Constructibility and mathematical existence / / Charles S. Chihara

• Autore: Chihara Charles S. <1932->
• Pubblicazione: Oxford, : Clarendon Press; New York, : Oxford University Press, 1990
• Edizione: 1st ed.
• Descrizione fisica: xv, 282 p. : ill
• Disciplina: 511
• Soggetto topico: Constructive mathematics; Logic, Symbolic and mathematical; Mathematics - Philosophy
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- I: The Constructibility Theory -- 1. The Problem of Existence in Mathematics -- 1. The Philosophical Problem -- 2. Quine's Platonism -- 3. Gödel's Platonism -- 4. Heyting's Intuitionism -- 2. The Constructibility Quantifiers -- 1. Introduction -- 2. The Language L -- 3. The Language L* -- 4. Some Objections Considered -- 3. Constructibility and Open-Sentences -- 1. The Constructibility of Open-Sentences -- 2. A Simple Type Theory for Open-Sentences -- 3. A Comparison with a Predicative System -- 4. The Logical Space of Open-Sentences -- 5. The Kinds of Open-Sentences to be Discussed -- 6. Quine's Objections to Modality -- 4. The Deductive System -- 1. The Language Lt -- 2. The Theory Ct -- 3. Objections to Type Theory -- 4. Objections to the Constructibility Theory -- 5. Cardinality and Number Theory -- 1. Formal Developments -- 2. Philosophical Amplifications -- 6. Measurable Quantities and Analysis -- 1. A Standard Development of Real Analysis -- 2. A Theory of Lengths -- 3. Geometrical Representations of Functions -- 4. Putnam's Case for Realism -- 5. Complex Analysis -- 6. Applications by Means of Structural Identity -- II: Philosophical Developments -- 7. Mathematical Structuralism -- 1. Introduction -- 2. The Structuralist View of Applications -- 3. Resnik on the Nature of Structures -- 4. An Evaluation of Shapiro's Account of Mathematics -- 5. An Evaluation of Resnik's Account of Structures -- 8. Science without Numbers -- 1. Introduction to Field's Instrumentalism -- 2. The Conservation Theorem -- 3. Field's Cardinality Theory -- 4. Field's Nominalistic Physics -- 5. Some Doubts about the Adequacy of Field's View -- 6. A Comparison with the Constructibility Theory -- 7. A Re-examination of Resnik's Reasoning -- 8. The Neo-Quinian Argument Reconsidered. ; 9. Why Burgess Is a Moderate Realist -- 1. A Dilemma for the Nominalist -- 2. A False Dilemma -- 3. Burgess's Objection to Field's Preference for Nominalism -- 10. Maddy's Solution to the Problem of Reference -- 1. Involved Platonists -- 2. Problems of Reference for Mathematical Platonism -- 3. Maddy's Solution -- 4. Doubts about Maddy's Solution -- 5. Concluding Comments -- 11. Kitcher's Ideal Agents -- 1. Kitcher's Account of Mathematical Knowledge -- 2. An Analysis of Kitcher's View: Details and Doubts -- 12. Deflationism and Mathematical Truth -- 1. Field's Deflationism -- 2. A Reconsideration of the Veridicality of Mathematics -- Appendix: Field's Nominalistic Logical Theory -- Postscript -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- V -- W -- Z.
• Sommario/riassunto: This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others. -;PART I: THE CONSTRUCTIBILITY THEORY: The Problem of Existence in Mathematics; The Constructibility Quantifiers; Constructibility and Open-Sentences; The Deductive System; Cardinality and Number Theory; Measurable Quantities and Analysis. PART II: PHILOSOPHICAL DEVELOPMENTS: Mathematical Structuralism; Science Without Numbers; Why Burgess is a Moderate Realist; Maddy's Solution to the Problem of Reference; Kitcher's Ideal Agents; Deflationism and Mathematical Truth. Appendix;Field's Nominalistic Logical Theory.
• Titolo autorizzato: Constructibility and mathematical existence
• ISBN: 0191520004; 9780191520006
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910971792403321
• Lo trovi qui: Univ. Federico II