Proofs and refutations : the logic of mathematical discovery
著者
書誌事項
Proofs and refutations : the logic of mathematical discovery
（Cambridge philosophy classics）
Cambridge University Press, 2015, c1976
Cambridge philosophy classics ed
- : pbk
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注記
"First published 1976, Cambridge philosophy classics edition 2015"--T.p. verso
Includes bibliographical references (p. 164-174) and indexes
内容説明・目次
内容説明
Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.
目次
- Preface to this edition Paolo Mancosu
- Editors' preface
- Acknowledgments
- Author's introduction
- Part I: 1. A problem and a conjecture
- 2. A proof
- 3. Criticism of the proof by counterexamples which are local but not global
- 4. Criticism of the conjecture by global counterexamples
- 5. Criticism of the proof-analysis by counterexamples which are global but not local. The problem of rigour
- 6. Return to criticism of the proof by counterexamples which are local but not global. The problem of content
- 7. The problem of content revisited
- 8. Concept-formation
- 9. How criticism may turn mathematical truth into logical truth
- Part II: Editors' introduction
- Appendix 1. Another case-study in the method of proofs and refutations
- Appendix 2. The deductivist versus the heuristic approach
- Bibliography
- Index of names
- Index of subjects.
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