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- Title
Some highs and lows of hylomorphism: on a paradox about property abstraction.
- Authors
Robertson Ishii, Teresa; Salmón, Nathan
- 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.
- Subjects
HYLOMORPHISM; CONTRADICTION; LIAR paradox; RESTRICTIONS; COMPREHENSION
- Publication
Philosophical Studies, 2020, Vol 177, Issue 6, p1549
- ISSN
0031-8116
- Publication type
Article
- DOI
10.1007/s11098-019-01274-4