variation, evolution, and heredity.
In addition to persons of interest, this book also explores topics in science and mathematics with broad appeal. For example, it engages with the perennial issue of how scientific knowledge is validated. By examining the successes and failures of the scientists featured in the text, it suggests that when a scientific paradigm cannot be relied on to establish the appropriateness of mathematical arguments, arguers can turn to beliefs and values outside of science. Further, it explores the question. “How reliable and successful are mathematics in describing real phenomena?” This query is central to our current public and scientific concerns as we turn to polls, statistics, and probabilistic assessments with increasing frequency to make decisions about products, cures, risks, and candidates. What this investigation reveals is that nineteenth and early twentieth century scientists approached new mathematical methods and their conclusions with a healthy dose of skepticism. They offered legitimate resistance to mathematically informed theories of variation, evolution, and heredity that had insufficient evidence or blatantly disregarded important aspects of biological phenomena. In a few instances, however, their rejections were premature and prejudiced by either their ignorance of mathematics or their personal commitments to other methods of analysis.
Whether you read this book for the characters or the concepts, the goal is the same: to scrutinize, using the tools of rhetoric, the texts, arguments, and contexts involved in the development of the relationship between biological investigations of variation, evolution, and heredity and mathematics from the middle of the nineteenth to the beginning of the twentieth century. In investigating these phenomena, it endeavors to show how Darwin’s and Mendel’s ideas about them influenced the transformation of biology from a predominantly qualitative science to one with a vital, mathematical component. It also reveals how difficult this transformation—which we now take for granted as the very essence of our modern sciences of genetics and evolution—really was. By approaching science from a rhetorical perspective as a process of argument and deliberation rather than a product (as it is so often presented in the popular media), we can develop a greater appreciation both for the value of mathematics as a source for knowledge about nature and for the difficult and sometimes circuitous path by which that confidence is earned.
1 Introduction
I assert . . . that in any special doctrine of nature there can be only as much proper science as there is mathematics therein. For . . . proper science, and above all proper natural science, requires a pure part lying at the basis of the empirical part.
—Immanuel Kant
In the twentieth and twenty-first centuries, there has been a substantial expansion in the number of fields applying mathematics to their investigations of natural and social phenomena. Areas of social research such as psychology and sociology, which had traditionally been qualitative, have developed robust quantitative components, such as standardized intelligence tests and statistical surveys to assess the habits, beliefs, and practices of populations. In addition, fields of natural investigation. particularly genetics and evolutionary biology, have expanded their methods as described in the Forward from observation and experiment to include mathematical descriptions of the genome and the change and distribution of variation within organic populations. As a result of this expansion, mathematics has become a ubiquitous aspect of what makes a discipline “scientific,” making Kant’s invocation that “there can only be as much proper science as there is mathematics therein” seem even more relevant today as it was when he wrote it in 1786.1
Although this mathematical expansion has helped us better understand social, psychological, and biological phenomena, the path to developing and adopting mathematics in science has not always straight or easy. One widely-cited example of a mathematical science with a turbulent beginning is population genetics. In the twenty- first century, this vital field of genetics research has its own textbooks, specialists, and places in the academy. Its recent success, however, obscures a less flourishing past. Although the basic scientific and mathematical foundations for population genetics were largely in place by the first decade of the twentieth century, almost thirty years elapsed before it garnered sufficient attention and support to establish itself as a field of research worthy of an individuated identity.
Historians interested in the intellectual foundations of population genetics and its transition into an important field of inquiry have reached back to Darwin and traced its development forward, hoping to understand the reasons why such a productive, modern field of study had such a difficult maturation. Perhaps the most well-known investigation into this mystery was undertaken by historian William Provine, whose groundbreaking book, The Origins of Theoretical Population Genetics, suggests that the turmoil associated with the rise of the field was largely the consequence of an ideological conflict between Darwinians and Mendelians (ix-x).
According to Provine, Darwin and his later followers, the biometricians, believed in continuous variation in which differences between members of a species arose by the slow accretion of small variations over long periods of time. Mendelians and the supporters of mutation theory, on the other hand, believed that variation was discontinuous: varieties appeared suddenly and could introduce dramatic changes into individuals and populations of organisms. By tracing these notions about variation from Darwin through the debates between the biometricians and the Mendelians, Provine concludes that it was only when the differences between these ideological positions were resolved in the work of R.A. Fisher, J.B.S. Haldane, and Sewall Wright, that a research field of population genetics emerged (Provine 131).
Although Provine and other historians rightfully devote attention to how ideological conflicts over variation complicated the development of population genetics, their focus excludes other elements that could have contributed significantly to population genetics’ “torturous” development (Provine ix). One important element that has not been considered is whether and to what degree the beliefs about the acceptability of using mathematics to make arguments about biological phenomena might have contributed to the difficulties in establishing the field.
Although it is difficult from a twenty-first century perspective to image mathematics not being a legitimate means of researching variation, evolution, and heredity, scrutiny of the work of early researchers such Charles Darwin, Gregor Mendel, Francis Galton, Karl Pearson, and R.A Fisher suggests that this has not always been the case. Attention to their work and its reception reveals that mathematical approaches to these phenomena were caught up in a cycle of development, conflict, and persuasion that lasted almost one hundred years, a cycle that has all but been forgotten as science looks to the future and eviscerates from memory the useless, blind allies and conflicts that led to its current position. In hoping to understand the development of scientific knowledge, however, we need to look at the process of making knowledge, not just the results. Investigating these long-forgotten conflicts can help us understand not only what people believed, but also how they were moved to change their beliefs, what they perceived were good reasons for accepting or rejecting a particular position, and what lines of argument dominated the scientific landscape.
Despite the importance of mathematics to scientific argument and epistemology, there have been few historical-philosophical, sociological, or rhetorical investigations of how scientists argue with or about the use of mathematics.2 In the history of science, the intersection between argument, science, and mathematics has been investigated by historian Peter Dear, whose book, Discipline and Experience: The Mathematical Way in the Scientific Revolution, examines sixteenth, seventeenth, and eighteenth century disputes among natural philosophers about whether mathematics could serve legitimately and authoritatively as a source for arguments about nature. In the book, Dear attempts to make sense—in the context of eighteenth century natural philosophy—of both the novelty of Newton’s physico-mathematical argument strategy and its importance to the development of a new paradigm for scientific research (248).
Although very few historians have examined the relationships between mathematics, science, and argument, there is evidence of a trend towards increasing attention to the
