John Venn's Evolutionary Logic of Chance

John Venn’s Evolutionary Logic of Chance Berna Kılıç Eden “So careful of the type she seems, so careless of the individual”. These verses from Alfred Tennyson’s “In Memoriam”, written between 1833 and 1850, served as an epigraph to John Venn’s 1866 treatise Logic of Chance. The latter work is taken by many modern historians as the first systematic account of the frequency theory of probability.1 According to this theory, all quantified uncertainties should mirror some external reality that can be expressed as the relative proportion with which a property occurs among objects of a certain class. This account of probability in its turn has been cherished by many contemporary statisticians as the objective interpretation of probability. Objectivity is thought to be attained when personal uncertainties are scaled to, and corrected by, statistical frequencies. It has been suggested that this notion of an objective probability was made possible by the expanding statistical practice in the nineteenth century that spawned a belief in statistical uniformity. In this paper I take issue with these claims by focusing on Venn’s work. In order to understand better the view of nature that was Venn’s point of departure, we may read Tennyson’s “In Memoriam” further: That I, considering everywhere Her secret meaning in her deeds, And finding that of fifty seeds She often brings but one to bear, (Tennyson, 1982, 79) In his query for an explanation of death, Tennyson intimated--in the stanza following the two lines Venn quoted--that the mystery of nature was played out in the contrasting destinies of the individual and the type: While individual lives flourished and vanished in utterly inexplicable and erratic ways, their type had a permanence, explicable by a 2 regularity--the average fecundity of the species--which emerged when the comparative frequencies among the aggregates ofbirths, lives and deaths were taken into account. Ultimately, Tennyson submitted, averages were all that Nature offered by way of an explanation of the death of a beloved one.2 Statistical concepts, such as an average fecundity, were booming in the first half of the nineteenth century when Tennyson wrote his poem. A burst of statistical activity in this period, what Ian Hacking has called an “avalanche of numbers”, indicated an ever widening range of mass phenomena which seemed to occur in regular periodic intervals (Hacking, 1990, vii). The notion of a statistical law became conceivable by the 1840s when those statistical regularities were projected beyond the confines of space and time (as well as paper and effort) encompassed by statistical tables. Demographers and their readers believed that they were confronted not simply with statistical facts, as for instance the kind that would be found through one single census, but with statistical laws, i.e., long term regularities of aggregate phenomena. By the mid-nineteenth century, statistical practice transformed moral sciences by presenting a new picture of society as the static or dynamic state of a massive entity that was the sum total of its members.3 Examples of statistical regularities, such as those concerning the yearly murder and suicide rates or instances of forgetfulness like misaddressing of letters, circulated widely in both the Continent and Britain, especially after they were popularized by Adolphe Quetelet in the 1830s. To many advocates of statistical methods in political economy, medicine and government, statistics provided a new way of understanding the tangle of mass phenomena: It revealed the constant causes behind surface variability. In Quetelet’s project for anthropological measurements, those constant causes were tantamount to the “human type”. Average men approximated that human type, as the number of measurements of actual men increased. By averaging out the accidents of time, place, individuality, etc., “the method of means” or “the numerical method”, as it was variously called, was thought to lay bare the essential uniformities. 3 It was to this enthusiasm over statistical laws and statistical determinism that Venn reacted in the 1860s, when he took Tennyson’s vision of nature as a wrong-headed assumption in the philosophy of probability. This may be surprising if the frequency account of probability is seen to be a theorizing of the concept of statistical uniformity brought about by the recent boom of statistical activity. But this suggestion, advanced by Hacking and Porter, needs to be qualified.4 Venn was influenced not only by the statistical view but also by the historicist approaches to nature and society. These two styles of thinking, the statistical and the genetic views as the historian John Theodore Merz called them, confluenced in Venn’s philosophy of probability, and created grave conceptual problems in the foundations of probability.5 As a result, not only the notion of a statistical law, but also the very conception of probability based on the existence of such laws became questionable. Venn did not agree with Tennyson’s poetic evocation that nature was more careful of her types than of her individuals. Contra Tennyson, Venn expounded in the Logic of Chance that nature was as hostile to a type as it was to an individual, since types also came into being and ceased to exist: “the type itself, if we regard it for a long time, changes and then vanishes and is succeeded by others” (Venn, 1866, 14). Types had histories just like individuals. I trace in this paper Venn’s concern with the “change of type” to biological theories of evolution, of which there was no shortage in the nineteenth century, the most celebrated one appearing in 1859 with Charles Darwin’s Origin of Species. Doing so, not only do I present a most significant ingredient of the Victorian culture in which Venn lived, but I also aim to highlight the conceptual significance of his concern with “change of type” for philosophy of probability. Indeed, what Venn called “the change of type” sat in the center of a whole range of questions in the foundations and applications of probability theory. If types changed, could one still read “constant causes” or envisage “the average man” from prolonged statistical compilations? Could one rely on Bernoulli’s theorem, which for many 4 mathematicians and statisticians was the watertight proof of the existence of constant causes? Could one still espouse an associationist mechanism of probabilistic reasoning, based--as advanced by David Hume--on “the constant conjunctions” within experience? More significantly, could one make sense of the frequency definitions of probability formulated in terms of an indefinitely prolonged series, stretching over millennia of change? The formulation of the frequency conceptions of probability always involves, implicitly or explicitly, some reference to universals. Obscured in the twentieth century by the use of set theory, this aspect of frequentism can be easily verified by a sampling of the vocabulary of nineteenth century frequentists, such as Robert Leslie Ellis, John Stuart Mill and Venn, which abound with the words “species”, “genus”, “kind” and “natural class”. These terms, all used to characterize the generic “event” the probability of which was sought, gave expression to some implicit assumptions underlying frequentism: To the extent that the frequency accounts of probability hinged upon long run behavior of mass phenomena, they presupposed a constant taxonomy of the world. And to the extent that frequentism had a claim to provide an objective account of probability, in whatever sense that objectivity is understood, that taxonomy should delineate genuine classes of entities-- objects, events or processes--which can sustain that objectivity. The issues I raise in this paper are thus based on the following tension: Theories of evolution undermined the belief in the fixity of species, as well as posing a threat to the assumption of the constancy of taxonomies. Venn appealed to the existence of “natural kinds” in order to explicate the notion of series, the infinitely repeated observations or experiments, that he introduced as the sine qua non of probabilistic reasoning. He was actually one of the first to introduce the expression “natural kind” into English language. How should we understand Venn’s “natural kinds” in the universe of flux the theories of evolution depicted? Were Venn’s natural kinds homogenous populations that endured the “change of type”? How could one have stable probabilities, when the very kinds which were used to tabulate statistical enumerations changed in time, just as biological species 5 did? I argue that Venn’s philosophy of probability was strained with the issue of temporality. Thereby appeared his disconcerting avowal that the frequency account of probability could not achieve that ideal of objectivity with which the twentieth century advocates of the theory glorified it. Venn denied the existence of “objective” probabilities. It was in this context that the reference class problem arose. I substantiate these claims by first presenting the statistical and the genetic views of nature in the works of Venn and his milieu. I then analyze the impact of the theories of evolution on Venn’s notion of natural kind. I end by discussing the bearing of Venn’s historicist concerns on the reference class problem and the interpretation of Bernoulli’s theorem. In this endeavor, I make use of Venn’s published works as well as an unpublished and little known autobiography of the author deposited in the Church Missionary Society archives.6 Venn and the Statistical View John Venn (1834-1923) came from a staunch Evangelical family that belonged to the Clapham sect of the Low Church (named after the London suburb of Clapham).7 Venn grew up in a highly secluded and puritan household, imbibing the Evangelical creed and unsuspecting of religious doubt. He entered Gonville and Caius College, Cambridge in 1853, and received a degree in mathematics in 1857.

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