Venn, John (1834–1923)

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The British logician John Venn was born at Drypool, Hull, the elder son of the Reverend Henry Venn, a prominent evangelical divine. After early education at Highgate and Islington proprietary schools, he entered Gonville and Caius College, Cambridge, in 1853. On graduating Sixth Wrangler in 1857, he became a fellow and remained on the foundation for sixty-six years, until his death. During the last twenty years of his residence he was also president of the college. Venn took orders in 1858 and served as a curate in parishes near London before returning to Cambridge as college lecturer in moral sciences in 1862. He married in 1867. In 1869 he was Hulsean lecturer and published thereafter a work titled On Some Characteristics of Belief (London, 1870), but contact with Henry Sidgwick and other Cambridge agnostics, plus the reading of Augustus De Morgan, George Boole, J. Austin, and J. S. Mill had the effect of transferring his interests from theology almost wholly to logic, and in 1883 he gave up his orders without altogether withdrawing from the church. In the same year he became a fellow of the Royal Society and took the degree of doctor of science.

Venn was among those responsible for the development of the moral sciences tripos at Cambridge and in the course of his teaching published successively the three works by which he is now remembered: The Logic of Chance (London, 1866; 3rd ed., 1888); Symbolic Logic (London, 1881; 2nd ed., 1894); and The Principles of Empirical or Inductive Logic (London, 1889; 2nd ed., 1907). In 1888 he presented his extensive collection of books on logic to the university library, and he turned in later years to antiquarian pursuits, writing the history of his college and his family and collaborating with his son, J. A. Venn, in the preparation of Part I of Alumni Cantabrigienses (4 vols., London, 1922). Venn was an accomplished linguist and throughout most of his long life an active botanist and mountaineer. In addition to designing a simple mechanical contrivance to illustrate his well-known logical diagrams, he is said to have invented a very successful machine for bowling at cricket.

Venn has no strong claim to be regarded as an original thinker. His general position in philosophy was that of an orthodox, though unusually cautious and skeptical, empiricist. Outside the fields of logic and methodology he contributed little of importance, and even within them his role was essentially that of a critic and expositor of ideas first mooted by other men. In that capacity, however, his writings are marked by an acumen, learning, and lucidity that rank them among the best productions of their day. Within its limits, therefore, his reputation is still a high one.


Venn was a follower of Boole and to a lesser extent of Mill and a defender of both against the criticisms of William Stanley Jevons on the one hand and of the idealist logicians on the other. His Symbolic Logic is an attempt to show not merely that the Boolean algebra "works" but also that it is in the main line of historical tradition and that its supposedly mathematical obscurities are in fact intelligible from a purely logical point of view. Like De Morgan, he is aware of the element of convention in the choice of a logical standpoint and hence of the possibility of alternative versions of the basic propositional forms. He thus contrasts the four Aristotelian (or "predicative") types of proposition with the eight forms of Sir William Hamilton (which reduce on analysis to the five possible relations of inclusion and exclusion between pairs of classes), and compares them both with the fifteen possibilities that arise on his own "existential" view, based on the emptiness or occupancy of the four "compartments" marked out by a pair of terms and their negatives. Unlike some of his predecessors, he sees the difference as one of convenience rather than correctness, and so finds it unnecessary to dispute the merits of the older logic in order to vindicate the claims of the new. A similar tolerance is apparent in his treatment of the vexed issue concerning the "existential import" of propositions, where, after careful discussion, he opts for the presumption that universal propositions do not imply the existence of members in the subject classa view that the great majority of writers from J. M. Keynes onward have since found reason to accept. Less open-minded, perhaps, is his attitude to Jevons's reforms of the Boolean calculus; but he made several improvements of his own, notably in the writing of particular propositions as inequations, and, by the introduction of his diagrammatic methods, he did more than anyone else to render the workings of that calculus intelligible to the nonmathematical mind.


The Logic of Chance is also a work of much value to those embroiled in the mathematical complications of the theory of probability. The rationalistic handling of this subject by earlier writers was not to Venn's taste, and he recognized more clearly than they did the difficulties of relating their a priori computations to the realities of uncertain reasoning in everyday life. Following the suggestions of Leslie Ellis, he therefore identifies the probability of events not with the amount of belief it is rational to have in them but with their statistical frequency of occurrence in the generic class of events to which they belong. He assumes, that is, that the world contains series of resembling events in which individual irregularity in the possession of properties is combined with aggregate regularity "in the long run." The assignment of probability to a type of event is thus a mere matter of ascertaining the relative frequency with which it tends, increasingly, to occur as the series is extended to large numbers; and this is, in principle, not a subjective affair but a perfectly empirical and objective type of inquiry into the properties of a certain kind of group. To define probability in this way is, as Venn realized, to restrict it more narrowly than is usually done. No meaning can properly be attached to the probability of a single event, and the notion becomes equally inapplicable to the large range of judgments expressing partial belief (in theories and the like) that had hitherto been dealt with under this head. There are difficulties, moreover (as he also recognized), in assuming that observed frequencies are a reliable clue to "long-run" or "limiting" frequenciesthat it is possible, in effect, on inductive grounds to arrive at such long-run frequencies by means of sample observations, however extended. For such a conclusion can itself be only probable, and that in a sense which Venn does not offer to define. Thus a knowledge of statistical frequency, even if obtainable, would be no sufficient ground for preferring one expectation to another. Probability, as Venn conceives it, is clearly not the guide of life.

Scientific Method

The frequency theory of probability has had able defenders since Venn's time and is now less vulnerable to criticism. His version of it remains, however, the classical one, and the majority of later exponents acknowledge their debt to him. By comparison, the scientific methodology set forth in Empirical Logic has suffered somewhat from its association with that of Mill, on which it is largely modeled and whose conclusions it largely accepts. Venn differs from Mill chiefly in setting greater store by laws of coexistence than by laws of causal succession. The idea of causation he considers too crude and popular in conception to be of much use in science, and he is accordingly skeptical as to the value of the inductive methods. So far from being a reliable instrument for the discovery of causes, Mill's canons of induction are effective, he thinks, only where the conditions of the problem and its possible solutions have been narrowly circumscribed in advance, and under ordinary circumstances this can seldom be done. Inductive procedures are thus by no means so conclusive as Mill supposed, though we are not therefore justified in assuming, with Jevons, that they can be rationalized by appeal to the calculus of probability. Judgments of probability themselves make use of induction, and the two must therefore be kept, so far as possible, distinct. More generally, the use of formal methods in the classification, ordering, and prediction of natural phenomena can never be more than approximate, owing to the number of simplifying assumptions necessary before it can get under way. Venn's subsidiary discussions of definition, division, hypothesis, measurement, and so on, are similarly concerned to stress the difficulties of applying principles to cases and the amount that is taken for granted in doing so. Though less closely acquainted than some other writers with the details of scientific practice, he is also less liable than most to mistake the logic of science for a description of its technique.

See also Austin, John; Boole, George; De Morgan, Augustus; Hamilton, William; Jevons, William Stanley; Logic Diagrams; Logic, History of; Mill, John Stuart; Mill's Methods of Induction; Probability and Chance; Sidgwick, Henry.


Venn has been somewhat neglected by historians of philosophy and no comprehensive study of him exists. For a serviceable brief account, see J. A. Passmore, A Hundred Years of Philosophy (London: Duckworth, 1957), pp. 134136. His views on probability are most fully criticized in J. M. Keynes, Treatise on Probability (London: Macmillan, 1921).

P. L. Heath (1967)