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 (which mirrors certain real developments in the history of mathematics) 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)

Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume II presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues. Imre Lakatos had an influence (...) out of all proportion to the length of his philosophical career. This collection exhibits and confirms the originality, range and the essential unity of his work. It demonstrates too the force and spirit he brought to every issue with which he engaged, from his most abstract mathematical work to his passionate 'Letter to the director of the LSE'. Lakatos' ideas are now the focus of widespread and increasing interest, and these volumes should make possible for the first time their study as a whole and their proper assessment. (shrink)

Alexander Rosenberg (1983) has argued, contrary to his previous work in the philosophy of economics, that economics is not science, and it is merely mathematics. The following paper argues that Rosenberg fails to demonstrate either of these two claims. The questions of the predictive weakness of modern economics and the cognitive standing of abstract economic theory are discussed in detail.

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...