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)

What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. Numerical taxonomists sought (...) to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

The twentieth century witnessed a dramatic increase in the use of statistics by biologists, including systematists. The modern synthesis and new systematics stimulated this development, particularly after World War II. The rise of "the statistical frame of mind " resulted in a rethinking of the relationship between biological and mathematical points of view, the roles of objectivity and subjectivity in systematic research, the implications of new computing technologies, and the place of systematics among the biological disciplines.

A numerical classification was performed on 69 elements with 54 chemicaland physicochemical properties. The elements fell into clusters in closeaccord with the electron shell s-, p- andd-blocks. The f-block elements were not included forlack of sufficiently complete data. The successive periods ofs- and p-block elements appeared in an ovalconfiguration, with d-block elements lying to one side. Morethan three axes were required to give good representation of thevariation, although the interpretation of the higher axes is difficult.Only 15 properties were scorable for (...) the noble gases, but despite thepaucity of properties reflecting chemical reactivity, analysis of the 69elements on these properties still showed the major features seen fromthe full set. (shrink)

It is time to escape the constraints of the Systematics Wars narrative and pursue new questions that are better positioned to establish the relevance of the field in this time period to broader issues in the history of biology and history of science. To date, the underlying assumptions of the Systematics Wars narrative have led historians to prioritize theory over practice and the conflicts of a few leading theorists over the less-polarized interactions of systematists at large. We show how shifting (...) to a practice-oriented view of methodology, centered on the trajectory of mathematization in systematics, demonstrates problems with the common view that one camp straightforwardly “won” over the other. In particular, we critique David Hull’s historical account in Science as a Process by demonstrating exactly the sort of intermediate level of positive sharing between phenetic and cladistic theories that undermines their mutually exclusive individuality as conceptual systems over time. It is misleading, or at least inadequate, to treat them simply as holistically opposed theories that can only interact by competition to the death. Looking to the future, we suggest that the concept of workflow provides an important new perspective on the history of mathematization and computerization in biology after World War II. (shrink)

Zoologist A. J. Cain began historical research on Linnaeus in 1956 in connection with his dissatisfaction over the standard taxonomic hierarchy and the rules of binomial nomenclature. His famous 1958 paper ‘Logic and Memory in Linnaeus's System of Taxonomy’ argues that Linnaeus was following Aristotle's method of logical division without appreciating that it properly applies only to ‘analysed entities’ such as geometric figures whose essential nature is already fully known. The essence of living things being unanalysed, there is no basis (...) on which to choose the right characters to define a genus nor on which to differentiate species. Yet Cain's understanding of Aristotle, which depended on a 1916 text by H. W. B. Joseph, was fatally flawed. In the 1990s Cain devoted himself to further historical study and softened his verdict on Linnaeus, praising his empiricism. The idea that Linnaeus was applying an ancient and inappropriate method cries out for fresh study and revision. (shrink)

Throughout the twentieth century calls to modernize natural history motivated a range of responses. It was unclear how research in natural history museums would participate in the significant technological and conceptual changes that were occurring in the life sciences. By the 1960s, the Museum of Vertebrate Zoology at the University of California, Berkeley, was among the few university-based natural history museums that were able to maintain their specimen collections and support active research. The MVZ therefore provides a window to the (...) modernization of natural history. This paper concentrates on the directorial transitions that occurred at the MVZ between 1965 and 1971. During this period, the MVZ had four directors: Alden H. Miller (Director 1940–1965), an ornithologist; Aldo Starker Leopold (Acting Director 1965–1966), a conservationist and wildlife biologist; Oliver P. Pearson (Director 1966–1971), a physiologist and mammalogist; and David B. Wake (Director 1971–1998), a morphologist, developmental biologist, and herpetologist. The paper explores how a diversity of overlapping modernization strategies, including hiring new faculty, building infrastructure to study live animals, establishing new kinds of collections, and building modern laboratories combined to maintain collections at the MVZ’s core. The paper examines the tensions between the different modernization strategies to inform an analysis of how and why some changes were institutionalized while others were short-lived. By exploring the modernization of collections-based research, this paper emphasizes the importance of collections in the transformation of the life sciences. (shrink)

The taxa that appear in biological classifications are commonly seen as representing information about the traits of their member organisms. This paper examines in what way taxa feature in the storage and retrieval of such information. I will argue that taxa do not actually store much information about the traits of their member organisms. Rather, I want to suggest, taxa should be understood as functioning to localize organisms in the genealogical network of life on Earth. Taxa store information about where (...) organisms are localized in the network, which is important background information when it comes to establishing knowledge about organismal traits, but it is not itself information about these traits. The view of species and higher taxa that is proposed here follows from examining three problems that occur in contemporary biological systematics and are discussed here: the problem of generalization over taxa, the problem of phylogenetic inference, and the problematic nature of the Tree of Life. (shrink)