| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910810174403321 |
|
|
Autore |
Shapiro Stewart <1951-> |
|
|
Titolo |
Philosophy of mathematics : structure and ontology / / Stewart Shapiro |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Oxford, : Oxford University Press, 1997 |
|
|
|
|
|
|
|
ISBN |
|
1-280-45096-7 |
9786610450961 |
0-19-802545-9 |
1-4237-6518-4 |
|
|
|
|
|
|
|
|
Edizione |
[1st ed.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (x, 279 p.) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Mathematics - Philosophy |
Mathematics |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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. |
|
|
|
|
|
|
|
| |