Proofs and Refutations 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 between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of (...) mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.

Our paper “Experimental Economics: Where Next?” contains a case study of Ernst Fehr and Klaus Schmidt’s work in which it is shown that the claims they make for the theory of inequity aversion are not supported by their data. The current issue of JEBO contains two replies, one from Fehr and Schmidt1 themselves, and the other from Catherine Eckel and Herb Gintis. Neither reply challenges any claims we make about matters of fact in our critique of Fehr and Schmidt on (...) inequity aversion, although it is clear that if they could have refuted any single factual sentence then they would have done so. Both replies therefore implicitly concede that the facts quoted in our case study are correct. All the other issues raised in the two replies are just so much dust kicked up to distract attention from the only question that matters: Is it scientific to proceed like Fehr and Schmidt or is it not? Fehr and Schmidt say yes. So do Eckel and Gintis. The implications are quite far-reaching for those like us who think it is obvious that the answer is no. What other claims asserted by the school of Gintis et al can we trust? (shrink)