LEADER 04449nam 2200565 450 001 996466402303316 005 20230508110638.0 010 $a3-030-88534-8 035 $a(CKB)4940000000615689 035 $a(MiAaPQ)EBC6799131 035 $a(Au-PeEL)EBL6799131 035 $a(OCoLC)1284875998 035 $a(PPN)258839023 035 $a(EXLCZ)994940000000615689 100 $a20220729d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFounding mathematics on semantic conventions /$fCasper Storm Hansen 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (259 pages) 225 1 $aSynthese Library ;$vv.446 311 $a3-030-88533-X 320 $aIncludes bibliographical references and index. 327 $aIntro -- Founding Mathematics on Semantic Conventions -- Preface -- Contents -- 1 Introduction -- 1.1 Overview and Guide to Partial Reading -- 2 Classical Mathematics and Plenitudinous Combinatorialism -- 2.1 Large Cardinal Axioms and Theorems of Arithmetic -- 2.2 Transfinite Ordinals -- 2.3 Transfinite Cardinals -- 2.4 The Continuum Hypothesis -- 3 Intuitionism and Choice Sequences -- 3.1 General Introduction -- 3.2 Brouwer on Freely Proceeding Choice Sequences -- 3.3 Constitution of Free Choice Sequences -- 3.4 Evaluation of Brouwer's Claim -- 3.5 Verificationism and Intuitionistic Logic -- 4 From Logicism to Predicativism -- 4.1 Frege -- 4.2 Russell -- 4.3 Weyl -- 4.4 Weyl's Failure to Include All Real Numbers -- 5 Conventional Truth -- 5.1 The Obvious Solution to the Liar Paradox -- 5.2 Conventional Truth Conditions -- 5.3 The Dogma -- 5.4 Possible Language Conventions -- 5.5 T-schemas and Expressive Strength -- 5.6 Dialectical Situation -- 5.7 The View from Nowhere -- 5.8 Comparison with Chihara's Position -- 5.9 Revenge -- 6 Semantic Conventionalism for Mathematics -- 6.1 Needs Assessment -- 6.2 Simple Arithmetic as a Conventional Language -- 6.3 Quine's Anti-Conventionalism -- 6.4 Rule-Following -- 6.5 Choice of Logic -- 7 A Convention for a Type-free Language -- 7.1 The Kripke Convention and Its Shortcomings -- 7.2 Reformulating the Kripke Convention -- 7.2.1 Collapsing Truth and Satisfaction of View-From-Nowhere Truth Conditions -- 7.2.2 Kleenification -- 7.2.3 Kripke Recursion -- 7.3 Adding a Conditional with Supervaluational Semantics -- 7.3.1 Supervaluation over All Possibilities -- 7.3.2 View-From-Nowhere Truth Conditions for the Strong Conditional -- 7.3.3 If the Supervaluation Criterion is Not Satisfied -- 7.3.4 Ensuring Quantification over All Possibilities in the Presence of Supervaluation. 327 $a7.3.5 Iteration of the Strong Conditional -- 7.3.6 Summary -- 7.4 Denoting Terms for Applied Mathematics -- 7.5 Meta-Theorems -- 8 Basic Mathematics -- 8.1 Logic -- 8.2 Natural Numbers -- 8.3 Integers -- 8.4 Rational Numbers -- 8.5 Classicality So Far -- 8.6 Classes -- 8.7 An Example of Applied Mathematics -- 9 Real Analysis -- 9.1 Functions -- 9.2 Real Numbers -- 9.3 Exponentiation -- 9.4 Completeness -- 9.5 Suprema, Infima, and Roots -- 9.6 Continuity -- 9.7 Operations on Functions -- 9.8 Differentiation -- 9.8.1 Calculating Derivatives -- 9.8.2 Uniform Differentiability -- 9.9 Integration -- 9.10 Unbounded Intervals and Piecewise Continuity -- 9.11 Completifications of Functions Generalized -- 9.12 Another Example of Applied Mathematics -- 9.13 Diagonalization -- 10 Possibility -- 10.1 All Possible Real Numbers -- 10.2 Modal Metaphysics -- 10.3 Conclusion -- References -- Index of Symbols -- General Index. 410 0$aSynthese Library 606 $aMathematics$xPhilosophy 606 $aLogic, Symbolic and mathematical 606 $aSemantics (Philosophy) 606 $aFilosofia de la matemātica$2thub 606 $aLōgica matemātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematics$xPhilosophy. 615 0$aLogic, Symbolic and mathematical. 615 0$aSemantics (Philosophy) 615 7$aFilosofia de la matemātica 615 7$aLōgica matemātica 676 $a510.1 700 $aHansen$b Casper Storm$01052511 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466402303316 996 $aFounding Mathematics on Semantic Conventions$92483844 997 $aUNISA