and Miller and Halloran). Their works explore different aspects of his rhetorical strategy in The Origin of the Species, including the use of analogy between the human breeder and nature, to help his audience understand the operation of natural selection and the importance of the rhetorical figures incrementum and gradatio in making the argument about variation and diversity among groups of organisms.
Despite the wide range of topics and issues in argument covered by rhetorical scholars, there has as yet been no substantive discussion about the rhetorical importance of mathematics in making arguments in The Origin of the Species. The purpose of this chapter is to offer arguments and analyses that suggest that Darwin relies heavily on mathematical elements such as quantification and basic arithmetical operations for support and invention of his arguments for dynamic variation, relation by descent, and the principle of divergence of character in The Origin of Species. It will also make the case that, by following the best practices of quantitative induction, Darwin hoped to establish an ethos of precision and rigor for his work which was commensurate with the rising importance of quantification to the study of biological phenomena in the middle of the nineteenth century.
Mathematical Darwin?
Though historians and philosophers of science have expended considerable effort tracing the development of different mathematical fields and examining their political, cultural, and even rhetorical influence (e.g., Cullen; Patriarca), they have not, with rare exceptions, taken up investigations into the role of mathematics in Darwin’s arguments. A survey of eleven books and nine articles published by historians, philosophers, and rhetoricians of science, most published in the last twenty-five years, reveals that few texts associate Darwin’s arguments with mathematical reasoning (Appendix A). Those texts that do associate the two predominantly comment either on the lack of mathematical reasoning in the text, or on Darwin’s inability to use mathematics to make his case (Ghislen; Hull; Gale; Depew and Weber). Only four assign any real importance to mathematics in Darwin’s arguments (Browne; Schweber; Parshall; Bowler).
Mathematics in The Origin of Species
The previous examination of selected books and articles in the history, philosophy, and rhetoric of science suggests that many modern scholars do not believe or have not considered mathematical argument as an important facet of Darwin’s persuasive strategy in The Origin of Species. These results raise the question, “If mathematics plays such an important role in Darwin’s argument, why is it that so few scholars in rhetoric and history bothered to write about it?”
A cursory review of the text itself reveals that there are very few places where mathematical symbols, numbers, tables, equations, etc. are used. This scarcity of mathematical notation is puzzling even to those who argue in favor of the importance of mathematics in The Origin of the Species, like historian Janet Browne, who comments on the scarcity of mathematics in the text:
That Darwin’s botanical arithmetic has been neglected by historians is partly his own fault. In On the Origin of Species, he barely referred to his botanical statistics or the long sequence of calculations which he had undertaken from 1854 to 1858. He compressed and simplified these into a few meager paragraphs, giving his reader only six pages of statistical data to fill out the discussion of “variation of nature” in Chapter II. (53)
Despite its absence in the actual text, a brief review of Darwin’s notebooks, letters, the published manuscript of his “big species book,” and Variation of Plants and Animals under Domestication, reveals the extent to which mathematics influenced the development of his theories.1 In these publications, Darwin supplies his readers not only with lists of quantitative evidence and calculations, but also with occasional glimpses of the degree to which these data and calculations helped him formulate his conclusions.
The existence of precisely quantified data and calculations in these extrinsic sources, however, still does not explain why, if they were so important to Darwin’s argument, the majority of them were left out of his text. The answer to this query is provided by Darwin himself in the introduction to The Origin of the Species.
I can here give only the general conclusions at which I have arrived, with a few facts in illustration, but which, I hope, in most cases will suffice. No one can feel more sensible than I do of the necessity of hereafter publishing in detail all the facts, with references, on which my conclusions have been grounded; and I hope in a future work to do this. (4)
Here Darwin explains that he is able to give only a general outline of his theory, and as a result, has to forgo presenting all of the data and discussion that he might have otherwise provided. The reason for this brevity is that he has been rushed into publication by the emergence of Alfred Russel Wallace’s theory of evolution which, for all intents and purposes, offered the same conclusions as his own. Additionally, Darwin’s lack of specific, quantitative detail may have been a strategy to make his work accessible to a wider readership for whom a text dense with quantitative data and arithmetical calculations would have seemed too formidable (Beer viii).
Besides the infrequency of quantified data and operations in The Origin of the Species, influential historians discussing the arguments in the text, notably David Hull, have made the case that Darwin could never have integrated mathematical reasoning into his arguments because this type of reasoning was deductive and could not be brought into the service of an inductive theory. In his book, Darwin and His Critics, Hull takes the position that because Darwin was developing arguments in the non-physical sciences, deductive mathematical reasoning could not aid him in prosecuting his argument:
Darwin could not help but know the crucial role which mathematics had played in physics, since Herschel had repeatedly emphasized it in his Discourse, but it did not seem to be in the least useful in his own work in biology. . . . For Darwin, mathematics consisted of deductive reasoning, and he distrusted greatly “deductive reasoning in the mixed sciences.” In his own work, he seldom was presented with a situation in which he could use such deductive reasoning. He was constantly forced to deal in probabilities, and no one could tell him how to compute and combine such probabilities. (12–13)
Hull’s assessment of the impossibility of Darwin’s use of mathematics rests on the assumption that Darwin believed that mathematical reasoning was deductive, and therefore could not be used in inductive arguments. Like Hull, rhetorical theorists most likely also miss the rhetorical dimension of the text because they assume that mathematical warrants are deductive. Though this does not preclude them necessarily from functioning in Darwin’s text, it does remove them, in the minds of most rhetorical analysts, from being the focus of a rhetorical investigation. To my knowledge there has been no explicit statement such as Hull’s that this consideration has kept rhetoricians from examining the mathematical aspects of Darwin’s arguments. However, this restriction is articulated in influential theoretical texts such as Philip Davis and Rueben Hersh’s “Rhetoric and Mathematics,” in which they write that, in the minds of most rhetorical scholars, “If rhetoric is the art of persuasion, then mathematics seems to be its antithesis. This is believed, not because mathematics does not persuade, but rather that it seemingly needs no art to perform its persuasion” (53).
Philosophers, historians, and rhetoricians of science have not recognized an important role for mathematics in Darwin’s arguments. However, careful examinations of early nineteenth century botany and geology, a detailed investigation of Darwin’s ideas in his notebooks and letters, and a close textual analysis of the arguments in The Origin of the Species, reveal that quantification and basic mathematics were important to his work. They show that mathematics played a central role in Darwin’s formulation and defense of his arguments, including his rhetorical efforts to establish an ethos of precision and rigor for his work.
Keeping Count: The Rise of Statistics in the Nineteenth Century
One of the fundamental characteristics of robust science in both modern and Victorian characterizations is quantification. Without the ability
