05326nam 2200625Ia 450 991045427460332120200520144314.01-281-94428-997866119442850-19-152022-5(CKB)1000000000721474(EBL)728976(OCoLC)309340984(SSID)ssj0000233595(PQKBManifestationID)11185586(PQKBTitleCode)TC0000233595(PQKBWorkID)10221086(PQKB)10491368(MiAaPQ)EBC728976(Au-PeEL)EBL728976(CaPaEBR)ebr10273215(EXLCZ)99100000000072147420000913d2000 uy 0engur|n|---|||||txtccrReason's nearest kin[electronic resource] philosophies of arithmetic from Kant to Carnap /Michael PotterOxford ;New York Oxford University Press20001 online resource (316 p.)Description based upon print version of record.0-19-825041-X Includes bibliographical references (p. [290]-298) and index.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 Grundlagen2.1 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 again4.2 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 ambiguity5.12 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 infinity6.13 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 Metamathematics9.6 Hilbert's programmeHow 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 ArithmeticPhilosophyMathematicsPhilosophyElectronic books.ArithmeticPhilosophy.MathematicsPhilosophy.510.1Potter Michael D59732MiAaPQMiAaPQMiAaPQBOOK9910454274603321Reason's nearest kin2172337UNINA