Abstract
In this chapter, I examine in some detail Gareth Evans’s famous one-page article ‘Can there be vague objects?’. I argue that Evans’s proof of the impossibility of vague identity (presented in his second paragraph) is flawed but suggest an alternative way in which Evans’s desired conclusion might be secured. I also point out some oddities in Evans’s final paragraph.
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Notes
- 1.
In his second sentence Evans implies that if the world is not vague, then vagueness is a ‘deficiency’ in our description of the world. This is tendentious. Those who deny the possibility of worldly vagueness do not have to see vagueness as any kind of linguistic deficiency (e.g. epistemicists such as Tim Williamson).
- 2.
D Lewis (1988) suggests that Evans intended his proof to be fallacious. But it is hard to square this interpretation with the text.
- 3.
Apart from some comments in his final paragraph, Evans says nothing about the logical properties of ‘Indefinitely’ (∇). I assume that Evans intends ∇ to indicate absence of truth and falsity. So ‘∇P’ means ‘it’s indefinite whether P’ and is true just if P is neither true nor false. This assumption allows us to make sense of Evans’s proof in a straightforward way. In that case, however, Evans’s proof and the (1a)–(4a) proof below exclude indeterminate identity even when the source of the indeterminacy is something other than vagueness.
- 4.
Some also question premise (3). I have heard the reaction: ‘But if a were a vague object, it would be indeterminate whether a = a’. However, I think (3) is hard to deny, and I agree with David Wiggins’s response (Wiggins 1986, p. 175): even if vague, a is exactly the right object to mate with a in order to ensure a perfect case of identity.
- 5.
- 6.
Why? If (4a) is true, it cannot have an indeterminate antecedent and false consequent. A case in which `x = y' is indeterminate would be a case in which (4a) had an indeterminate antecedent and a false consequent. Since (4a) is true, it follows that `x = y' can never be indeterminate in truth value.
- 7.
Even gerrymandered designators of concrete objects such as ‘A-at-t1’ do not count as precise. In cases of multiple personality or monstrous two-headed births, for example, it may well be indeterminate whether A at t1 = B at t1. What of an apparent diachronic or cross-temporal identity sentence such as ‘C-at-t3 = D-at-t4’? On the four-dimensional view of ordinary continuants, the canonical truth condition of this sentence is, C-at-t3 is part of the same four-dimensional entity (ship, person, etc.) as D-at-t4. If it is vague whether C-at-t3 = D-at-t4, and both singular terms are precise, then the vagueness must lie with the part/whole relation (not with identity). But I take it there is nothing paradoxical in the possibility: (∃x)(∃y)(∃z) ∇ (x and y are both parts of z).
- 8.
See Pelletier (1984).
- 9.
Does the imprecision of ‘Everest’ mean, e.g. that it is not determinately true that Hillary climbed Everest? No; that is determinately true because it is determinately true that Hillary climbed A, determinately true that Hillary climbed B, and so on.
- 10.
Thanks to Peter Roeper, Daniel Nolan and an audience at ANU in October 2012 for useful comments. (After writing this chapter, I came across Barnes (2009) which presents an interesting counterpart-theoretic treatment of the determinacy/indeterminacy operators, according to which Evans's proof is invalid. Barnes's article requires careful study.)
References
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Barnes, E. (2009). Indeterminacy, identity and counterparts: Evans reconsidered. Synthese, 168, 81–96.
Evans, G. (1978). Can there be vague objects? Analysis, 38, 208.
Kripke, S. (1971). Identity and necessity. In M. K. Munitz (Ed.), Identity and individuation (pp.135–164). New York: New York University Press.
Lewis, D. (1988). Vague identity: Evans misunderstood. Analysis, 48, 128–130.
Pelletier, F. J. (1984). The not-so-strange modal logic of indeterminacy. Logique et Analyse, 108, 415–422.
Wiggins, D. (1986). On singling out an object determinately. In P. Pettit & J. H. McDowell (Eds.), Subject, thought and context (pp. 169–180). Oxford: Oxford University Press.
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Garrett, B. (2014). Some Comments on Evans’s Proof. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_13
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