Proofs and Refutations

Proofs and Refutations

Proofs and Refutations is a book by the philosopher Imre Lakatos expounding his view ofthe 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, butoften have to be patched up in the light of later insights, in particular failed proofs.This gives mathematics a somewhat experimental flavour.

The pupils in the book are named after letters of the Greek alphabet.

Many important logical ideas are explained in the book. For example the difference between a counterexample to a proof (local counterexample) and a counterexample to a conjecture (global counterexample) are discussed.

The 1976 book has been translated into more than 15 languages worldwide, including Chinese, Korean and Serbo-Croat, and went into its second Chinese edition in 2007.

References

*Lakatos (1976). "Proofs and Refutations". Cambridge: Cambridge University Press. ISBN 0-521-29038-4


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