1 Much of the line of reasoning presented here was developed during long conversations I enjoyed with McLaughlin, Brian discussions which resulted in a joint paper, ‘Distinctions Without a Difference,’ Southern Journal of Philosophy, 33, supplement (1995) 203-51Google Scholar. I would also like to thank Catherine Elgin and Ralph Wedgwood for helpful discussions.

2 London and New York: Routledge 1994

3 Even if you think that all vagueness is either linguistic or mental in origin, you can still make sense of the claim that Kilimanjaro is a vague object, by understanding ‘vague object’ in a derivative sense: A vague object is one that is, considering the purposes that are likely to arise in practice, especially apt to be named by a vague term. This derivative sense is not what we shall have in mind when we discuss the thesis that Kilimanjaro is a vague object. Instead, the thesis will be that the vagueness of Kilimanjaro is part of what the mountain is, independent of human language and thought.

4 In principle, one might hold that ‘Kilimanjaro’ suffers from both kinds of indeterminacy: It is a vague term whose reference is indeterminate among a number of vague objects. It is doubtful that anyone will find such a Baroque position attractive, however, since the principal motive for postulating vague objects is to avoid (as much a possible) the difficulties that come with vague singular terms.

5 See Zadeh, Lofti ‘Fuzzy Logic and Approximate Reasoning,’ Synthese 30 (1975) 407-28.CrossRefGoogle Scholar

6 Word and Object (Cambridge, MA: MIT Press 1960), ch. 2, and ‘Ontological Relativity’ in Ontological Relativity and Other Essays (New York: Columbia University Press 1969), 26-68

7 Analysis 38 (1978) 208

8 Salmon, Nathan(Reference and Essence (Princeton: Princeton University Press 1981), 243-45)Google Scholar uses the same formal argument (discovered independently of Evans) as a demonstration of the conclusion that identity is not a vague relation. There is a misstep in Salmon's argument. Having assumed ‘a= b’ as a premiss for reductio ad absurdum, Salmon characterizes ‘a = b’ as “an assumption - something we are taking to be determinately the case for the sake of argument“ (244n). But assuming a statement for the sake of a reductio or conditional proof is not at all the same as assuming that that statement is determinately true. Indeed, if assumptions we made for the sake of conditional proofs could be presumed to be determinately true, we could prove outright that no statement is indeterminate in truth value, as follows:

9 A useful and careful investigation of the logic of Evans's argument can be found in Richard Heck's ‘That There Might Be Vague Objects (So Far As Concerns Logic),’ which is part of his 1991 MIT Ph.D. thesis.

10 Another worry about existential generalization comes from the fact that, in natural languages, there are denotationless proper names. This worry is less serious, since it can be soothed by adopting the premiss, ‘Kilimanjaro exists,’ then proceeding in free logic.

11 Supervaluations were invented by Fraassen, Bas van ‘Singular Terms, Truth Value Gaps, and Free Logic,’ Journal of Philosophy 63 (1966) 464-95Google Scholar. Their application to problems of vagueness is due to Fine, Kit ‘Vagueness, Truth, and Logic,’ Synthese 30 (1975) 265–300CrossRefGoogle Scholar. Their application to Evans's specific argument about vague identity statements is due to Lewis, David ‘Vague Identity: Evans Misunderstood,’ Analysis 48 (1988) 128-30.CrossRefGoogle Scholar

12 In van Fraassen's original terminology, for each acceptable U-model, the function that assigns to each sentence its truth value in is called a classical valuation, while the function that assigns the value true to those sentences true in every acceptable U-model is called a supervaluation.

13 If I read them correctly, Fodor, Jerry and Lepore, Ernest (‘What Cannot Be Evaluated Cannot Be Evaluated, and It Cannot Be Supervalued Either,’ Journal of Philosophy 93 (1996) 516-35)Google Scholar and Timothy Williamson (op. cit., §5.7) have succumbed to this misunderstanding.

14 See Chang, C. C. and Keisler, H. J.Model Theory, 3rd ed. (Amsterdam: North Holland 1990), §2.2.Google Scholar

15 Details aside, this was the program announced by Field, Hartry in ‘Quine and the Correspondence Theory,’ Philosophical Review 83 (1974) 200-28.CrossRefGoogle Scholar

16 To precisely specify a referent for ‘Kilimanjaro,’ we have to determine not only what its parts are, but what its parts would have been if the comet Kohoutek had crashed on its summit; for this purpose, we have to look at worlds other than our own.

17 On the Plurality of Worlds (Oxford and Cambridge, MA: Blackwell 1986), 211-3. See also Quine, Theories and Things (Cambridge, MA, and London: Harvard 1981), 8–13.Google Scholar

18 Lewis, op. cit., 212