Strong Homomorphisms, Category Theory, And Semantic Paradox

Jonathan Wolfgram, Roy T. Cook

Research output: Contribution to journalArticlepeer-review

Abstract

In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox: Strong-homomorphisms. In particular, we show that (i) strong-homomorphisms between constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of constructions can be recast as special cases of our central result regarding strong-homomorphisms, and (iii) that we can use strong-homomorphisms to provide a simple demonstration of the paradoxical nature of a well-known paradox that has not received much attention in this context: The McGee paradox. In addition, along the way we will highlight how strong-homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the framework and the methods and tools of category theory.

Original languageEnglish (US)
Pages (from-to)1070-1093
Number of pages24
JournalReview of Symbolic Logic
Volume15
Issue number4
DOIs
StatePublished - Dec 30 2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s). Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

Keywords

  • Liar paradox
  • McGee paradox
  • category theory
  • language of paradox

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