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Proofs and Refutations
The Logic of Mathematical Discovery

$93.99 (P)

Part of Cambridge Philosophy Classics

Paolo Mancosu
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  • Date Published: November 2015
  • availability: In stock
  • format: Hardback
  • isbn: 9781107113466

$ 93.99 (P)

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About the Authors
  • 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.

    • Unique to Cambridge, this classic book has been revived and rebranded for a twenty-first-century readership
    • Offers a new generation of readers access to Imre Lakatos's influential theory on the nature of mathematical discovery and methodology
    • Proposes a philosophy of mathematics that accounts for both the static and dynamic complexities of mathematical practice
    • Features a specially commissioned Preface written by Paolo Mancosu
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    Reviews & endorsements

    "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."

    "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

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    Product details

    • Date Published: November 2015
    • format: Hardback
    • isbn: 9781107113466
    • length: 196 pages
    • dimensions: 237 x 152 x 15 mm
    • weight: 0.41kg
    • contains: 27 b/w illus. 2 tables
    • availability: In stock
  • Table of Contents

    Preface to this edition Paolo Mancosu
    Editors' preface
    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
    Index of names
    Index of subjects.

  • Author

    Imre Lakatos
    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.


    John Worrall

    Elie Zahar


    Paolo Mancosu

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