The Argument from Vagueness is Unjustified

100009963 Argument from Vagueness Unjustified

The Argument from Vagueness is Unjustified

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I. Introduction

The thesis of restricted composition (RC) has been

powerfully argued against via the argument from vagueness

(AV). The strongest version of AV is widely thought to be

from Theodore Sider (2001, pp. 120-139), which is an

improvement of the one established by David Lewis (2006, pp.

212-213). However, even the Siderian version of AV has

fallen under heavy criticism. Kathrin Koslicki (2003) argues

that his third premise begs the question in favor of

universalism. But perhaps AV can be justified from the

thesis of Composition-as-Identity (CAI). In this essay, I

argue that AV is indeed unjustified, both on Sider's account

and with CAI justifying AV, and, as such, the thesis of RC

should remain on the table for discussion. The essay

proceeds in the following way.

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First, I go over Sider's account of AV. Following this,

I discuss Koslicki's challenge to the justification of the

third premise of his argument. After that, I analyze Sider's

response to her argument and conclude it does not hold. I

then consider if there is another, separate argument that

might justify (P3). The candidate that presents itself is

the thesis of Composition-as-Identity (CAI). It is

independently motivated and not justified via mereological

terms, but rather by the logic of identity. And it is

supposed to settle the Special Composition Question (SCQ) in

favor of universalism. Perhaps this could underwrite the

third premise in AV. I then consider Ross Cameron's (2012)

argument that demonstrates that not only does CAI not settle

SCQ in favor of universalism, but that it is also compatible

with RC and nihilism. Moreover, the reason it does not

settle SCQ is because of what a holder of RC and a

universalist are debating over in the first place. That is,

one has to decide on RC, nihilism, or universalism

independently of AV and CAI on pain of vicious circularity.

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There are two interrelated concerns that I want to

address before starting. The first concern is that it might

seem that if CAI settles SCQ in favor of universalism, there

is no reason to bother with AV. But secondly, if CAI does

not settle SCQ in favor of universalism, how could it be

used to justify AV? Suppose that CAI did settle SCQ in favor

of universalism. Would that make AV superfluous? Not

necessarily. Most arguments should enjoy several avenues of

evidence from different angles. AV would simply highlight

another angle by which to look at the composition question.

But what if CAI does not settle SCQ in favor of universalism

(as indeed it does not)? Does this mean that it cannot be

used to justify AV? Not necessarily. If CAI and AV are

independently plausible, their combined power could deliver

a stronger case for universalism (after all, how many

independent knock-down argument actually exist, especially

in metaphysics?). However, I am going to show that while

both CAI and AV are plausible, they are not plausible in a

way that could settle SCQ; rather the critical parts of each

only serve to highlight the debate between the universalist

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100009963 Argument from Vagueness Unjustifiedand the holder of RC. If this is right, then the question of

composition better be settled some other way on pain of

vicious circularity. I conclude that AV is currently

unjustified. I do not conclude that it must always remain

so; just that RC is a viable option for now.

II. The Argument from Vagueness (Non-Temporalized Version)

Sider's version of AV is a stronger reformulation of a

similar argument made by David Lewis (1986, pp. 212-213).

Sider's (2001) three premises are:

(P1) If not every class has a fusion, then there must

be a pair of cases connected by a continuous series such

that in one, composition occurs, but in the other,

composition does not occur.

(P2) In no continuous series is there a sharp cut-off

in whether composition occurs.

(P3) In any case of composition, either composition

definitely occurs, or composition definitely does not

occur (pp. 123-125).

I borrow the conclusion of this argument from James Van

Cleve (2008), which he puts in a disjunction: "either

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100009963 Argument from Vagueness Unjustifiedcomposition always occurs [mereological universalism] or it

never occurs [mereological nihilism]" (p. 328; 336 fn 27).

(Since this essay is concerned with composition, I will

generally leave the nihilist version to one side throughout

the course of this essay. I bring it up only as needed.) The

problem with RC is that if composition sometimes occurred

and sometimes did not, there would be cases where it was

vague whether composition occurred, which according to (P3),

cannot be the case. For example, suppose I purchase a model

sea vessel. Call it "Little Theseus." and begin putting it

together. At what point is it a model vessel? When I glue

the last piece of plank on? But surely it is a boat before

that; does one piece matter? In terms of (P1), (if not every

class has a fusion) the pile of ship parts at the very

beginning is the case in which composition definitely does

not occur. The finished product is the composite ship. In

terms of (P2), there is no fact of the matter when the non-

composite pile stops being non-composite and forms a further

object. One might think there is; when the last plank is

glued on. But is this right? Consider this. The series can

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100009963 Argument from Vagueness Unjustifiedwork the other way. Let's start with the finished product.

Is it a ship if I take just one part away? Sure. What about

two? Yes. And so on. There is no determinate point at which

it stops being a ship. Perhaps (P3) is faulty. Could I ask

if it is true that composition either definitely occurs or

definitely does not occur?

No. Lewis (1986) says it is impossible that composition

could be a vague matter because vague composition would have

the consequence that existence could be vague (p. 212). This

is intolerable, especially considering there is a far better

explanation of vagueness, which is "semantic indecision"

(Lewis, 1986, p. 212). That is, vagueness is a feature of

our thought and language (p. 212). His example is that of

the Outback in Australia; there is no fact of the matter

which precise borders all the way around properly

circumscribe the region known as the Outback (p. 212). This

is not because the Outback is vague, but our concept of it

and our extensions are. But the linguistic account of

vagueness is not available in the case of composition. Lewis

(1986):

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"But not all of language is vague. The truth-

functional connectives aren't, for instance.

Nor are the words for identity and difference, and for the

partial identity of overlap. Nor are the

idioms of quantification, so long as they are

unrestricted. How could any of these be vague" (p. 212)?

The reason, for Lewis, why composition cannot be vague is

that vagueness is a feature of concepts and language;

moreover, composition issues can be cast in non-vague

language (Koslicki, 2003, pp. 113; 116). So the seeming

indeterminacy of when Little Theseus comprises a model ship

(or fails to) is a vague feature of my language and/or

conceptual framework. However, the ship pieces are not a

vague feature of the world and their sum is therefore not

vague either. Thus, we have a many (ship parts)-one (Little

Theseus) relationship. So RC is blocked by AV because

existence cannot be a vague matter.

But, as Koslicki rightly notes (2003), Lewis made a

move that is circular (p. 116).1 In justifying (P3), Lewis

1 See also: (Sider, 2001, pp. 126-127).

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100009963 Argument from Vagueness Unjustifiedclaims that 'partial identity and overlap' belong in the

non-vague part of language. Koslicki says: "an argument

which concerns the question of whether composition could

ever be vague cannot take for granted that the notion of

overlap is not vague, since composition can be defined in

terms of overlap" (p. 116). This is the point at which Sider

attempts a better justification of (P3). But as we shall see

his move is still circular.

II.1. Sider's Justification of (P3)

Sider attempts to use logic, and in particular

numerical sentences, to justify (P3). Sider's (2001) first

move, for reductio, is to assume for argument's sake that

(P3) were false--" that is, that it can be vague whether a

given class has a fusion" (p. 127). Consider all the objects

in a class. And suppose, then, that it could be

indeterminate whether the fusion of the class is another

entity (p. 127). In a finite world with a finite number of

concrete objects, this would mean that "some numerical

sentence--a sentence asserting that there are exactly n

concrete objects, for some finite n--would be indeterminate.

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100009963 Argument from Vagueness UnjustifiedBut numerical sentences need contain only logical terms and

the predicate 'C' for concreteness" (p. 127). Following

this, Sider (2001) argues convincingly for the plausible

claim that "logical words are never a source of vagueness"

(p. 128). Thus, he justifies (P3) with logical notions

rather than mereological ones. To complete the reductio, if

(P3) were false, logic words would be a source of vagueness.

Koslicki (2003) says that justification for (P3) can now

shift from Lewis's circular (C) statement:

"(C) Composition is never vague" to Sider's (allegedly)

non-circular

to Sider's (N) below:

"(N) No numerical sentence of the form 'There are n

concrete objects' (for some finite value of 'n') is ever

indeterminate in truth-value" (p. 117).2

By recasting the debate in logical terms, Sider seems to get

what he wants. Koslicki (2003) observes that if (N) contains

2 Koslicki (2003) thinks his use of the concrete predicate 'C' is illegitimate. One reason for this is that she thinks 'C' is "implicitly mereological" (p. 131 fn 14), making it circular like Lewis. Since what follows is sufficient to show his justification still does not work, I set this to one side. Koslicki (2003) also shows the converses of (C) and (N) (p. 117).

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100009963 Argument from Vagueness Unjustifiedno mereological vocabulary, in conjunction with the

assumption that logic is not vague, in conjunction with

concreteness-predicate's non-vagueness, then Sider should

get the conclusion that (N) is true (p. 118). But Koslicki

(2003) argues that (N) and (~N) only reformulates what the

holder of RC and the universalist disagree on in the first

place. Because of this, Sider's move is circular in a

similar way as Lewis (pp. 119-120). This is the topic of the

next section.

III. Koslicki's Arguments Against Sider's Justification of

(P3)

Before discussing her arguments, I follow her in

granting Sider the following points. Koslicki (2003) grants

the truth of (P1) and (P2) and also the presuppositions that

1) the only plausible account of vagueness is "semantic

indecision" and 2) that logic is never a source of vagueness

(though with the caveat that this requires care in defining

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100009963 Argument from Vagueness Unjustifiedwhat this means in this context) (p. 115).3 These play a

role in her analysis, which follows.

Say there is a numerical sentence (X) of the form

'There are n concrete objects' (for some finite value of

'n') over which a universalist and proponent of RC are

disagreeing (Koslicki, 2003, p. 118). What could they be

disagreeing over? (X), Sider argues, only contains logical

terms including the existential quantifier, logical

connectives and the identity-relation. None of these,

according to Sider, are likely candidates for vagueness. So

it seems that if one grants that logic is non-vague, (X)

must have a determinate truth-value. However, Koslicki

argues (and Sider (2003, p. 137) agrees)), they are actually

arguing about the existential quantifier (EQ). Specifically,

they could agree 1) on what EQ means, "in the sense that

they can agree on which logical operation is denoted by the

symbol '∃'", and 2) that EQ is not vague, "in the sense that

it can be precisely specified which logical operation it

3 Koslicki (2003) grants him two other points that I need not mention here (p. 115). Also, as Koslicki (2003) also notes, there are those who argue against the truth of (P2) (p. 130 fn 11).

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100009963 Argument from Vagueness Unjustifieddenotes" (Koslicki, 2003, p. 118). Agreeing on meanings,

however, does not at all mean agreeing on the range. Two

philosophers may still debate about "the size and the nature of the

domain quantification (while both of them are talking about

unrestricted quantification)" (Koslicki, 2003, p. 118).

This is the situation between the holder of RC and the

universalist. They disagree on what exists and the number of

things that exist; in short they disagree on what it means

to be an object. Mutatis mutandis for fusions. Two

philosophers can agree on the meaning of 'fusion,' and

disagree about which fusions there are. The upshot is that

nothing has been gained in casting the debate in terms of

(N) or (~N) because the truth-value of a numerical sentence

cannot be settled unless one has already taken a position on

RC or universalism. The ontological dispute must be settled

some other way. So just as Lewis' move was illicit because

he assumed mereological vocabulary in theorizing about

composition, so similarly Sider's move is illicit since "one

also cannot take for granted that no numerical sentence of

the form 'There are n concrete objects' (for some finite

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100009963 Argument from Vagueness Unjustifiedvalue of 'n') is ever indeterminate in truth-value, since

that is merely a re-statement of what is at issue" (pp. 119-

120). Thus, the justification for (P3) in terms of numerical

sentences turns out to fail. If (P3) remains unjustified, in

terms of my dialectic, AV cannot be used to block RC. But

maybe Sider can respond.

III.1. Sider's Response

Sider (2003) answers 'no' to the following question:

"can quantifiers be vague" (p. 137)? He offers two

arguments. The first is to show that vague quantifiers would

be very different from familiar cases of vagueness; vague

quantifiers may be possible but require an altogether

different model. But what is in dispute is the existential

quantifier and how to understand it. This has no power to

overturn Koslicki's argument since Sider's line of reasoning

serves here to demarcate the debate, rather than settle it.

He even sketches three ways someone could attempt building

these new models.4 I set this first argument to one side

since it does not really get at Koslicki's point.

4 Sider, of course, is not hopeful about those projects.

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Sider's (2003) second argument is stronger and has

three premises before the conclusion:

"1. Vagueness requires multiple precisifications

2. Wherever there is a unique natural kind, there are

no multiple precisifications

3. (Unrestricted) existence is a unique natural kind

________________

Therefore, 'exists' and '∃' are not vague" (p. 142-

143).

I want to focus on Premise 3 (assuming 1 and 2 are valid).

Interestingly, Sider (2003) chooses not to argue for 3; he

just says that existence being a natural kind is "crucial to

the rebuttal of Carnapian ontological relativity and hence

to the whole enterprise of ontology" (p. 144). Is this true?

No. In fact, it is a very strange claim. The reason is that

it is a perfectly defensible view to say that while there

may be different "linguistic frameworks," there could also

be a fact of the matter of which one is right. Rather than

relativity, this position would assume legitimate disputes

among those with the different "frameworks." So one possible

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100009963 Argument from Vagueness Unjustifiedscenario is a holder of RC and a universalist agreeing on

the meaning of '∃' and still disagreeing on its range.

Another is that they may even agree that (unrestricted)

existence is a unique natural kind and still disagree to

what that extends. Or they may even disagree on how to use

the existential quantifier (it may be vague). But none of

this requires ontological relativity; rather, they are

seeking to establish what exists and what does not.

Therefore, if the universalist and the holder of RC are

having a legitimate dispute, there need not be any concern

of Carnapian relativity (for more information, see: (Sider,

2001, pp. xviii-xxiv)).

Koslicki's argument remains valid. The debate centers

on the existential quantifier and there is nothing in her

account that requires Carnapian (or indeed, any) relativity.

But maybe there is another way of justifying (P3) in

AV. If successful, AV remains a powerful argument against

RC. If unsuccessful, the debate between the universalist and

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100009963 Argument from Vagueness Unjustifiedholder of RC continues. The best possible candidate for this

is the thesis of composition as identity (CAI).5

IV. Composition as Identity and (P3)

CAI, according to Aaron Cotnoir (forthcoming), is a

thesis that accounts for "the intuitive notion that the

whole 'is nothing over and above' its parts--that the whole

is the same as its parts" by claiming simply that "the whole

is identical, in some sense or other, to its parts" (p. 2). To

understand the motivations and benefits of the theory, I

will be appealing to the following example; a pizza with

eight slices.6

Suppose I did not hold to some form of CAI and my

philosophic friends wanted to joke on me. They tell me that

I can have the whole pizza, but each of the eight of them

gets a slice. What am I left with? The idea is that those

eight slices just are the pizza. The pizza just is those

eight slices. Ross Cameron (2012) notes that one important

advantage of CAI is that it is supposed to "settle certain

5 I am deeply indebted to a discussion with a colleague in what follows.6 This pizza example is based on (Baxter, 1988, p. 579). For discussion,see: Cotnoir (forthcoming, pp. 1-2).

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100009963 Argument from Vagueness Unjustifiedmereological claims...by the logic of identity" (p. 532).

Cameron (2012) explains that if parthood is a primitive

relation, then it is an open question whether Xs can compose

two different things; but CAI claims that to be a part of Y

is to be among the things that, taken together, are

identical to Y, which means that 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" (p. 532).

Cameron (2012) says that another important benefit of

the theory is that it is supposed to settle SCQ.7 Cameron's

(2012) puts SCQ this way: "under what conditions do a

collection of objects compose some further object" (p. 532)?

Universalists says always and a holder of RC says

sometimes.8 The orthodox view is that CAI settles the

question in favor of universalism, and does so without

appealing to mereological terms; rather CAI uses logic of

identity terms (Cameron, 2012, p. 531).

7 First asked by Peter van Inwagen (1990). 8 A nihilist says never.

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Perhaps we can add another benefit to CAI. Perhaps it

can be used to justify (P3) above. If it can, then not only

is SCQ settled in favor of the universalist, but there is

also a strong corroborating argument from AV. Koslicki

thinks that the debate between the holder of RC and the

universalist has to be settled another way. Maybe CAI is

this way. Lewis was unable to settle the debate because of

using mereological terms in order to settle mereological

issues. Sider was similarly circular because recasting the

debate in terms of numerical sentences just re-stated the

issue between the holder of RC and universalism. But maybe

re-casting the debate in terms of identity will get the

justification required to wield AV against RC.

As a very crude attempt, I could recast

"(P3) In any case of composition, either composition

definitely occurs, or composition definitely does not

occur" as

"(P3*) in any case of identity, either identity

definitely occurs, or identity definitely does not

occur."

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100009963 Argument from Vagueness UnjustifiedAs stated, (P3*) of course makes little sense. But here is

what I am driving at. CAI is supposed to commit us only to

what there is in the first place. With regard to the pizza,

there are the eight slices that just is the pizza. The pizza

is just the eight slices. So it can never be vague as to

what exists because facts about existence are just facts

about identity. Once we have agreed that the eight slices

exist, it cannot be vague whether the pizza exists, unless

it is vague whether or not the pizza is identical to the

eight slices. Something exists or it does not. If it does

exist, it is identical with its parts. As David Lewis (1991)

says "...composition -- the relation of part to whole, or,

better, the many-one relation of many parts to their fusion

-- is like identity. The 'are' of composition is, so to

speak, the plural form of the 'is' of identity" (p. 82).

(P3) is then underwritten by identity.9

This approach fails for two reasons. First, as Cameron

(2012) demonstrates, CAI does not solve the SCQ question in

favor of universalism. And secondly, one needs to decide on 9 For a good overview of the various motivations of CAI, see: (Cotnoir, forthcoming, pp. 1-7).

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100009963 Argument from Vagueness UnjustifiedRC or universalism without CAI on pain of vicious

circularlity. If this is right, CAI cannot justify (P3),

weakening AV significantly.10

V. CAI Does Not Settle SCQ in Favor of Universalism

This section is heavily based on (Cameron, 2012).

Cameron (2012) argues that CAI only states 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" (p. 533). This does nothing to settle when composition

occurs. Cameron (2012) says that only the following

biconditional is settled: "they compose iff there is some

one to which the Xs is identical" (p. 533).

The following terms are germane to the discussion in

this section: 'mere many' and 'many-one.' Cameron (2012)

defines them this way: "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" and "call the Xs a many-one if there's

10 Cotnoir (forthcoming) notes that there are at least three "strengths"of CAI: weak, moderate, and strong (p. 9). Sider (2007) even discusses asuperstrong version of CAI (pp. 59-69). Might some of them justify (P3) better? I do not think so. Insofar as the discussion centers on the use of the existential quantifier, is insofar as it relates to all versions of CAI.

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100009963 Argument from Vagueness Unjustifiedmore than of the Xs and they are not a mere many...they are

a plurality that is identical to some one thing" (p. 533).

Cameron's (2012) thesis is that both of these are

conceptually possible even given CAI. The debate between the

universalists, holders of RC, and nihilists can be restated

with these terms if composition is identity. A universalist

says that every many is a many-one; the holder of RC says

some many is a many-one and some many is a mere many; and

the nihilist says every many is a mere many. All of these

are compatible with CAI.

The first step in showing why this is so is to show why

assuming universalism with CAI is circular. If the coherence

of a mere many is granted, then a further argument must be

added to the universalist account, Cameron (2012) says,

which is that there are no mere manys (p. 534). But this is

equivalent to saying that every many is a many-one, which is

begging the question (pp. 534-535). This shows quite well

that CAI does not entail universalism, since one has to

assume universalism to get the desired conclusion.

Moreover, the holder of RC can accept CAI since for her

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100009963 Argument from Vagueness Unjustifiedit simply means that there are some Xs that are identical to

some one thing. In effect, argues Cameron (2012), "if CAI is

true, answering SCQ is simply tantamount to answering the

question of when a plurality of things is identical to some

one thing" (p. 535). Note that any of the three responses,

given CAI, has a response to the question. CAI seems to be

doing no real work and the question of composition remains

as intractable as ever.

There are two other arguments that Cameron (2012)

examines that are supposed to show that CAI entails

universalism. The one I focus on, he calls the "Merricks-

Sider" argument (pp. 536). It is extracted from Merricks

(2005) and Sider (2007). Cameron (2012) formalizes it in

seventeen steps (pp. 536-539). With one of the premises

being CAI, the conclusion of the Merricks-Sider argument is

that "for every collection of things, there's some thing

that is the sum of those things" (p. 538).

There are six logical statements in the seventeen-step

argument that bear on what follows (Cameron, 2012, p. 538):

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100009963 Argument from Vagueness Unjustified3) ∀x1 . . . xn P(x♢ 1 . . . xn)

[Poss Comp]

5) ∀x☐ 1 . . . xn(P(x1 . . . xn)↔∃x(x=x1 . . . xn))

[Nec of CAI]

12) A= a1 . . . an [From

11, E]☐

13) ∃x(x= a1 . . . an)

[From 12, ∃I]

14) P(a1 . . . an)↔∃x(x= a1 . . . an)

[From 5, E, ∀E]☐

15) P(a1 . . . an) [From

13, 14↔E]

Cameron (2012): "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" (p. 536). Cameron (2012)

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100009963 Argument from Vagueness Unjustifiedsays that step (12) "establishes the truth of the identity

claim" and that at 13, "we existentially generalize and

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

an instance of the embedded biconditional in Nec of CAI"

which allows us to infer the left hand side (p. 543).

Cameron (2012) has many good arguments about the logic

(pp. 539-545). I focus here on one point he makes: there

comes a time when one needs to decide how the existential

quantifier is behaving in step 5.

Consider:

'∃x(Φ)'( where 'Φ' is an open sentence).

Does it mean that "there is at least one individual--some one

thing--that satisfies the open sentence Φ, or does it mean

that there is some thing or are some things that satisfy Φ"

(Cameron, 2012, p. 543)? If one decides on the former than

the step from 12 to 13 is unsound. All that is proven is the

truth of the identity claim A= a1 . . . an (Cameron, 2012,

p. 543). Given that CAI does not pick out universalism,

Cameron (2012) says that "'A' might not actually name any

individual but merely actually plurally refer to a

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100009963 Argument from Vagueness Unjustifiedcollection of things" (p. 543). Thus, one cannot

existentially generalize on A because the existential

quantifier on this was to refer only to some individual thing.

But if the latter move ("are some things...") is

chosen, the question is begged in favor of universalism, no

matter how one goes about it. Here is how. Let us suppose

that the existential quantifier picked up terms that refer

singularly or plurally. In this case 13 could follow from

12, but all 13 is then saying is that "there is some thing

or there are some things identical to a1 . . . an" (Cameron,

2012, p. 543). But composition occurs when some many is

identical to some one; therefore we cannot get 15 unless Nec

of CAI is tightened up on this usage of the existential

quantifier. CAI in premise 14 says that "composition occurs

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

the many" (Cameron, 2012, p. 543). The problem for the

universalist is that this formulation ignores the many-one

composition she wanted. To get what she wants, a

universalist can introduce a special quantifier which only

means an individual, or she can "introduce a predicate 'I(x1

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100009963 Argument from Vagueness Unjustified. . . xn)' that x1 . . . xn only satisfy if there is some

individual which is identical to x1 . . . xn" (Cameron,

2012, p. 544).

This would mean that Nec of CAI would need modifying;

either the quantifier needs to be swapped for the special

one introduced, or swapped for the new predicate. The

consequence for this move is that step 15 cannot follow from

13 and the claim at step 14. What is needed is either of the

following two claims: I(a1 . . . an), or S∃x(x=a1 . . . an)

(where 'S∃' means the specially introduced quantifier)

(Cameron, 2012, p. 544). But since all this says is that

there is "some one thing identical to a1 . . . an," a great

circle has been drawn; this is the very thing under

discussion in the first place.

We might want to say the above-mentioned statements are

possible, given step 3, and we could derive them if a

premise was added that meant that any possible individuals

are essentially individuals. But Cameron (2012) wonders why

this should be accepted given step 5 because "if

individuality is essential to every possible many that is

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100009963 Argument from Vagueness Unjustifiedidentical to some one, why is non-individuality not essential

to those possible collections of things that are not

identical to some one" (p. 544)?

The upshot is this. Just as numerical sentences do not

settle (P3) in favor of universalism, so the logic of

identity does not settle SCQ in favor of it either. The

central point of debate is the existential quantifier. One

must settle SCQ by some other way since this is what is in

dispute. It is not that CAI or Sider's numerical sentences

are outlandish or unbelievable, but just that they do not

settle SCQ. Once someone accepts universalism for other

reasons, then AV and CAI might be used to bolster their

position given that they have reasonable premises. In other

words, AV and CAI preach to the choir, but they do not

convert the heathen.

There is one other point to draw from this. One might

think that CAI might not settle SCQ in favor of

universalism, but it could lend support of whatever strength

to (P3); that is, it can still justify (P3) to some degree.

But this is incorrect given the above. The reason that CAI

28

100009963 Argument from Vagueness Unjustifieddoes not settle SCQ in favor of universalism is because of

considerations about the existential quantifier. But this is

what is being debated between a holder of RC and a

universalist in the first place. CAI lends the wrong kind of

support for AV.

V.1. Possible Universalist Responses

Cameron (2012) considers an objection that one who

thinks CAI entails universalism might make (pp. 545-547).

Consider Lewis's (1991) double-counting thought and the

pizza from earlier (p. 81). It would be double-counting to

count the slices and then the one thing, the pizza. Those

who think that CAI entails universalism would argue that

Cameron's (2012) two ways of understanding the quantifier

discussed above is illegitimate because there is "no

distinction between the many and the one: the one just is

the many counted as an individual instead of as a plurality"

(p. 545). On this view, the idea of mere manys is incoherent

"because to make sense of a mere many we need to make sense

of a many not being a one" (p. 545).

29


But the interesting claim of the ontological thesis of

CAI is the many-one identity (Cameron, 2012, p. 547). That

is, not only is it the case that everything is identical

with itself and that every collection of things (like the

pizza slices) is identical to that collection, but the

further claim is that there "are collections of things

identical to some one thing;" for example, the pizza slices

(collection) is identical to one thing, namely the pizza

(Cameron, 2012, p. 547). And according to CAI orthodoxy,

there is always the sum; there is always a many-one. This

would have been the interesting entailment of CAI (but as

seen from Cameron's work, this is not entailed).11

VI. Conclusion

I conclude that AV cannot be justified by numerical

sentences (Sider) or the logic of identity (CAI). The reason

is that the debate over RC and universalism centers on the

existential quantifier and its range. Neither can settle the

11 Cameron (2012) argues convincingly that without many-one identity, mere many talk collapses into "fancy-talking" nihilism (pp. 545-547). Cameron (2012) then discusses another argument developed by Ted Sider (p. 548-552). But Cameron's (2012) above proof lays the groundwork for rejecting this line of argument too (p. 548).

30

100009963 Argument from Vagueness Unjustifieduse of the existential quantifier in favor of universalism

without first assuming universalism in the first place. This

is true whether the attempted justifier of (P3) is numerical

sentences or the logic of identity. Since no non-circular

justification has yet been found for (P3), RC remains a

viable theory of composition. This is also why AV and CAI

could not jointly lend more credibility to universalism.

Like the numerical sentences, CAI does not settle the debate

between the universalist and the holder of RC.

None of this is to say that some non-question begging

way of settling SCQ in favor of universalism is impossible.

Rather, with numerical sentences and the logic of identity

set aside, it is difficult to see what shape an argument

like this would take. Whatever could justify AV must not

contain any mereological terms and be independently

motivated. Until this is found, if it can be, I conclude

that the thesis of RC remains a viable option for

consideration as a solution to SCQ.

31


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100009963 Argument from Vagueness UnjustifiedCotnoir, A. J. (forthcoming). Composition as Identity:

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The Argument from Vagueness is Unjustified

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