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02647aam a2200313Ii 4500 001 FD79A17C010B11EEB5B5CDCD2BECA4DB 003 SILO 005 20230602010835 008 211222t20222022enka b 001 0 eng d 020 $a 1009045385 020 $a 9781009045384 035 $a (OCoLC)1289735767 040 $a YDX $b eng $e rda $c YDX $d UKMGB $d OCLCO $d OCLCF $d EAU $d YDX $d QGJ $d XII $d SILO 050 4 $a BC71 R47 2022 100 1 $a Restall, Greg, $d 1969- $e author. $4 aut 245 10 $a Proofs and models in philosophical logic / $c Greg Restall. 264 1 $a Cambridge, United Kingdom ; $b Cambridge University Press, $c 2022. 300 $a 82 pages ; $c 23 cm. 490 1 $a Elements in philosophy and logic 504 $a Includes bibliographical references. 520 $a 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. 505 0 $a Cover -- Tilte Page -- Coypright Page -- Proofs and Models in Philosophical Logic -- Contents -- 1 Context -- 1.1 Proofs and Models -- 1.2 Paradoxes -- Example 1: The liar paradox -- Example 2: The sorites paradox -- 1.3 The Plan -- 2 Proofs -- 2.1 Proof Structures -- 2.2 Inference Rules as Definitions -- 2.3 Structural Rules -- 2.4 Other Proof Structures -- 3 Models -- 3.1 Two Truth Values -- 3.2 Beyond Two Truth Values -- 3.3 Worlds: Possible and Impossible -- 4 Connections -- 4.1 Soundness and Completeness -- 4.2 Paradoxes, Proofs and Models -- 4.3 Where to, from Here? 650 0 $a Logic. 776 08 $i ebook version : $z 9781009040457 830 0 $a Cambridge elements. $p Elements in philosophy and logic. 941 $a 1 952 $l USUX851 $d 20231004011249.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=FD79A17C010B11EEB5B5CDCD2BECA4DB 994 $a C0 $b IWAInitiate Another SILO Locator Search