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Reason's nearest kin [[electronic resource] ] : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Reason's nearest kin [[electronic resource] ] : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Autore Potter Michael D
Pubbl/distr/stampa 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.
ISBN 1-281-94428-9
9786611944285
0-19-152022-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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
Record Nr. UNINA-9910454274603321
Potter Michael D  
Oxford ; ; New York, : Oxford University Press, 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Reason's nearest kin [[electronic resource] ] : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Reason's nearest kin [[electronic resource] ] : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Autore Potter Michael D
Pubbl/distr/stampa Oxford ; ; New York, : Oxford University Press, 2000
Descrizione fisica x, 305 p
Soggetto topico Arithmetic - Philosophy
Mathematics - Philosophy
ISBN 9780191520228
0191520225
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Altri titoli varianti Philosophies of arithmetic from Kant to Carnap
Record Nr. UNINA-9910795712703321
Potter Michael D  
Oxford ; ; New York, : Oxford University Press, 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Reason's nearest kin : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Reason's nearest kin : philosophies of arithmetic from Kant to Carnap / / Michael Potter
Autore Potter Michael D
Edizione [1st ed.]
Pubbl/distr/stampa Oxford ; ; New York, : Oxford University Press, 2000
Descrizione fisica x, 305 p
Disciplina 513/.01
Soggetto topico Arithmetic - Philosophy
Mathematics - Philosophy
ISBN 9780191520228
0191520225
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- 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.
5.10 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.
L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.
Altri titoli varianti Philosophies of arithmetic from Kant to Carnap
Record Nr. UNINA-9910962305803321
Potter Michael D  
Oxford ; ; New York, : Oxford University Press, 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui