Synopses & Reviews
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
Synopsis
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Synopsis
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Synopsis
A novel introduction to the philosophy of mathematics, mostly in the form of a discussion between a group of students and their teacher. It combats the positivist picture and develops a much richer, more dramatic progression.
Description
Bibliography: p. 155-165.
Table of Contents
Editors' preface; Acknowledgments; Author's introduction; 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; Appendices; Bibliography; Index of names; Index of subjects.