Recombination and Paradox

Philosophers' Imprint 15 (2015)
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Abstract

The doctrine that whatever could exist does exist leads to a proliferation of possibly concrete objects given certain principles of recombination. If, for example, there could have been a large infinite number of concrete objects, then there is at least the same number of possibly concrete objects in existence. And further cardinality considerations point to a tension between the preceding doctrine and the Cantorian conception of the absolutely infinite. This paper develops a parallel problem for a variety of possible worlds accounts of modality which eschew the commitment to a plethora of possibly concrete objects. Moreover, the difficulty is importantly different from more familiar threats of paradox exemplified by certain descendants of Russell's paradox of propositions and Kaplan's paradox

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Gabriel Uzquiano
University of Southern California

Citations of this work

In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
Cantor, Choice, and Paradox.Nicholas DiBella - forthcoming - The Philosophical Review.
Alternative Logics and Applied Mathematics.Timothy Williamson - 2018 - Philosophical Issues 28 (1):399-424.
A Purely Recombinatorial Puzzle.Fritz Peter - 2017 - Noûs 51 (3):547-564.

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