Philosophy of mathematics : structure and ontology / / Stewart Shapiro

• Autore: Shapiro Stewart <1951->
• Pubblicazione: Oxford, : Oxford University Press, 1997
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (x, 279 p.)
• Disciplina: 510/.1
• Soggetto topico: Mathematics - Philosophy; Mathematics
• Note generali: Originally published: 1997.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Contents -- Introduction -- PART I: PERSPECTIVE -- 1 Mathematics and Its Philosophy -- 2 Object and Truth: A Realist Manifesto -- 1 Slogans -- 2 Methodology -- 3 Philosophy -- 4 Interlude on Antirealism -- 5 Quine -- 6 A Role for the External -- PART II: STRUCTURALISM -- 3 Structure -- 1 Opening -- 2 Ontology: Object -- 3 Ontology: Structure -- 4 Theories of Structure -- 5 Mathematics: Structures, All the Way Down -- 6 Addendum: Function and Structure -- 4 Epistemology and Reference -- 1 Epistemic Preamble -- 2 Small Finite Structure: Abstraction and Pattern Recognition -- 3 Long Strings and Large Natural Numbers -- 4 To the Infinite: The Natural-number Structure -- 5 Indiscernibility, Identity, and Object -- 6 Ontological Interlude -- 7 Implicit Definition and Structure -- 8 Existence and Uniqueness: Coherence and Categoricity -- 9 Conclusions: Language, Reference, and Deduction -- 5 How We Got Here -- 1 When Does Structuralism Begin? -- 2 Geometry, Space, Structure -- 3 A Tale of Two Debates -- 4 Dedekind and ante rem Structures -- 5 Nicholas Bourbaki -- PART III: RAMIFICATIONS AND APPLICATIONS -- 6 Practice: Construction, Modality, Logic -- 1 Dynamic Language -- 2 Idealization to the Max -- 3 Construction, Semantics, and Ontology -- 4 Construction, Logic, and Object -- 5 Dynamic Language and Structure -- 6 Synthesis -- 7 Assertion, Modality, and Truth -- 8 Practice, Logic, and Metaphysics -- 7 Modality, Structure, Ontology -- 1 Modality -- 2 Modal Fictionalism -- 3 Modal Structuralism -- 4 Other Bargains -- 5 What Is a Structuralist to Make of All This? -- 8 Life Outside Mathematics: Structure and Reality -- 1 Structure and Science-the Problem -- 2 Application and Structure -- 3 Borders -- 4 Maybe It Is Structures All the Way Down -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q. ; R -- S -- T -- U -- V -- W -- Z.
• Sommario/riassunto: This text argues that both realist and anti-realist accounts of mathematics are problematic. It articulates a structuralist approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers.
• Titolo autorizzato: Philosophy of mathematics
• ISBN: 1-280-45096-7; 9786610450961; 0-19-802545-9; 1-4237-6518-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910810174403321
• Lo trovi qui: Univ. Federico II