¹ Lewis, David, On the Plurality of Worlds (Oxford: Blackwell, 1986), Ch. 3Google Scholar. Ersatzism also goes by the name of ‘ersatz modal realism’, ‘actualism about possible worlds’, ‘abstractionism’, and ‘moderate modal realism’.

² See: Plantinga, Alvin, The Nature of Necessity (Oxford: Clarendon Press, 1974), Ch. 4Google Scholar, and ‘Actualism and Possible Worlds’, reprinted in Loux, Michael (ed.), The Possible and the Actual (Ithaca: Cornell University Press, 1979), 253–73Google Scholar; Robert Stalnaker, ‘Possible Worlds’, reprinted in Loux, op. cit., 225–34, and Inquiry (Cambridge, Mass.: MIT Press, 1984), 43–58; Robert Adams, ‘Theories of Actuality’, reprinted in Loux, op. cit., 190–209; Kripke, Saul, Naming and Necessity (Oxford: Blackwell, 1980), 15–20, 43–53Google Scholar.

³ Possible-world discourse can mix quantification over possible worlds and possible individuals with the modal idioms drawn from ordinary modal discourse – e.g., ‘There could have been more worlds than there are’. What is important for us, however, is only that possible-world discourse involves, while ordinary discourse does not involve, quantification over possibilia.

⁴ Modalists claim that this can be done. See: Forbes, Graeme, The Metaphysics of Modality (Oxford: Clarendon Press, 1985)Google Scholar and Languages of Possibility (Oxford: Blackwell, 1989) for a defence; and Melia, Joseph, ‘Against Modalism’, Philosophical Studies, 68 (1992), 35–56CrossRefGoogle Scholar, and Modality (UK: Acumen, 2003), Ch. 4 for dissent.

⁵ See: Javier Kalhat, ‘Has Lewis Reduced Modality?’, European Journal of Philosophy (forthcoming); William Lycan, ‘The Trouble with Possible Worlds’, reprinted in Loux (ed.), op. cit. note 2, 274–316, ‘Review of On the Plurality of Worlds’, Journal of Philosophy, 85 (1988), 42–7, ‘Two–No, Three–Concepts of Possible Worlds’, Proceedings of the Aristotelian Society, 91 (1991), 215–27, and ‘Pot Bites Kettle: A Reply to Miller’, Australasian Journal of Philosophy, 69 (1991), 212–13; Shalkowski, Scott, ‘The Ontological Ground of the Alethic Modality’, Philosophical Review, 103 (1994), 669–88CrossRefGoogle Scholar; McGinn, Colin, Logical Properties (Oxford: Clarendon Press, 2000), Ch. 4CrossRefGoogle Scholar.

⁶ Lewis, op. cit. note 1, 5ff.

⁷ Cf. Lewis, op. cit. note 1, 3–5

⁸ Lewis, David, Counterfactuals (Oxford: Blackwell, 1973), 87Google Scholar.

⁹ Ibid.

¹⁰ In the metaphysical rather than in the chemical sense, of course.

¹¹ Cf. Lewis, op. cit. note 1, 2.

¹² In Quinean fashion, of course, the metaphysician might be able to tell the scientist what he – the scientist – takes there to be.

¹³ See also Lewis' discussion of this matter, op. cit. note 1, 108–15. Tellingly, Quine defended the existence of sets on the grounds that they are central to mathematics, and mathematics is central to science (to physics, in particular) rather than to philosophy. For more discussion on the methodological issues touched on here, see e.g., Divers, John, Possible Worlds (London: Routledge, 2002), Ch. 9Google Scholar, and Daniel Nolan, David Lewis (UK: Acumen), 203–13.

¹⁴ I have ignored here the fact that non-reductive modal realism discerns impossible as well as possible concrete worlds among that plurality. This is, of course, an additional problem for non-reductive modal realism (though not for Lewis).

¹⁵ Stalnaker, Robert, ‘Modalities and Possible Worlds’, in Kim, Jaegwon and Sosa, Ernest (eds.), A Companion to Metaphysics (Oxford: Blackwell, 1995), 336–7Google Scholar.

¹⁶ Oderberg, David, Real Essentialism (London: Routledge, 2007), 2–4CrossRefGoogle Scholar.

¹⁷ Lewis, David, ‘Counterpart Theory and Quantified Modal Logic’, reprinted in his Philosophical Papers, Volume 1 (Oxford: Oxford University Press, 1983), 28Google Scholar.

¹⁸ Fine, Kit, ‘Introduction’, Modality and Tense (Oxford: Clarendon Press, 2005), 2CrossRefGoogle Scholar.

¹⁹ Fine, op. cit. note 18, 1–2.

²⁰ Naming and Necessity, op. cit. note 2, 45 n13; see also Plantinga, The Nature of Necessity, op. cit. note 2, 116ff.

²¹ Hazen, Allen, ‘Counterpart Theoretic Semantics for Modal Logic’, Journal of Philosophy, 76 (1979), 321CrossRefGoogle Scholar.

²² Hazen, op. cit., note 21, 321–2, and Divers, Possible Worlds, op. cit., note 13, 129.

²³ Possible Worlds, op. cit. note 13, 131.

²⁴ Of course, the fact that Humphrey might have won entails the fact that Nixon might have lost, but this does not make either fact relational in nature.

²⁵ Op. cit. note 21, 323–4.

²⁶ Plantinga, , ‘Two Concepts of Modality: Modal Realism and Modal Reductionism’, reprinted in his Essays in the Metaphysics of Modality (Oxford: Oxford University Press, 2003), 221CrossRefGoogle Scholar; cf. Lewis, op. cit. note 1, 241.

²⁷ Possible Worlds, op. cit. note 13, 132.

²⁸ See note 2 above for references.

²⁹ Forrest's conception of possible worlds as structural universals might be an exception; see Forrest, Peter, ‘Ways Worlds Could Be’, Australasian Journal of Philosophy, 64 (1986), 15–24CrossRefGoogle Scholar. For discussion, see Forbes, Languages of Possibility, op. cit. note 4, 80–2.

³⁰ To clear up a potential elementary confusion: for the ersatzist all possible worlds actually exist, but only one of them is actual. For a world to be actual (non-actual) is for it to represent (fail to represent) things the way they are. Some ersatzists, such as Plantinga, take the actual world to be the same kind of entity as the merely possible ones, viz., an abstract entity. (Plantinga thus distinguishes between the actual world and physical reality – i.e., ‘us and our surroundings’). Other ersatzists take the actual world and merely possible worlds to be different kinds of entity – Stalnaker, for example, takes a merely possible world to be a property, but takes the actual world to be the entity that instantiates one such property.

³¹ The sense that the ersatzist confuses the order of explanation is particularly acute in Adams' version of ersatzism, according to which possible worlds are sets of maximal consistent propositions (‘Theories of Actuality’, op. cit. note 2). On Adams' view, ‘For me to feel a pain in some possible world is just for a proposition, to the effect that I feel pain, to be a member of a certain kind of set of propositions (namely, of some world-story)’ (‘Theories of Actuality’, 205). It follows from this that I am possibly in pain just in case the proposition that I am in pain is a member of a certain kind of set (a world-story). But I am not possibly in pain in virtue of the fact that the proposition ‘I am in pain’ is a member of some world-story, anymore than I am in pain in virtue of the fact that ‘I am in pain’ belongs to the set of actually true propositions. Rather: the proposition ‘I am in pain’ belongs to the set of actually true propositions in virtue of the fact that I am indeed in pain. And similarly, the proposition ‘I am in pain’ is a member of some world-story in virtue of the fact that I am indeed possibly in pain.

³² An object x exists in a world w only in the following sense: if w had been actual, x would have existed simpliciter (Plantinga, The Nature of Necessity, op. cit. note 2, 46ff; cf. Stalnaker, ‘Modalities and Possible Worlds’, op. cit. note 15, 336).

³³ Oderberg appears not to distinguish between the two when he makes a similar complaint to mine: ‘… the question arises as to how what is true of that kind of thing [a possible world construed as an abstract object] can have any bearing on the modal properties of a concrete material object such as a man, a mouse or a mountain’ (Real Essentialism, op. cit. note 16, 3; emphasis added).

³⁴ Indeed, not just when it comes to modality. Witness, for example, Lewis' and Stalnaker's identification of propositions with sets of possible worlds where they hold true. This is patently inadequate: propositions can be true or false; sets can be neither (cf. Plantinga, ‘Two Concepts of Modality’, op. cit. note 26, 207).

³⁵ I do not mean to imply, of course, that it is indeed correct to identify the fact that Humphrey might have won with the fact that Humphrey himself wins in another possible world (anymore than it is correct to identify mental facts with physical facts). In order for Humphrey himself to win in another possible world, that world would have to be concrete, since Humphrey is concrete and he would be literally a part of it. But as I argued in section 2, there are no concrete possible worlds. And even if there were, Humphrey could not exist in two of them (as the present identification would require), for no concrete object can be in two different places at the same time.

³⁶ Modality, op. cit. note 4, 108; cf. Lewis, op. cit. note 1, 196 and Divers, Possible Worlds, op. cit. note 13, 129, 134–5.

³⁷ Rosen's fictionalism about worlds, which is itself a form of anti-realism rather than realism about possible worlds, is also susceptible to the objection from irrelevance (Rosen himself observes this; see his ‘Modal Fictionalism’, Mind, 99 (1990), 349–54). According to fictionalism, facts about what is possible and necessary are identical with facts about the content of the story PW – the hypothesis of a plurality of concrete worlds. Thus, the fact that Humphrey might have won is (supposedly) identical with the fact that according to PW, there is a world in which a counterpart of Humphrey wins. Rosen candidly brings out the implausibility of this identification by noting that it calls for a radical shift in our patterns of modal interest and concern. Thus, if fictionalism is correct, Humphrey must now care deeply about what happens to a certain fictional character (his winning counterpart) in the story PW. This is implausible. I also note that, as observed earlier, the issue of concern presupposes the issue of irrelevance. Humphrey cannot be expected to care deeply about the fate of a certain fictional character because facts about that character are simply irrelevant to what is true of Humphrey, namely, that he might have won. The fictional character, and the world he inhabits, represent Humphrey as winning, and are therefore at best evidence that Humphrey might indeed have won. (For a general overview of fictionalism, see Nolan, ‘Modal Fictionalism’, Standford Encyclopedia of Philosophy, E. Zalta (ed.), (http://plato.stanford.edu/entries/fictionalism-modal/).)

³⁸ I will not consider the issue of whether possible worlds (construed as abstract objects) can be useful in philosophical accounts of concepts other than modality, though I have already indicated that one such additional use (propositions) is problematic (see footnote 15 above).

³⁹ Whether this lack of ‘ontological seriousness’ is harmless is an important question, but one which I leave for another occasion.

⁴⁰ Paul Teller, ‘Supervenience’, in Kim and Sosa (eds.), op. cit. note 15, 485.

⁴¹ For an accessible account of this use of possible worlds, see Michael Loux, ‘Introduction: Modality and Metaphysics’, in Loux (ed.), op. cit. note 2, 16–30.

⁴² Loux, op. cit. note 41, 19.

⁴³ Although Carnap had already done some pioneering work in his Meaning and Necessity, first published in 1947 (Chicago: Chicago University Press).

⁴⁴ Kripke, Saul, ‘Semantical Considerations on Modal Logic’, reprinted in Linsky, Leonard (ed.), Reference and Modality (Oxford: Oxford University Press, 1971), 63–87Google Scholar.

⁴⁵ Here a remark by Kripke is apposite: ‘The apparatus of possible words (sic) has (I hope) been very useful as far as the set-theoretic model-theory of quantified modal logic is concerned, but has encouraged philosophical pseudo-problems and misleading pictures’ (Naming and Necessity, op. cit. note 2, 48 n15).

⁴⁶ Lewis, op. cit. note 1, 18ff.

⁴⁷ To deny that the possible-worlds semantics is the right semantics for our ordinary modal discourse is not to deny, of course, that ordinary modal claims can be about worlds. If I say that the world could have been a better place, for example, I am evidently making a claim about the actual world. But according to the possible-worlds semantics, I am in fact making a claim about a different world – one which exists, but is not actual – for what I am saying is that there is a possible world which is indeed a better place than the actual world. It is this sort of analysis that I am rejecting.

⁴⁸ See Lewis, op. cit. note 8, 84.

⁴⁹ Cf. van Inwagen, , ‘Two Concepts of Possible Worlds’, reprinted in his Ontology, Identity and Modality (Cambridge: Cambridge University Press, 2001), 208Google Scholar; Loux, op. cit. note 41, 30ff. Stalnaker is an exception; see his ‘Possible Worlds’, op. cit. note 2, 226–227.