Towards a Philosophy of Real Mathematics
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Lieferzeit: Print on Demand - Lieferbar innerhalb von 3-5 Werktagen I
ISBN-13:
9780521817226
Veröffentl:
2005
Einband:
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Erscheinungsdatum:
22.12.2005
Seiten:
300
Autor:
David Corfield
Gewicht:
642 g
Format:
235x157x22 mm
Sprache:
Englisch
Beschreibung:
David Corfield provides a variety of innovative approaches to research in the philosophy of mathematics. His study ranges from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics to the use of analogy; the prospects for a Bayesian confirmation theory; the notion of a mathematical research program; and the ways in which new concepts are justified. This highly original book will challenge philosophers as well as mathematicians to develop the broadest and most complete philosophical resources for research in their disciplines.
Corfield sets out a variety of approaches to new thinking about the philosophy of mathematics.
Preface; 1. Introduction: a role for history; Part I. Human and Artificial Mathematicians: 2. Communicating with automated theorem provers; 3. Automated conjecture formation; 4. The role of analogy in mathematics; Part II. Plausibility, Uncertainty and Probability: 5. Bayesianism in mathematics; 6. Uncertainty in mathematics and science; Part III. The Growth of Mathematics: 7. Lakatos's philosophy of mathematics; 8. Beyond the methodology of mathematical research programmes; 9. The importance of mathematical conceptualisation; Part IV. The Interpretation of Mathematics: 10. Higher dimensional algebra; Appendix; Bibliography; Index.