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Proofs and Models in Philosophical Logic

Published online by Cambridge University Press:  25 March 2022

Greg Restall
Affiliation:
University of St Andrews, Scotland

Summary

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits.
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Online ISBN: 9781009040457
Publisher: Cambridge University Press
Print publication: 21 April 2022
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© Greg Restall

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Proofs and Models in Philosophical Logic
  • Greg Restall, University of St Andrews, Scotland
  • Online ISBN: 9781009040457
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Proofs and Models in Philosophical Logic
  • Greg Restall, University of St Andrews, Scotland
  • Online ISBN: 9781009040457
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Proofs and Models in Philosophical Logic
  • Greg Restall, University of St Andrews, Scotland
  • Online ISBN: 9781009040457
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