LEADER 05326nam 2200625Ia 450 001 9910454274603321 005 20200520144314.0 010 $a1-281-94428-9 010 $a9786611944285 010 $a0-19-152022-5 035 $a(CKB)1000000000721474 035 $a(EBL)728976 035 $a(OCoLC)309340984 035 $a(SSID)ssj0000233595 035 $a(PQKBManifestationID)11185586 035 $a(PQKBTitleCode)TC0000233595 035 $a(PQKBWorkID)10221086 035 $a(PQKB)10491368 035 $a(MiAaPQ)EBC728976 035 $a(Au-PeEL)EBL728976 035 $a(CaPaEBR)ebr10273215 035 $a(EXLCZ)991000000000721474 100 $a20000913d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aReason's nearest kin$b[electronic resource] $ephilosophies of arithmetic from Kant to Carnap /$fMichael Potter 210 $aOxford ;$aNew York $cOxford University Press$d2000 215 $a1 online resource (316 p.) 300 $aDescription based upon print version of record. 311 $a0-19-825041-X 320 $aIncludes bibliographical references (p. [290]-298) and index. 327 $aContents; 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 327 $a2.1 Axiomatization2.2 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 327 $a4.2 The context principle in Grundgesetze4.3 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; 5.10 The hierarchy of propositional functions in the Introduction; 5.11 Typical ambiguity 327 $a5.12 Cumulative types5.13 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 327 $a6.13 A transcendental argument6.14 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 327 $a9.6 Hilbert's programme 330 $aHow do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as 606 $aArithmetic$xPhilosophy 606 $aMathematics$xPhilosophy 608 $aElectronic books. 615 0$aArithmetic$xPhilosophy. 615 0$aMathematics$xPhilosophy. 676 $a510.1 700 $aPotter$b Michael D$059732 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454274603321 996 $aReason's nearest kin$92172337 997 $aUNINA