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