Philosophical Studies 177 (6):1549-1563 (2020)

Authors
Nathan Salmon
University of California at Santa Barbara
Teresa Robertson Ishii
University of California at Santa Barbara
Abstract
We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs.
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DOI 10.1007/s11098-019-01274-4
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References found in this work BETA

A Puzzle About Belief.Saul A. Kripke - 1979 - In A. Margalit (ed.), Meaning and Use. Reidel. pp. 239--83.
Hylomorphism.Mark Johnston - 2006 - Journal of Philosophy 103 (12):652-698.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
Hylomorphism Reconditioned.Michael C. Rea - 2011 - Philosophical Perspectives 25 (1):341-358.

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