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Against Lewisian Modal Realism from a Metaontological Point of View

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Abstract

Modal realism is an ontological position made familiar by David Lewis, according to which there exist possible worlds other than the actual world that we inhabit. It is hard to uphold modal realism, and indeed modal realism has only a few advocates. However, as most contemporary metaphysicians agree, this does not mean that it is easy to refute modal realism. In this paper, I argue against modal realism from a metaontological point of view. First, I provide a precise formulation of modal realism based on Lewis’ discussion of modal realism. Second, I argue that modal realism is undermined unless it incorporates a view of metaontology known as ontological realism. Third, I point out that if modal realism incorporates ontological realism, it comes into conflict with its own formulation.

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Notes

  1. Cf. Lewis (1986, p. 2).

  2. Cf. Lewis (1986, pp. 81–2). Lewis himself carefully avoids using the term “concrete” in his explanation of possible worlds. But his position is often construed in terms of concrete worlds. See, e.g., Sider (2003, Sec. 3.5).

  3. Cf. Lewis (1986, p. 86). This is actually the “naïve version” of Plenitude (Pigden and Entwisle 2012, p. 158). Lewis claims that the naïve version is not a good principle for modal realists to uphold because of the unclarity of what the term “way” means, and adopts the Principle of Recombination instead of Plenitude (e.g., Lewis 1986, pp. 86–8). I use Plenitude rather than the Principle of Recombination because, as I argue later, even if Plenitude is established (by the Principle of Recombination or some other principle), modal realism faces a serious trouble. I am not (at least not primarily) concerned with the validity of the Principle of Recombination, and hence I ignore the objections to modal realism that are based on the principle’s inadequacy (e.g., Pigden and Entwisle (2012)’s). Furthermore, Lewis seems to use this principle simply to obtain Plenitude; thus its inadequacy is not fatal for modal realism.

  4. Cf. de Rosset (2009a, p. 998).

  5. To avoid using modal notions, it suffices to characterize possible worlds using mereological notions and spatiotemporal relations, as Lewis himself does. However, it implies that the actual world is ontologically on a par with possible worlds since the characterisation can apply to the actual world too.

  6. Two examples of these are combinatorialism (e.g., Armstrong (1989)) and ersatz modal realism (e.g., Plantinga (1974); Adams (1974)).

  7. This is called “modalism”. See Forbes (1985).

  8. Chalmers (2009, p. 77) defines metaontology in the way described here.

  9. See, especially, Sider (2009) and Chalmers (2009) for details of this dispute. Ontological anti-realism is sometimes called “ontological deflationism” (e.g., Sider (2011)).

  10. Cf. van Inwagen (1990).

  11. Ontological anti-realism does not claim that there are different meanings or interpretations of a crucial predicate used to express the Special Composition Question, such as “compose”. See Sider (2011, Chap. 9.4) for this point.

  12. More precisely, suppose that in our actual use of language, u 1, there is a modal truth, p, such that p is true if and only if a certain possible world, w, exists, according to Correspondence. In a different use, u 2, w does not exist, so that p is false according to Correspondence. This case can be construed in such a way that u 2 makes p false. However, there may well be a case in which p is true while w does not exist; it at least seems difficult for ontological anti-realism to deny this.

  13. The term “grounding” may be more popular. In fact, fundamentality can be defined in terms of grounding, as shown below. I believe that the difference is a matter of terminology. I use “fundamentality” here because this can be appropriately contrasted with “existence”.

  14. Cf., e.g., Schaffer (2009b).

  15. Schaffer calls this stance “permissive about existence.” See Schaffer (2009b, pp. 356–362).

  16. Schaffer also crafts the notion of derivativeness, which is dual to the notion of fundamentality: x is derivative if and only if something grounds x. Fundamentality and derivativeness are exhaustive and exclusive to each other; thus, everything is either fundamental or derivative, and nothing is both fundamental and derivative.

  17. There are other notions in the same vein. For example, ontological dependence and truthmaking may be regarded as versions of grounding, by which other notions of fundamentality could be defined.

  18. Fundamentality may well be gradual, in which case the following conditions can be used instead of No-Collapse: something is more fundamental than others.

  19. This problem is pointed out in Cameron (2009) and Kalhat (2008). Ross P. Cameron argues for a deflationistic view regarding the existence of possible worlds. O-modal realism, however, can respond to his argument by accepting impossible world as well as possible worlds. Javier Kalhat interprets Lewis’ argument as showing that he is almost committed to impossible worlds, and argues that it follows from this interpretation that his reduction of modality is circular. While I agree with this interpretation, I do not agree with what follows from it. See note 23.

  20. Kalhat calls this “The Utility Argument for Impossible Worlds”. See Kalhat (2008, p. 10). See also Berto (2013, Sec. 1); Yagisawa (2010, Ch. 8.3–8.5).

  21. This is how Cameron argues for his deflationist view of modality. He holds that the distinction between possible and impossible worlds is “a highly unnatural distinction” (Cameron 2009, p. 13) in the sense that we draw this because of our interests.

  22. Some might think that there is a way to distinguish possibility and impossibility that is unavailable for linguistic ersatzers. Impossible worlds may fall into a different category from possible worlds. For instance, the former is abstract while the latter is concrete (as Concrete states). Linguistic ersatzers cannot accept this distinction because for linguistic ersatzers the actual world is the only concrete world. However, there is no good reason to think that any kinds of possible worlds are concrete entities (and correspondingly any kinds of impossible worlds are abstract entities), given that there are many kinds of possibility and the distinction between possibility and impossibility is unnatural. See note 21.

  23. This is how Cameron construes Lewis’ response to the accusation that his reduction is circular by being implicitly committed to a modal notion—the distinction between possibility and impossibility. See Cameron (2012, p. 10); See also Sider (2003, Sec. 3.9).

  24. The notion of fundamentality might be regarded as offering support for O-modal realism. For example, if there were a single fundamental logic, this could be used to draw the fundamental distinction between possibility and impossibility. Unfortunately, this line of defence of O-modal realism is not very promising because there are many different logics: we have classical, intuitionistic, and relevant logic, as well as other less well-known logical systems. There seems to be no good reason to choose one logic with which to draw the fundamental distinction between possibility and impossibility. Thus, I take many different logics to raise at least a prima facie problem, just as many kinds of possibility do.

  25. See Yagisawa (1988, 2010) for extended modal realism. It is less popular than the standard (Lewisian) modal realism, but frequently discussed when the topic of discussion is related to impossible worlds.

  26. A reason to accept extended modal realism is, some argue, that Plenitude allows for a world that creates a serious problem for L-modal realism. Charles Pigden and Rebecca E. B. Entwisle argue that their interpretation of Plenitude entails the existence of “spread worlds”, which “spread through logical space and exclude all alternatives” so that “there is only one way the world could be” (Pigden and Entwisle 2012, p. 163). This objection to L-modal realism can be blocked if there are impossible worlds and this spread is limited to certain impossible worlds.

  27. Correspondence, too, should be slightly modified to be relative to some criteria of possibility. An example of this as follows:

    • Extended-Correspondence It is possible relative to c that p if and only if there is a w such that w is a world that is a member of the class specified by c, and ‘p’ is true at w,

    where c is a criterion of possibility and specifies a class of worlds relevant to a given kind of possibility. Yagisawa (2010, p. 177) presents the truth conditions of modal statements in a similar way.

  28. I ignore the difference between genuine and analogous spatiotemporal relations described in Lewis (1986, pp. 75–76).

  29. Priority monism is an ontological position according to which there is only one fundamental entity among concrete entities. See Schaffer (2014) for details.

  30. The condition for priority monism is the following:

    • Priority Monism ∃x(x is fundamental &∀y(y is fundamental → x = y))

  31. Sum-Priority suggests a different version of E-modal realism with the thesis that the logical space — the maximal sum of absolutely everything—is fundamental, instead of Extended-Fundamentality. This version might appear to resemble priority monism more than Monism-like E-modal realism does; however, it faces the same problem as Monism-like E-modal realism.

  32. For details of junky worlds, see Bohn (2009, Sec.I). The notion of “junky” is the converse of the notion of “gunky”. See also note 39.

  33. Schaffer holds that a junky world is metaphysically impossible. See Schaffer (2010, pp. 64–5).

  34. Cf., e.g., Varzi (2015, Sec. 4.4). The original formulation is found in Leonard and Goodman (1940).

  35. It seems obvious that the problem of junky worlds can be avoided simply by rejecting Lewisian-World. However, this is not easy for E-modal realists to do, since E-modal realism is motivated by the definition of possible worlds that Lewis himself endorses. Moreover, a similar problem would presumably arise insofar as a world is defined as an “aggregate” in some formal sense.

  36. Cf. Lewis (1994). Lewis actually uses the term “fundamental” for properties and relations on which truths supervene. For example, “any contingent truth whatever is made true, somehow, by the pattern of instantiation of fundamental properties and relations” (ibid., p. 473).

  37. The definition of an atom is as follows: x is an atom if and only if x has no proper part.

  38. It can retain Lewisian-World but not Sum-Priority, which must be replaced by something like the following thesis:

    Part-Priority Proper parts are more fundamental than their sums.

  39. See Sider (1993). As I mentioned in note 32, the notion of “junky” is the converse of the notion of “gunky”.

  40. E-modal realists might actually be able to deny the ontological difference between sums and their parts if they accept non-fundamental abstract entities. Such abstract entities are not part of worlds, since worlds are concrete, according to Concreteness. (I am grateful to Ted Sider for suggesting this option to me.) In pursuing this line of response, E-modal realists must explain exactly how different abstract entities are from concrete objects and the nature of the relationship between them. More particularly, any alleged distinction between abstract and concrete objects must satisfy Objectivity. This requirement is not easy to meet.

  41. Although the argument against E-modal realism I gave in this section presupposes Schafferian ontological realism, related arguments can be constructed for other versions of ontological realism. As for Sider’s version, for example, Monism-like E-modal realists must say that their “world view”’s ontology includes not only worlds (including junky ones) and entities that are asserted to be their parts in non-fundamental languages but also other entities similarly asserted a junky world is a part of. There seems no way to obtain these entities since the latter entities violate Lewisian-World. Nihilism-like E-modal realists face a similar problem. They need entities that are asserted to be proper parts of point-sized possibilia but they violate Atom-Fundamentality.

    As for Fine’s version, Monism-like E-modal realists would say that a fact about the existence of any contingent object is grounded in the fact that there exists a world that it is a part of and that the latter fact is fundamental (there is no grounding fact for it). However, it cannot be true for a junky world. If it is true, objects in a junky world are parts of it. In this case, the junky world is not fundamental because the fact about its existence should be similarly grounded in a fact that there exists something that the junky world is a part of. Nihilism-like E-modal realists would similarly say that a fact about the existence of any possible object is grounded in the fact that there exist point-sized possibilia that are parts of it and that the latter fact is fundamental, but in a gunky world, since even point-sized possibilia have a proper part, the fact about their existence is not fundamental in the same way.

    Other versions may require more different and complicated arguments. Still, it seems plausible that my argument relies on only basic features of the relevant notion of fundamentality.

  42. This is a response to the concern that although metaphysicians do discuss junky worlds and gunky worlds, this might be because junky worlds and gunky worlds are merely conceivable rather than possible or impossible. In fact, Williams (2006) argues that we conceive of gunky worlds but that their existence is only an illusion. In response, I argue that gunky worlds are not merely conceivable; this is not plausible since both kinds of worlds are characterised in terms of a formal system. I am grateful to Masashi Kasaki for raising this concern.

  43. It may be worse, since there are objections to modal realism that can be easily blocked for E-modal realists. See note 26.

  44. Such critics include Lycan (1988); Shalkowski (1994); and Pigden and Entwisle (2012). (More precisely, they discuss the Principle of Recombination, the elaborated version of Plenitude. See also note 3.) Replies to their criticisms are found in Sider (2003) and Cameron (2012).

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Acknowledgements

This work was supported in part by JSPS Grant-in-Aid for Young Scientist (B), Grant Number 24720012 and for Scientific Research (C), Grant Number 15 K02001. Earlier versions of this paper were presented at the First Conference on Contemporary Philosophy in East Asia, Academia Sinica, Taiwan, October 2012; CAPE Workshop on Meta-metaphysics, Kyoto University, Japan, August 2014; A Workshop on David Lewis’s On the Plurality of Worlds, Kyoto University, Japan, March 2015. I would like to thank the audiences on those occasions for helpful discussion. I would like to especially thank Masashi Kasaki and Ted Sider for their help and encouragement, without which this paper would not exist.

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    Tora Koyama

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Koyama, T. Against Lewisian Modal Realism from a Metaontological Point of View. Philosophia 45, 1207–1225 (2017). https://doi.org/10.1007/s11406-017-9824-1

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