Proofs and Refutations: The Logic of Mathematical Discovery / Edition 1

by Imre Lakatos, John Worrall, Elie Zahar

Overview

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.

Product Details

ISBN-13:	9780521290388
Publisher:	Cambridge University Press
Publication date:	01/01/1976
Edition description:	New Edition
Pages:	188
Product dimensions:	5.47(w) x 8.46(h) x 0.51(d)

About the Author

Imre Lakatos (1922–74) was one of the twentieth century's most prominent philosophers of science and mathematics, best known for his theory of the methodology of proof and refutation in mathematics.

Table of Contents

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.

Editorial Reviews

"For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963–4 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material … the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised."
Michael Dummett, Nature

"The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level."
C. W. Kilmister, The Times Higher Education Supplement

"In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics … The arguments presented are deep … but the author's lucid literary style greatly facilitates their comprehension … The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught."
Education

"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

From the Publisher