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. His interest in mathematics waned as soon as he graduated from Cambridge; in 1857, in a fit of reaction against his narrow mathematics education in Cambridge, he sold most of his mathematics books, and began his career of a clergyman. He was ordained curate in 1858 and priest in 1859. Under the influence of a domineering father, Henry Venn (who was the founder of the Church Missionary Society), John Venn could not conceive of any other vocation but divinity. My creed, he wrote in his Autobiography, “had been accepted as a whole, and was only held together by my emotions, of which emotions one of the chief was reverence for my father” (Autobiography, 105). It was only at a distance from his father’s influence, when 6 he entered a new world of friends and “radical” literature in the late 1850s, was Venn able to think for himself, and start doubting Evangelicalism.8 His interest in probability theory was awakened in this period by readings in history and political philosophy, in particular, by the writings of Henry Thomas Buckle and John Stuart Mill.9

Conceived in 1858, Venn’s work in probability theory, Logic of Chance, appeared in 1866. Venn’s central contention in this book was that the probability of an event was the limiting relative frequency with which that event occurred in a population of wide extent and of long duration. The book was intended as a popular exposition of the subject, and had little to do with mathematical subtleties, such as a rigorous notion of limit. Venn found it sufficient to illustrate his position by explanations such as: “When we say, for instance, that it is an even chance that an unvaccinated person recovers from the smallpox, the meaning of this assertion is that in the long run each alternate person attacked by that disease does recover” (Venn, 1866, 109). This viewpoint, which has been later termed frequentism, was not novel with Venn. Already in the 1840s, a number of mathematicians and philosophers, the British Robert Leslie Ellis and John Stuart Mill, the French Antoine Augustin Cournot, and the German Jacob Friedrich Fries, advanced the view that the concept of probability could be best understood in terms of relative frequencies.10 Those authors were critical of the prevailing Laplacian framework--classical probability as Lorraine Daston called it-- in which probabilities were couched in terms of the ratios among equally likely outcomes that could be assigned to an event prior to its taking place (Daston, 1988). So, the probability of having an ace with a die would be evaluated by a Laplacian probabilist as 1/6 solely on the grounds that the die had a physical symmetry or that one was totally ignorant of the prospects of any outcome. A frequentist, on the other hand, would assign 1/6 or another numerical value to the probability of having an ace by observing the actual proportion of outcomes on a long run of trials. The issue, of course, was not simply that of evaluating probabilities for gambling devices--the opposition between frequentism and the Laplacian outlook involved more essentially the nature of 7 evidence and its quantification. In the eighteenth century, the calculus of probabilities was seen by many as a promising way of evaluating evidence, in situations ranging from the distributions of stars and courtroom decisions to insurance policies and error analysis. Opposing the readiness of the classical probabilists to accommodate a variety of types of evidence, frequentists maintained that evidence could be quantified on no other grounds than relative frequencies observable in a population of similar entities.11

Venn’s term for that population of entities was “series”. A series, such as the one constituted by the repeated throws of a die, was to be determined by a set of attributes, universally applicable to its members. A series, according to Venn, had a “nominal identity”: “That which gives its unity to the succession of groups is the fact of some of these substances or attributes being common to the whole succession” (Venn, 1866, 11- 12). Probability judgments were thus essentially assertions about classes. And as such, “a system of classification” was indispensable (ibid., 180). But a system of classification was not to be based on the existence of types. Venn argued against typological realism, especially as it was advanced by Quetelet. The notion of type appeared most prominently in the writings of the Belgian astronomer and statistician Quetelet, the foremost popularizer of the practice in the nineteenth century. Quetelet’s vision of a new science of society based on statistics-- ”social physics” as he called it--bore the stamp of his early interest in error theory as an astronomer, and his later fascination with the regularities of statistical tables, such as those exhibited in Compte général de l’administration de la justice criminelle, published by the

French government from 1827 onwards.12 As Quetelet presented his agenda in his 1835

Sur l’homme et le développement de ses facultés, ou essai de physique sociale, social physics--more like meteorology than physics--would disclose a miscellany of laws regulating the social body, including: the laws of human reproduction, growth, and physical force--growth of his intellectual powers, and of his disposition, more or less great, to good or evil; the laws regulating the development of his passions and tastes; the mode of succession of the materials he produces or consumes; the laws of human mortality, etc.13 8

The evidence of the statistical tables boosted Quetelet’s confidence that there were general laws to be found in each of these specified aspects of society, once the suitable surveys were carried out. He further invested those laws with a peculiar metaphysical significance. Just as in error theory, where the mean value of measurements approximated the true value of the measured magnitude--because the measured values were assumed to be scattered erratically around that true value--in demographic phenomena, population averages were to be regarded as reflecting an inherent truth about that population, akin to the true value of repeated measurements. Quetelet glorified those average physical, moral and intellectual traits of a given society by praising the “average man”, an expression he put into circulation in his 1835 treatise. His exaltation of the average man was undergirded by an analogy he employed in order to explicate how nature and error theory corresponded. Accordingly, nature engendered variety in the same way in which an assembly of human artists would do inadvertently when copying a classical sculpture. Just as the human artists reproduced the original sculpture with slight alterations here and there, nature generated human beings from an ideal human type, but with random modifications. Quetelet’s belief in this analogy was reinforced by his discovery that various anthropomorphic measurements, such as the chest sizes of Scottish soldiers, had a roughly normal distribution, the distribution that had been the staple of error theory.14

Venn’s philosophy of probability had no room for this anthropomorphic conception of nature. He found untenable the analogy Quetelet drew between the average height of men and the average value of the measurements of a fixed magnitude. There was no fixed type of men that was analogous to the fixed magnitude in question. Venn protested: when, on comparing the group which these attempted measures compose, we find that they correspond roughly to the actual heights of a large number of different men taken at random, and go on to assume, as M. Quetelet does, that these actual heights must be in some way modelled on a type common to all: what is this but the reappearance of the realistic doctrine? (Venn, 1866, 43) 9

And Venn was a staunch critic of realism, the belief that there were fixed archetypes grounding universals in nature or in thought. Metaphorical or otherwise, the analogy Quetelet drew between the human artists copying a certain statue and nature endlessly producing its phenomena on fixed types was unacceptable to Venn’s philosophy of nature. As I argue further below, Venn’s conception of nature contained no telos of the kind ascribable to an artist.

Genetic View of the World Venn’s case against realism was to a large extent historicist. True, he conceded, statistical practice has revealed many approximate uniformities in population phenomena, such as those pertaining to the average duration of life or the birth ratios of different sexes. But could any such uniformity be projected beyond the narrow confines of time over which they were recorded? Venn was more than cautious. He noted that the average duration of life in England must have been much shorter a few centuries ago, and with the improvement of sanitary conditions it may get considerably longer in the future. One could not even hope to find a linear growth here, for: this uniformity (as we have hitherto called it) has varied, and, under the influence of future eddies in opinion and practice, may vary still; and this to any extent, and with any degree of irregularity (Venn, 1866, 14-15). On that count, Venn opposed not only Quetelet’s speculation on types but also the historian Henry Thomas Buckle’s promotion of statistical determinism. Buckle, like many British intellectuals and public officials, was greatly influenced by Quetelet’s program.15 In a work of wide popularity, History of Civilization in

England, the first and second volumes of which appeared respectively in 1857 and 1861, Buckle celebrated statistical regularities as the manifestation of natural law in society, and as the touchstone for a truly scientific history.16 Statistics, according to Buckle, “though still in its infancy, has already thrown more light on the study of human nature than all the 10 sciences put together” (Buckle, 1934, 24-5). Statisticians, according to Buckle, were the first to provide proofs for the uniformity of human affairs. Buckle’s conviction in the deterministic course of social life paralleled that of Pierre-Simon Laplace’s in the determinacy of the natural realm. Asking “[a]re the actions of men, and therefore of societies, governed by fixed laws, or are they the result either of chance or of supernatural interference?”, Buckle dismissed, as Laplace had done, theology and chance in the explanation of social processes (ibid., 6). In what he thought to be the remarkable stability of social numbers, Buckle saw the verification of social determinism. Taking a rather controversial step, he interpreted that determinism as the refutation of the doctrine of free will. The uniformity of the rate of suicides showed, according to Buckle, that suicide is merely the product of the general condition of society, and that the individual felon only carries into effect what is a necessary consequence of preceding circumstances. In a given state of society, a certain number of persons must put an end to their own life. This is the general law; and the special question as to who shall commit the crime depends of course upon special laws; which, however, in their total action, must obey the large social law to which they are all subordinate (ibid., 20). In another controversial move, Buckle distinguished between the moral and intellectual laws of society, noting in this regard that “if we contrast this stationary aspect of moral truths with the progressive aspect of intellectual truths, the difference is indeed startling” (ibid., 130). He maintained that morality (moral systems, moral instincts) was constant whereas the intellectual condition of a nation was variable, and that social progress was measured by the different levels of that intellectual state (ibid., 127-131). Buckle took the regularity of moral statistics to be proving the former claim, and the advance of European civilizations documenting the latter. In his vision of social change, the average man remained the same in his moral attributes, but progressed as an intellectual.17

Buckle’s dismissal of free will, teleology and theology in his account of historical process positioned him against the prevailing historicist positions in Britain, especially against the “Liberal Anglicans”.18 The latter historians, including Thomas Arnold, Julius 11

Charles Hare, Connop Thirlwall, Henry Hart Milman and Arthur Penrhyn Stanley, conceived of cultural change (including intellectual transformations) in terms of cycles-- civilizations waxed and waned--while they held the true progress to lie in the moral and spiritual perfection of mankind. For Romantic historians such as Thomas Carlyle, the historian must capture “the inward condition of life”, which was not the same in any two ages, by immersing into the past, by endeavoring to enter different mental worlds.19 For most of those historians, statistical history, if not an oxymoron, would have been a most superficial way of understanding the past. Buckle thus became a highly controversial figure among the British historians. He was more welcome among the radical liberals and Utilitarian social theorists, such as Thomas Babington Macaulay, who were also intent on explaining mass phenomena by general laws. However Buckle received criticism from those circles too, especially in connection with his denial of free will and his decoupling of moral and intellectual laws. James Fitzjames Stephen, an outspoken Utilitarian journalist and jurist, criticized Buckle on the first count, while John Stuart Mill was skeptical about the second point. Leslie Stephen, the brother of James Fitzjames Stephen, was altogether critical of Buckle’s alleged historical approach, for its lack of appreciation of the organic growth of societies.20

Venn’s interest in probability theory arose in the midst of these controversies surrounding the reception of Buckle’s work. The brothers James Fitzjames Stephen and

Leslie Stephen, well-known men of letters of the period, were cousins of John Venn.21 In his first attempt to formulate his dissent from Buckle, Venn wrote an article in 1862, announcing several reasons why sociology could not unearth social laws that were on a par with physical laws. Venn argued there that the practitioners of sociology and history had to recognize the impact they would have by publishing their prophecies. As a counterpoint to Buckle, Venn noted in this article that social predictions can be self- fulfilling or self-defeating: for instance, announcing that the future of scientific activity lay 12 in natural sciences, everybody would abandon the study of social science, and thereby disrupt the existing regularities.22 According to Venn, history and sociology were essentially different from astronomy or meteorology, where predictions did not react upon the system as a new cause. Social life had a plasticity and dynamics incompatible with the static outlook of Buckle. The statistical view rested on “the supposition that the ways and thought of men are, in the long run, invariable, or subject only to periodic changes. On the assumption of a steady progress in society either for the better or the worse, the argument falls to the ground at once” (Venn, 1866, 248).

Change of Type in Biology Historical change was not confined to the social realm. Venn was emphatic in his Logic of Chance that a “type, that is, which shall be in the fullest sense of the words, persistent and invariable is scarcely to be found in nature” (Venn, 1866, 16). The roots of his deep concern over the mutability of types became more explicit in the second edition of the Logic of Chance in 1876. There Venn propped his case against typological realism by invoking evolution. He declared, “no one who gives the slightest adhesion to the Doctrine of Evolution could regard the type, in the qualified sense of the term, as possessing any real permanence and fixity” (Venn, 1876, 42). Venn could tolerate the notion of type as employed by comparative anatomists, so long as that notion did not have realist implications: With them [comparative anatomists] it is nothing more, I apprehend, than a statement of resemblances which are actually found to subsist between different species. If any additional hypothesis be intended, I presume it would be one of a causal nature as to the process by which these species and their varieties had been produced (Venn, 1866, 44). The prevailing use of the notion of type among the nineteenth-century naturalists was indeed conformable to that nonmetaphysical view of types Venn could tolerate. By the time Venn was writing in 1866, at least three different notions of type were available in natural history: Types may exist as ideal archetypes, as extant or idealized prototypes, or 13 as extinct progenitors. For many practicing naturalists, types were specimens, existing in herbaria or natural history collections, designated by the community of naturalists as a reference material for the purposes of identification. Another widespread use of the notion of type within natural history rendered it as an extant or idealized prototype--a variety, species, or genus--used as a heuristic device for the purposes of classification (Stevens, 1994). Especially when used for the latter purpose, types were protostatistical objects: they exhibited roughly averaged out and weighted properties. Their function was to orient the naturalist in the immense diversity of nature by reducing variability.23 These uses of the notion of type within natural history did not need to take them to be fixed entities within or behind nature. They can be easily squared with Venn’s contention that types are historical entities. Venn’s opposition to statistical determinism was motivated by his rejection of the alternative account of types as ideal archetypes, an account that was readily associated with natural theology, as in the writings of William Whewell or Richard

Owen.24

Notions of type and archetype were also present in Charles Darwin’s Origin of Species, but invested with radically new meanings. Those meanings derived from Darwin’s central emphasis on the mobility of nature and the genealogy of species. Nothing in nature was constant in Darwin’s framework, except the tendency of organisms to vary and diverge. Centrifugal rather than centripetal forces permeated the laws of development--species arose by deviating from the norm rather than by conforming to it. Darwin’s metaphor for this kind of change, which he described both in words and in diagrams, was a tree, branching endlessly and unpredictably through the history of life. The essentialist taxonomies, such as that of Linneaus, recording the diversity of life on the variation of a few characteristics, were doomed to failure in this boundless spread and ramification of species, “for no part of the organization is universally constant” (Darwin, 1859, 417). The task of the systematist in this universe of flux was to chronicle life rather than to regiment it. In Darwin’s vision of nature, where all species “may metaphorically 14 be called cousins to the same millionth degree,” (ibid., 421) the notion of an “archetype” found an explanation in terms of extinct ancestors. Archetypes, as Darwin used the word, did not beckon to ideas of creation; they referred to the earthly creatures of distant past, which had also their own archetypes as ancestors. Furthermore, the archetypes of the future offshoots of the present species did not need to be the same as those of the present species. Thus, it was possible to say in this Darwinian framework that (arche)types changed. Darwin’s theory, although the most respectful and the most influential, was nonetheless one of the many efforts in historicizing nature in a long tradition of evolutionary theories dating from the eighteenth century. Immanuel Kant’s nebular hypothesis of the solar system as well as the geological theories of the history of earth predated the historicizing of organic life. Historicism had many faces; it was a conglomerate of several outlooks and approaches to the natural and moral realm. The geologist Charles Lyell’s uniformitarianism as a resistance to historicism could have been understood on three different counts: as “law” uniformitarianism (the laws of nature have not changed over time), as “kind” uniformitarianism (the kinds of geological causes have not changed over time), or as “degree” uniformitarianism (the intensity of geological causes have not changed over time).25 This multiplicity aside, many scholars of Victorian intellectual history agree that the period around the mid-century was marked by an heightened historicist sensibility.26

It is beyond the scope of my work to delimit the intricate relation between evolutionism and historicism. Nor can it be documented fully the extent to which Venn adopted Darwin’s specific theorizing. The very term evolution does not entirely specify the reference of Venn’s inspiration, since the word appeared in a variety of contexts in the nineteenth century. Early in the century, evolution was used commonly to denote the embryological processes of development as well as the succession of the fossil record, without necessarily implying any commitment to the transmutation of species (Bowler, 15

1975). Only in the second half of the nineteenth century the term evolution acquired a more specific meaning, especially when it was used in phrases such as the theory or hypothesis of evolution. Herbert Spencer was one of the first to employ the phrase “Theory of Evolution” to refer to the transmutation of species in his collected essays which appeared between 1857 and 1862 (ibid., 367). Beginning in the late 1860s, evolution came to be associated more exclusively with that meaning. For instance, Louis Agassiz’s posthumously published paper of 1874, “Evolution and permanence of type”, was unmistakably aimed at Darwin. Still, the phrase “doctrine of evolution” did not need to refer specifically to Darwin’s theory. Starting from 1860s Herbert Spencer also used the theory of evolution to refer to his grand theory of development in every sphere of matter and life, from cosmology to mind. Notwithstanding the ambiguities in the phrase “doctrine of evolution”, or Venn’s reticence in naming Darwin explicitly in the 1876 edition of his Logic of Chance, his Autobiography testifies that it was Darwin’s Origin of Species and the ensuing controversy in the 1860s that made a lasting impact on his life. In 1860 Venn read the Origin of Species and the Essays and Reviews, which created an uproar immediately after its publication.27 Venn did not have an immediate reaction, and continued his curacy in

Mortlake, a dutiful Evangelical clergyman his father taught him to be. Yet, as he wrote in his Autobiography, his religion was “being actively attacked on every side by nearly all the books I was reading, and implicitly contradicted by much of my conversation with my friends” (Autobiography, 104-5). The uneasiness caused by these publications was followed by misgivings, and a gradual separation between Venn’s public and private lives. As he recalled, “there was no insincerity, in the sense of my saying in public what I did not believe, but I must admit that there was reserve, in the sense of not saying a great deal which I did believe” (ibid., 105). Subsequently, Venn could no longer preach with certain voice of religion: “I could not talk for hours together with such men as J.R. Seeley, W. 16

Berkley, A. Blunt, and my cousin Albert Dicey, without recognizing that what I said to them was not the same as what I said in the pulpit.”28

The condition of doubt persisting, Venn resigned his position as a curate in 1862, and returned to his alma mater Caius College, where he was made Catechist, a post later converted into a more permanent Moral Science Lectureship.29 He attended the British

Association Meeting of 1862 in Cambridge when Thomas Henry Huxley attacked fiercely the creationism of Richard Owen.30 By 1864, Venn wrote in his Autobiography, “[a]ll that was distinctive of evangelicalism had now fallen off me” (Autobiography, 138-9).

Thereafter he considered himself to be “a very moderate Broadchurchman”.31 His 1869 lectures on the nature of religious belief, collected in On Some of the Characteristics of Belief, Scientific and Religious, were attempts to accommodate religious belief to the scientific one. Denying any special epistemology to religious knowing, Venn defended there the significance of critical and historical examinations of the scripture and thereby expounded the Broad Church position.32 In 1883, even less in sympathy with the church orthodoxy, he took advantage of the provisions of the Clerical Disabilities Act, and resigned orders.33

In this long process of reconciliation with Darwinism, Venn became fully receptive to the historical method. Both the biological theories of evolution as well as historical geology informed his discussion of the change of type. Not only the heights and sizes of men were subject to change, but also diseases, yield of crops, and weather, to cite some of the examples Venn dwelled on. Concerning the short-term regularities that could be discerned in agricultural production, Venn noted, in the third edition of his Logic of Chance in 1888: The reader must be reminded again that this fixity is only temporary, that is, that even here the series belong to the class of those which possess a fluctuating type. Those indeed who believe in the fixity of natural species will have the best chance of finding a series of the really permanent type amongst them, though even they will admit that some change in the characteristic is attainable in length of time. In the case of the principal natural agencies [e.g. wind and weather], it is of course 17

incontestable that the present average is referable to the present geological period only. Our average temperature and average rainfall have in former times been widely different from what they now are, and doubtless will be so again (Venn, 1962, 64-5). Of course, some of those changes in question, for instance, the geological ones, were supposed to be extended over an enormous time period, with the slowest pace imaginable. That may be a comfort to the social statistician, but to the frequentist, who like Venn maintained that an indefinitely extendible series was involved in the reference of any judgment of probability, geological time scales were no less alarming. It was the intractable potency of time, rather than that of nature, that more than anything else in the contemporary historicist and evolutionist outlooks inspired Venn. Stabilizing or eruptive, smoothening or disruptive, sorting or scrambling, time did matter. The multiplicity of the historicist outlooks or even theories of evolution do not therefore pose a real problem in interpreting Venn’s concern with temporality. It does not seem to matter much which specific theory of evolution Venn upheld. Whether adaptation was a result of the inheritance of acquired traits or the result of natural selection, or even whether one species really derived from another, an evolutionary vision that precluded permanent organic kinds sufficed to challenge the assumption that timeless types permeated reality. Of course, Darwin’s theory did not imply that all groups of entities had a volatile existence. Maxwell’s molecules did not change their type. As James Clerk Maxwell put it in a lecture in 1873: The molecules are conformed to a constant type with a precision which is not to be found in the sensible properties of the bodies which they constitute. In the first place, the mass of each molecule, and all its other properties, are absolutely unalterable. In the second place, the properties of all molecules of the same kind are absolutely identical. (Maxwell, 1965, Vol.2, 374) Yet Maxwell needed to add “[n]o theory of evolution can be formed to account for the similarity of molecules”, and provide evidence for why molecules of the same kind were not altered in cosmological history.34 By challenging the assumption of the immutability of nature, an evolutionary view left the burden of proof on those who claimed otherwise. Venn vigorously drove home this ontological challenge of evolutionism, exclaiming in a 18 later work: “We should indeed require a whole volume if we proposed to discuss the ways in which historic explanation has cast a light on many difficult problems of the present” (Venn, 1994, 338-9). Historicism was not only a challenge to the traditional conception of an immutable ontology; it also had epistemological consequences. Those consequences were articulated in more detail in Venn’s later work Empirical and Inductive Logic, where the charge against realism was coupled with that against conceptualism: “Realists held the fixity of the archetypes corresponding to ideas. Conceptualists still hold the fixity of ideas, even if there are no corresponding archetypes”.35 How could our general terms be imbued with that aura of finality if the things classified under one kind could assume a different set of attributes in the future? Diseases were a case in point. Venn noted on several occasions that the type of disease or its treatment may evolve in the future.36 A cluster of symptoms making up a disease at the present could turn into a different set of symptoms in the future. Venn pressed this issue in his account of kinds and classifications.

Natural Kinds Venn’s point of departure in his account of classification was that of traditional nominalists such as Leibniz. While nature provided some clues, classification was nonetheless a by-product of the discriminative effort of human cognition. Venn noted: Nature, as we have seen, and as Leibnitz was fond of insisting, never exactly repeats herself. But she does the next best thing to this for us. She gives us repetitions,--sometimes very frequent, sometimes very scarce, according to the nature of the phenomena,--of all the important elements, only leaving it to us to decide what these important elements are (Venn, 1994, 98).

No classification deserved to be called natural if the aim thereby was to deny the constitutive human contribution to taxonomy. Yet, one could assess the worth of different classification procedures. Venn’s proposal was to distinguish special purpose classifications from general purpose ones (ibid., 323). Special purpose classifications, such as those employed to catalogue the plants of one single country or the books in a 19 library, reflected only one point of view. General purpose classifications, on the other hand, reconciled all points of view. To the extent a classification was able to achieve that perspectival agreement, thought Venn, it recommended itself as the objective or natural one: A special classification, being conditioned by this or that object, or the wants of this or that class of persons, is in a measure a personal or subjective one: let us therefore aim at a truly objective classification, which shall hold good for all persons, and which shall therefore deserve to be called a natural one (ibid., 332). One of the perspectives Venn’s ideal of an objective classification would have to take into account was no doubt the evolutionary viewpoint. And this viewpoint required considerations of temporality: There is an enormous increase in historic interest and investigation. There is the introduction, so to say, of a third dimension into our subject. Existing classes could be symbolized, and their affinities indicated, on a superficial diagram; but if we are to take account of the past, and to represent the connection of the individuals and classes which are now extinct with all those which can be proved to have arisen as modifications of them, we should need a solid figure as a suitable representation (ibid., 338). Indeed Venn intimated how such a three-dimensional representation of biological taxonomy could be imagined. His starting point was the visual representation of the affinities between extant species provided by the zoologist William Henry Flower in his

Introduction to the Osteology of the Mammalia.37 In Flower’s map-like diagram, lake-line contours corresponded to different species, and the distances between those contours represented the degree of resemblance among species.38 Venn proposed augmenting this illustration by the time-dimension: I should have thought that the most appropriate illustration of the introduction of the additional, or time element, would have been afforded by regarding each of these separate lake-outlines as being the base of a sort of cone standing on the diagram. As we traced these cones upwards from the surface we should find the adjacent ones continually merging into each other, so that successive horizontal sections displayed fewer and fewer species. Each such succession would then represent the mutual relation of the species at some prescribed epoch. If we supposed that all life originated from one primordial form we should have to make all these cones spring ultimately from one common vertex (Venn, 1994, 338-9). 20

In this way, the Venn diagrams of synchronous life were to be integrated to Darwin’s tree diagrams of becoming. Classifications had a time index, however intractable that time dependence may be. Notwithstanding his Darwinian approach, Venn did not abandon the use of the term kind. Just as he adopted a qualified notion of type, he also made use of a circumscribed notion of kind. In point of fact, Venn was one of the first to employ the expression “natural kind” in English in his 1866 treatise on probability.39 Venn invoked natural kinds precisely for the purpose of delineating the populations which could exhibit statistical regularities. The uniformity of statistical enumerations, Venn noted, was “owing, much more than is often suspected, to this arrangement of things in natural kinds, each kind containing a large number of individuals.”40 It may be instructive here to consider an alternative world Venn imagined in his Empirical or Inductive Logic where no probabilistic reasoning could be justified. If an all powerful “ingenious and malicious” agent wished to put a stop to all human inference, probabilistic or demonstrative alike, what should he do? Venn proposed the following trick: [L]et each animal and plant and fruit, and so forth, be unique of its kind, like the fabled phœnix,--we might add to the number of species in proportion as we diminished the number of their representatives, so as to keep up the quantity of individuals and add to the consequent perplexity,--and nearly all the generalizations and inductive extensions upon which we depend for guidance in daily life would be gone at once (Venn, 1994, 97).

If only that agent pushed Earth’s orbit into a hyperbolic one, speculated Venn, so that “we should never again have any one summer or winter or day or night which would be an exact repetition of the preceding one”, all probabilistic inference would be frustrated at once (ibid., 97). With the disruption of daily or yearly uniformities, never “would an average of any number afford safe guidance as to the repetition of such an average again” (ibid., 97). Frequentism was not compatible with all possible worlds.

Reference Class Problem 21

The existence of kinds was a sine qua non of statistics. Yet Venn’s natural kinds were not the enduring populations pre-Darwinians such as John Stuart Mill had thought ultimate real kinds to be. Since Venn held that both the natural and the human ways of coercing entities into kinds may change, his kinds had a life trajectory as well: They could come into being and perish. As a consequence, Venn was extremely guarded in the way he related statistics to probability. He presumed, on the one hand, that the existence of natural kinds grounded the relation between an individual and its series. The prospects of an individual member of a series having a given attribute, such as John Smith’s probability of dying at a given age, were intimately tied to the properties of the natural kind, in this case man, with which the individual shared some important attributes (Venn, 1866, 181). On the other hand, observed Venn, the longevity of mankind was in all probability different in different epochs of history. Statistics of death from smallpox or accusations of witchcraft showed how unrepresentative such figures would be for long term tendencies. Venn was emphatic that regularity over the course of a couple of decades was no guarantee of uniformity in the long run: We shall, in the vast majority of instances ... find that the numerical proportions, which by their persistence produce the uniformity, gradually change, and this to such an extent that the term uniformity at last becomes inappropriate (ibid., 24).

Unlike the previous generations of statisticians, Venn saw neither nature nor society as the source of vast uniformities. So arose the problem of the reference class, i.e., the problem of determining or characterizing the population from which to glean reliable statistical ratios. As Venn put it: If the type were fixed we could not have too many statistics, but if it vary, our extra labour may be worse than wasted. The danger of stopping too soon is easily seen, but in avoiding it we must not fall into that of going on too long (ibid., 38). Statisticians were thus faced with a fundamental dilemma: to shrink or to enlarge statistical counts. In Venn’s words, "whilst we may fall into error by taking too few instances we may also fail in our aim ... by taking too many" (ibid., 16). But what was too few and what was too many? Venn could not provide a conceptually sound answer, only leaving the decision to the good judgment of the practicing statistician. He concluded: 22

[T]he limits within which we collect our statistics are to a certain extent arbitrary; we must exercise our judgment in deciding where we will draw the line and what we will include within it.41

Although the reference class problem was grounds for hesitation in the use of statistics from early on, Venn deserves the credit for the formulation of these problems with full clarity.42 These problems, moreover, had an unprecedented urgency for his account of probability. Venn’s frequency account rested on a series consisting of homogeneous entities--coming from a natural kind--which should be presumed indefinitely extended. Since no natural kind could encompass an infinity of entities existing in a finite duration of time, a series spanned an infinite time. Not only social change but even geological or cosmic change could not be neglected in those eons of millennia a series was supposed to extend through. Confronted with that problem, Venn suggested, at least for the purposes of mathematical reasoning, to have recourse to idealization. Instead of a real series developing in actual time, he proposed considering what he called a “substituted series”, imagined to extend a finite segment of the real series. An ideal series was to remedy the defects of an actual series--the latter was possibly inhomogeneous, whereas the ideal series “must be regarded as indefinitely extensive in point of number or duration” (Venn, 1866, 19). The calculations concerning games of chance, for instance, had their reference to a “substituted series”. One reasoned, wrote Venn, “not from the fragment given to us; from potential, therefore, not from actual experience” (ibid., 298). Venn introduced the ideal series to explain the reasoning and the content of beliefs associated with probabilistic statements, not to challenge the practical necessity of equating observed relative frequency with probability. An ideal series was assumed to be a potentially infinite sequence of objects belonging to one single type. In his attempt to adjust the tension between the statics of frequentism and the dynamics of the world, Venn thus ended up transforming the ideal types of the realists to the ideal space of the mathematician. 23

Bernoulli’s Theorem and Objective Probability It is no wonder then that Venn denied the existence of an “objective probability”. Venn understood by an objective probability some potentiality (propensity, facility or possibility) that inhered in the individuals making up a universal. His denial that such a thing existed went hand in hand with his opposition to realism. As he put it: The doctrine of an objective probability almost necessarily presupposes a fixed type. It seems merely the realistic doctrine of an ideal something which is perpetually striving, and gradually, though never perfectly, succeeding in realizing itself in nature. Against this the view of a changeable type is, of course, distinctly antagonistic; still more so when, as I maintain, the type not merely changes, but has in many cases an actual origin and conclusion (Venn, 1866, 37-8). Probabilistic ascriptions, in Venn’s view, derived from idealized features of mass phenomena--neither the attributes of an individual entity nor those of a group of entities included something that could be properly called probabilistic. He thus disagreed with Laplace that statistical uniformities could be seen as “the development of the respective probabilities of the simple events” (ibid., 33). Even the stability of gambling devices, such as dice, did not warrant the reduction of statistics to an objective probability--inhering e.g. in the physical make-up of the dice. Statistics, for Venn, was the outcome of various conditions producing mass phenomena; it could not be simply counted among the universal properties of the individuals of a series (ibid., 35). Venn’s rejection of Bernoulli’s theorem on these grounds proves how deep-seated his antirealist-cum-historicist convictions were. Given the preeminence of this theorem in the mathematical literature of a century and a half, his proclamation against it was remarkably daring: “This theorem of Bernoulli seems to me one of the last remaining relics of Realism, which after being banished elsewhere still manages to linger in the remote province of Probability” (ibid., 36). Jacob Bernoulli’s theorem appeared in the author’s posthumously published Ars Conjectandi of 1713, and was celebrated by the later mathematicians as the most powerful result in the calculus of probabilities.43 A version of this theorem is nowadays called the weak law of large numbers. The theorem linked probability to relative frequencies, asserting that with moral certainty the probability of an 24 event can be approximated by the relative frequency with which it occurs after a finite number of observations.44 The theorem passed the scrutiny of a distinguished line of mathematicians, including Abraham De Moivre, Pierre-Simon Laplace and Siméon-Denis Poisson; was modified and generalized; and at the end declared to be not only a mathematical theorem but an all pervasive law of nature.45 While the precise import of

Bernoulli’s theorem had been a topic of controversy from early on, it was nonetheless thought by many to disclose a hidden structure of phenomena whereby statistical uniformities were made intelligible.46

In the Logic of Chance, Venn took issue with the theorem head on, not analyzing in detail the subtleties of its interpretation. He regarded it to be establishing a link between the probability of a single event and limiting frequencies. In his words, the theorem stated that “in the long run all events will tend to occur with a frequency proportional to their objective probabilities” (Venn, 1866, 35). As such, it was unacceptable. Bernoulli's theorem was, for Venn, “an illustration of the inveterate tendency to objectify our conceptions even in cases where the conceptions had no right to exist at all” (ibid., 36). This tendency to reify concepts manifested itself in the attribution of an “objective probability” to the single occurrence of an event as the underlying constant cause for the statistical uniformities observed in nature or society. In a universe where types changed perpetually, as the “Doctrine of Evolution” suggested, one could not accept a mathematical theorem which entailed eternal regularities to unfold from a property inhering in a single entity. It was not that Venn found fault with the derivation of Bernoulli’s theorem. It was rather the case that, as he put it, “the basis on which the mathematics rest is faulty, owing to the fact of there really being nothing which we can call the objective probability” (ibid., 36). Although proposing an ideal space of ontology for mathematical considerations, Venn could not conceive of a fictitious realm in which Bernoulli’s theorem would be valid. The material conditions of Venn’s reality had a dearth of statistical regularities, and the 25 ideal space of mathematics had to heed those conditions. Unlike Poisson, who saw in Bernoulli’s theorem the all-pervading law of large numbers, Venn could not see an endless recurrence of that law in the social or natural realm. An “objective probability”, as presupposed by Bernoulli’s theorem, gestured towards fixed types and timeless essences, thereby undermining its intelligibility. Venn described aptly the historicist outlook underlying his approach in the analogy he drew between the probabilist and the land- surveyor in a mountainous terrain, “the surface of which is all broken up into crag and boulder and gully”. He continued: “although there is disorder over any very small space, and disorder again of another kind over a very large space (for then we may get out of the plain), there is between these extremes an extent of order” (ibid., 19-20). Inhabiting an analogous position in history, the statistician had nothing better than this confined view of the land-surveyor.

Conclusion In 1873 the Victorian essayist Leslie Stephen observed, in connection with the biological theories of evolution, “the new theories will transform the mode in which men interpret the universe to themselves.”47 Darwinism ushered in a new method, the application of which went far beyond biology. According to Stephen, the new interpretation of the universe spawned by Darwinism included: [T]he acceptance of the corollary that we must seek for the explanation of facts or ideas by tracing their history instead of accounting for them by some short a priori method; and thus of the adoption of the historical method in all manner of investigations into social, and political, and religious problems (ibid., 106). The historical method that was consolidated by Darwin’s theory was crucial in Stephen’s revolt against Christianity in the 1860s.48 Not as rebellious, Venn was nonetheless under the sway of this intellectual tide. The turmoil of the 1860s transformed the life of an Evangelical clergyman of a parochial background--Venn became a liberal academician. The reference class problem, which undermines the attempt to ascribe a unique probability to the occurring of a single event, arose in this context. In order to explicate 26 the notion of probability in terms of an unending series of similar events, Venn needed to characterize the class to which an individual entity belonged. Unlike the twentieth century accounts of the frequency view, for instance that of Richard Von Mises from the 1920s, which are usually based on set theoretic considerations for characterizing a random sequence, Venn’s starting point was a search for a natural substratum which could ground statistical assertions.49 He soon realized, however, that there was no iron-clad rule about the determination of that substratum. Because the mobility of nature defied sharp boundaries, there were, in principle, an infinity of populations to which an individual entity belonged. Not being able to provide a general rule about the determination of the reference class, Venn left the decision about which statistical frequencies to employ to a large extent arbitrary. The problem of characterizing the populations that can provide reliable statistical information called into question the objectivity of probabilities. This question, the reference class problem, is ever since a difficulty in the foundations of frequentism.

Acknowledgements: I am grateful to Lorraine Daston, Stephen Stigler and Zeno Swijtnik for many helpful suggestions. I thank Dr. Mark Nicholls of Department of Manuscript and University Archives, Cambridge University, and the archivists of the Special Collections at the University of Birmingham for facilitating this research. This work was made possible by the financial support I received from the Fishbein Center for the History of Science and Medicine, and the Conceptual Foundations of Science Program at the University of Chicago, as well as the Max-Planck-Institut für Wissenschaftsgeschichte in Berlin. 27

BIBLIOGRAPHY Agassiz, Louis (1874) “Evolution and Permanence of Type”. The Atlantic Monthly, Vol. 33: 92-101. Annan, Noel Gilroy (1977) Leslie Stephen: His Thought and Character in Relation to his Time. (Reprint. New York: AMS Press). Bernoulli, Jakob (1966) Ars conjectandi: Translations from James Bernoulli. (Translated by Bing Sung. Harvard University Department of Statistics Technical Report No. 2. 12 February). Bowler, Peter J. (1975) “The Changing Meaning of “Evolution”” and “Herbert Spencer and ‘Evolution’--An Additional Note. Journal of the History of Ideas, 36: 95-114, 367. Buckle, H.T. (1934) History of Civilization in England. (2 vols. in one. New York: Appleton-Century Co.) Candolle, Augustin-P. de (1819) Théorie élémentaire de la botanique, ou exposition des principes de la classification naturelle et de l’art de décrire et d’étudier les végétaux. (Paris: Deterville). Canguilhem, Georges (1991) The Normal and the Pathological. (New York: Zone Books). Cannon, Susan Faye (1978) Science in Culture: The Early Victorian Period. (New York: Dawson). Carrithers, David (1995) “The Enlightenment Science of Society.” In Christopher Fox, Roy Porter and Robert Wokler (eds), Inventing Human Science: Eighteenth-Century Domains, (Berkeley: Univ. of California Press). Chadwick, Owen (1966) The Victorian Church. (2 vols. London: Adam & Charles).

Cournot, Antoine Augustin (1984) Exposition de la théorie des chances et des probabilités. Reprinted as vol. 1 of Cournot’s Oeuvres complètes. (Paris: J.Vrin). Crowther, M.A. (1970) Church Embattled: Religious Controversy in Mid-Victorian England. (Great Britain: David & Charles). Darwin, Charles (1859) On the Origin of Species. (Facsimile of the First Edition. Cambridge: Harvard Univ. Press). Daston, Lorraine (1987) “Rational Individuals versus Laws of Society: From Probability to Statistics” in The Probabilistic Revolution, Vol. 1: Ideas in History, pp. 295-304. (1988) Classical Probability in the Enlightenment. (Princeton, Princeton University Press). De Moivre, Abraham (1967) The Doctrine of Chances. (. Reprint of 3d ed. in 1754. New York: Chelsea Publishing Co). Desmond, Adrian and James Moore (1991) Darwin. (New York: Warner Books). Dupree, A. Hunter (1986) “Christianity and the Scientific Community in the Age of Darwin” in David C. Lindberg and Ronald L. Numbers eds. God and Nature: Historical 28

Essays on the Encounter between Christianity and Science. (Berkeley: University of California Press). Eden, Berna Kılıç (1997) The One and the Many of Frequentism. (Ph. D. dissertation, the University of Chicago). Ellis, Robert Leslie (1844) “On the Foundations of the Theory of Probabilities”. Transactions of the Cambridge Philosophical Society, Vol.8, Part 1: 1-6. Read Feb. 14, 1842. Essays and Reviews (1860). (London: Parker and Son). Eyler, John M. (1979) Victorian Social Medicine: The Ideas and Methods of William Farr. (Baltimore: The Johns Hopkins University Press). Francis, Henry Thomas (1923) “In Memoriam: John Venn”. The Caian, Vol.31, No.3. Flower, William Henry (1966) An Introduction to the Osteology of the Mammalia. (Reprint of the 3d ed. in 1885 Amsterdam: Asher & Co.) Forbes, Duncan (1952) The Liberal Anglican Idea of History. (Cambridge at the University Press). Fries, J.F. (1842) Versuch einer Kritik der Principien der Wahrscheinlichkeitsrechnung. (Brunswick). Gregory, Frederick (1986) “The Impact of Darwinian Evolution on Protestant Theology in the Nineteenth Century” in David C. Lindberg and Ronald L. Numbers eds. God and Nature: Historical Essays on the Encounter between Christianity and Science. (Berkeley: University of California Press). Hacking, Ian (1990) The Taming of Chance. (Cambridge, England). (1991) “A Tradition of Natural Kinds”. Philosophical Studies 61: 109-126. Heyck, T.W. (1982) The Transformation of Intellectual Life in Victorian England. (London: Croom Helm). Hilts, Victor L. (1978) “Aliis exterendum, or, the Origins of the Statistical Society of London”. Isis, 69 (No. 246): 21-43. (1981) Statist and Statistician. (Originally presented as the author’s thesis, Harvard, 1967; New York: Arno Press). Laplace, Pierre-Simon (1995) Philosophical Essay on Probabilities. (Trans. from the 5th French ed. of 1825 by Andrew I. Dale. Springer-Verlag). Laudan, R. (1987) From Mineralogy to Geology. (Chicago: University of Chicago Press). Maxwell, James Clerk (1965) “Molecules” in W.D. Niven ed. The Scientific Papers of James Clerk Maxwell, Vol.2, (2 vols. bound as one. New York: Dover), pp. 361-378. Merz, John Theodore (1965) A History of European Thought in the Nineteenth Century. (4 vols. Reprint of 1904-1912 original, New York: Dover). Mill, John Stuart ( 1974) A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. 29

J.M. Robson. ed. Collected Works of John Stuart Mill. Vols. 7 and 8. (Toronto: Univ. of Toronto Press). von Mises, Richard (1919) “Grundlagen der Wahrscheinlichkeitsrechnung”. Mathematische Zeitschrift 5: 52-99. von Plato, Jan (1994) Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective. (Cambridge University Press). Poisson, Siméon-Denis (1837) Recherches sur la probabilité des jugements en matière criminelle et en matière civile. (Paris). Porter, Theodore (1986) The Rise of Statistical Thinking, 1820-1900. (Princeton: Princeton Univ. Press).

Quetelet, Lambert Adolphe Jacques (1991) Sur l’homme. Fayard. (1842) A Treatise on Man and the Development of his Faculties. (Trans. by R. Knox. from the 1835 original, Sur L'homme et le developpment de ses facultes, ou essai de physique sociale. New York: Burt Franklin). (1849) Letters addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha, on the Theory of Probabilities as applied to the Moral and Political Sciences. (Trans. from the 1846 original. London: Charles & Edwin). Robertson, John Mackinnon (1895) Buckle and his Critics: A study in sociology. (London: Swan Sonnenschein). Salmon, Wesley C. (1980) “John Venn’s Logic of Chance” in J. Hintikka, D. Gruender, and E. Agazzi (eds.), Pisa Conference Proceedings, Vol. II, pp.125-138. Stephen, Leslie (1880) “An attempted philosophy of history”. Fortnightly Review, n.s. Vol. 27: 672-695. (1905) Essays on Freethinking and Plainspeaking. (G.P. Putnam’s Sons: New York and London). (1950) The English Utilitarians. (3 vols. Reprint of 1900. New York: Peter Smith). Stevens, Peter F. (1994) The Development of Biological Systematics: Antoine-Laurent de Jussieu, Nature, and the Natural System. (New York: Columbia University Press). Stigler, Stephen (1986) The History of Statistics: The Measurement of Uncertainty before 1900. (Cambridge: Harvard University Press). (1996) “Adolphe Quetelet: Statistician, Scientist, Builder of Intellectual Institutions”. (Paper presented in the Quetelet Bicentenary; Brussels, 24-25 October 1996). Stocking, George W. (1987) Victorian Anthropology. (New York: The Free Press). Stockton, William Kenneth (1980) The Venn Family since the Mid-eighteenth Century. (Ph.D. dissertation, Brandeis University). Tennyson, Alfred (1982) In Memoriam. (Oxford: Clarendon Press). Thomson, William (1860) An Outline of the necessary Laws of Thought: A Treatise on Pure and Applied Logic. (4th ed.)

Torretti, Roberto (1990) Creative understanding : philosophical reflections on physics. (Chicago: University of Chicago Press). 30

Venn, John (1862) “Science of History”. Fraser’s Magazine, May: 651-660. (1866) The Logic of Chance. (London: Macmillan and Co.) (1876) The Logic of Chance. (2d ed. London: Macmillan and Co.) (1990) On Some of the Characteristics of Belief Scientific and Religious (The Hulsean Lectures for 1869. Reprint of 1870 original, Bristol: Thoemmes Publications). (1962) The Logic of Chance. (4th ed. identical with the 3d ed.from 1888. New York: Chelsea). (1994) The Principles of Empirical or Inductive Logic. (Reprint of the 1889 original, Bristol: Thoemmes Press). (1904) Annals of a Clerical Family. c. 1903. Autobiographical Sketch. Venn Papers in the Church Missionary Society Archives held at the Special Collections, the University of Birmingham. Wise, Norton M. and Crosbie Smith (1989) “Work and Waste: Political Economy and Natural Philosophy in Nineteenth Century Britain (I)”. History of Science, xxvii: 263- 301, 391-449. xxviii, 221-261. 31

ENDNOTES

1. Two more editions of Venn’s Logic of Chance appeared in 1876 and 1888. Most references in this paper are to the first edition in 1866. For an assessment of Venn’s significance in the history of probability, see Salmon (1980).

2. Tennyson began writing “In Memoriam” after the death of his beloved friend Arthur Hallam in 1833. See Dictionary of National Biography, s.v. “Alfred Tennyson”.

3. See Daston (1987), Porter (1986), and Hacking (1990).

4. See Hacking (1990), 208 and Porter (1986), Ch. 3.

5. See Merz (1965) Vol.2, 276-367, 548-626.

6. Venn’s manuscript is classified as Autobiographical Sketch in the Church Missionary Society archives currently held at the University of Birmingham, Special Collections. In this paper, it will be referred to as Autobiography. Composed c. 1903, Venn’s autobiography was not completed--his recollections, presented in a chronological order, terminated brusquely in the year 1866.

7. All biographical information in this paper is drawn from Venn’s Autobiography unless otherwise stated.

8. For an analysis of Venn’s relation with his father, see Stockton (1980), Ch. 9 and 12.

9. Venn was introduced to most of this literature by his close friend Charles Henry Monro, who attended Gonville and Caius College, Cambridge at about the same years as Venn 32 did, becoming a scholar of classics and linguistics. See The Dictionary of National Biography, s.v., “Charles Henry Monro”.

10. Fries presented his approach in (Fries, 1842). In the same year Ellis read “Foundations of the Theory of Probabilities” to the Cambridge Philosophical Society, which was later published as (Ellis, 1844). Cournot (1984) and Mill (1974) formulated similar viewpoints in 1843. Venn acknowledged both Mill and Ellis as influences.

11. For an analysis of the motivations lying behind frequentism, see Eden (1997), Ch. 2.

12. See Porter (1986), 49.

13. Quetelet (1842), 8. For the original French version, see Quetelet (1991), 46. The influence of meteorology on Quetelet’s approach to social science is discussed in Stigler (1996).

14. On Quetelet’s analogy between nature and artists, and his interpretation of anthropomorphic measurements, see Quetelet (1849), 90-3, 276. Quetelet here relied on the 5,738 measurements given in the Edinburgh Medical Journal in 1817.

15. Quetelet’s On Man was translated into English in 1842. For the rise and reception of statistical thinking in Britain, see Eyler (1979), Hacking (1990), Hilts (1978, 1981) and Porter (1986).

16. Buckle (1821-1862) was a historian without academic training or affiliation, making his education largely through traveling foreign countries. He already had a rough draft of his History of Civilization in England by 1853, but continued to work on it until 1857. The first volume was an instant success. It was reprinted in 1858, 1861 and 1864. The 33 second volume was reprinted in 1864 and 1867. The work was republished as History of Civilization in England, France, Spain and Scotland in 1866, 1868, 1869, 1871, 1872, 1873 and 1878. In 1860 it was translated into German, in 1868 into French and Russian. See Dictionary of National Biography, s.v. “Henry Thomas Buckle” by Leslie Stephen.

17. Ibid., 131. On Buckle’s differentiation between moral and intellectual laws, see also Stephen (1950), Vol.3, 344-375.

18. The phrase “Liberal Anglican” is from Forbes (1952).

19. See Forbes (1952), 132-3; Heyck (1982), Ch. 5.

20. Leslie Stephen, in his biography of Buckle in The Dictionary of National Biography, observed that the History of Civilization “won for its author a reputation which has hardly been sustained”, and that “[s]pecialists in every department of inquiry will regard him as a brilliant amateur rather than a thorough student.” He noted the want of “historical method” in Buckle’s approach, and complained of his “entire want of sympathy with earlier stages of civilization”. See also Leslie Stephen’s acrimonious attack on Buckle in (Stephen, 1880). For J.F. Stephen’s criticism of Buckle, see Porter (1986), 166-7. On Buckle’s popularity in this period as well as the criticisms he received, consult Porter (1986), 164-7; Robertson (1985); Heyck (1982), Ch. 5; Stocking (1987), Ch 4.

21. James Fitzjames Stephen grew up in the same household as Venn. See the table “Pedigree V” for a family tree of Devonshire Venns in Venn (1904). Venn was thus a great cousin of Virginia Woolf, Leslie Stephen’s daughter.

22. See Venn (1862), 658. A substantial part of this article was included in Venn (1866), 344-7. 34

23. See, for instance, Candolle (1819), 188. See also Stevens (1994), 137-143.

24. For a discussion of Whewell’s typological realism, see Eden (1997), Ch. 5.

25. See Laudan (1987), 205.

26. For instance, Wise and Smith (1989) argue that a historicist outlook was deeply ingrained in the individual psychologies of British enterprenours, both intellectual and business-minded ones, whose daily lives witnessed all the impact of mechanization and industrial revolution. Concentrating mostly on political economy and physics, Wise and Smith situate that shift in around 1830s.

27. Essays and Reviews appeared in 1860 three months after the Origin of Species. Consisting of seven essays written by six Anglican clergymen and a layman, it voiced the liberal theological outlook that condoned Darwin and argued against miracles. The contributors were Frederick Temple, Rowland Williams, Baden Powell, H.B. Wilson, C.W. Goodwin, Mark Pattison and Benjamin Jowett. Several of them were later tried for heresy. See Desmond and Moore (1991), 500; Crowther (1970), 20.

28. Ibid., 117. John Robert Seeley, who held later the Regius Professorship of Modern History in Cambridge, became famous with his historical study of the life and teaching of Christ, Ecce Homo (1865). Albert Venn Dicey, later Vinerian Professor at Oxford, was a cousin of the Stephen brothers, and a distant cousin of Venn.

29. In this position, Venn lectured in ethics, political economy and logic to prepare students for the Moral Science Tripos. Only towards the end of 1860s could he specialize his teaching to logic. 35

30. Autobiography, 122. Henry Thomas Francis, a fellow of Caius College and a friend of Venn, attended the same meeting, and recounted the outcome in his memorial notice of Venn thus: “The truth of Darwin’s proposition ... seems to have been proved by this controversy and, however, reluctantly, we have to accept it, and to acknowledge our kinship with the ape on the physical side.” (Francis, 1923, 23). For a brief account of the Thirty-Second Meeting of the British Association for the Advancement of Science in Cambridge, see The Athenæum, No. 1822, (Sept. 27, 1862): 391-4 and No. 1824 (Oct. 11, 1862):463-8.

31. Ibid., 139. Broad Church was not an organized church party, but a movement emerging during the mid-nineteenth century among liberal Anglican divines aiming to assess critically both the authority of Bible and the authority of the church. As such it was positioned against Evangelicalism and the High Church. See Chadwick (1966), Vol. 1, 544-5. Venn’s intellectual life in Cambridge was enriched by his participation in the “Essay Club” of John Grote, Professor of Moral Theology. Comprising Joseph Mayor, Aldis Wright, Henry Sidgwick and J.R. Mozley, the club activities continued until 1866. See Francis (1923), 24-5.

32. While adhering to one shared epistemology for belief, Venn did not deny the possibility of different truths (Cf. Cannon, 1978). Religious belief differed from the scientific one in its complexity; the first as opposed to the latter turned around a “theory of life” (Venn, 1872, 72). An individual’s theory of life--a body of beliefs held tacitly or explicitly--oriented his or her reception of new beliefs. Venn’s account of change of belief was non-monotonic: New beliefs could modify or subvert old beliefs. While the complexity of religious belief thus contrasted with scientific belief, Venn did not construe that difference as a radical distinction, but as a matter of degree. 36

33. Dictionary of National Biography, s.v. John Venn. This item was written by Venn’s son, John Archibald Venn.

34. Ibid., 376. In the same article Maxwell referred to the spectroscopic evidence provided by distant stars as proof that hydrogen molecules were identical across stellar space.

35. Ibid., 287. Conceptualism was regarded to be a doctrine intermediate between realism and nominalism, according to which universals corresponded to some privileged mental concepts. See Thomson (1860), 118-120.

36. See for instance, Venn (1866), 109. Venn here anticipated several of the arguments mustered by Canguilhem against the use of statistics in medical ideology. Cf. Canguilhem (1991), Ch. 3.

37. Published in 1870, 1876 and 3rd ed. with Hans Gadow in 1885. Venn did not specify which edition he made use of.

38. See Figure 1 in Flower (1966), 11.

39. See Hacking (1991). One of the first attempts to explicate the notion of kind on pragmatic grounds, independently from the realism versus nominalism controversy, was that of John Stuart Mill in the System of Logic. There Mill defined the notion of a “real kind” as a class which possessed a multitude of properties in addition to the few that were used in its characterization. See Mill (1974), Vol.7, 126. Venn thought Mill’s definition was inadequate vis-a-vis historical change: “Mill, as we all know, writing in præ- Darwinian days, greatly overrated the distinctness and the ultimate or primitive character of these various attributes.” (Venn, 1994, 82-3). Mill’s reluctance to incorporate the 37

Darwinian point of view was also noted by Leslie Stephen, who found it curious that Mill did not change his notion of kinds in the last edition of his System of Logic in 1872, “after the first Darwinian controversies” (Stephen, 1950, Vol.3, 130). On Mill’s notion of kinds, see Hacking (1991) and Eden (1997).

40. Venn (1866), 246. See also ibid., 249-250.

41. Ibid., 24. For a more detailed discussion of Venn’s deliberations on the characterization of the reference class, see Eden (1997).

42. See, for instance, Leibniz’s worries over the use of statistics in his letter to Jacob Bernoulli on December 3, 1703 (Bernoulli, 1966, 72).

43. Bernoulli died in 1705, and the manuscript he left behind was edited by his nephew Nicholas Bernoulli.

44. The theorem dealt with conjectures about the number of times a given event would be observed when many trials were performed under similar conditions. In Bernoulli’s example, a pebble was drawn, its color was observed, and then replaced in an urn which contained thirty white and twenty black pebbles; and this trial was repeated many times. The probability of drawing a white pebble in a single trial is three fifths, or 30/50, as all the classical probabilists would agree. Bernoulli specified a lower and upper bound of 29/50 and 31/50 around the probability 30/50 of drawing a white pebble, which he called a fertile case, and asserted that "so many trials can be run such that it will be more probable than any given times (e.g., c times) that the number of fertile observations will fall within these limits rather than outside these limits". (Bernoulli, 1966, 60) Indeed, when an event r had probability (because r cases favored it and s cases opposed it, as the thirty white r + s 38 pebbles in the above example favored the outcome white, and the twenty black pebbles opposed that outcome), and when a positive number c was specified, Bernoulli could determine an upper bound, N, for the number of times an experiment needed to be repeated so that the probability that the relative frequency with which that event would be r - 1 r + 1 observed in N trials would fall within and could be made c times larger than r + s r + s the probability that it would not. Bernoulli’s theorem can be rendered in modern notation as follows:

X X P(| - p| < e) > cP(| - p| > e), N N where X is the number of observed fertile cases when N experiments are carried out, p= r 1 , is the probability of success in each experiment, e = , the desired margin of r + s r + s approximation, and c the intended degree of certainty. In the above example, where there were thirty white and twenty black pebbles in an urn, and c was chosen to be one thousand, Bernoulli computed that 25,550 trials were sufficient in order to insure that, with a probability of 1000/1001, the observed frequency of the event after that many trials would deviate from the ratio 3/5 by at most 1/50. For further details, consult Stigler (1986).

45. See De Moivre (1967), Laplace (1995), and Poisson (1837).

46. For an examination of the interpretations of Bernoulli’s theorem and its reception by the frequentists, see Eden (1997).

47. Stephen (1905), 104. As noted earlier, Stephen was a cousin of Venn. 39

48. See Annan (1951). On the impact of Darwinism on religious controversy in this period, see Dupree (1986) and Gregory (1986). These authors underline the complexity of factors which contributed to the growing tension between traditional religion and the new scientism. While the impact of Darwinism on the ongoing religious controversies may have been indeed exaggerated by early historiography, this is no reason to overlook its role as a transforming experience in the lives of several Victorians.

49. See von Mises (1919). For accounts of twentieth century frequentism, consult Torretti (1990) and von Plato (1994).