Proofs and Models in Philosophical Logic (Elements in Philosophy and Logic) - Softcover

Restall, Greg

Softcover

ISBN 10: 1009045385 ISBN 13: 9781009045384

Publisher: Cambridge University Press, 2022

Synopsis

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2022
• Language: English
• ISBN 10: 1009045385
• ISBN 13: 9781009045384
• Binding: Paperback
• Number of pages: 92