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Mathematics and the Image of Reason.
A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Hoboken :
Taylor and Francis,
2013.
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| Collection: | Philosophical issues in science.
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| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- 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