We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to (...) formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. (shrink)

Defending Robert Rosen’s claim that in every confrontation between physics and biology it is physics that has always had to give ground, it is shown that many of the most important advances in mathematics and physics over the last two centuries have followed from Schelling’s demand for a new physics that could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but progressive (...) tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico echemical morphology research program, the biosemiotics movement, and the relational biology of Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics. (shrink)

Many years after the publication of “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Warren McCulloch gave Walter Pitts credit for contributing his knowledge of modular mathematics to their joint project. In 1941 I presented my notions on the flow of information through ranks of neurons to Rashevsky’s seminar in the Committee on Mathematical Biology of the University of Chicago and met Walter Pitts, who then was about seventeen years old. He was working on a mathematical theory of (...) learning and I was much impressed. He was interested in problems of circularity, how to handle regenerative nervous activity in closed loops....For two years Walter and I worked on these problems whose solution depended upon modular mathematics of which I knew nothing, but Walter did.. In this paper, we will fill in some of the details regarding Pitts’s interest in problems of circularity, regenerative activity in closed loops of neurons, and modular mathematics, and the way in which they relate to “A Logical Calculus.”. (shrink)

This paper aims at bridging a gap between the history of American animal behavior studies and the history of sociobiology. In the post-war period, ecology, comparative psychology and ethology were all investigating animal societies, using different approaches ranging from fieldwork to laboratory studies. We argue that this disunity in “practices of place” explains the attempts of dialogue between those three fields and early calls for unity through “sociobiology” by J. Paul Scott. In turn, tensions between the naturalist tradition and the (...) rising reductionist approach in biology provide an original background for a history of Edward Wilson’s own version of sociobiology, much beyond the William Hamilton’s papers usually considered as its key antecedent. Naturalists were in a defensive position in the geography of the fields studying animal behavior, and in reaction were a driving force behind the various projects of synthesis called “sociobiology”. (shrink)

The paper examines Pierre Bourdieu’s extensive writings on the production of scientific knowledge. The study shows that Bourdieu offered not one but two - significantly different - approaches to scientific knowledge production, one formulated in his theoretical, or programmatic, writings on the subject, the other developed in his empirical writings. Addressing the question as to the relevance of Bourdieu’s work for science studies, the analysis argues that the former of these two approaches is at once very visible in Bourdieu’s work (...) but characterized by limitations from the standpoint of scholarship in STS, whereas the latter approach is less conspicuous but of broader empirical value. (shrink)