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Towards a Philosophy of Real Mathematics

Sprache: Englisch.
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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 a … weiterlesen
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Produktdetails

Titel: Towards a Philosophy of Real Mathematics
Autor/en: David Corfield

ISBN: 0521817226
EAN: 9780521817226
Sprache: Englisch.
CAMBRIDGE UNIV PR

Dezember 2005 - gebunden - 300 Seiten

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.

Inhaltsverzeichnis

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.

Portrait

David Corfield holds a Junior Lectureship in Philosophy of Science at the University of Oxford.

Pressestimmen

'Corfield's book as a whole is itself a fine specimen of a philosophical approach to mathematics that takes its questions and its resources from 'real' mathematics, showing convincingly the richness and fruitfulness of such an approach.' Philosophia Mathematica 'I found this book interesting and it is certainly worth looking at if only to increase one's sense of the possibilities for the philosophy of mathematics.' Metascience 'What is really special about the book under review is that it demonstrates a philosopher struggling to grapple with modern mathematics as it is actually carried out by practitioners. This is what the author means by 'real mathematics' as quoted in the book title.' Zentralblatt MATH
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