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