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Overall similarity, natural properties, and paraphrases

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I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that anti-resemblism is true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch.

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Fig. 1

Notes

  1. See e.g. Quine (1961, p. 155), Paul (2004).

  2. Lewis (1983b, p. 42).

  3. See Lewis (1983a, c).

  4. See Lewis (1983b, pp. 42–43).

  5. See Lewis (1983c, pp. 51–52).

  6. See Lewis (1973, p. 48).

  7. Lewis (1973, pp. 93–94).

  8. See Lewis (1986a, p. 252; 1986b, p. 52).

  9. Lewis (1986b, pp. 53–54).

  10. Goodman (1972, pp. 443–445) and Lewis (1973, pp. 91–92).

  11. Lewis (1999a, p. 10).

  12. Lewis (1986b, p. 53).

  13. See Goodman (1972, pp. 443–444) and Lewis (1986b, p. 53).

  14. Notice that this traditional argument in favour of anti-resemblism does not take into account the role played by the similarity of properties in the evaluation of overall similarity. However, the similarity of properties plays a central role in my argument to the conclusion that Lewis’s mature doctrine yields a form of resemblism.

  15. See e.g. Armstrong (1978, pp. 7–94).

  16. See Lewis (1999a, p. 13; 1986a, pp. 59–60). Notice that in this article I follow Lewis in using “resemblance” and “similarity” synonymously.

  17. See Lewis (1999a, p. 14).

  18. See e.g. Sider (2011, pp. 1–8).

  19. See below on degrees of naturalness.

  20. Lewis (1986a, pp. 159–165).

  21. Lewis (1999a, pp. 13–14).

  22. Lewis (1986a, pp. 59–60).

  23. See, for instance, Hall (2010), Nolan (2005, p. 24), and Taylor (2006, p. 104).

  24. Nolan (2005, p. 24).

  25. Lewis (1999a, p. 13).

  26. Lewis (1999a, pp. 13–14, note 7). Notice that by rejecting Armstrong’s structural universals in (Lewis 1999b) Lewis thereby rejected Armstrong’s solution to the problem of resemblance of universals, which consists in conceiving of resembling universals as structural ones. However, this does not mean that Lewis changed his mind on the link between degrees of naturalness and the similarity of perfectly natural properties. He might have preferred another account of this link. For instance, an account that consists in taking modal realist paraphrases for predications of similarity to properties (see below) as genuine analyses.

  27. “The different shapes resemble each other: they are all shapes. Furthermore, one (sort of) shape may resemble another more closely than it resembles a third. Triangularity is more like quadrilaterality than it is like circularity. (…) Our task is to give an account of resemblances such as these.” Armstrong (1978, p. 101); see also Eddon (2007).

  28. If the similarity of natural properties is not determinate or fine-grained, then the relative naturalness of some natural properties is not fine-grained either, given the link Lewis draws between similarity of natural properties and degrees of naturalness. But the Lewisian denies that the joints of nature are indeterminate. So the Lewisian must agree that the similarity of natural properties is a determinate matter.

  29. (1) and (2) could be taken as primitives or as derived from “F is at least as similar G as it is to H”.

  30. Lewis (1986a, p 86). Although it is doubtful that completeness can be achieved, I shall assume it for the sake of my demonstration; see Divers and Melia (2002).

  31. Lewis (1999a, pp. 16–17, 1986a, p. 13).

  32. Perfect duplicates share all their perfectly natural properties; near duplicates share almost all their perfectly natural properties; see Lewis (1999a, pp. 25–29).

  33. Todd Buras (2006) has defended a similar conclusion. However, Buras’s argument is based on the belief that, according to Lewis, shared perfectly natural properties (or shared maximally natural properties) are the privileged respects of similarity; see Buras (2006, pp. 35–36). From this belief, Buras concludes that the ontology assigns a privileged role to some specific relation of comparative overall similarity which is wholly determined by the number of shared perfectly natural properties independently of any contextual specification; see Buras (2006, pp. 32, 36, and 40, 41). But my reading of Lewis and the model I gave show that the belief that shared perfectly natural properties are the privileged respects of similarity is wrong in Lewis’s realism about natural properties. In Lewis’s system, similarity of perfectly natural properties does not count less than commonality of perfectly natural properties in determining objective facts of overall similarity—otherwise b′ and c′ would be equally similar to a, which is not the case.

    Notice that Buras would agree with me that, in the model I offered at the end of Sect. 3, it is true independently of any context that i and j are equally similar to k. However, the reason why Buras would maintain that i and j are equally similar to k is different from mine and does not fit with Lewis’s doctrine. Buras would conclude that i and j are equally similar to k because i and j share the same number of perfectly natural properties with k. By contrast, according to my reading of Lewis, i and j are equally similar to k because i, j, and k are exactly similar in every perfectly natural respect except for the fact that i has F 1, j has F 2, and k has F 3 and because F 1 and F 2 are equally similar to F 3.

  34. The simplest model is the following. Consider three worlds, w 1 , w 2 , and w 3 that differ in exactly one natural respect: w 1 has F 1, w 2 has F 2, and w 3 has F 3. Then suppose that, objectively, F 1 is more similar to F 2 than it is similar to F 3.

  35. Lewis (1999a, pp. 16–17; 1986a, p. 13).

  36. See for instance Rodriguez-Pereyra (2002, pp. 91–92).

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Acknowledgments

Thanks to Alexander Bown, Fabrice Correia, Filipe Drapeau Contim, Stephan Leuenberger, Kevin Mulligan, Frédéric Nef, the members of eidos (the Genevan research group in metaphysics), the audience and organisers of the conference “Another world is possible” on David Lewis in Urbino, and the editors and reviewer at Philosophical Studies for helpful comments on this paper or the ideas it presents.

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Guigon, G. Overall similarity, natural properties, and paraphrases. Philos Stud 167, 387–399 (2014). https://doi.org/10.1007/s11098-013-0105-y

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