TY - BOOK ID - 101225653 TI - Proofs and models in philosophical logic PY - 2022 SN - 1009040456 1009045385 1009050303 1009050508 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Logic. KW - Intellect KW - Philosophy KW - Psychology KW - Science KW - Reasoning KW - Thought and thinking KW - Argumentation KW - Deduction (Logic) KW - Deductive logic KW - Dialectic (Logic) KW - Logic, Deductive KW - Methodology UR - https://www.unicat.be/uniCat?func=search&query=sysid:101225653 AB - 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. ER -