Mathematical progress: Between reason and society

Summary

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.