Salmón, Nathan (2018) A Paradox about Sets of Properties. [Preprint]

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Abstract

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed.

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Item Type:	Preprint
Creators:	Creators Email ORCID Salmón, Nathan nsalmon@ucsb.edu 0000-0002-3551-7435
Additional Information:	To appear in Synthese (2021).
Keywords:	Grelling's paradox; impredicative definition; lambda abstraction; ramified type theory; Russell's paradox; Russell-Myhill
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Depositing User:	Prof. Nathan Salmón
Date Deposited:	04 Aug 2021 21:33
Last Modified:	04 Aug 2021 21:33
Item ID:	19404
DOI or Unique Handle:	SYNT-D-21-00022R2
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics
Date:	2018
URI:	https://philsci-archive.pitt.edu/id/eprint/19404

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