LEADER 05770nam 2200553Ia 450 001 9910962305803321 005 20200520144314.0 010 0 $a9780191520228 010 0 $a0191520225 035 $a(MiAaPQ)EBC7035348 035 $a(CKB)24235058200041 035 $a(MiAaPQ)EBC728976 035 $a(Au-PeEL)EBL728976 035 $a(CaPaEBR)ebr10273215 035 $a(OCoLC)309340984 035 $a(OCoLC)42745457 035 $a(FINmELB)ELB164036 035 $a(Au-PeEL)EBL7035348 035 $a(OCoLC)748207452 035 $a(EXLCZ)9924235058200041 100 $a20000913d2000 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReason's nearest kin $ephilosophies of arithmetic from Kant to Carnap /$fMichael Potter 205 $a1st ed. 210 $aOxford ;$aNew York $cOxford University Press$d2000 215 $ax, 305 p 320 $aIncludes bibliographical references (p. [290]-298) and index. 327 $aIntro -- Contents -- Introduction -- 0.1 Arithmetic -- 0.2 The a priori -- 0.3 Empiricism -- 0.4 Psychologism -- 0.5 Pure formalism -- 0.6 Trivial formalism -- 0.7 Reflexive formalism -- 0.8 Arithmetic and reason -- 1 Kant -- 1.1 Intuitions and concepts -- 1.2 Geometrical propositions -- 1.3 Arithmetical propositions -- 1.4 The Transcendental Deduction -- 1.5 Analytic and synthetic -- 1.6 The principle of analytic judgements -- 1.7 Geometry is not analytic -- 1.8 Arithmetic is not analytic -- 1.9 The principle of synthetic judgements -- 1.10 Geometry as synthetic -- 1.11 Arithmetic as synthetic -- 1.12 Arithmetic and sensibility -- 2 Grundlagen -- 2.1 Axiomatization -- 2.2 Arithmetic independent of sensibility -- 2.3 The Begriffsschrift -- 2.4 Frege's conception of analyticity -- 2.5 Numerically definite quantifiers -- 2.6 The numerical equivalence -- 2.7 Frege's explicit definition -- 2.8 The context principle again -- 2.9 The analyticity of the numerical equivalence -- 3 Dedekind -- 3.1 Dedekind's recursion theorem -- 3.2 Frege and Dedekind -- 3.3 Axiomatic structuralism -- 3.4 Existence -- 3.5 Uniqueness -- 3.6 Implicationism -- 3.7 Systems -- 3.8 Dedekind on existence -- 3.9 Dedekind on uniqueness -- 4 Frege's account of classes -- 4.1 The Julius Caesar problem yet again -- 4.2 The context principle in Grundgesetze -- 4.3 Russell's paradox -- 4.4 Numbers as concepts -- 4.5 The status of the numerical equivalence -- 5 Russell's account of classes -- 5.1 Propositions -- 5.2 The old theory of denoting -- 5.3 The new theory of denoting -- 5.4 The substitutional theory -- 5.5 Russell's propositional paradox -- 5.6 Frege's hierarchy of senses -- 5.7 Mathematical logic as based on the theory of types -- 5.8 Elementary propositions -- 5.9 The hierarchy of propositional functions in * 12. 327 $a5.10 The hierarchy of propositional functions in the Introduction -- 5.11 Typical ambiguity -- 5.12 Cumulative types -- 5.13 The hierarchy of classes -- 5.14 Numbers -- 5.15 The axiom of reducibility -- 5.16 Propositional functions and reducibility -- 5.17 The regressive method -- 5.18 The Introduction to Mathematical Philosophy -- 6 TheTractatus -- 6.1 Sign and symbol -- 6.2 The hierarchy of types -- 6.3 The doctrine of inexpressibility -- 6.4 Operations and functions -- 6.5 Sense -- 6.6 The rejection of class-theoretic foundations for mathematics -- 6.7 Number as the exponent of an operation -- 6.8 The adjectival strategy -- 6.9 Equations -- 6.10 Numerical identities -- 6.11 Generalization -- 6.12 The axiom of infinity -- 6.13 A transcendental argument -- 6.14 Another transcendental argument -- 7 The second edition of Principia -- 7.1 Logical atomism and empiricism -- 7.2 The hierarchy of propositional functions -- 7.3 Mathematical induction -- 7.4 The definition of identity -- 8 Ramsey -- 8.1 Propositions -- 8.2 Predicating functions -- 8.3 Extending Wittgenstein's account of identity -- 8.4 Propositional functions in extension -- 8.5 Wittgenstein's objections -- 8.6 The axiom of infinity -- 9 Hilbert's programme -- 9.1 Formal consistency -- 9.2 Real arithmetic -- 9.3 Schematic arithmetic -- 9.4 Ideal arithmetic -- 9.5 Metamathematics -- 9.6 Hilbert's programme -- 10 Gödel -- 10.1 Incompleteness -- 10.2 Formal theories -- 10.3 The unprovability of outer consistency -- 10.4 The demise of Hilbert's programme -- 10.5 The unprovability of consistency -- 10.6 Axiomatic formalism -- 11 Carnap -- 11.1 Language and symbolism -- 11.2 The rejection of the Tractatus -- 11.3 Conventionalism -- 11.4 Completeness -- 11.5 Consistency -- 11.6 Semantics -- 11.7 Pragmatics -- Conclusion -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K. 327 $aL -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z. 330 $aReason's Nearest Kin is a critical examination of the most exciting period there has been in the philosophical study of the properties of the natural numbers, from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world. 517 3 $aPhilosophies of arithmetic from Kant to Carnap 606 $aArithmetic$xPhilosophy 606 $aMathematics$xPhilosophy 615 0$aArithmetic$xPhilosophy. 615 0$aMathematics$xPhilosophy. 676 $a513/.01 700 $aPotter$b Michael D$059732 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962305803321 996 $aReason's nearest kin$94463834 997 $aUNINA