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Record Nr. |
UNINA9910783041003321 |
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Autore |
Tiles Mary |
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Titolo |
Mathematics and the image of reason / / Mary Tiles |
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Pubbl/distr/stampa |
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London ; ; New York : , : Routledge, , 1991 |
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ISBN |
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1-134-96771-3 |
1-134-96772-1 |
1-280-53925-9 |
9786610539253 |
0-203-02836-8 |
0-203-32706-3 |
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Descrizione fisica |
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1 online resource (198 p.) |
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Collana |
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Philosophical issues in science |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 178-183) and index. |
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Nota di contenuto |
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Cover; MATHEMATICS AND THEIMAGE OF REASON; Title Page; Copyright Page; Table of Contents; Acknowledgements; Introduction; 1 AXIOMATIZATION, RIGOUR AND REASON; Rigour and Proof; Deserting Euclidean Standards; The Return to Euclidean Standards; 2 FREGE: ARITHMETIC AS LOGIC; Calculation and Reasoning; Numbers and the Nature of Arithmetical Truths; Numbers as Objects; The Natural Numbers; Word Games?; 3 RUSSELL: MATHEMATICS AS LOGIC; Geometry and Relational Structures; Paradoxes and Logical Types; Empiricism, Logical Positivism and the Sterility of Reason |
4 HILBERT: MATHEMATICS AS A FORMULA-GAME?Formalism and Hilbert's Programme; Geometrical Rigour; Forging the Formal Chains of Reason; Successes and Failures; Logic and its Limitations; Appendix - Recursive Functions; 5 IDEAL ELEMENTS AND RATIONAL IDEALS; Formulae, Symbols and Forms; Ideal Elements and Ideals; Geometry: Diagrams and Rigour; Pragmatism, Axiomatization and Ideals; Logic and the Objects of Mathematical Knowledge; Lack of Closure and the Power of Reason; Glossary of Symbols; Further Reading; Bibliography; Index |
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Sommario/riassunto |
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A thorough account of the philosophy of mathematics. In a cogent |
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