This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Social revolutions--that is critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. But can the idea of revolutionary upheaval be extended to the world of ideas and theoretical debate? The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began in the United States in the mid-1970's as to whether the concept of revolution could (...) be applied to mathematics as well as science. Michael Grove declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave some examples. This book is the first comprehensive examination of the question. It reprints the original papers of Grove, Dauben, and Mehrtens, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics, who each discuss an important episode and consider whether it was a revolution. The whole question of mathematical revolutions is thus examined comprehensively and from a variety of perspectives. This thought-provoking volume will interest mathematicians, philosophers, and historians alike. (shrink)

Suppe, F. The search for philosophic understanding of scientific theories (p. [1]-241)--Proceedings of the symposium.--Bibliography, compiled by Rew A. Godow, Jr. (p. [615]-646).

The standard reading of Kuhn's philosophy attributes to him the view that the incommensurability of rival theories and theory-ladenness of observation make rational debate about competing paradigms nearly impossible. If this reflects his real view, then he has claimed something prima facie absurd, and easily refuted with historical counter-examples. It is not the incommensurability thesis per se that is easily refutable, but Kuhn's gestelt interpretation of it. The gestalt interpretation, moreover misrepresents his more fundamental ideas on paradigms, and is in (...) itself confused. The incommensurability thesis can be explained and defended without invoking gestalts, and this reconstructed view can be used to show that familiar criticisms, such as those of Davidson and Laudan, and unwelcome endorsements, such as that of Barnes, which are based on the assumption that Kuhn must be an extreme relativist, are all directed at views that he need not, and should not, hold. (shrink)

This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Is mathematical knowledge the product of a method fulfilling temporally and locally invariant criteria and thus manifesting a rationality which sets it entirely apart from all other cultural products? Or is it a socially constructed product, sharing in the accidental and conventional nature of all historically contingent cultural products? In order to be able to take the latter point of view at all seriously into consideration, the most sophisticated and historically informed methodological model is carefully and critically examined. This (Lakatosian) (...) model, however liberal and history-directed it may seem, turns out to incorporate the former, (methodo)logical view of the development of mathematics. It will be demonstrated that the basic assumption underlying Lakatosian methodology is both unwarranted and superfluous for the rational explanation of the growth of mathematical knowledge. This leads to the provisional conclusion that the relevant question is not whether mathematical progress derives ultimately from irreducibly cognitive or from irreducibly social factors, but how cognitive and social factors are interrelated and together, in their indivisible unity, are constitutive of the development of mathematical knowledge. In the forthcoming second part of the article, a model of this socio-cognitive interplay, relying heavily on empirical analyses, will be presented. (shrink)