| Document Type
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BL
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| Record Number
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873690
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| Main Entry
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Chihara, Charles S.,1932-
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| Title & Author
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Constructibility and mathematical existence /\ Charles S. Chihara.
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| Publication Statement
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Oxford :: Clarendon Press ;New York :: Oxford Univ. Press,, ©1990.
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| Page. NO
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1 online resource (xv, 282 pages) :: illustrations
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| ISBN
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0191520004
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: 0191597198
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: 9780191520006
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: 9780191597190
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01982481720198239750
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9780198239758
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9780198248170
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| Bibliographies/Indexes
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Includes bibliographical references (pages 273-278) and index.
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| Contents
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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.
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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.
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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.
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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.
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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.
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| Abstract
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Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.
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| Subject
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Constructive mathematics.
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Logic, Symbolic and mathematical.
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Mathematics-- Philosophy.
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Logique symbolique et mathématique.
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| Subject
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Mathématiques constructives.
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| Subject
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Mathématiques-- Philosophie.
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Constructive mathematics.
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Filosofia da matemática.
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Logic, Symbolic and mathematical.
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| Subject
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Lógica matemática.
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Matemática construtiva.
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MATHEMATICS-- Infinity.
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| Subject
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MATHEMATICS-- Logic.
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Mathematics-- Philosophy.
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| Subject
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Constructieve wiskunde.
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| Subject
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Filosofie.
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| Subject
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Ontologie (filosofie)
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| Dewey Classification
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511.3
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| LC Classification
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QA8.4.C45 1990eb
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| NLM classification
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31.02bcl
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