Vol. 41 No. 2 (2021)
Thematic section

A Nontransitive Theory of Truth over PA

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  • Jonathan Dittrich
Jonathan Dittrich
Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität, Munich, Germany
DOI: https://doi.org/10.36446/af.2021.456

Published 2021-11-01

Keywords

  • Corte,
  • Paradojas,
  • Mentiroso,
  • Verdad
  • Cut,
  • Paradox,
  • Liar,
  • Truth
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Abstract

David Ripley has argued extensively for a nontransitive theory of truth by dropping the rule of Cut in a sequent calculus setting in order to get around triviality caused by paradoxes such as the Liar. However, comparing his theory with a wide range of classical approaches in the literature is problematic because formulating it over an arithmetical background theory such as Peano Arithmetic is non-trivial as Cut is not eliminable in Peano Arithmetic. Here we make a step towards closing this gap by providing a suitable restriction of the Cut rule, which allows for a nontransitive theory of truth over Peano Arithmetic that is proof-theoretically as strong as the strongest known classical theory of truth.

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