Proofs and Refutations

The Logic of Mathematical Discovery

AvImre Lakatos,John Worrall

Inbunden, Engelska, 2015

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-10-15
Mått:156 x 235 x 15 mm
Vikt:410 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Philosophy Classics
Antal sidor:196
Förlag:Cambridge University Press
ISBN:9781107113466

Utforska kategorier

Naturvetenskapens filosofi inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.