about what audiences might have thought about a particular application of a mathematical argument to some aspect of variation, evolution, and heredity, each chapter includes close readings of audience responses to the texts of the featured arguers. These responses are primarily from book reviews written at or around the time a featured text was released or, in the cases of journal articles, private or public responses offering commentary on the research. All audience responses are assessed by close textual analyses, singling out the reasons given by respondents for supporting or challenging the featured arguments. In addition, the reasons are compared to the featured arguer’s theory of his audience to draw conclusions about why they may have succeeded or failed in their persuasive endeavor.
Preview of Chapters
Each chapter in the book is dedicated to investigating some aspect of the relationship between science, mathematics, and argument. In the first three chapters, the focus is on articulating the general conventions and limitations of mathematical argument in science. The remaining three chapters explore the rhetorical dimensions of making mathematical arguments in science.
Chapter 2, “A Proper Science,” explores nineteenth century epistemological and ontological commitments about the appropriate relationship between mathematics and science by examining the philosophies of two of the period’s most influential, natural philosophers. A close reading of William Whewell’s, Philosophy of the Inductive Sciences (1840), and John Herschel’s, Preliminary Discourse on Natural Philosophy (1831), suggests that quantification and mathematical reasoning were considered assets in the production of knowledge about nature because they contributed precision and rigor to scientific research and reasoning. Investigations of these texts also reveal the stages in which quantification and mathematical reasoning contributed to science and the process by which mathematical arguments might be elevated from hypothetical analogies to deductive laws of nature. The views of these two, influential philosophers about the status of mathematical arguments in science provides a framework for assessing the status of mathematical arguments, the choices of arguers as they seek to defend them, and the reactions of nineteenth century audiences as they move to accept or reject mathematical arguments as a legitimate means for making knowledge about nature.
The third chapter, “A New Species of Argument,” examines the rise of the mathematical treatment of variation and evolution in Charles Darwin’s work, The Origin of the Species (1859). It makes the case, contrary to most current scholarship on Darwin, that his work relies on common mathematical warrants—generally accepted lines of reasoning for making mathematical arguments in science—both to support and invent arguments about dynamic variation, relation by descent, and the principle of divergence of character. In addition, the chapter suggests that his use of mathematics for support and invention may have been a rhetorical move on Darwin’s part to establish an ethos of precision and rigor for what he knew would be controversial positions. An examination of popular philosophies of science, which had been read by Darwin and were revered by many nineteenth century philosophers, suggests that the naturalist had attempted to follow the conventions for developing robust scientific arguments through the use of quantification and mathematical operations.
Whereas Chapter 3 investigates the use of common mathematical warrants as a means of enhancing the credibility of an argument, the fourth chapter, “Hidden Value,” explores Gregor Mendel’s reliance on special mathematical warrants—mathematical principles and formulae previously unsanctioned for argument about a particular subject—in his attempts to persuade his contemporaries to accept his theory of uniform particulate inheritance. Careful scrutiny of Mendel’s arguments in “Experiments in Plant Hybridization” (1865) suggest that the mathematical principles of probability and combinatorics—mathematics “relating to the arrangement of, operation on, and selection of discrete mathematical elements belonging to finite sets or making up geometric configurations”—rather than being resources for description or verification of his experimental results, act as sources of invention for his experiments (“Combinatorial” Def. 2.). As a consequence, the mathematics function rhetorically as a creative analogy for imagining and arguing about nature before reasonable certainty had been established about its applicability to the case. I will argue that Mendel’s confidence that other members of his audience would embrace the analogy as more than creative conjecture plays a central role in his failure to persuade them of the validity of his hereditary theory.
In addition to examining the analogical characteristics of mathematics in Mendel’s argument, the chapter also investigates the complex network of ontological commitments which may have affected the reception of his mathematical arguments. A comparison of Mendel’s ontological commitments with those of his contemporaries suggests that the principles on which Mendel founded his theory were, in many cases, directly at odds with those of mainstream studies of hybridization. As a consequence, the mathematical arguments, despite their analytical rigor, could be challenged on a number of grounds unrelated to their technical execution or their verification by experiment. This vulnerability suggests that Mendel’s mathematical warrants existed in a competitive hierarchy of truths and values, some of which were either singly or collectively more compelling to his audience than the mathematical proofs which Mendel held in high esteem.
While Chapters 2, 3, and 4 probe the general divide between what was considered conventional or unconventional in mathematical arguments for mid-nineteenth century Continental and Victorian biological researchers, Chapters 5, 6, and 7 examine cases wherein explicit efforts are made to argue for the acceptance of special mathematical warrants as reliable descriptors of nature. These efforts reveal not only the reasons for the success or failure of particular attempts, but also further illuminate the scope of issues thought pertinent to, and reasons believed legitimate for, accepting or rejecting mathematical argument in science.
Chapter 5, “Probable Cause,” investigates the rhetorical success of Charles Darwin’s cousin, Francis Galton, in his endeavors to promote an analogy between the probabilistic law of error (as embodied in the bell curve) and the distribution of hereditary outcomes in human populations. Evidence from Galton’s campaign to promote this analogy in his groundbreaking book, Natural Inheritance (1889), suggests that analogies between mathematics and nature had to be argued for, and that non-analytic rhetorical strategies played a substantive role in securing their acceptance.
To make this case, the fifth chapter investigates the rhetorical strategies in Natural Inheritance, the context of its publication, and its reception. An examination of the context of publication reveals that, like Mendel. the mathematical arguments Galton relied on to establish his conclusions about variation, evolution, and heredity were considered special warrants by his audience. A close textual analysis of Natural Inheritance reveals that Galton, unlike Mendel, was aware of the lack of common acceptance of his warrants and looked for argument strategies and good reasons outside of the confines of the specialist discourse community of biological researchers to defend his conclusions. The use of general argument strategies such as narrative, visual argument, synonymia, and appeals to the values of his English Victorian readers are identified in his text, and evidence of their efficacy is presented from reviews of Galton’s work.
Whereas Chapter 5 examines a successful effort to promote a novel mathematical approach amongst conventional biological audiences, Chapter 6 investigates the failure to expand it. “Behind the Curve” explores the mathematician Karl Pearson’s efforts to develop—based on the success of Galton’s arguments in Natural Inheritance—a purely mathematical model of inheritance based on the principle of probability. This exploration reveals that Pearson’s dogged insistence that mathematics, and mathematics alone, was the key to understanding variation and evolution in natural populations, alienated his audience despite their general sympathy for Galton’s analogy between the mathematical law of error and heredity. This failure suggests that even though the suitability of the analogy had been accepted, when mathematics was advanced as a value for doing science it could be challenged rhetorically.
The final chapter, “Weightless Elephants on Frictionless Surfaces,” explores the early, twentieth century statistician R.A. Fisher’s efforts to revitalize mathematical
