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Lewis' Indexical Argument for World-Relative Actuality

  • Richard M. Gale (a1)


David Lewis has shocked the philosophical community with his original version of extreme modal realism according to which “every way that a world could possibly be is a way that some world is”. Logical Space is a plenitude of isolated physical worlds, each being the actualization of some way in which a world could be, that bear neither spatiotemporal nor causal relations to each other. Lewis has given independent, converging arguments for this. One is the argument from the indexicality of actuality, the other an elaborate cost-benefit argument of the inference-to-the-best explanation sort to the effect that a systematic analysis of a number of concepts, including modality, causality, propositions and properties, fares better under his theory than under any rival one that takes a possible world to be either a linguistic entity or an ersatz abstract entity such as a maximal compossible set of properties, propositions or states of affairs. Lewis' legion of critics have confined themselves mostly to attempts at a reductio ad absurdum of his theory or to objections to his various analyses. The indexical argument, on the other hand, has not been subject to careful critical scrutiny. It is the purpose of this paper to show that this argument cannot withstand such scrutiny. Its demise, however, leaves untouched his argument from the explanatory superiority for his extreme modal realism.



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1 Lewis, David, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), 2.

2 For Lewis, the Kantian thesis that necessarily all times (spaces) are temporally (spatially) related holds intra- but not inter-world.

3 This argument forms the substance of chapters 1 and 3 of On the Plurality of Worlds.

4 The notable exception is Peter van Inwagen's excellent Indexicality and Actuality”, Philosophical Review 89 (1980), 403426.

5 Lewis, David, “Anselm and Actuality”, Nous 4 (1970), 175188; reprinted, with added postscripts, in Lewis, David' Philosophical Papers, vol. 1 (New York: Oxford University Press, 1983).

6 See 92–93 of Lewis' Plurality of Worlds and 86 of Lewis' Counterfactuals (Cambridge, MA: Cambridge University Press, 1973) which chapter is reprinted in Loux, Michael, ed., The Possible and the Actual (Ithaca, NY: Cornell University Press, 1979), 182189. Future references are to the pagination in the latter.

7 Lewis, , “Anselm and Actuality”, 187.

8 Lewis, , Plurality of Worlds, 93.

9 Ibid.: he adds that “The ‘actual at’ relation between worlds is simply identity”.

10 Lewis, , Plurality of Worlds, 2.

11 Lewis, , Counterfactuals, 183. That Lewis commits a category mistake in conjoining this definition with his insistence that worlds are maximal spatiotemporal aggregates is made by Stalnaker, Robert, “Possible Worlds”, Nous 10 (1976), 6575, and van Inwagen, , “Indexicality”, 407.

12 That other words are no more abstract or linguistic entities than is the actual worlds is asserted in footnote 3 on 7 of Lewis, Plurality of Worlds: “But worlds, as I understand them, are not like stories or story-tellers. They are like this world; and this world is no story, not even a true story.” A possible strategy; for Lewis to make his claim that a possible world is a way things could have been compatible with his claim that other worlds are just like our world, which is a maximum spatiotemporal aggregate, is to use his indexical argument to justify a revisionary analysis of “a way things could have been” as “a maximal spatiotemporal aggregate”.

13 Lewis, , “Indexicality and Actuality”, 407.

14 See Lewis, , Counterfactuals, 182.

15 Lewis, , “Anselm and Actuality”, 184185, my italics.

16 Ibid., 185.

17 Adams, Robert M., “Theories of Actuality”, Nous 8 (1974), 211231. Reprinted in Loux, , The Possible and the Actual, 205. Future references are to the pagination in the latter.

18 This point seems to be missed by the charges of inconsistency raised by Michael Loux in his introduction to The Possible and the Actual, 47, and William Lycan in “The Trouble with Possible Worlds”, which is printed in the Loux anthology, 289.

19 Lewis, , “Anselm and Actuality”, 186187.

20 Lewis, , On the Plurality of Worlds, 94.

21 Lewis, , Counterfactuals, 185.

22 Adams, , “Theories of Actuality”, 195. Lewis' response is on 125 of On the Plurality of Worlds.

23 Hazen, Allen, in “One of the Truths about Actuality”, Analysis 39 (1977), denies that there is any connection between them: “Semantically, logically, the indexical theory is the truth. This does not answer the metaphysical question about the nature of possible worlds; it is a metaphysical question.” (3).

24 Lewis, , “Anselm and Actuality”, 186187.

25 Ibid., 184–185.

26 Ibid., 185.

27 This is the analogy that Lewis himself uses. It makes no difference to the argument if the analogy is drawn with some other indexical term. It might seem to some that the analogy is closer if it is drawn to “here”, since a possible world is a place. This is wrong: a world, i.e., a maximal spatiotemporal aggregate, although it contains places, is not itself a place.

28 See his Indicators and Quasi-Indicators”, American Philosophical Quarterly 4 (1967), 85100, and my criticisms of his position in Omniscience-Immutability Arguments”, American Philosophical Quarterly 23 (1986), 328331.

29 See 22 of Lewis' Postscript to “Anselm and Actuality”, in his Philosophical Papers, 22, as well as “Anselm and Actuality”, 185, and Plurality of Worlds, 94.

30 Lewis, , Plurality of Worlds, 94.

31 The following discussion builds upon 418–419 of the van Inwagen article.

32 For a full discussion of these issues see Gale, Richard, The Language of Time (London: Routledge and Kegan Paul, 1968), chap. 2.

33 Lewis fails to see the need to relativize truth to a world, as is done in 9′, when he says that “This is the actual world' is true whenever uttered in any possible world”. My italics. Lewis, “Anselm and Actuality”, 186.

34 Van Inwagen explores this strategy on 422 of his essay, “Indexicality”.

35 Lewis, , “Anselm and Actuality”, 188. A similar remark is made, but in an inaccurate way, on 184 of Counterfactuals: “My indexical theory of actuality exactly mirrors a less controversial doctrine about time. Our present time is only one time among others. We call it alone present not because it differs in kind from all the rest, but because it is the time we inhabit.” But we do not inhabit just one time (although we might inhabit only one world). That we inhabit more than one time is true whether we conceive of ourselves as enduring substances or bundles of successive person-stages.

36 My discussion here is indebted to Adam's article, “Theories of Actuality”, especially 160.

37 A parallel problem plagues a simple property theory of being now or the present according to which “X is now” is analyzed into “X has the property of nownessP, in which the latter means “X now has the property of nowness”. An examination of McTaggart's vicious infinite regress argument against any individual being present is instructive in this connection.

38 I am deeply indebted to two very astute referees for Dialogue. Their probing objections required me to spend an entire year reworking this paper. I wish to both thank and curse these people!

Lewis' Indexical Argument for World-Relative Actuality

  • Richard M. Gale (a1)


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