Four-Dimensionalism and the Puzzles of Coincidence
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Often cited in defense of four-dimensionalism about the persistence of material objects is its treatment of the so-called puzzles of coincidence. These puzzles include the statue/lump, the ship of Theseus, Tibbles the cat, and the various fission and fusion puzzles in the personal identity literature. In their original versions, the puzzles involve changes which seem either to produce or terminate coincidence between material objects (the lump is flattened, the cat's tail is cut off, etc.), but each of the puzzles also has a modal variant in which the relevant change could have occurred but does not. 4Dists standardly take themselves to have an edge over 3Dists in the treatment of these puzzles. They claim that the original puzzles are answered easily and painlessly under 4Dism, and that their modal variants can be answered by something like counterpart theory. By contrast, they claim, 3Dists have no easy way with the originals, and no better way with the modal variants. My aim here is to determine whether this is correct. I will argue that it is not, and in fact that the puzzles are every bit as challenging for the 4Dist as they are for the 3Dist. In a final section, I will tentatively suggest that reflecting on the puzzles may provide us with reason to reject 4Dism.
McGrath, M. "Four Dimensionalism and the Puzzles of Coincidence," Oxford Studies in Metaphysics, Vol. 3 (2007, D. Zimmerman, ed.), pp. 143 - 176.