The ArgumentWhile there has been muchattention given to experiment in modern science studies, there has been astoundingly little concern spared over the practice ofquanitataivemeasurment.Thus myths about the unreasonable effectiveness of mathematice in science still abound. This paper presents: An explicit mathematical model of the stabilization of quantitative constants in a mathematical science to rival older Bayesian and classical accounts;a framework for writing a history of pracitces with regard to treatment of quantitative measurement erroe; resourece for the comparative sociology of differing (...) discipliness in this regard;and a prolegonmena to a critique of orthodox economics and accounting theories. The key to all these diverse themes is the realization that no one individual alone is capable of fixing the magnitude of a quantitative error estimate, and therefore the social construction of error must be given a more precise meaning, an therefore the social construction of error must be given a more precise menaing, and that this occurs through the istrumentality of meta-analysis. (shrink)

The ArgumentIn the minds of many, the Bourbakist trend in mathematics was characterized by pursuit of rigor to the detriment of concern for applications or didactic concessions to the nonmathematician, which would seem to render the concept of a Bourbakist incursion into a field of applied mathematices an oxymoron. We argue that such a conjuncture did in fact happen in postwar mathematical economics, and describe the career of Gérard Debreu to illustrate how it happened. Using the work of Leo Corry (...) on the fate of the Bourbakist program in mathematics, we demonstrate that many of the same problems of the search for a formalstructurewith which to ground mathematical practice also happened in the case of Debreu. We view this case study as an alternative exemplar to conventional discussions concerning the “unreasonable effectiveness” of mathematics in science. (shrink)

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

The literature of economic theory, like that of philosophy, abounds in prefaces and prolegomena. Methodology and analysis of concepts take an important place in a science which has not found the sure path of development. But there is no sure path for methodology either. The selfconscious methodology of social science has been largely a borrowing from that of physical science, where procedures have developed to a stage of considerable maturity. But the analogy falls down where guidance is most needed, at (...) the points where social science is most likely to develop new concepts and new types of structure. Philosophers have not been lacking, indeed, to belittle the entire enterprise, and to deny the possibility of anything that could strictly be called social science. (shrink)