Some Highs and Lows of Hylomorphism: On a Paradox about Property Abstraction

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

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.

Author Profiles

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

Analytics

Added to PP
2019-03-13

Downloads
235 (#66,039)

6 months
113 (#36,950)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?