https://orcid.org/0000-0002-2385-096X
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ABSTRACT
I defend the thesis that Composition Entails Identity (CEI): that is, a whole is identical to all of its parts, taken together. CEI seems to be inconsistent, since it seems to require that the parts of a whole possess incompatible number properties (for instance, being one thing and being many things). I show that these number properties are, in fact, compatible.
Disclosure Statement
No potential conflict of interest was reported by the author.
Notes
1 Compare Baxter [Citation1988a, Citation1988b].
2 CEI is weaker than the more familiar thesis, ‘Composition as Identity’ (CAI). I say that xx = y if xx compose y; CAI adds that xx = y only if xx compose y. Only the weaker CEI is relevant to the problem discussed here.
3 For a detailed survey, see Oliver and Smiley [Citation2016].
4 On one view, that ‘a@b’ denotes a and b implies both that ‘a@b’ denotes a and that it denotes b. On a competing view, ‘a@b’ denotes a and b together, and doesn’t denote either of them individually. I remain neutral on this dispute; see Oliver and Smiley [Citation2016: ch. 6] for discussion.
5 See Baxter [Citation1988a: 193], Lewis [Citation1991: 87], Cotnoir [Citation2013: 301], Varzi [Citation2014: 49], and especially Yi [Citation2014: 179–80].
6 For example, if a@b = c, then a@b@c = a@b@a@b, which are just a@b again.
7 See Baxter [Citation1988b: 578], van Inwagen [Citation1994: 213–14], and Koslicki [Citation2008: 42].
8 See, e.g., Rothstein [Citation2017: 28–35] and sources cited therein.
9 Compare Barker-Plummer et al. [Citation2011: 375–88].
10 Note that ‘Iaa’, or ‘∃x(x = aa)’, isn’t trivially true. Granting aa = aa, what follows is ‘∃xx(xx = aa)’. This is consistent with, but doesn’t entail, ‘∃x(x = aa)’.
11 You might think that this is already secured, since ‘#≼’ is a function. But see Oliver and Smiley [Citation2016: 4–7] on multi-valued functions.
12 More formally: ∃xx1 … ∃xx4(Axx1 & … & Axx4 & xx1 ≠ xx2 & … & xx3 ≠ xx4 & ∀yy(yy ≼ aa ⊃ (yy = xx1 ∨ … ∨ yy = xx4))).
13 We needn’t assume CEI here, since we needn’t think that a pair of shoes is a composite object. Instead, we might think that ‘pair of shoes’ is grammatically singular but applies only to pluralities [Oliver and Smiley Citation2016: 305–7].
14 This analysis gives the ‘exact’ reading of ‘aa are n Fs’. To say that aa are at least n Fs, but possibly more —say, that there are n Fs such that those Fs, together with some (possibly identical) Fs, are collectively identical to aa. For example, aa are at least one F just in case ∃xx∃yy(Fxx & Fyy & xx@yy = aa), while aa are least two Fs just in case ∃xx1∃xx2∃yy(Fxx1 & Fxx2 & Fyy & xx1 ≠ xx2 & xx1@xx2@yy = aa).
15 ‘Ipseity’ is derived from the Latin ‘ipse’ (roughly equivalent to ‘self’) and means ‘identity’ or ‘self’. The term is sometimes used, e.g., in the phenomenological tradition, to refer to a subject’s sense of themselves as a unified self or consciousness. No such connotation is intended here.
16 It’s crucial that ‘F’ be read collectively in the definition of ‘#=(F, aa, n). Otherwise, e.g., the fifty-two cards in a deck will count as one card (since they’re identical to some xx such that ‘card’ is true of xx on the distributive reading). Thanks to an anonymous referee for discussion.
17 ‘#=(F, aa, n)’ is true only if there are some Fs, xx1–xxn, to which aa are collectively identical. Since identity is mutual inclusion, it follows that xx1@ … @xxn ≼ aa, from which it follows that xx1 ≼ aa & … & xxn ≼ aa.
18 Recall that ‘aa are n individuals’ implies that there are at least n individuals among aa, and so to say that the parts of a whole are at least two individuals implies that there are at least two individuals among them.
19 See also Koslicki [Citation2008: ix] and Spencer [Citation2017: 866].
20 I defend this view in more detail elsewhere [Citationforthcoming a].
21 Since ‘#=(I, aa, n)’ doesn’t imply ‘#≼(I, aa) = n’, (5*) doesn’t imply (5).
22 Since ‘#≼(I, aa) = n’ entails ‘#=(I, aa, n)’, (7) entails that there are two things distinct from c to which a@b are collectively identical:
23 See also Kleinschmidt [Citation2012].
24 One might insist that the identity predicate, ‘=’, which I used to define ‘I’, is illegitimate, by adopting Geach’s [Citation1967] doctrine of relative identity: nothing is ever identical to anything else simpliciter, but only relative to a concept, property, or kind. However, that view faces serious difficulties, and Bohn himself rejects it: ‘Relative identity is worse than death’ [Citation2014: 146n10].
25 Baxter [Citation2005: 378] and Varzi [Citation2014: 52] anticipate this point.
26 Spencer doesn’t consider the Counting Argument as I’ve presented it; he considers only the Many-One Argument. However, his response to the latter naturally extends to the former.
27 Thanks to David Liebesman for this point.
28 Lipman [Citationforthcoming: 4] anticipates this point.
29 Wallace [Citation2011: 820–1] only discusses quantificational number claims—i.e. claims of the form ‘There are n Fs.’ Here, I consider an extension of her view to number ascriptions.
30 See also Cotnoir [Citation2013: 313–17], Calosi [Citation2018: 282–7], and Loss [Citationforthcoming: 4].
31 That is, aa1 are an F, and aa2 are an F, and … and aan are an F.
32 That is, if xx are an F, then either xx = aa1 or xx = aa2 or … or xx = aan.
33 Early versions of this material were presented to the Department of Philosophy at the University of Alberta, the Department of Philosophy at Bilkent University, the 2019 Vendler Group’s Philosophy and Linguistics Workshop at the University of Calgary, the Philosophy Graduate Colloquium at the University of Calgary, the 2019 meeting of the Society for Exact Philosophy, and the 2020 meeting of the American Philosophical Association, Central Division. Thanks to all of those audiences. Special thanks to David Liebesman for extensive feedback on earlier drafts of this paper, and to Roberta Ballarin and Daniel K. Rubio for helpful discussion. “Thanks also to the Editor and three anonymous referees at the Australasian Journal of Philosophy.”