Paradoxes, Intuitionism, and Proof-Theoretic Semantics

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Abstract

In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.
Original languageEnglish
Title of host publicationPeter Schroeder-Heister on Proof-Theoretic Semantics
EditorsThomas Piecha, Kai F. Wehmeier
Place of PublicationCham
PublisherSpringer
Pages363-374
Number of pages12
ISBN (Electronic)978-3-031-50981-0
ISBN (Print)978-3-031-50983-4
DOIs
Publication statusPublished - Feb 2024

Publication series

NameOutstanding Contributions to Logic
PublisherSpringer
Volume29
ISSN (Print)2211-2758
ISSN (Electronic)2211-2766

Keywords

  • Definitional freedom
  • Intuitionism
  • Liar
  • Paradoxes
  • Proof-theoretic semantics

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