Proofs and Refutations
The Logic of Mathematical Discovery

This influential book discusses the nature of mathematical discovery, development, methodology and practice, forming Imre Lakatos's theory of 'proofs and refutations'.

Imre Lakatos (Author), John Worrall (Edited by), Elie Zahar (Edited by)

9781107113466, Cambridge University Press

Hardback, published 15 October 2015

196 pages, 27 b/w illus. 2 tables
23.5 x 15.6 x 1.5 cm, 0.41 kg

'How is mathematics really done, and - once done - how should it be presented? Imre Lakatos had some very strong opinions about this. The current book, based on his PhD work under George Polya, is a classic book on the subject. It is often characterized as a work in the philosophy of mathematics, and it is that - and more. The argument, presented in several forms, is that mathematical philosophy should address the way that mathematics is done, not just the way it is often packaged for delivery.' William J. Satzer, MAA Reviews

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.

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.

Subject Areas: Philosophy of science [PDA], Philosophy of mathematics [PBB]