failed attempts to persuade conventional biologists to side with their quantitative vision of variation, evolution, and heredity over Mendel’s. This chapter concludes that Fisher believed he needed to construct and maintain a credible ethos for his own work as well as for the general program of mathematical argument in science to reestablish biometry as a viable approach to generating new knowledge about natural selection and evolution. An investigation of his early papers and seminal book, The Genetical Theory of Natural Selection (1929), suggests that by making his complex mathematical arguments accessible to scientists with limited mathematical training, and by arguing that mathematical arguments had the virtues of practicality and inductivity, Fisher made important strides in overcoming some of the final obstacles in the long and difficult road towards the synthesis of Mendelian genetics and Darwinian natural selection that were required for the emergence of population genetics.5
A Rhetorical Approach to Mathematics, Argument, and Science
By exploring the complexity of arguing mathematically in the study of variation, evolution, and heredity from the middle of the nineteenth to the beginning of the twentieth century, this book hopes to contribute to the understanding of mathematical argument in science and its rhetorical dimensions. What it reveals about mathematics in science is that its status as a warrant for making scientific arguments is not always secure, and in some cases, requires conventional and unconventional support to be accepted as legitimate. It also advances the possibility that mathematical descriptions and arguments in-and-of-themselves may not be sufficient reasons to accept a particular scientific conclusion. Instead, mathematics exists as one node in a complex hierarchy of good reasons in competition with other values, beliefs, and truths. These conclusions illustrate the rhetorical dimensions of mathematical argument, and should thereby further encourage rhetorical investigation into mathematics not only in science, but also in other areas, such as public policy, politics, and even theoretical mathematics.
Finally, this book is dedicated to showing how a rhetorical approach to argument analysis might contribute to the efforts of historians, philosophers, and sociologists of science in their quest to understand scientific knowledge. By carefully attending to the language, organization, and argument of specific texts, and the interrelations between texts, arguers, audiences, and contexts, rhetoricians offer methods for providing concrete textual evidence to support robust characterizations of the process of argument and knowledge-making in science that are contextually sensitive and empirically grounded.
2 A Proper Science: Mathematics, Experience, and Argument in Nineteenth-Century Science
Philosophy is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.
—Galileo 1
In the last twenty years, two major trends have emerged in the analysis of the rhetorical features of science, one taxonomic and another constructivist. In taxonomic approaches to analysis, scientific argument is identified and its effects explained using traditional concepts and terms from canonical treatises of rhetoric. This particular approach is employed in well-known rhetoric of science investigations, such as Lawrence Prelli’s Rhetoric of Science: Inventing Scientific Discourse, and Jeanne Fahnestock’s Rhetorical Figures in Science. While taxonomic approaches rely on established catalogues of topoi, tropes, and figures for analysis, constructivist investigations of argument, such as those undertaken by genre and action network theorists, focus on the features of communication and argument as they emerge and change in response to shifting needs within communities. In their analyses of scientific communication and argument, scholars like Carol Berkenkotter, Thomas Huckin, and John Swales, examine the conventions for scientific communication as well as how social, cultural, and institutional circumstances actively shape them (Genre Knowledge; Genre Analysis).
The analytical approach used in this book combines both of these theoretical perspectives and contributes a new set of resources for argument analysis. Throughout the text, taxonomic methods are employed to describe and explain the strategies for arguments used by researchers attempting to advance mathematical approaches to the study of variation, evolution, and heredity. For example, Chapter 3 examines Darwin’s use of the commonplace “the more and the less” to make his case for dynamic variation in species.
Whereas the taxonomic aspect of this analysis provides language and a conceptual framework for describing argument, its constructivist dimension seeks real-world evidence of the conventions for arguing with mathematics in science. To understand this facet of argument, I turn to philosophies/methodologies of science—which have not, to my knowledge, been exploited as analytical resources—to understand conventions for arguing mathematically in science. To provide a context for the discussion in later chapters, this chapter examines in detail the two, nineteenth-century works on the philosophy and methodology of science: John Herschel’s Preliminary Discourse on the Study of Natural Philosophy (1831) and William Whewell’s Philosophy of the Inductive Sciences (1840). The conventions of mathematical argument described in these works provide a context for assessing not only the legitimacy of strategies used by arguers to advance mathematical approaches to variation, evolution, and heredity, but also the reasons for the success and failure of those strategies with nineteenth century, scientific audiences.
John Herschel and William Whewell
Scientific philosophies provide a valuable resource for understanding the choices scientists make when they argue. The influence of such philosophical texts was particularly strong in the nineteenth century, a period when the philosophy of science was not divorced from its practice. Philosophies of natural science were written by influential educators and practitioners who included in their works the latest information about the methods and state of knowledge in a broad range of scientific fields. As a result, they were not only read as theoretical documents, but also as handbooks describing the state of the discipline and the practice of science.
John Herschel (1792–1871) and William Whewell (1794–1866) were two of the nineteenth century’s most eminently qualified writers on natural philosophy. They were both actively engaged in scientific research and publication, and both vigorously participated in developing important institutions of British science.2 John Herschel is, and was regarded, as one of the great figures of Victorian science not only because of his tireless efforts in discovering and cataloguing astronomical phenomena, but also because of his ability to write lucidly about the finest points of scientific philosophy (Partridge xii-xiv). His skills of adaptation are exemplified in Preliminary Discourse on the Study of Natural Philosophy (1830), in which he presents readers with a thorough introduction to scientific philosophy and a clear explanation of scientific method.
The significant influence that the book had on Victorian science is evidenced not only by the fact that the text went through twelve editions, but also by the quality of the Victorian thinkers who vouched for its importance in the development of their own scientific thought. John Stuart Mill, for example, used it as the basis of his own work on scientific theory in his System of Logic (1843) (Partridge xiv; Canon, “John Herschel” 220–221). It also influenced James Clerk Maxwell’s work in the Discourse on Molecules, and William Whewell’s Philosophy (Canon, “John Herschel” 220; Kemsley).
Although not as eminent a producer of scientific knowledge as Herschel, William Whewell had a significant impact on mathematical and scientific education and natural philosophy in Britain. As an influential member of the faculty and administration of Cambridge from 1828–1866, Whewell pushed for the introduction of analytical mathematics at Cambridge, a move which brought the archaic mathematics curriculum at Cambridge up to date with Continental mathematical practices. He also supported the creation of a new Tripos for the natural
