Some highs and lows of hylomorphism: on a paradox about property abstraction

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

Nathan Salmon
University of California at Santa Barbara
Teresa Robertson Ishii
University of California at Santa Barbara

Citations of this work

A Paradox About Sets of Properties.Nathan Salmón - 2021 - Synthese 199 (5-6):12777-12793.
Hylomorphisms.Christopher Shields - 2022 - Ancient Philosophy Today 4 (1):96-127.

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References found in this work

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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