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By Lukas M. Verburgt


The Montréal Review, October 2022


By Lukas M. Verburgt
(University of Chicago Press, 2022)


John Venn (1834-1923) is remembered as the inventor of the Venn diagram, widely used today in education as well as in social media memes. The fame of the diagram has long eclipsed Venn’s own status as one of the most accomplished English logicians of his day. Praised by John Stuart Mill as a “highly successful thinker” with much “power of original thought,”1 Venn had a profound influence on 19th century scientists and philosophers, ranging from Mill and Francis Galton to Lewis Carroll and Charles Sanders Peirce. Venn was heir to a clerical Evangelical dynasty, but religious doubts led him to resign Holy Orders and instead dedicate himself to an academic career. He went on to write influential textbooks on probability theory and logic – read, several decades later, by the likes of Bertrand Russell and W.V. Quine – became a Fellow of the Royal Society, and advocated for educational reform at Cambridge, including that of women’s higher education. Moreover, through his students, a direct line can be traced from Venn to the early analytic philosophy Russell and G.E. Moore, and family ties connect him to the famous Bloomsbury group (Virginia Woolf was the daughter of his cousin Leslie Stephen).

In my recently published book, John Venn: A Life in Logic, I tell the story of Venn’s life and work, taking the reader on Venn’s journey from Evangelical son to Cambridge don. What I would like to do in this essay is zoom in on Venn’s professional life, and more specifically on certain key aspects of his career as a self-made logician – telling, as these are, of the little-studied history of English philosophy in the second half of the 19th century. To tell this part of the story, I will have to start at the beginning, with Venn’s time as a student and young fellow at Cambridge.


It is easy to forget that Venn’s generation of Cambridge philosophers was not trained in philosophy or logic. Venn himself was a product of what he called the “old system”2 at the University of Cambridge: while in the period from the late 1840s it had become possible for students to graduate in other subjects, mathematics still dominated in the 1850s, not in the last place owing to its prestige.3 For serious reading men like Venn it meant that studying at Cambridge boiled down to three and a half years of preparing for the so-called Mathematical Tripos, the honours examination which de facto determined who would compete for a college fellowship. Venn graduated Sixth Wrangler in 1857, and was soon elected Fellow of Gonville and Caius College. But he strongly felt the “evil side”4 of the system, which in his case was – and here I quote from Venn’s autobiography – “displayed in the re-action and disgust which [ensued] when the examination is over. I felt this myself very strongly, and whereas, before coming to Cambridge and for my first year or two, I had a real enjoyment in the subject [i.e. mathematics], I never made any study of it afterwards: and in fact felt almost a repulsion towards it.”5 Again, like so many men of his generation, Venn had gone up to Cambridge and competed for a fellowship not to pursue an academic career, but to eventually become a clergyman. Indeed, between 1857 and 1862, Venn worked as an Evangelical curate at several parishes not far from Cambridge.

During these curacies, Venn nonetheless continued to read widely, partly as a counter-reaction against mathematics and partly from a wish to become well-versed in theology and philosophy. The dominating influence in these years was John Stuart Mill, with whose work he was made acquainted in 1860, at the age of 26. In fact, Venn then first heard not of Mill’s work merely, but even of his very name. As Venn recalled: “I remember the occasion vividly. [A friend] had come down to spend a night with me a few weeks after my arrival at Cheshunt, and had brought with him the then recently published On Liberty. We began talking about the subject, and my only association with the name was that there had been a theological professor or preacher called Mill at Cambridge some years before, and I wondered if it was the same man.”6

Venn was unhappy as a curate, and in 1862 an opening presented itself at Cambridge which he seized. Venn returned to Caius to work as a catechist, an ancient college teaching post re-created in response to a recent reconstruction of the Moral Sciences Tripos. The story of this particular Tripos is a fascinating one all in itself, touching directly upon the emergence of philosophy as an academic discipline in Britain.7 It had been founded between 1848 and 1851 to tone down the dominance of mathematics at Cambridge, which was then going through a period of internal (and later external) reform. The new Tripos initially consisted of five subjects: moral philosophy, political economy, modern history, general jurisprudence, and the laws of England. During its first decade, it was not popular at all, which is understandable as it initially did not lead to the award of a degree: a student needed to do the first part of the Mathematical Tripos before going on to honours in the Moral Sciences, which of course ruled it out as a course of study for the bulk of undergraduates. In 1861, following a year in which zero candidates took the examination, the university’s Senate upgraded the Tripos’s status to become a three-year degree course in its own right, also setting up a Board of Moral Sciences (the precursor of the current Faculty of Philosophy) to oversee it and to change the curriculum. This created an exciting opportunity for men like Venn. It allowed him to work alongside Henry Sidgwick and others to promote and advance topics like logic and (utilitarian) ethics at Cambridge and, thereby, to play their part in their alma mater’s broader reform from a mathematical seminary to a place of wide-ranging, intercollegiate teaching and learning.

As said, Venn himself was not trained in the subjects on which he now had to lecture. We find him in the Long Vacation of 1862 preparing for the texts on which he was to teach three times a week staring in October. Like his colleagues, Venn himself was initially not more than an “amateur” and “diligent learner” in the Moral Sciences.8 Indeed, many of the titles appearing on the ‘List of Books’ agreed upon by the Board of Moral Science Studies were at first totally unfamiliar to him. Similarly, upon his appointment as one of the examiners for the Moral Sciences Tripos in 1863, Venn wrote that “[t]here is not any very formidable amount of work recognized for it, but as to some of the subjects or authors I am not very familiar with, I shall have to brush them up during the vacation.”9 Looking back on the Moral Sciences in the 1860s-70s, Venn would later conclude: “I am certain that we did not know anything like so much as the average lecturers [later did], but we had a naif [sic] interest in subjects which were opening out before us. I cannot but suspect that something of what our pupils lost by our lack of learning they must have found replaced by our sympathetic interests in their own struggles.”10

One of the major benefits of the situation was that Venn and his colleagues had the management of the ‘Faculty’ to themselves. This meant, among other things, that they were free to arrange the curriculum as they saw fit, allowing them to introduce new topics, authors and books into Cambridge. Venn, for one, for many years taught courses on Elementary and Advanced Logic, put the work of George Boole on the curriculum, and himself wrote three logical textbooks appearing on the ‘List of Books’ for Moral Sciences students in the 1870s-90s and beyond. Venn’s Logic of Chance (1866) and Symbolic Logic (1881), for instance, were read by Moore and Rusell when they sat for the Moral Sciences Tripos. It is already for this reason that Venn arguably deserves the name of “grandfather of analytic philosophy” at Cambridge.

A lot more can be said about Venn’s work for the Moral Sciences Tripos in this period, and I do so in chapters 5 (‘Moral Scientist’) and 10 (‘Dereverend Believer and Amateur Scientist’) of my book. But let me now turn from Venn the teacher to Venn the researcher.


This shift is easily made in Venn’s case, as there was a direct and intimate connection between these two identities. Venn was a representative of the first generation of Cambridge fellows to pursue a professional academic career in a sense we can still recognize today: he took teaching as serious as research, and actively sought to bring them into contact,also with an eye to his own academic preferment. More specifically, all three of Venn’s textbooks were based on material first presented and developed in the lecture-room and they made him the leading expert in the fields he himself introduced into Cambridge.

On my interpretation, all Venn’s contributions to logic bore the stamp of Mill’s influence in one way or another. This fits with the fact that Venn was seen by his colleagues at Cambridge – as well as by fellow members of the ‘Grote Club’ 11 – as Mill’s most dedicated follower. The most helpful and fruitful way of making sense of Venn’s career as a logician is to see it falling into three periods of engagement with Mill’s groundbreaking System of Logic (1843): support (1860s), criticism (1870s) and disillusion (1880s).

During the 1860s, Venn published one article – a commentary on the discussion between Auguste Comte, Henry Thomas Buckle and Mill on the possibility of a social science – and one book, The Logic of Chance. The book was explicitly written as a systematization of Mill’s definition of probability as the frequency of like events in the long run. The years from 1876 to 1880 was the period in which Venn published almost all his journal articles, some dozen in total, many of which appeared in the newly-founded philosophical journal Mind, of which he became associate editor around 1891. After a review of a recent book  by William Stanley Jevons, there followed a steady stream of increasingly critical discussions of the so-called “material outlook” on logic, founded by Mill and further elaborated by the today little-studied philosophers Alexander Bain, Herbert Spencer, Carveth Read and John Neville Keynes. Venn was too much of an empiricist to walk over to the enemy’s camp – that of the ‘conceptualists’, who held that logic dealt with laws of the human mind. But he did abandon the ideal of a purely objective treatment of logic, one in which logic deals solely with inferences from and about matters of fact. Instead, Venn developed what I call in the book, for lack of a better term, a pragmatic, quasi-conventionalist alternative, which said that logic’s subject matter is the world as constructed from assumptions and conventions borrowed from other disciplines. This alternative would be fleshed out in Principles of Empirical Logic (1889), where Venn discussed all the subjective and objective postulates needed to construct “the universe as the logician regards it.”12 The book was considered a failure by its reviewers. But for Venn, however, thinking through the basic position put forward in it had opened a theoretical door: it allowed him to engage with the recent developments in formal logic associated with Augustus De Morgan and George Boole. Venn had first read Boole’s Laws of Thought (1854) in the late 1850s, and it took him several decades to make sense of it and, especially, to see how Boole’s abstract calculus of deductive reasoning could possibly be reconciled with Mill’s down-to-earth, empiricist outlook on logic. This problem situation, I argue in the book, stood at the hearth of Venn’s oeuvre: it was essentially a tension between scientific reasoning and formalization – a tension that would haunt analytic philosophers in the early 20th century and that is today surfacing again, for instance, in the battle between formal and material theories of induction.13 The problem is by no means an easy one to solve, especially not for someone like Venn who wished to remain loyal to both Mill and Boole, who in many ways were complete opposites, philosophically speaking. As always, Venn’s strategy was to come up with a compromise, a middle road, based on a criticism of Mill and an opinionated reading of Boole.

The matter is a bit technical, but I’ll here sketch it briefly, as it is key to understanding not just Venn’s work but British logic in the second half of the 19th century as such. Venn believed that Mill’s claim that there is no process of reasoning involved in deductive arguments (‘All men are mortal / Socrates is a man / Hence, Socrates is mortal’), was due to his “over-objectifying”14 of logic. There was a crucial difference, Venn emphasized, between the subjective recognition of facts and what is given in the objective facts themselves: to go from the premises to the conclusion always requires a mental step. For this reason, Venn argued, any tool that can aid us in recognizing what conclusions can be drawn from given premises is welcome, especially when dealing with cases far more complex than those considered by Mill. For over 2000 years this tool had been Aristotle’s syllogism. What Venn took Boole’s application of algebra to logic to have done was nothing less, but also nothing more, than this: to generalize traditional logic in such a way that it can deal with more complex cases of deductive reasoning. Unlike Boole, however, Venn remained committed to the view that deductive logic is just a formal tool. The premises from which we reason are drawn from, and the conclusions we arrive at ultimately concern, the observable world around us.

This was, roughly put, the position Venn elaborated in Symbolic Logic – the book the book which contains his famous diagrams – and in Principles. By the time the latter book was published, Venn had already quit logic, donating his private collection of some 1100 logical books to Cambridge University Library, where they are still held today.15


Perhaps the biggest challenge in writing my book, at least when it comes to Venn’s professional life, concerned his legacy. For what, if any, is Venn’s legacy as a logician? All things considered, my answer is twofold. First, I think that, from a broad-angle view, Venn climaxed a number of traditions. And, in keeping with the standard elements of plot, after a “climax” necessarily comes the “falling action”, when things start falling apart after having come to a dramatic high point. Indeed, the traditions which Venn climaxed – Mill’s inductive logic, Boole’s deductive logic – soon went out of fashion. The former owing to the emergence in the 1890s of British Idealism as the dominant philosophical school in Britain, and at Oxford and Cambridge in particular; and the latter because of the arrival of the new logic, based on quantification theory, of Gottlob Frege and Bertrand Russell. (Venn incidentally reviewed Frege’s Begriffschrift, unable to make much sense of it.)

On this basis, one could conclude that Venn left no significant legacy and has been rightfully forgotten. However, when approached from the local perspective of Cambridge, things look decidedly different. Taking this perspective asks for another kind of history of philosophy, one less focused on ideas and more on social, institutional and material factors. During the period between the 1860s and 1890s Venn was without any doubt the most eminent logician teaching and working at Cambridge. Moreover, in his role as textbook author, lecturer, member of the Board of Moral Science Studies, and examiner in the Moral Sciences Tripos, he contributed much to the creation of what C.D. Broad in the early 20th century called the “local historical background of contemporary Cambridge philosophy.”16 This should come as no surprise. Of the pioneering reformers of the Moral Sciences, Venn was the one who introduced and lectured on inductive logic, probability theory and formal logic at Cambridge. Venn was also the teacher of both W.E. Johnson and John Neville Keynes, the philosophers who counted Moore and Russell among their pupils and with whom they discussed Venn’s textbooks. Moore and Russell would come to look upon Venn’s generation as the “out of date” old guard.17 But this was due largely to the influence of figures like J.M.E. McTaggart, who sought to replace everything that came before by his new philosophical outlook. After their flirt with idealism, Moore and Russell would walk the road paved by Venn, using new tools to work on the subjects he had put on the philosophical agenda and to face some of the problems he had been the first to address.


Cambridge philosophy was not created by Venn. But one cannot help but wonder whether it would have been possible to create it (the way it actually was) without Venn’s trailblazing.


Lukas M. Verburgt is Gerda Henkel Stiftung Research Scholar and affiliated as Research & Project Associate to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS). He is the author of John Venn: A Life in Logic (2022) and (co-)editor of several volumes, including the forthcoming Cambridge Companion to John Herschel.


1 John Stuart Mill to John Venn, 16 April 1872, in Lukas M. Verburgt, ed. John Venn: Unpublished Writings and Selected Correspondence (Cham: Springer, 2022): p. 159.

2 John Venn, Annals: Autobiographical Sketch, p. 47, in Verburgt, Venn, p. 31.

3 See, in this regard, Alex D.D. Craik, Mr Hopkin’s Men: Cambridge Reform and British Mathematics in the 19th Century (London: Springer-Verlag, 2008), andPeter Searby, A History of the University of Cambridge: Volume 3, 1750-1870 (Cambridge: Cambridge University Press, 1997), chapters 5 and 6.  

4 Venn, Annals, p. 73, in Verburgt, Venn, p. 45.

5 Ibid.

6 Venn, Annals, p. 96, in Verburgt, Venn, p. 56.

7 On the Moral Sciences Tripos see David Palfrey, The Moral Sciences Tripos at Cambridge University, 1848-1860 (Cambridge University PhD Dissertation, 2002).

8 Venn, Annals, p. 124, in Verburgt, Venn, p. 73.

9 John Venn to Henry Venn [father], 8 May 1863, Gonville and Caius College Library, Venn Papers, C40/18. Quoted with kind permission from the Master and Fellows of Gonville and Caius College, Cambridge.

10 Venn, Annals, p. 124, in Verburgt, Venn, p. 73.

11'On the 'Grote Club' see John Gibbins, John Grote, Cambridge University and the Development of Victorian Thought (Exeter: Imprint Academic, 2007).'

12 John Venn, The Principles of Empirical or Inductive Logic (London: Macmillan and Co., 1889), p. 1.

13 See, for instance, Peter Achinstein, ‘The war on induction: Whewell takes on Newton and Mill (Norton takes on everyone)’, Philosophy of Science 77.5 (2010): 728-739; John P. McCaskey, ‘Reviving material theories of induction’, Studies in History and Philosophy of Science Part A 83 (2020): 1-7.

14 Venn, Principles, p. 374.

16 C.D. Broad, ‘The local historical background of contemporary Cambridge philosophy’, in C.A. Mace, ed. British Philosophy in the Mid-Century: A Cambridge Symposium (London: George Allen & Unwin, 1957), 11-61.

17 See Bertrand Russell, My Philosophical Development (New York: Routledge, 2022 [1959]), p. 29.


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