Evolution by the Numbers. James Wynn
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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 sciences, which allowed students to focus their attention on the study of nature by relieving them of the extraordinary burden of having to have expert knowledge of mathematics to obtain honors in their studies (Herivel xiii).3
In addition to being in the avant-garde of institutional reform, Whewell was also a leader in nineteenth century discussions about the history, philosophy, and methodology of science and its relationship to mathematics. In 1837 he published History of the Inductive Sciences, which was “aimed at being, not merely a narration of the facts in the history of science, but a basis for the philosophy of science” (viii). In the text, Whewell traces the history of natural philosophy from the Greeks through the Middle-Ages and into the nineteenth century, critiquing the shortcomings and praising the advancements in scientific thought as it developed.
Whereas History of the Inductive Sciences explored and assessed the empirical development of a proper system for obtaining scientific knowledge, Whewell elaborates the epistemological characteristics of that system in Philosophy of the Inductive Sciences (1840). In part one, “Of Ideas,” he offers an expansive discussion of scientific epistemology that addresses the relationship of thought and experience to the production of credible scientific knowledge. In part two, “Of Knowledge,” Whewell describes the process by which he believed scientific knowledge was constructed and the specific methods by which knowledge of nature is obtained.
Although the philosophical positions in Whewell’s History and Philosophy proved to be more controversial than Herschel’s Discourse, they were nonetheless seriously regarded as important scholarship on scientific history, philosophy, and method by nineteenth century scientists. Both History and Philosophy ran three editions, and contributed to a lively debate about the foundations of scientific knowledge, which engaged important nineteenth century figures such as John Stuart Mill, Charles Darwin, and John Herschel.4
Because of their substantial influence on Victorian science and their attention to the role of mathematics in making scientific argument, the philosophies of science by Whewell and Herschel can be considered credible guides for understanding the challenges and benefits of making scientific arguments with mathematics. In addition, they represent opinions on two sides of an important philosophical division in the nineteenth century: between nativism, whose adherents believed that the source of knowledge about nature resides in the mind of the scientist; and empiricism, whose supporters suppose that the truth of nature inhered in nature itself, and could only be uncovered through experience and experimentation (Richards 2–3). Because they represented opposing sides of this debate, Whewell, nativism, and Herschel, empiricism, a combined analysis of their work affords a comprehensive view of the spectrum of opinion on correct procedure in Victorian science as well as common ground on the role of mathematics in making scientific arguments.
Rationality and Reality: The Stakes for Mathematical Argument
Whewell