Page count: 251 pages
Category: from English
Proofs anf Refutation is essential reading for all those interested in the methodology, the philosophy, and the history of mathematics. Much of the book takes the form of a discussion betweewn a teacher and his students. They propose various solutions to some mathematical problems and investigate the strenghts and weaknesses of the solutions. Their discussion (wich mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativy.
Imre Lakatos is concerned throughout to combat the classical picture if mathematical truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creativa hypotheses by attempts to "prove" them and by criticism of these attempts: the logic of proofs and refutations.
The book is derived from a series of articles first published in the British Journal for the Philosophy of Science.
Imre Lakatos revised and expanded this material substantially, but died before completing the task.
- "Lakatos's contribution to the philosophy of mathematics was, to put it simply, definitive: the subject will never be the same again. (...) Lakatos made us think instead about what most research mathematicians do. He wrote an amazing philosophical dialogue around the proof of a seemingly elementary but astonishingly deep geometrical idea pioneered by Euler. It is a work of art - I rank it right up there with the dialogues composed by Hume or Berkeley or Plato. He made us see a theorem, a mathematical fact, coming into being before our eyes." - Ian Hacking, in a review of For and Against Method by Lakatos/Feyerabend (see our review), in the London Review of Books (20/1/2000)
- "Proofs and Refutations has the impact it does because Lakatos knows the mathematics -- or as much of it as he chooses to know -- and can take the reader through it. The question is how he came to jettison so much of his intellectual past, and to believe himself a friend of reason, while making his living out of a project fundamentally irrational." - James Franklin, in a non-review of For and Against Method by Lakatos/Feyerabend (see our review), in The New Criterion (5/2000)