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A Paradox about Sets of Properties

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:
CreatorsEmailORCID
Salmón, Nathannsalmon@ucsb.edu0000-0002-3551-7435
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-dev.library.pitt.edu/id/eprint/19404

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