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 to “translate” natural phenomena into the language of numbers, induction leading to the formation of empirical laws could not commence. It was, therefore, the first step in the formation of any science to discover the method or system of measure on which quantitative induction could be founded.
Although various attempts had been made in the eighteenth century by Linnaeus and others to quantify certain aspects of biological research (such as the classification of leaves and reproductive organs in plants), they were all considered, at least by nineteenth century standards, artificial, and therefore not sufficient for the basis of a quantitative science. At the beginning of the nineteenth century, however, two important developments afforded new opportunities for advancing quantitative investigations of organic phenomena. The first was the increased interest in and use of statistics. The second was the discovery of fossils of extinct organisms, whose forms were completely alien from existing flora and fauna, which focused attention on questions about the origin and dispersion of organic forms. In his search of evidence and arguments for The Origin of Species, Darwin was influenced by both of these developments, which inspired him to cultivate quantitative evidence and mathematical arguments to support his theories of variation and evolution.
Though vital statistics (numbers of births and deaths) had been collected since the seventeenth century by religious and political organizations, the number of investigations and degree of attention to their results was limited to very small audiences.2 At the beginning of the nineteenth century, however, social, political, and economic contingencies converged to create what statistical historian Harald Westergaard dubs the “The Era of Enthusiasm” for statistics (136), and Ian Hacking calls a period with “a professional lust for measurement” (5).
There is no single, agreed upon cause for this sudden interest in and collection of statistics. Some historians attribute it to the need to for precise measurement required by the Industrial Revolution, which gathered momentum at the beginning of the nineteenth century (Hacking 5). Others argue that it was the result of a sudden increase in the availability of statistical information that followed the end of the Napoleonic wars (Chatterjee 267). Yet others contend, perhaps most convincingly, that the supply of statistical data increased to meet a greater demand by governments who required quantitative data in order to make better informed political decisions and more persuasive policy arguments (Westergaard 141; Cullen 19–20; Patriarca 13–14). In particular, governments required statistics on birth and death rates as well as the resources of their domain and the domains of other nations to make rational economic policy decisions.
The statistical fever that had grabbed hold of politicians and moral philosophers in the early decades of the nineteenth century also infected geologists and botanists who were exploring the vast biodiversity of the Americas and Australia. Like political economists, they began in earnest to gather quantitative data on organic populations and the conditions under which they thrived. However, unlike their counterparts, the ends for their statistical efforts were affected by important scientific questions raised by new geological theories which assumed a dramatically older earth and grappled with new fossil evidence of organisms unlike any flora or fauna known to Victorian science. These discoveries, which challenged the tenants of the Christian doctrine of creation, encouraged investigations attempting to reconcile, to some extent, the scientific evidence with religious doctrine.
These efforts gave rise to a new field of biogeography, whose aim was to answer fundamental questions about organic populations, including: “What causes influence the thriving or extinction of particular species?”; “What is the distribution of species and genera upon the globe?”; “What is the population of any given species?”; “How can we account for the appearance of new species throughout geological time?”; and “What are the laws by which plants and animals of different parts of the earth differ?”3
Part of the spirit of this new field was that these questions needed to be answered not through classification of organisms and minerals, but rather through the juxtaposition of quantitative facts about climate, population, and location. Alexander von Humboldt, one of the early founders of biogeography, proclaims this goal in Aspect of Nature in Different Lands and Different Climates (1849):
Terrestrial physics have their numerical element, as has the system of the universe, or celestial physics, and by the united labors of botanical travelers we may expect to arrive gradually at a true knowledge of the laws which determine the geographical and climactic distribution of vegetable forms. (108)
The path towards a new biogeographical physics was laid down in works such as Alphonse de Candolle’s “Essai Elementaire de Geographie Botanique” (Elementary Essay on Botanical