Proofs and Refutations: The Logic of Mathematical Discovery
Author
Imre Lakatos
Genre
Philosophy of mathematics
Published
1976
ISBN
978-0-521-29038-8
Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour. At the end of the Introduction, Lakatos explains that his purpose is to challenge formalism in mathematics, and to show that informal mathematics grows by a logic of "proofs and refutations".
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in mathematics, and to show that informal mathematics grows by a logic of "proofsandrefutations". The 1976 book ProofsandRefutations is based on the...
mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction...
philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofsandrefutations" in its pre-axiomatic...
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and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his ProofsandRefutations aimed...
mathematics. In ProofsandRefutations: The Logic of Mathematical Discovery (1976), philosopher Imre Lakatos implemented mathematical proofs into what he...
additional proofs, see Eppstein (2013). Multiple proofs, including their flaws and limitations, are used as examples in ProofsandRefutations by Lakatos...
arguments for the existence of God. Imre Lakatos ProofsandRefutations is a 1976 book on the logic of discovery and progress in mathematics. It is written as...
Realism and the Aim of Science, 1956–57 (as privately circulated galley proofs; published as a book 1983), ISBN 0091514509 Conjectures andRefutations: The...
825–835. Imre Lakatos, ProofsandRefutations Cambridge University Press, 1976, ISBN 0521290384 James Franklin and Albert Daoud, Proof in Mathematics: An...
School of Mathematics and Statistics, University of St Andrews, Scotland. May 2000. Lakatos, Imre (1976). ProofsandRefutations. Cambridge University...
Doron Zeilberger A.J. Han Vinck Borwein integral Computer-aided proofProofsandRefutations Experimental Mathematics (journal) Institute for Experimental...
published. July 11 – Keuffel and Esser manufacture the last slide rule in the United States. Imre Lakatos' ProofsandRefutations: the Logic of Mathematical...
MAA. pp. 218–227. ISBN 978-0-88385-747-2. Lakatos, Imre (1976). Proofsandrefutations: the logic of mathematical discovery. Cambridge University Press...
of science by Karl Popper and Imre Lakatos. In particular, it initially made use of Lakatos' work on proofsandrefutations. Subsequently, development...
N.S. 10 pp. 1–26 as cited by Imre Lakatos (1976) in ProofsandRefutations p. 9. (John Worrall and Elie Zahar, eds.) Cambridge University Press ISBN 0-521-21078-X...
ISBN 9780465037704. Lakatos, Imre (1976). Worrall, J.; Zahar, E. (eds.). ProofsandRefutations:The Logic of Mathematical Discovery. Cambridge University Press...
Bookstore. p. 184. ISBN 978-0-8218-2623-2. Lakatos, Imre (1976). ProofsandRefutations. Cambridge University Press. pp. 141. ISBN 978-0-521-21078-2. Rudin...
first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation complete—given unlimited resources and a fair derivation strategy, from...
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politics contains many examples of proofs by assertion. This practice can be observed in the use of political slogans, and the distribution of "talking points"...
above-mentioned correspondence says that proofs in a theory translate to sequences of short proofs in the corresponding proof system, a form of the opposite implication...
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