John Neville Keynes was born in Salisbury, Wiltshire on 31 August 1852 and died in Cambridge on 15 November 1949. The only son of John Keynes and his wife, Anna Maynard Neville, he was educated at Amersham Hall School, University College London and Pembroke College, Cambridge, from which he graduated in 1875 with a first class degree in the Moral Sciences Tripos. That same year he was elected a fellow of University College London, and then of Pembroke College a year later. In 1884 he was appointed university lecturer in moral science, a position he held until 1911, when he resigned it to accept the post of Registrary of Cambridge University. Until his retirement in 1925 he solved the problems students brought to him in an orderly and sympathetic way, and thus earned both their affection and their gratitude. His wife, Florence Ada Brown, whom he married in 1882, served a term as mayor of Cambridge, and their sons, John Maynard (Keynes) and Geoffrey, both had very distinguished careers. He died in 1949 and the next year his wife published a delightful memoir, Gathering up the Threads: A Study in Family Biography. As a schoolboy in 1864 Keynes began to keep a diary and continued it until 1917. It has proved a rich source for historians of the period, especially those interested in the history of economics at Cambridge during Alfred Marshall's tenure as professor from 1885 to 1908.
Henry Sidgwick (later Knightbridge Professor of Moral Philosophy), who was one of his teachers, had an important influence on both his writing style and his philosophical method. Both influences are plain to see in ‘On the Position of Formal Logic’, which Keynes published in 1879. It is a careful critique of the positions taken by Archbishop Whately, Sir William Hamilton, Henry Mansel, John Stuart Mill, William Whewell, George Boole, Augustus De Morgan, John Venn and William Stanley Jevons on the question whether ‘Formal Logic is yet satisfactorily established on an intelligible and independent basis’ (‘On the Position of Formal Logic, p. 362). Their various answers to the question are quoted and critically examined, and from the residue Keynes formulates ‘provisionally’ - in a very Sidgwickian way - a definition of the term: ‘Formal Logic is the science which treats of the nature and conditions of the conformity of symbolical with positive thought, and which is therefore chiefly concerned with the nature and conditions of the conformity of the expression of thought in ordinary language with thought itself (ibid., p. 370). He remarks that a systematic investigation of this kind of thought-symbolism is likely to prove useful. On the vexed question of the relationship between formal logic and psychology, he argues that his conception of logic avoids entangling the two: ‘Logic treats of language in entire subordination to mental processes and mental laws which have been previously established by Psychology’ (ibid., p. 371). In the course of his essay he distinguishes his view from the empirical logic of Mill and his followers and the symbolic logic of Boole and De Morgan. The care shown in this essay, as well as the respect accorded those whose views he is examining, is typical of all of Keynes's work. He was a panner of gold in the works of others, rather than an original thinker.
In 1884 Keynes gave his position the full treatment in Studies and Exercises in Formal Logic, which he intended as a supplement to the existing logic textbooks. Despite this limitation, it proved to be popular, largely because it was clearly written and avoided symbolism. One of its most innovative parts is an extensive discussion of the existential import of propositions, a topic then coming to the fore among logicians. Between the first and the fourth editions of the book the space devoted to this topic expanded from thirteen to thirty-eight pages. Throughout his discussion he defended the view that the subject terms of universal propositions do not imply the existence of what they denote, but they do in particular propositions. The developers of quantification theory, which includes syllogistic logic as an early phase, adopted this solution to the problem. The final part of his book goes beyond the syllogism to deal with arguments involving complex propositions of the sort that Boole and De Morgan used equations to solve. Keynes uses everyday language in his treatment of these arguments. John Venn, in his review of the book, opined that Keynes avoided symbolism by translating the discoveries of the symbolic logicians into ordinary language:
I feel tolerably sure that Mr. Keynes himself would not have worked out his scheme unless he had been a thorough adept in the more symbolic methods, and I rather doubt if there are many of the adherents of the old scheme who will be able, without his training, adequately to appreciate these very ingenious modifications of it.
(Venn, p. 304)
Keynes revised the book three times, the fourth edition being published in 1906. The successive editions of the book thus provide us with a record of what was taught under the rubric ‘logic’ at Cambridge in the years before Alfred North Whitehead's and Bertrand Russell's great work altered logic forever.
Keynes is equally well known as the author of The Scope and Method of Political Economy (1891), a critical examination of the logical problems inherent in that subject. Keynes read widely in political economy and then undertook to reconcile the two principal methodological positions revealed in its literature. His task turned out to be the bridging of the gap between two schools of economists, one of which insisted that induction was the proper method and the other of which insisted on deduction. Writers on both sides sometimes took rather extreme positions, arguing that induction alone or deduction alone was all that was required in their work. Keynes showed that both sorts of logic were used by the best authors of the competing sides and that both were required: induction to establish the premises of the subject, and deduction to draw out the consequences of these premises. As he did in his examination of the nature of formal logic, his discussion of the literature of political economy was both sympathetic and critical, with his own conclusions clearly stated. This book went through three editions and was widely used by students.
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