Reason's nearest kin [[electronic resource] ] : philosophies of arithmetic from Kant to Carnap / / Michael Potter

• Autore: Potter Michael D
• Pubblicazione: Oxford ; ; New York, : Oxford University Press, 2000
• Descrizione fisica: 1 online resource (316 p.)
• Disciplina: 510.1
• Soggetto topico: Arithmetic - Philosophy; Mathematics - Philosophy
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [290]-298) and index.
• Nota di contenuto: 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 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 ; 4.2 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 ; 5.12 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 ; 6.13 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 ; 9.6 Hilbert's programme
• Sommario/riassunto: How 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
• Titolo autorizzato: Reason's nearest kin
• ISBN: 1-281-94428-9; 9786611944285; 0-19-152022-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910454274603321
• Lo trovi qui: Univ. Federico II