in the study of history and philosophy of science—titled, “Ten Problems in the History and Philosophy of Science,” historian and philosopher Peter Galison lists a lack of understanding of the “Technologies of Argumentation” as problem number three for philosophers and historians of science. He raises the following questions for them to pursue:
When the focus is on scientific practices (rather than discipline-specific scientific results per se), what are the concepts, tools, and procedures needed at a given time to construct an acceptable scientific argument? . . . Cutting across subdisciplines and even disciplines, what is the toolkit of argumentation and demonstration—and what is its historical trajectory? (116)
For rhetoricians of science, whose interests lay predominantly in the study of scientific argument and communicative practices, answering these sorts of questions about the relationship between mathematics, science, and argument would seem to be an important and fruitful undertaking. Despite the natural fit between scholarly interest and subject matter, however, very few rhetoricians have made efforts to examine the intersection between these three subjects. One notable exception is the work of Alan Gross, Joseph Harmon, and Michael Reidy in, Communicating Science: The Scientific Article from the 17th Century to the Present. In this book, the authors examine the developing conventions of argument and style in the scientific article, including brief descriptions of the use of mathematics.
Though the works of Dear, Gross, Harmon and Reidy begin a conversation about the role of mathematics in scientific argument, there are many important avenues currently unexplored. Questions—such as, “Do new mathematical methods have a different status of reliability as a source for arguments in science than existing ones?”; “If mathematical methods are not assumed a priori to be reliable, how do scientists make a case for their use in science?”; and “Can the reliability of mathematical methods and their use be debated and secured using methods outside of a framework of analytical argument?”— still remain and represent substantial lacunae in or understanding of the subject. The primary goal of this book is to explore these questions.
Just as scientists rely on rare diseases amd aphasias to understand the functioning of genes and language, this investigation turns its attention to a special case of the mathematization of a scientific field to find answers to these questions. Specifically, it examines the development of the mathematical study of variation, evolution, and heredity from the middle of nineteenth to the beginning of the twentieth century which eventually culminates in the emergence of important mathematical subfields of biology, including population genetics, quantitative genetics, and biostatistics. This development provides a unique opportunity to observe the nuances and difficulties in the relationships between mathematics, science, and argument.
By examining the conventions for arguing mathematically about natural phenomena and the successes and failures of advocates for a mathematical approach, I intend to advance four conclusions about the relationship of mathematics to scientific/biological argument:
that novel mathematical arguments used to make claims about natural phenomena do not necessarily compel acceptance,
that scientists arguing for novel mathematical warrants rely on a range of resources for generating good reasons to support their use,
that arguments about and with mathematics in science can have non-analytical, rhetorical dimensions, and
that conflicts over the appropriateness of using mathematics have complicated the development and acceptance of biomathematical fields such as population genetics.
A Rhetorical Approach to Scientific Epistemology
Any effort to discuss scientific argument and knowledge-making requires some explanation of one’s philosophy of scientific epistemology. The epistemological perspective guiding this rhetorical investigation can be understood by contrasting it with positions on the subject that have been previously taken up by historians, philosophers, and sociologists of science.
In the last century, notions of scientific epistemology have tended either towards logical positivist/empiricist models of science or towards social constructivist models. For the logical positivist/empiricist, scientific propositions and theories are thought to be systematically verified or falsified by appealing to physical evidence in conjunction with logical-linguistic constructs and deductions. For the social constructionist, rationality is located in the commitments of a scientific community to seeing nature in a particular way. Although logical positivist/empiricist approaches to scientific epistemology were extremely influential in the late decades of the nineteenth and the early decades of the twentieth century, they met a series of challenges from philosophers such as Karl Popper, W.V. Quine, and Ludwig Wittgenstein, culminating in Thomas Kuhn’s The Structure of Scientific Revolutions, which substantially decreased their appeal. Kuhn’s investigation offered a fairly comprehensive vision of scientific knowledge-making that rejected the possibility that fixed, rational principles could be appealed to in times of epistemic crisis. From Kuhn’s paradigmatic perspective, major changes in the conceptual framework of a scientific community could only occur when an existing paradigm had become so troublesome that its adherents began the process of developing alternative paradigms to replace it. This feature of paradigmatic change precludes falsification or verification by rejecting the possibility of a rational, external position from which a paradigm could be judged (145).
One of the consequences of Kuhn’s model of scientific epistemology is that it not only eliminates the possibility for “objective” logical-linguistic constructs and deductions to guide argument and decision-making in science, but also the prospects for any reasonable common ground to exist between members of old and new paradigms. The absence of a third position, or alternative reasonable perspective, from which arguments supporting or challenging a paradigm over its alternative can be made or judged, raises important questions such as: “How is it that researchers working in a particular field during a time of revolution choose one paradigm over another?” and “How do communities of scholars with different points of view decide that one school of thought’s natural metaphysic is sufficiently better than its competitors’ and should be embraced as a paradigm?”
In response to the first question, Kuhn argues that the choice of a paradigm is made on the basis of a personal rather than a communal calculus. Novices entering a field with conflicting paradigms, for example, choose a paradigm to apprentice under according to their own individual sensibilities about which one they more closely identify with. Similarly, established participants in an existing paradigm either remain steadfast in their support for it, or experience a sudden, personal conversion to the alternative. In both cases, the transformation cannot be compelled by any commonly held good reasons for preferring one position over the other (Kuhn155). In response to the second question, Kuhn offers no criteria at all, stating only that “to be accepted as a paradigm, a theory must seem better than its competitors” (17).
As a challenge to logical positivist/empiricist approaches to scientific epistemology, Kuhn’s concept of paradigm adoption swings away from what the rhetorical theorist Kenneth Burke, in the Rhetoric of Motives, calls a grammatical stance: a search for a set of universal propositions and procedures which would account for its epistemological robustness (21–23). In correcting the perceived errors of the grammatical position, however, Kuhn moves towards a radically opposed symbolic stance in which rationality is bound to idiosyncratic, personal reasons for choice rather than some loci of rationality shared by the larger community. The perspective on knowledge and argument employed in this investigation takes an epistemological middle ground between the universal and the idiosyncratic. This middle path is uniquely fitted to a rhetorical perspective because it rejects, on the one hand, analytical self-evidence by embracing the centrality of audience in argumentation, and in so doing, the necessarily communal and probabilistic nature of argument (Perelman and Olbrechts-Tyteca 1–10). On the other hand, it takes up the position that discourse communities overlap and interconnect and, as a consequence, good reasons can exist outside of a single
