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Grim, Omniscience, and Cantor’s Theorem

100%

Lembke M.

Forum Philosophicum

2012

tom 17

nr 2

211-223

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscience is sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an enormously untoward side effect, but it is self-referentially incoherent as well.

Composition as identity and plural Cantor's theorem

100%

Bohn E. D.

2016

tom 25

nr 3 Mereology and Beyond (II)

411-428

In this paper, I argue that the thesis of Composition as Identity blocks the plural version of Cantor’s Theorem, and that this in turn has implications for our use of Cantor’s theorem in metaphysics. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano, and might be turned around to become an abductive argument for Composition as Identity