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Published online by Cambridge University Press: 12 April 2010
It seems to be an obvious truth that
(1) There could be something that doesn't actually exist.
That is, it seems to be obiously true that
(1a) ◊∃×(Actually ∼ (× exists)).
It is sufficient for the truth of (1) that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of (1) that there could be some pepole, or trees, or cars that are distinct from all those that actually exist. Do (1) and suchlike statements involve a commitment to possibilia, to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which (1) and its ilk commit us? These simple little questions are at the tip of an iceberg.
1 Davies, Martin, ‘Weak Necessity and Truth Theories’, Journal of Philosophical Logic 7 (1978), 415–39CrossRefGoogle Scholar; Gupta, Anil ‘Modal Logic and Truth’ Journal of Philosophical Logic 7 (1978), 441–72CrossRefGoogle Scholar; Peacocke, Christopher ‘Necessity and Truth’ Journal of Philosophical Logic 7 (1978) 473–500CrossRefGoogle Scholar.
2 The model theory is that in Kripke, Saul, ‘Semantical Considerations on Modal Logic’ repr. in Reference and Modality, ed. L., Linsky (Oxford: Oxford University Press, 1971).Google Scholar
3 ‘Semantical Considerations’, p. 64.
4 In this respect, I am in agreement with Timothy Williamson ‘Bare Possibilia’, Erkenntnis 48 (1998) 257–73, at, p. 263Google Scholar.
5 For remarks on the varieties of modalism, see my Being Known (Oxford: Oxford University Press, 1999)Google Scholar Chapter 4, section 4, and the references therein.
6 The next few sentences briefly summarize the approach of Chapter 4 of Being Known.
7 Fine, Kit, ‘Postscript’ in Arthur, Prior, Worlds, Times and Selves (London: Duckworth, 1977), pp. 122, 144Google Scholar. As Fine summarizes the semantics of Vlach's operators: '†allows one to keep or “store” a reference to the world of evaluation, while enables one to pick up this reference’ (p. 144).
8 For discussion of world-propositions and their significance, see Worlds, Times and Selves, Chapter 2, Fine's ‘Postscript’ thereto, and Review, Kripke's, in the Journal of Symbolic Logic, 48 (1983), pp. 486–88Google Scholar, of Fine's paper ‘Failures of the Interpolation Lemma in Quantified Modal Logic’ Journal of Symbolic Logic, 44 (1979), 201–206CrossRefGoogle Scholar.
10 This point parallels one made by Donald Davidson concerning the indicative character of theories of truth, and their possible role as meaning-theories in his ‘Reply to Foster’ in Truth and Meaning ed. Gareth, Evans and John, McDowell (Oxford: Oxford University Press, 1976)Google Scholar.
11 Lewis, David, On the Plurality of Worlds (Oxford: Blackwell, 1986), esp. pp. 87–92Google Scholar.
12 Marcus, Ruth ‘Possibilia and Possible Worlds’, in her Modalities: Philosophical Essays (Oxford: Oxford University Press, 1993)Google Scholar.
13 See the last but one paragraph before that containing the displayed quote.
14 Henceforth I ignore the case of meiotic division. Although taking it into account complicates the correct formulations, it does not bring new issues of principle. An individual who results from meiotic division originates essentially in the first cluster of cells that is not subject to later meiotic division. No individual who results from non-meiotic division could result from meiotic division.
18 Though it is not within the letter of that doctrine, which requires that modal operators be primitive. The spirit is retained by the weaker position that there are constraints which something must satisfy to be a possible world, and which are explanatorily prior to the notion of a possible world.
19 Wright, Frege's Conception of Numbers as Objects.
21 ‘Postscript’, pp. 122–3.
22 ‘E(ξ)’ is a first-level existence predicate. For anyone uneasy about its use, it would suffice for present purposes to replace it by ‘∃y(y=ξ)’, where the existential quantifier has the inner, actualist reading within modal operators. The points of the text still go through under this replacement.
23 This prima facie impression could be overturned if the opposing view could cite some other cases, outside issues of possibilia, that give us reason to reject (B). Considerations of uniform theory might then point in a different direction.
24 I thank Gideon Rosen and Timothy Williamson for stimulating discussions on modal matters, and to Justin Broackes and Kit Fine for valuable comments on an earlier draft of this paper.
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