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Verificationism and Classical Realizability

  • Alberto Naibo
  • Mattia Petrolo
  • Thomas Seiller
Part of the Logic, Argumentation & Reasoning book series (LARI, volume 8)

Abstract

This paper investigates the question of whether Krivine’s classical realizability can provide a verificationist interpretation of classical logic. We argue that this kind of realizability can be considered an adequate candidate for this semantic role, provided that the notion of verification involved is no longer based on proofs, but on programs. On this basis, we show that a special reading of classical realizability is compatible with a verificationist theory of meaning, insofar as pure logic is concerned. Crucially, in order to remain faithful to a fundamental verificationist tenet, we show that classical realizability can be understood from a single-agent perspective, thus avoiding the usual game-theoretic interpretation involving at least two players.

Keywords

Verificationism Realizability semantics Classical logic Untyped proof theory Axiomatic theories 

Notes

Acknowledgements

We would like to thank Marco Panza for the interest he manifested in our work and Luiz Carlos Pereira for the valuable discussions about the verificationist aspects of classical logic. This work has been partially funded by the French-German ANR-DFG project BeyondLogic (ANR-14-FRAL-0002) and by the CAPES-COFECUB project Preuve, démonstrations et représentation (Sh813–14).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.IHPST (UMR 8590), CNRS, ENSParisFrance
  2. 2.PPS (UMR 7126), CNRSParisFrance

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