within it (Aristotle, Rhetoric I, ii 15–25). This allows for alternative avenues of rationality and common ground to exist, even in cases where different paradigms or schools of thought compete, and dispenses with the necessity of reverting to personal calculi to make decisions in these types of crises.
Rhetorical Method
From a rhetorical perspective, foci for analysis can include, but are certainly not limited to: (1) the good reasons and forms of evidence and argument that discourse communities find acceptable, (2) the effects of these dimensions of argument on the choices that speakers and writers make in constructing arguments, and (3) the ways that audiences judge their choices. Analyses centered on these foci address questions like, “Who is the audience for a scientific argument?”; “What conventions govern the way researchers participating in a particular scientific discourse community are expected to argue?”; “What facts, beliefs, and values do participants within a particular research community use to judge the validity and reliability of methods and conclusions?”; and “What broader sets of facts, beliefs, and values might influence the making or judging of arguments?”
Historical Analysis
This investigation relies on several different methods of analysis, including historical analysis, close textual analysis, and audience response analysis to draw conclusions about the relationship between scientific and mathematical arguments in the development of mathematical approaches to the study of variation, evolution, and heredity. Historical analysis is used to establish the dimensions of the scientific debates surrounding these phenomena and the perceived role of mathematics in the debate from the middle of the nineteenth to the beginning of the twentieth century. This aspect of analysis draws on a wide range of sources, including archived letters, scientific articles, philosophies of science, reader reviews of primary texts, and secondary historical accounts to establish the contours of the debate. These resources also supply evidence for characterizing the role of mathematical argument in science during the period under investigation.
Using philosophies of science to establish the conventions for scientific arguing in a particular historical period is not, to my knowledge, a method that has been previously exploited by rhetoricians of science. Current rhetorical work analyzing scientific argument relies either on a scientific figure’s knowledge of rhetoric or on second-hand accounts of the conventions of scientific argument. In Jean Dietz Moss’s work on the Copernican controversy, Novelties in the Heavens, for example, Moss offers readers historical evidence that scientific figures such as Galileo and Kepler had studied and/or taught rhetoric. This evidence proves a particular connection between rhetorical treatises and a scientist’s use of characteristically rhetorical strategies of argument—such as the employment of ornamental language to gain the attention and admiration of the reader. While this approach offers a robust connection between specific rhetorical training and argument, it limits the rhetorical analyst to cases in which scientists can be proven to have had a rhetorical education. Though these limitations are not prohibitive in investigations of Renaissance science, they become severely restrictive for science in the nineteenth century—a time when rhetoric was largely absent from standard education and during which no new substantive treaties on rhetoric were published (Houlette ix). Further, by restricting rhetorical investigations to facets of argument learned through a rhetorical education, the range of scientific argument that can be explored is unnecessarily narrowed based on distinctions between dialectic and rhetoric, which are practically very difficult to maintain.
Other rhetorical analysts of science have adopted a broader sense of the argumentative territory open to rhetorical discussion and analysis. However, in their efforts to identify the conventions of scientific argument, they depend on secondary rather than primary sources. In Lawrence Prelli’s substantive work on the rhetoric of science, A Rhetoric of Science: Inventing Scientific Discourse, for example, he relies on Thomas Kuhn’s discussions in The Structure as the source for his problem-solution topoi and evaluative topoi.3 Though Kuhn is certainly considered a reputable source for understanding scientific argument, neither he nor Prelli offer any primary source evidence to corroborate that scientists endorsed these lines of reasoning as conventional places for finding arguments in science.
The methodological contribution of this book is in its use of primary source material, specifically the writings of nineteenth century philosophers of science, as sources for constructing a robust description of the conventions for arguing with mathematics during this period. By relying on primary source material, it avoids problems of reliability and contextual sensitivity. In addition, it broadens the scope of materials available to rhetoricians for analyzing scientific argument and offers a means by which the division between common and special lines of argument can be made. These divisions are formulated positively based on examinations of the actual conventions articulated by a scientific discourse community rather than negatively as anything not existing in a particular treatise or set of treatises on rhetoric. Investigating the articulated conventions of science in conjunction with scientific arguments provides a broader and more accurate picture of what constitutes or does not constitute a common or special line of argument, and thereby what aspects of scientific argument are or are not being employed rhetorically.
Close Textual Analysis
While the historical analyses in the book are aimed primarily at establishing the conventions for mathematical and scientific argument, close textual analyses of the works of featured arguers offer insight into their specific choices of language, organization, and argument. These choices illuminate not only the persuasive goals and strategies of arguers, but also what these arguers may have believed about their audiences.
This type of analysis is conducted in this investigation using a number of pre-existing analytical categories in modern and classical rhetoric, such as ethos, stases, loci, value hierarchies, etc. as well as a detailed assessment of choices in language, organization, and argument in the text. The applications of these analytical categories are intended—in addition to their utilitarian function of illuminating the character and structure of the argument—to illustrate that categories for analyzing discourse and argument exist within rhetoric that might be profitably used to expand our understanding of the role of mathematics in scientific argument.
Audience Response Analysis
Finally, unlike the two previous analytical methods, which are primarily designed to illuminate argument conventions and strategies, the third method, audience response analysis, is designed to provide insight into persuasion. As some rhetoricians have pointed out, rhetorical analysts have made bold pronouncements about the persuasive affects of texts without supplying evidence from the audience to support their contentions.4 The analysis in this book endeavors to make claims about the reasons that late nineteenth and early twentieth century biological researchers judged mathematical concepts and formulae to be reliable or unreliable grounds for arguments about variation, evolution, and heredity. As a consequence, it is necessary not only to discuss the conventions of scientific argument, but also the specific reasons given by audiences for accepting or rejecting them.
Examining the responses of individual audience members in conjunction with the conventions of scientific argument has a number of benefits. First, by examining the two together, it is possible to know whether members of a particular audience were or were not appealing to convention to support their praise or excoriation of a scientific argument. This knowledge provides a method of checking whether scientific conventions were taken seriously, considered unreasonable ideals, or not considered applicable in particular situations. Second, by examining individual responses it is possible to understand whether sources of good reasons for accepting or rejecting mathematical argument were limited to the conventions outlined in scientific philosophies. If alternative good reasons exist, their presence suggests that there may be values, beliefs, and truths from outside the confines of a specific scientific discourse community impacting the development of scientific knowledge. Their existence would indicate that broader, rhetorical lines of argument are implicated in reasoning about the validity of mathematical warrants in making scientific arguments about biological phenomena.
