Many problems of the many
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Many problems of the many Hao Hong1 Received: 30 November 2019 / Accepted: 19 October 2020 © Springer Nature B.V. 2020
Abstract David Lewis (Papers in metaphysics and epistemology: volume 2. Cambridge University Press, Cambridge, pp 164–182, 1993) offers two solutions to the problem of the many, one of which relies on supervaluationism and the other on the notion of “almostidentity” for the most part. In this paper, I argue that Lewis’ other metaphysical views constitute reasons to prefer his second solution to the first one. Specifically, Lewis’ theory of propositions and his counterpart theory give rise to two similar problems of the many, which I call “the problem of many propositions” and “the problem of many counterparts” respectively. While both Lewis’ solutions may solve the problem of the many with respect to objects in the actual world, I argue that only his second solution can solve the problem of many propositions and the problem of many counterparts. Therefore, for anyone who accepts Lewis’ metaphysical views on propositions and counterparts, they should embrace Lewis’ second solution to the problem of the many for the reason of unification. Keywords The problem of the many · Supervaluationism · Almost-identity · Propositions · Counterparts Many material objects do not have precise boundaries. Some of philosophers’ favorite examples of such objects include cats, mountains, and clouds. Consider Tibbles the cat on the mat.1 Some hairs are definitely parts of Tibbles and some are definitely not. But there are some hairs that may or may not be counted as parts of Tibbles. Assume that there are 1000 “boundary hairs” h1 , h2 ,…, h1000 . Let c be the cat-like entity that has all these 1000 hairs. Let c1 be the cat-like entity that has all these 1000 hairs except for h1 ; and similarly for c2 ,…, c1000 . We have 1001 cat-like entities with minute and insignificant differences. Further, the differences among the 1001 cat-like entities are so minute that they seem not sufficient to single out one of them as a real cat, Tibbles, 1 The specific description of this example is borrowed from Lewis (1993).
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Hao Hong [email protected] Department of Philosophy and Honors College, University of Maine, 5776 The Maples, Orono, ME 04469, USA
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while others being merely “cat-like”.2 Thus, if there are cats at all, it seems that what is really the case is that there are 1001 cats, rather than just one, on the mat. It is not hard to see that we face a couple of problems if we admit that there are 1001 cats on the mat. First, we have a strong intuition (which is sometimes called the “counting intuition”3 ) that the number of cats on the mat is one rather than 1001. To accommodate this intuition about the number of cats, we have to either find a way to deny that there are 1001 cats on the mat or give an explanation why we count the number of cats as one while there are indeed 1001 cats. Second, we have a similar intuition about the number of Tibbles: there is one Tibbles rather than many. If there are 1001 c
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