some one, they compose that one.

But this doesn’t tell us whether, given some Xs, they in fact compose;

it only settles the biconditional: they compose iff there is some one to

which the Xs is identical.

CAI only entails universalism if we add the thesis that for any

collection of things, there is some one to which that collection of things

is identical. But then, if CAI is true, the doctrine of universalism simply

is the claim that for any plurality of things, there’s a one to which that

plurality is identical, so assuming this claim is tantamount to simply

begging the question in favour of universalism.

To bring this point out, let’s introduce some terminology. Call the

Xs a mere many if there’s more than one of the Xs, and there is no one

thing to which the Xs is identical. Call the Xs a many-one if there’s

more than one of the Xs and they are not a mere many: that is, if they

are a plurality that is identical to some one thing. I claim that both

mere manys and many-ones are conceptually possible, given CAI.

(Note: I don’t claim that there are mere manys. That would beg the

question against the universalist. I only claim that it’s coherent to say

that there are mere manys.) This claim is so important to what follows

that we should give it a name.

Thesis: It’s conceptually possible that there are mere manys

and it’s conceptually possible that there are many-ones.

The second conjunct of Thesis should be uncontroversial to those

who accept CAI and reject compositional nihilism: if identity can be

many-one, as it must be if CAI is true and nihilism false, then it’s

conceptually possible that there are many-ones. It follows simply from

the definition of a many-one that if we have a case of many-one


identity – Xs=A, say – that A is a many-one, since ex hypothesi

there are more than one of the Xs and they are identical to some one

thing and are hence not a mere many. But the first conjunct of Thesis

should be accepted as well, even by the defender of CAI: it’s concep-

tually possible that there are mere manys. Admitting the coherence of

many-one identity does not commit us to denying the coherence of a

many identical to no one. The orthodox view held by those who

deny many-one identity is that every many is a mere many. It’s

implausible that the defender of CAI can’t make sense of the ortho-

dox view. They know what they are denying when they claim that

there are cases of many-one identity: they are denying that every

many is a mere many. So they had better be able to make sense of

the notion of a mere many.

There’s obviously more that can be said on that last point, and in

section 4 I will consider in more detail the potential objection that the

defender of CAI shouldn’t admit the coherence of mere manys. But for

the moment, let’s assume that they do grant the coherence of this

notion.

If composition is identity, then the theses of universalism, restrictiv-

ism and compositional nihilism can be restated as follows:

UniversalismCAI: Every many is a many-one.

RestrictivismCAI: Some many is a many-one and some many is a

mere many.

NihilismCAI: Every many is a mere many.

My claim is that each of these three theses is compatible with CAI.

Allowing that identity can be many-one simply doesn’t tell us how

ubiquitous cases of many-one identity are. So return to the above

argument that CAI entails universalism. We said: of course whenever

you’ve got some things, the Xs, you’ve got their sum, for their sum

just is the Xs. That’s a mistake: the sum just is the Xs if the Xs are

a many-one, but if the Xs are a mere many then there simply is no

sum. And again, I do not assume that there are any mere manys,

for that would be to beg the question; I simply assume that the

notion of a mere many is coherent. If the coherence of a mere many

is granted, we need to add to the above argument the premise that

there are no mere manys to guarantee the conclusion that every col-

lection composes. But the claim that there are no mere manys is

equivalent to the claim that every many is a many-one, so this

534 ROSS P. CAMERON

would be simply to assume UniversalismCAI, which just begs the

question.8

The moral of the story is that if CAI is true, answering SCQ is sim-

ply tantamount to answering the question of when a plurality of things

is identical to some one thing. Call this latter question the special iden-

tity question (SIQ). I see no reason to think that any of the proposed

answers to SCQ are incoherent as answers to SIQ: we could be organi-

cists, and hold that there’s only a one identical to the many when the

many participate in a life; we could hold that the many is only identical

to some one when they are fastened together; etc. Admitting the coher-

ence of many-one identity simply does not settle SIQ. And while admit-

ting that there are instances of many-one identity rules out

mereological nihilism, it leaves it open whether or not every many is

identical to some one: to say that there are cases of many-one identity

does not settle how ubiquitous it is. And so restrictivism – which, given

CAI, is the doctrine that there are some collections of things identical

to some one thing but some collections of things identical to no one

thing – is not ruled out by CAI. And not only are these rival answers

to SIQ each consistent with CAI, I see no reason to think that SIQ is

an easier question to answer, given CAI, than SCQ is without it. Hence

the debate over when composition occurs is no less intractable given

CAI, giving us one less reason to believe it.

8 What if the CAIist holds not that composition is identity, but simply that composi-

tion and identity are coextensive (either as a matter of necessity or merely as a

matter of fact)? In that case the claim that there are no mere manys isn’t simply

tantamount to the claim that every collection of entities composes some thing; but

it would, I think, still beg the question to assume it. An argument begs the ques-

tion if warrant for the premises presupposes warrant for the conclusion. One way

in which that can be the case is if one of the premises is simply tantamount to the

conclusion, but it’s not the only way. What warrant could one have for thinking

that there are no mere manys independent of warrant for thinking that every col-

lection of entities composes some thing? Given Thesis, it’s coherent that there are

mere manys, so how can we rule out the claim that there are any without relying

on the claim that every collection composes and mere manys don’t compose? I

can’t see how it could be done. I will concede that I am hostage to fortune here,

though. Call the theory that says that while composition is not the same as iden-

tity, there is a correspondence between cases of composition and cases of identity

‘Composition With Identity’ (CWI). If the CAIist is willing to abandon CAI for

CWI, and if she can give an independent reason for denying that there are mere

manys, then I will concede that CWI entails universalism, and that this is a mark

in its favour. But I very much doubt she will be able to do this. I also think that

CWI would be an unattractive theory – worse that CAI: if composition and iden-

tity are not simply one and the same, why is there a correspondence between cases

of composition and cases of identity? Why should we think they go hand in hand

if they’re not one and the same relation? The unattractiveness of CWI would out-

weigh, I think, any advantage gained even if its proponent did manage to non-

question-beggingly argue for universalism.


2. The Merricks-Sider Argument

Here is another argument that CAI entails universalism. The argument

was first put forward, to the best of my knowledge, by Trenton Mer-

ricks9, and is discussed and tentatively endorsed by Ted Sider10, so I’ll

call it the Merricks-Sider argument. Suppose for reductio that CAI is

true and universalism false. Then there is a collection of things, the

Xs, that do not compose. But they could compose. So consider an arbi-

trary world in which they do compose, call it w. CAI, if true, is neces-

sary (it’s a thesis about what composition is, not the thesis that

composition and identity in fact coincide), so it is true in w. So since

the Xs compose in w, there is, in w, some one thing to which the Xs is

identical, call it A. Given the (necessity of the) necessity of identity,

identities that hold in w hold in the actual world.11 So the Xs is

actually identical to A. Which, given CAI, is just to say that the Xs

actually compose A, contrary to our initial assumption. So CAI entails

universalism.

Let’s formalise the Merricks-Sider argument; let ‘P(Xs)’ say that the

Xs have a sum. We have the following premises:

Nec of CAI: h"x1 . . . xn(P(x1 . . . xn)M$x(x= x1 . . . xn))

Nec=: "x1 . . . xn"y1 . . . yn()x1 . . . xn= y1 . . . yn fi hx1 . . .

xn= y1 . . . yn)

Poss Comp: "x1 . . . xn)P(x1 . . . xn)

Nec of CAI says that, necessarily, there is something composed of the

Xs if and only if there is some thing to which the Xs is identical.

Notice that this is weaker than what CAI says: this premise says simply

that there’s a necessary coincidence between cases of composition and

cases of many-one identity – it does not tell us that the thing composed

9 Merricks (2005, p630).10 Sider (2007).11 Provided the entity exists in the actual world, of course. I used to think this was

the way to resist this argument. (See Cameron (2007), p104-6.) The thought was,

the argument told us just that the Xs is actually identical to A if A exists, but that

whether A exists is exactly what is up for debate. I now think this is wrong. If

A=B is a possibly true identity, to know that it holds at a world w we just need to

know that either A or B exists at w. For suppose A=B at a world w but that there

is a world at which the identity fails because, say, A exists but not B. Then at w A

has a property B lacks: the property of being able to exist without B existing.

Hence, by Leibniz’s law, A and B cannot be identical in w after all. So since in our

case we know ex hypothesi that the Xs actually exist, the possible identity of A

and the Xs forces us to accept the actual identity of A and the Xs.

536 ROSS P. CAMERON

is the one to which the composing many is identical. There are various

ways we could cash out the stronger claim intended by CAI theorists:

that what it is for the Xs to compose some thing is for them to be iden-

tical to some one thing; that saying that the Xs compose some thing

means the same as saying that there is some one thing identical to

them; that the truth of <there is something composed of the Xs>

obtains in virtue of the truth of <there is some one thing identical to

the Xs>; etc. I don’t want to take a stand on how exactly CAI should

be formulated: suffice it to say, on any of these understandings of CAI,

CAI entails that composition occurs iff there is some one identical to

the many, and that’s the claim of CAI that is doing the work in the

Merricks-Sider argument. None of the extra claims allow us to patch

what I will argue is the flaw in the Merricks-Sider argument; so there is

no understanding of CAI that entails universalism.12

Nec= is the necessity of the necessity of identity generalised to

collections of things: it says that if there’s a possibly true identity

fact – be it many-many, many-one, or one-one – then that identity is

necessary. The familiar principle of the necessity of identity follows

from this: just let the Xs have one member, a, and the Ys have one

member, b. Since a=b entails )a=b we can substitute the former for

the occurrence of the latter in the resulting instance of Nec of Identity

to get (a=b) fi (ha=b). And Poss Comp simply says that for any

collection of things, it’s possible that there exist some thing that is

their sum.

The Merricks-Sider argument then goes as follows:

1) $x1 . . . xn(�P(x1 . . . xn)) [Ass]

2) �P(a1 . . . an) [From 1, $E]

3) "x1 . . . xn)P(x1 . . . xn) [Poss Comp]

12 Okay, that’s too strong. Obviously if by CAI one simply meant the doctrine that

for any collection of things there is some one to which those things are identical,

and that that one thing is the sum of the many things, this doctrine entails univer-

salism. But by making it analytic of CAI that for any many there’s a one to which

the many are identical, this doctrine has simply built in universalism from the start,

so the question simply becomes: why hold this view? And the problem with this

view is that it is not motivated simply by the thought that composition is identity:

that motivates only the weaker claims, since they also hold that composition is

identity, they just apparently leave it open that identity is less ubiquitous. Arguing

that one should accept this view because it settles SCQ would be no better than

arguing that one should accept universalism because it settles SCQ. True in each

case; but if we don’t have independent reason for holding the doctrine, we can’t

claim to have advanced the debate.


4) )P(a1 . . . an) [From 3, "E]

5) h"x1 . . . xn(P(x1 . . . xn)M$x(x= x1 . . . xn)) [Nec of CAI]

6) h(P(a1 . . . an)M$x(x= a1 . . . an)) [From 5, "E]

7) )$x(x=a1 . . . an) [From 4,6, ME]

8) )(A=a1 . . . an) [From 7, $E]

9) "x1 . . . xn"y1 . . . yn()x1 . . . xn= y1 . . . yn fi hx1 . . . xn=

y1 . . . yn) [Nec=]

10) )(A=a1 . . . an) fi h(A=a1 . . . an) [From 9, "E]

11) h(A=a1 . . . an) [From 8,10 fi E]

12) A=a1 . . . an [From 11, hE]

13) $x(x= a1 . . . an) [From 12, $I]

14) P(a1 . . . an)M$x(x= a1 . . . an) [From 5, hE,"E]

15) P(a1 . . . an) [From 13,14 ME]

16) ^ [From 2,15]

17) �$x1 . . . xn(�P(x1 . . . xn)) [From 1,16]

Every line up until (16) rests on the assumption at (1). (17) rests on no

assumptions and says that there’s no collection of things such that

there’s no thing that is their sum: that is, that for every collection of

things, there’s some thing that is the sum of those things. That is uni-

versalism; so one who denies the entailment from CAI to universalism

had better say either where this argument goes wrong or which of the

three premises she rejects.

One might quibble with Poss Comp – the assumption that any col-

lection of objects which don’t compose could compose. Kris McDaniel13

argues that CAI obviously doesn’t entail universalism, since one who

believes that mereological nihilism is a necessary truth and who holds

that necessarily coextensive properties and relations are identical

13 McDaniel (2010).

538 ROSS P. CAMERON

thereby holds that composition is identity.14 He is right; and obviously

the believer in the necessity of mereological nihilism will resist the

above argument by denying (at least) the premise that composition

could occur even if it in fact does not. But even so, it would still be

interesting, and a mark in favour of CAI, if it settled SCQ in favour of

the disjunction of universalism or nihilism.15 The incompatibility of

CAI and restrictivism would still be big news; and the premise that any

collection of things could compose, while certainly not mandated by

acceptance of restrictivism, at least doesn’t look ridiculous given it.

(The thought being, just vary the conditions of the world so the Xs are

in the right conditions to compose. If they need to be in contact to

compose, move them closer together, etc.16)

3. The Merricks-Sider Argument Refuted

But CAI and restrictivism are perfectly compatible. Even granting that

any collection of objects could compose, the above argument fails. The

bad step is from ‘the Xs is actually identical to A’ to ‘the Xs actually

compose A’. CAI says that for a collection of objects to compose is for

them to be identical to some one thing, so it only follows that the Xs

actually compose if A is actually a one to which the Xs is identical.

But all we know is that A is possibly a one; we have no right to assume

that it actually is.

Remember Thesis: both mere manys and many-ones are conceptu-

ally coherent. We know that the Xs compose in some world, so we

know that they could be a many-one. A is the possible individual that,

in that other world, is that many-one, and the necessity of identity

tells us that A actually exists and is actually identical to the Xs. But

nothing tells us that A is actually a many-one; A might actually be a

14 Mereological nihilism being equivalent to the doctrine that the Xs compose A iff

there’s exactly one of the Xs, and it is A.15 One might, for example, think that if these are the only possible answers then we

have strong reason to accept universalism, given the Moorean truth that, e.g., I

exist and have more than one part. I myself am not sympathetic to such a style of

argument, but one can see at least how ruling out restrictivism could be useful in

answering SCQ given one’s background beliefs.16 Even then, whether this is plausible depends on what kind of restricted composition

you hold. If you think contact between the Xs is what’s needed for them to com-

pose, then it’s not implausible that any collection of things (any collection of mate-

rial things, in any case: and universalism restricted to material objects would still

be an interesting consequence of CAI) could be in contact and hence compose; if,

on the other hand, you think that what’s necessary is that the Xs participate in a

life (as does Van Inwagen (1990)), it’s a lot less obvious that any collection of

objects could so do. But I won’t quibble over this premise; as we will see, the argu-

ment fails even granting it.


mere-many, in which case, by Leibniz’s law, the Xs are actually a mere

many, in which case they don’t actually compose.

Let’s unpack this response. Given CAI, restrictivism is precisely the

view that some manys are mere manys but that some are many-ones.

In being asked to assume that some collection of objects which don’t

compose could compose, then, the restrictivist is being asked to assume

the following:

(1) Some mere many might have been a many-one.

That is, in going along with the assumption Poss Comp, the restrictivist

is allowing that some collection of things’ being a mere many and not

a many-one is not essential to that collection of things. Given this,

there seems to be no reason for them to deny the following:

(2) Some many-one might have been a mere many.

If some many that is identical to no one thing might have been identi-

cal to some one thing, couldn’t some many that actually is identical to

some one thing have been identical to no one thing? If being a mere

many is contingent to a plurality, wouldn’t being a many-one be like-

wise contingent?

But if (2) is true, so is (3):

(3) Some one thing might have been a mere many.

(3) says that there are individuals that might not have been individuals;

that is, there are individuals that might have been a mere plurality of

things, identical to no one thing. (3) follows from (2) by Leibniz’s law.

When we’ve got a many-one, the many is the one; so if the many that

is in fact identical to some one thing might have been a many that is

identical to no one thing, so might the individual that is in fact identi-

cal to some one thing (itself) have been a mere many, identical to no

one thing.

(3) does not say that an individual might not have been identical to

itself, at least not in any objectionable manner. If many-one identity

makes sense, then there can be cases of trans-world identity that are

many-one. (Trans-world identity is, after all, identity.) Allowing the

truth of (1) is to allow that while some many isn’t actually identical to

any one thing, it is trans-world identical to some one thing in some

other world. Likewise, (3) says that some individual is trans-world

identical to some plurality of things that is not, in this new world, iden-

tical to any one thing in that world. The only sense then in which (3)

540 ROSS P. CAMERON

says that an individual might not have been identical to itself is that it

might be inappropriate to speak of a mere many as ‘itself’. (3) is per-

fectly compatible with the necessity of self-identity. Saying that some

individual A might have been a mere many is compatible with saying

that A is necessarily identical to A: it’s just that in some worlds ‘A’

refers to a one – an individual – and in some worlds it plurally refers

to a mere many – a many that is identical to no one. And of course,

this does not mean that ‘A’ is not a rigid designator. For ‘A’ to be a

rigid designator just requires that whenever ‘A’ refers in two worlds w

and v, what ‘A’ refers to in w is trans-world identical to what ‘A’ refers

to in v. If there can be cases of many-one trans-world identity, then,

this is compatible with ‘A’ plurally referring to a mere many in w and

singularly referring to an individual in v.

So to recap, given the truth of (1) – which our hypothetical defender

of CAI and restrictivism is being asked to accept by the proponent of

the above attempted reductio of that conjunction, since (1) follows

from Poss Comp and the assumption that there are some objects that

don’t compose – there is no reason for our hypothetical defender to

rule out (3). But if the possibility of (3) is allowed then that reductio is

unsound. For if there are individuals that might have been mere

manys, perhaps this is the status A has in w. Ex hypothesi, A is the

possible individual that is identical to the many Xs in the (arbitrarily

chosen) possible situation in which the Xs happen to compose. The

necessity of identity tells us that A is also identical to the Xs in the

actual world. But it only follows that the Xs actually compose – thus

we only get our reductio – if A is actually a one. If on the other hand

A in w is a one that might have been a mere many – as is allowed if

we grant (3) – then we’ve got no reason to suppose that A isn’t actually

a mere many. Hence, we’ve got no reason to suppose that the Xs

(being identical to A) aren’t actually a mere many. Hence we’ve got no

reason to suppose that there’s actually a one to which the Xs is identi-

cal, and hence no reason to suppose that the Xs actually compose some

thing.

To guarantee that the Xs actually compose we have to insist that A

is essentially an individual; i.e. that A is essentially not a mere many.

But why should this be? If we grant (1) – that a mere many might have

been identical to some individual – why should we not grant (3) – that

an individual might have been a mere many? And if we don’t grant (1)

we should resist the above argument as soon as it says some collection

of objects which don’t compose could compose. So either we should

reject one of the premises of the attempted reductio – Poss Comp – or

we should grant that it proves that the Xs are actually identical to A

but deny that this proves that there is actually a one to which the Xs is


identical. Either way, then, we shouldn’t accept that the Merricks-Sider

argument shows that the combination of restrictivism and CAI is ruled

out.

Normally, of course, the essentiality of individuality – that no one

thing could have been a mere collection of things; i.e. that every indi-

vidual is essentially an individual: essentially identical to some one

thing – is an extremely attractive principle. But my claim is that accep-

tance of CAI opens up room to doubt this principle: room for doubt

that is lacking if we don’t accept the coherence of many-one identity.

Suppose, as we normally think, that it’s of the essence of the identity

relation that it is a one-one relation. Then trans-world identity is a

one-one relation. (Trans-world identity is identity.17) So any one thing

A in any world w can only bear the relation of trans-world identity to

some one thing in any other world v: so A is essentially an individual

(given that a property is essential to A iff, at every world w, if A is

trans-world identical to some thing in w, that thing has that property).

But once we accept CAI and allow for cases of many-one identity, we

also thereby allow for cases of many-one trans-world identity. (Again,

trans-world identity is identity.) So just as within a world, A can be

identical to the Xs, so can A in world w be trans-world identical to the

Xs in world v. If the Xs in v are a mere many then A is, in w, an indi-

vidual that might not have been an individual, and the Xs are, in v, a

mere many that might have been an individual.18 So whilst the logic of

identity entails the essentiality of individuality if identity is one-one, the

defender of CAI has no such reason to accept the essentiality of indi-

viduality. They would need to provide us with such a reason, then; and

moreover, they would need to provide us with a reason for the essenti-

ality of individuality which did not undercut the case for Poss Comp. It

is this that I think cannot be done. Poss Comp should only be accepted

by the restrictivist if they deny the essentiality of non-individuality: the

17 There are views on which trans-world identity is not identity, of course, but some-

thing weaker, like counterparthood. But we can legitimately ignore such views for

present purposes: if one accepts counterpart theory one can resist the Merricks-

Sider argument simply by denying the necessity of identity.18 Assuming for the sake of argument that the accessibility relation between worlds is

symmetric. One possible route for breaking the symmetry between the two essen-

tialist claims – the essentiality of individuality and the essentiality of non-individu-

ality – would be if you held that the accessibility relation between worlds was not

symmetric. But this move is not going to help the proponent of the Merricks-Sider

argument, since the move from the possible identity of A and the Xs to the actual

identity of A and the Xs via the necessity of identity relies on the symmetry of the

accessibility relation. Without symmetry, it might be necessary in the possible world

w that A=Xs, but not actually true that A=Xs, because the actual world is not

possible relative to w, even though w is, ex hypothesi, possible relative to the actual

world.

542 ROSS P. CAMERON

claim that a mere many couldn’t have been an individual. Perhaps both

essentialist claims are true, perhaps they are both false: my claim is

simply that they should stand or fall together. If one accepts Poss

Comp then one should (if one has restrictivist sympathies, at least)

abandon the essentiality of non-individuality and hence abandon the

essentiality of individuality, in which case the argument doesn’t succeed

in establishing its conclusion. On the other hand, if one accepts both

essentialist theses then one should deny Poss Comp (at least if one has

restrictivist sympathies) and hence the argument has a false premise.

Either way, the argument should not convince the restrictivist to aban-

don their position.

To return then to the formalised argument, the point at which it

goes wrong, given the above, is either the move from step (12) to (13)

or in the statement of Nec of CAI. At step (12) we have established the

truth of the identity claim A=a1 . . . an. At (13) we existentially gener-

alise and conclude $x(x= a1 . . . an); this is the right hand side of an

instance of the embedded biconditional in Nec of CAI, thus allowing

us to infer the left hand side of that instance, which is P(a1 . . . an),

which is what we need for our reductio.

Given what’s been said above, we need to make a decision about

how to use the existential quantifier. Does ‘$x(F)’ mean that there is at

least one individual – some one thing – that satisfies the open sentence

F, or does it mean that there is some thing or are some things that

satisfy F? This is simply a matter of how we choose to use it. If we

choose the former, then the step from (12) to (13) is unsound. All we

have proven is the truth of the identity A= a1 . . . an. But given what

was said above, ‘A’ might actually not name any individual but merely

actually plurally refer to a collection of things. In that case, one cannot

existentially generalise on A, given that the existential quantifier is to

mean ‘there is some individual such that . . .’. On the other hand, we

can choose to use the existential quantifier so that it is blind as to

whether terms refer singularly or plurally. In that case we can conclude

$x(x= a1 . . . an) from A= a1 . . . an, but all the former says is that

there is some thing or there are some things identical to a1 . . . an.

Composition is when the many is identical to some one, so this should

not let us conclude P(a1 . . . an). So if we have this liberal understand-

ing of the existential quantifier then we were too loose in our statement

of Nec of CAI. CAI, as this premise states it, entails P(a1 . . .

an)M$x(x= a1 . . . an). But this is a bad formulation of this commit-

ment of CAI if we’re using the liberal quantifier: it says that composi-

tion occurs if there is some thing or there are some things identical to

the many. This ignores the thought that composition is a many-one

relation: to capture this thought we must either introduce a special


quantifier ‘$ ’ which does mean ‘there is an individual such that . . .’ or

introduce a predicate ‘I(x1 . . . xn)’ that x1 . . . xn only satisfy if there is

some individual which is identical to x1 . . . xn. Then Nec of CAI

should be replaced with one of the following:

Nec of CAI*: h"x1 . . . xn(P(x1 . . . xn)M$x(x= x1 . . . xn))

Nec of CAI›: h"x1 . . . xn(P(x1 . . . xn)MI(x1 . . . xn))

But of course, if Nec of CAI is thus replaced we won’t be able to derive

step (15) from (13) and the resulting claim at step (14). In addition to

(13) we’d need the claim I(a1 . . . an), or $x(x=a1 . . . an). But, of

course, what those claims say is that there’s some one thing identical to

a1 . . . an, which is exactly what is up for debate, and so this can’t be

simply assumed without begging the question. We can conclude that

both those claims are possible, given Poss Comp, and so would be able

to derive them if we added the premise "x1 . . . xn[)I(x1 . . .

xn) fi h($x(x= x1 . . . xn) fi I(x1 . . . xn))] or "x1 . . . xn[)$x(x= x1 . .

. xn) fi h($x(x= x1 . . . xn) fi $x(x=x1 . . . xn))]. But what these

claims both say is that possible individuals are essentially individuals:

that is, that if a thing A is an individual in some world then, in any

world w, if there is some thing or are some things in w identical to A,

then there is some one thing (an individual) in w identical to A. And as

I said above, it’s hard to see why we should accept this whilst also

accepting Poss Comp. If individuality is essential to every possible many

that is identical to some one, why is non-individuality not essential to

those possible collections of things that are not identical to some one?

And of course, there are versions of the necessity of identity that

would simply build in the required essentialist claim. The argument

would work if we replaced Nec= with a principle that said that if it’s

possible that there be a many-one identity between the Xs and A then

it’s necessary that there’s a many-one identity between the Xs and A: that

is, the necessity of identity itself forces the individuality of A in the

worlds in which A is identical to the Xs. The argument will then be valid,

but of course I would reject this version of the necessity of identity.

Think about the argument for the necessity of identity in the case

where identity is always one-one. Suppose a=b. a has the property

being necessarily self-identical, so necessarily a is identical to itself, so

since it is a it has the property being necessarily identical to a. So by

Leibniz’s law, b also has the property being necessarily identical to a.

Hence, necessarily, a=b. Now run through this with a many-one iden-

tity a=Xs. Should we now accept the claim that a has the property

being necessarily self-identical. Yes, if all that means is that in every

544 ROSS P. CAMERON

world in which there is some thing or are some things trans-world iden-

tical to a that that thing or those things are self-identical in that world;

but no if it means that a is necessarily identical to an individual that is

itself, for that begs the question that a is essentially an individual. But

if we run through the argument with the acceptable version, the only

conclusion we will get out is that the Xs have the property being neces-

sarily identical to some thing or some things that are A. There’s going to

be no argument for the version of the necessity of identity that gives us

what is needed without simply building in the essentiality of individual-

ity from the start.

So to sum up, there are many ways in which one could plug the

Merricks-Sider argument to get the desired conclusion, but they all

smuggle in the premise, somewhere or other, that possible individuals

are essential individuals: a premise one shouldn’t accept if one accepts

the other necessary premise Poss Comp – since this entails, together

with the assumption of restrictivism, that non-individuals might have

been individuals.

4. Objection: Distinguishing Between the Many and the One isIllegitimate

The defender of the entailment from CAI to universalism might object

to my insistence of treating individuals differently from pluralities. In

diagnosing where the argument went wrong I distinguished between

two ways of understanding the existential quantifier: as saying that

some one thing satisfies the open sentence or as saying that some one

thing or some things satisfy it; I distinguished two versions of the

necessity of identity, one which says that if the Xs are possibly identical

to an individual A then they are necessarily identical to some one thing

that is A and another which says that they are necessarily identical to

some one thing that is A or some things that is A. But, the defender of

the entailment might object, such distinctions are inappropriate given

CAI, since according to CAI there is simply no distinction between the

many and the one: the one just is the many counted as an individual

instead of as a plurality. Any ideology that allows us to make the

distinction I want to make, she might object, is suspect by the CAI

theorist’s lights. According to this objection Thesis is false: mere manys

are not coherent because to make sense of a mere many we need to make

sense of a many not being a one, and there is, according to this objection,

no sensible distinction to be made between the many and the one.

Similarly, I granted that the Merricks-Sider argument establishes the

truth of A= a1 . . . an; but, I said, this doesn’t establish that a1 . . . ancompose anything because composition is when the many is identical

to the one, and we don’t know that ‘A’ singularly refers to a one or


whether it merely plurally refers to a many that is identical to no one.

But again, the defender of the entailment might object that this is to

make a distinction that the believer in composition as identity should

be blind to. CAI doesn’t say that composition is many-one identity, it

says that composition is identity, simpliciter. So all we need to know in

order to know that the Xs compose is that there’s a true identity claim

with the Xs on one side of the identity. We don’t need to know any

more: to insist on more is to deny that composition is identity and to

insist that composition is identity under certain conditions, but this

isn’t what CAI says: it says just that composition and identity are one

and the same relation.

But I don’t think the CAI theorist should hold that all cases of iden-

tity are cases of composition; and if she does, I think she loses what is

metaphysically interesting about her theory. Our notion of composition

is of many things coming together to make one thing. If the CAI theo-

rist doesn’t allow us ideology enough to say this, then I don’t see why

we should grant that they mean what we do by ‘composition’ (and so

of course I’m not going to be persuaded to accept their theory on the

grounds that it settles SCQ, if they mean something different by the

‘C’). Of course there will be cases of many-many identity that are cases

of composition if CAI is true. To take the example from the beginning

of the paper, if A is the sum of the Xs and B the sum of the Ys, then

the sum of A and B, if there is one, is A,B. And A,B= x1, x2, . . . xn,

y1, y2, . . . yn. And of course, this many-many identity is a case of com-

position: the Xs and the Ys compose A,B. But I’m only happy to say

that because I know, ex hypothesi, that there is a one to which A,B is

identical. Even in the cases of many-many identity, it needs to be the

case that at least one of those manys is a many-one in order for this to

be a case of some many composing something. For composition to be

going on, it must be that there’s some one thing being composed; so if

composition is identity, for composition to be going on it must be that

some one thing features in a true identity claim: identities between some

many, the Xs, and some many, the Ys, can be cases of composition,

but only if there’s a one to which the Xs or the Ys is identical.

Furthermore, even if we allow that all that it takes for the Xs to

compose is for there to be a true identity claim with ‘the Xs’ on one

side, no matter what is on the other side (be it a plurally referring

expression or a singular term) then I think we should simply insist that

universalism can no longer be stated simply as the doctrine that every

collection of things compose. The interesting thesis is that for any

collection of things there is some individual that has exactly those things

as parts: that is, given CAI, that for any collection of things there is

some one thing which is identical to them. Call that thesis universalism

546 ROSS P. CAMERON

or don’t, but it is this claim that I think would be the interesting entail-

ment of CAI. But this claim is not entailed by CAI, as we have seen.

Let me elaborate on this last point. Suppose we start with the mere-

ological nihilist’s ontology: reality is one of simple entities lacking

proper parts. Now there’s a question of how to describe that reality.

We allow ourselves names for the individual atoms and also plural

names (like ‘The Beatles’) for pluralities of those atoms. We allow one-

one identities, such that ‘a=b’ is true iff ‘a’ and ‘b’ name the same

atoms, and we allow many-many identities such that ‘Xs=Ys’ is true iff

every one of the Xs is a Y and vice-versa. We have an existential quan-

tifier that can quantify over both atoms and pluralities of atoms, so that

$x(F) is true iff either some atom satisfies F or some plurality of atoms

collectively satisfy F. Our rules governing this existential quantifier

allow us to infer a=a for any singular term ‘a’ and Xs=Xs for any plu-

rally referring term ‘the Xs’. We then say that the term ‘composition’

picks out the relation of identity, and so since we can plurally refer to

any collection of atoms with ‘the Xs’, and infer as a result Xs=Xs, we

can now say that every collection of atoms composes.

Well, that theorist might talk the CAI-ist talk, but it’s clear that they

have the mereological nihilist’s ontology, and that everything else is

just a way of talking. But CAI is not meant to be mereological nihilism

with some fancy talk, it’s meant to be a radical ontological thesis. It

seems to me that what distinguishes CAI as an interesting ontological

thesis from the above nihilist theory is their additional claim that not

only is everything identical to itself and that every collection of things

is identical to that collection of things, but that there are collections of

things identical to some one thing. That is, it is the postulation of

many-one identity that makes CAI interesting – that distinguishes it

from mereological nihilism with some fancy talk. If the composition as

identity theorist doesn’t allow me the resources to distinguish between

the many and the one then they lose what seems to me metaphysically

interesting about their thesis – I have no way of distinguishing them

from the fancy talking nihilist!

And once I’m allowed the resources to distinguish between the many

and the one then even if the CAI theorist says that any case of identity

is a case of composition (rather than just those cases of identity that

are many-one), I can still ask after what seem to me to be the interest-

ing cases of composition: those cases when the many compose some

one; I can still ask what we can call the Very Special Composition

Question (VSCQ): under what conditions do the many compose some

one thing. The CAI theorist can choose to play funny business with the

term ‘composition’ if she likes, and thus ‘settle’ SCQ trivially, but the

interesting metaphysical question, VSCQ, is left unsettled.


5. On Being Nothing Over and Above One’s Parts

I responded to the Merricks-Sider argument by distinguishing between

the Xs being a mere many and the Xs being a many-one. Such a dis-

tinction also lets us respond to another argument that Ted Sider offers.

(Sider thanks Karen Bennett when he offers this argument, so I’ll call

it the Bennett-Sider argument.)

Unless composition is unrestricted, it is in general an open

question whether some Xs compose something. But then in

cases where some Xs do compose something, the composed

object seems to be something ‘‘over and above’’ the Xs. For it

is an open question whether the object exists given that the Xs

do, whereas it is not an open question whether the Xs exist

given that the Xs do. Finally, opposition to unrestricted com-

position — distrust of scattered objects and the like — is

undermined by the idea that the whole is ‘‘nothing over and

above the parts’’.19

There are two distinct thoughts here: the first might be taken as an

argument that CAI entails universalism, the second is an argument that

if you accept CAI you should accept universalism (even if CAI doesn’t

entail universalism). I’ll discuss these two thoughts in turn.

We can extract the following argument from the first part of the

Bennett-Sider thought.

1) If composition is restricted, then it is an open question whether

there is a sum of the Xs, given that the Xs exist.

2) It is not an open question whether the Xs exist, given that the

Xs exist.

3) If it is an open question whether there is a sum of the Xs, given

that the Xs exist, but it is not an open question whether the Xs

exist, given that the Xs exist, then the sum of the Xs, if there is

one, is something over and above the Xs.

4) So, if composition is restricted, then the sum of the Xs is some-

thing over and above its parts. (from 1, 2, 3)

5) But, if CAI is true, then the sum of the Xs, if there is such a

thing, is not something over and above its parts.

19 Sider (2007, p72–73).

548 ROSS P. CAMERON

6) So, If CAI is true, then composition is not restricted. (from 4, 5)

Premises (1), (2) and (5), I am perfectly happy to accept. On any sensi-

ble understanding of ‘___ is something over and above ___’, surely

nothing is something over and above itself; so since CAI says that sums

are identical to their parts, no sum is something over and above its

parts, which gives us (5). Premise (2) is obvious: it’s never an open

question whether p, given p. And (1) seems utterly innocuous: if com-

position is restricted, we need to know whether the conditions for com-

position are met to know whether composition occurs. The conditions

for the Xs to compose can’t simply be the existence of the Xs, for that

would be universalism not restrictivism, so it must be an open question

whether the Xs compose if all we’re given is that the Xs exist. So the

only point of resistance to this argument, since it is valid, is premise

(3). Thankfully, I think we have a good reason to reject (3).

We need to distinguish between the claim that something more needs

to happen for the Xs to compose and the claim that if the Xs compose,

the thing they compose is something over and above the Xs. What is

acceptable is not (3) but (3*):

(3*) If it is an open question whether there is a sum of the Xs,

given that the Xs exist, but it is not an open question whether

the Xs exist, given that the Xs exist, then something more needs

to happen for the sum of the Xs to exist than that the Xs exist.

If composition is restricted and the Xs fail to compose, then there’s a

difference between our world and a world in which the Xs do compose.

Something else needs to happen for them to compose. But it doesn’t

thereby follow that if that something else happens, the complex object

that thereby exists is a new entity. It’s not: it’s identical to the Xs and

hence is nothing over and above them.

Of course, the defender of CAI is likely to insist that they think that

nothing more does need to happen for there to be a sum of the Xs than

that there be the Xs. Well, they can claim that, but they do not get to

simply stipulate it! I have an argument that something more needs to

happen: there needs to be a one to which the Xs is identical. Given

Thesis, I think I can make sense of there being no such one to which

the Xs is identical, and I’ve seen no convincing argument to the effect

that there being such a one is guaranteed simply by the existence of the

Xs, so I think it’s appropriate for me to continue to believe that there

being such a one is a further requirement on the world. But were there

such a one, it wouldn’t be anything over and above the Xs, of course,

precisely because the Xs would be identical to it.


Considering the temporal case might help. Whilst nothing I’ve said

above entails this, it’s natural to think, given Thesis and what I’ve said

above, that the Xs can fail to compose at a time t but come to com-

pose something at a later time t*.20 So something more needs to be the

case at t* than was the case at t. What has changed? A mere many has

become a many-one. That’s all that’s changed. Nothing exists at t* that

didn’t exist at t.21 A complex object exists at t* and no complex object

exists at t, of course, but it’s not true that a complex object exists at t*

that didn’t exist at t. The complex object that exists at t* did exist at t:

it just wasn’t a complex object at t, it was a mere many. The many-one

that exists at t* is diachronically identical to the mere many that exists

at t. Nothing new has come into being, and nothing exists at t* over

and above what exists at t. What’s going on is simply that the Xs are

fundamentally different at the two times: at t the Xs are a mere many

and at t* they are a many-one.

Think of the view as follows: there is a fundamental property of

being an individual that can be had by a collection of things, but need

not be (at least, it’s conceptually possible that it not be had by some

collection of things). For a collection of things to have this property is

for them to be a many-one; for a collection to lack it is for them to be

a mere many. The more that has to happen for the Xs to compose is for

the Xs to have this fundamental property. God has to do more to

make the Xs compose than to make the Xs: He must make the Xs have

this property: He must grant them individuality! If God gives the Xs

this property He thereby ensures that there is an individual that has

20 This possibility would be ruled out by a temporal version of the Merricks-Sider

argument, were the original successful. On the face of it, one can argue that if CAI

is true then any collection of entities that ever compose always compose (provided

they are still around). For suppose the Xs composed A in the past. Then Xs=A

was true, so by the eternality of identity, Xs=A is always true, so the Xs always

compose A. Now of course, this temporal analogue of the Merricks-Sider argument

isn’t going to get you universalism, since the temporal analogue of Poss Comp –

namely, that any collection of entities compose at some time or other – is certainly

not something the restrictivist can be forced to accept. Nonetheless, the claim that

if some things ever compose then they never exist and don’t compose would still be

an interesting consequences of CAI. But as should be obvious, I don’t think even

this follows. If there can be many-one identity facts, then there can be many-one

diachronic identities. ‘A’ and ‘The Xs’ might presently both refer to a mere many

which is diachronically identical to the many-one that ‘A’ and ‘The Xs’ did refer

to. Without the premise that individuality cannot be temporary – that is, the pre-

mise that if there’s a time at which there’s some individual identical to A then, at

all times t, if there are some things identical to A at t then there is some one thing

identical to A at t – this argument will fail for analogous reasons as the modal

version.21 Assume, for ease of presentation, that the only change that took place is what’s

necessitated by the Xs having come to compose.

550 ROSS P. CAMERON

this property. But it simply doesn’t follow that He’s brought some new

thing into being: the individual is identical to the collection that existed

before and lacked the property. It’s just that these things are funda-

mentally a different way: they are now an individual whereas they wer-

en’t before.22

The second thought extractable from the Bennett-Sider passage is

that if CAI is true then, even if universalism is not entailed, it is war-

ranted: that is, that while CAI might not settle SCQ in favour of uni-

versalism (in the sense of entailing that answer), if CAI is true,

universalism is the answer we have reason to accept. Were this thought

right then this might still provide us with sufficient reason to accept

CAI: even though the case for universalism is now fallible, we still

might think we’re given more traction on SCQ than we are without

CAI.

The reasoning seems to be this: that the only reason to object to uni-

versalism is the intuition against such ontological exotica as the sum of

Hitler’s left ear, Scotland, and an atom in the sun. But, so the thought

goes, if this sum is identical to Hitler’s left ear, Scotland, an atom in

the sun, then – since we’re happy with the existence of each of the lat-

ter – we should also be happy with the sum as well.

I don’t think this second thought survives the dissolution of the first.

Once we allow that it can take more for there to be a sum of the Xs

than for there to be the Xs, namely that there be some one thing to

which the Xs is identical, it’s not clear why intuitions against the exis-

tence of these exotic sums shouldn’t translate into intuitions against

there being some one to which those manys are identical. That is, if

you find the existence of the sum of Hitler’s left ear, Scotland and an

atom in the sun counterintuitive, shouldn’t you let this count against

the claim that there is some one thing identical to Hitler’s left ear,

Scotland, an atom in the sun, if CAI is true, to just the same extent as

you would let it count against the claim that those object compose, if

CAI is false?

22 An analogy may help. Some people think mental properties like being conscious are

fundamental. If that is so, then God has to do more to make some organism con-

scious than to make the organism. It’s an open question, then, whether or not an

organism A is conscious given that A exists. But it’s not an open question whether

or not an organism A exists, given that A exists. So we can conclude that some-

thing more has to happen for A to be conscious than that it exists. What has to

happen? A has to have the fundamental property being conscious. It obviously

doesn’t follow, however, that were God to make A conscious He brings something

new into existence. That might be the case, but it doesn’t follow. All that follows is

that A is fundamentally different from how it would be were it to exist and not be

conscious. The case with a mere many becoming a many-one is exactly analogous,

so far as I can see.


So intuitions against universalism seem to me to still hold some

weight if CAI is true, assuming they do if it is false. Certainly, univer-

salism doesn’t bring an additional ontological commitment over restric-

tivism if CAI is true, since the ‘extra’ entities are not really extra

entities at all, but things we already had; but it does bring an addi-

tional metaphysical commitment: we must believe in more many-one

identity facts. And it seems to me that all the usual moves made with

respect to SCQ on the assumption that CAI is false can still be made if

CAI is true: CAI-universalists can claim to have the simplest and least

arbitrary theory, CAI-restrictivists can complain about the unintuitive-

ness of there being some one identical to Hitler’s left ear, Scotland, an

atom in the sun, etc, etc. Adopting CAI just doesn’t seem to me to

advance this debate.

6. Identity and Existence

I responded to the Bennett-Sider argument by arguing that although a

complex object is nothing over and above its parts, given CAI, there

being a complex object does indeed demand something of the world over

the existence of the parts. There is a conceptual gap between the

existence of the Xs and the existence of there being a sum of the Xs, and

this is enough to make intuitions against universalism not incoherent.

But this conceptual gap can be used to form an objection to CAI.

Jason Turner argues that if CAI is true, the existence facts don’t settle

the identity facts; but it’s a conceptual truth about existence and iden-

tity that the existence facts do settle the identity facts, so CAI is a con-

ceptual falsehood.23

The sense of ‘settle’ here is tricky, since the CAI theorist, even if she

is my theorist who both accepts CAI and denies universalism, can hold

that the facts about what there is necessitate the facts about what is

identical to what. Turner’s thought is rather that the existence facts

must apriori entail the identity facts, and that CAI invalidates this.

Suppose CAI is false. If God tells you that each of a1 . . . an all exist

and that nothing exists other than a1 . . . an, then this apriori entails all

the identity facts: there is no room for doubt about what is identical to

what once you know that this is all that there is. The existence facts

settle the identity facts in that the former apriori entail the latter. And

if God tells you that exactly one thing other than a1 . . . an exists, call

it b, this still settles all the identity facts: you know b is distinct from

each of a1 . . . an and identical to b. And this, you might think, must

be the case: the existence facts must apriori entail the identity facts. But

23 Turner (ms.).

552 ROSS P. CAMERON

if what I’ve said is right then, if CAI is true, it is not the case. God can

tell you that each of a1 . . . an all exist and that there is exactly one

thing, b, that is not identical to any one of a1 . . . an. The existence

facts are now settled, but the identity facts are not: there is room for

conceptual doubt as to what is identical to what. Of course each of b=

ax is false; but what about b= a1,a2 or b= a3,a4? We have no idea.

Perhaps b is identical to some subplurality of a1 . . . an, perhaps not.

We just don’t know, and even if we knew it was so identical, we

wouldn’t know to which subplurality it was identical. The existence

facts are settled, the identity facts not, in that the latter are not apriori

entailed by the former. God must decree identity facts in addition to

decreeing existence facts; the fact that CAI makes this a conceptual

possibility, one might think, is a reason to be suspicious of it.

Here’s the objection put another way. As I said above, if CAI is true

then SCQ simply becomes SIQ: when composition occurs is reduced to

when manys are identical to ones. One way of hearing Turner’s com-

plaint is that there simply shouldn’t be a special identity question! Once

the question concerning what there is is settled, there should simply not

be a question remaining concerning what is identical to what. If CAI is

true then there is; so there’s a problem with CAI.

7. Conclusion

Composition as identity, I have argued, is compatible with restricted

composition as well as universalism. CAI does not settle SCQ in that

the rival answers to SCQ on the assumption that CAI is false are still

rival answers on the assumption that it is true; furthermore, it’s not

clear that any one of the potential answers to SCQ is even more war-

ranted given CAI than not. If CAI is true, SCQ is simply reduced to

SIQ: under what conditions is there a one identical to some many?

And all the answers to SCQ are still on the table for SIQ. And so

whether or not we adopt CAI does not make the question as to when

composition occurs more tractable: it just replaces it with the seemingly

equally intractable question of when many-one identities occur. Thus

what may have seemed like a potential benefit of CAI – its resolution

of a potentially intractable metaphysical problem – is not one after all,

giving us one less reason to believe it. Furthermore, the very legitimacy

of the special identity question is doubtful: the fact that SIQ is an open

question if CAI is true might give us positive reason to reject CAI. So

if what I’ve said in this paper is correct, the case for CAI is under-

mined, and in seeing why it is undermined we reveal an objection to

CAI. Not only has one potential reason to accept CAI been rejected,

we have discovered a reason to reject it.


References

Cameron, Ross, (2007), ‘The Contingency of Composition’, Philosophi-

cal Studies Vol. 136, No. 1, p 99–121.

Lewis, David, (1991), Parts of Classes, Oxford: Blackwell.

McDaniel, Kris, (2010), ‘Composition As Identity Does Not Entail

Universalism’, Erkenntnis, Vol. 73, No. 1, p 97–100.

Merricks, Trenton, (2005), ‘Composition and Vagueness’, Mind, Vol.

114, p 615–637.

Sider, Theodore, (2007), ‘Parthood’, The Philosophical Review, Vol.

116, p 51–91.

Turner, Jason, (ms.), ‘Composition as Identity and Conceptual Confu-

sion’.

Van Inwagen, Peter, (1990), Material Beings, Ithaca: Cornell University

Press.

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Composition as Identity Doesn't Settle the Special Composition Question

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