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William Ernest Johnson

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For other people named William Johnson, see William Johnson (disambiguation).

W. E. Johnson
FBA
Johnson, c. 1902[1]
Born
William Ernest Johnson

(1858-06-23)23 June 1858
Cambridge, England
Died14 January 1931(1931-01-14) (aged 72)
Northampton, England
OccupationsPhilosopher, logician, economist
SpouseBarbara Keymer Heaton
Academic background
Alma materKing's College, Cambridge
Academic advisor
Henry Sidgwick
Academic work
InstitutionsKing's College, Cambridge
Notable students
Susan Stebbing, C. D. Broad

William Ernest Johnson (23 June 1858 – 14 January 1931), usually cited as W. E. Johnson, was a British philosopher, logician and economic theorist.[2] He is mainly remembered for his 3 volume Logic which introduced the concept of exchangeability.[3][4]

Life and career

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Johnson was born in Cambridge on 23 June 1858 to William Henry Farthing Johnson and his wife, Harriet (née Brimley), half-sister of the essayist George Brimley.[5] He was their fifth child.[5] The family were Baptists and political liberals.[6]

He attended the Llandaff House School, Cambridge where his father was the proprietor and headteacher, then the Perse School, Cambridge, and the Liverpool Royal Institution School.[5] At the age of around eight he became seriously ill and developed severe asthma and lifelong ill health. Due to this his education was frequently disrupted.[6]

In 1879 he entered King's College, Cambridge to read mathematics having won a scholarship and was placed 11th Wrangler in 1882.[7] He stayed on to study for the Moral Sciences Tripos from which he graduated in 1883 with a First Class degree.[7] He was also a Cambridge Apostle.[8]

In 1895 he married Barbara Keymer. After her sudden death in 1904 his sister Fanny moved in with him to care for his two sons.[5]

Having failed to win a prize fellowship, he taught mathematics. His first teaching post was as a lecturer in Psychology and Education at the Cambridge Women's Training College, which he held for several years.[6] He was a University Teacher of Theory of Education 1893–1898 and, from 1896 until 1901, University Lecturer in Moral Sciences at the University of Cambridge.[6][7] In 1902 he was elected a Fellow of King's College, and appointed to the newly created Sidgwick Lectureship, positions he held until his death.[7][5] In 1923 he was elected a Fellow of the British Academy.[7][5]

Johnson's students included I. A. Richards,[9] Dorothy Wrinch,[4] C. D. Broad,[2] R. B. Braithwaite[6] and Susan Stebbing.[10] Frank Ramsey is sometimes described as one of his students. However, as John Aldrich notes, Johnson lectured to, and supervised, moral science students and had no official duties toward students of mathematics and there is no evidence Ramsey attended his lectures.[11] Ramsey though, as Sahlin notes, "knew the work of Johnson extremely well".[12] He would review the second part of Johnson's Logic in 1922 and referred to Johnson multiple times in his 1925 paper on 'Universals'.[13]

In 1912 (at Bertrand Russell's request) Johnson attempted to 'coach' Ludwig Wittgenstein in logic but this was an arrangement that was both brief and unsuccessful.[14] They had strong disagreements on logic and philosophy, but got on well when they did not speak about these things.[15] Wittgenstein anonymously committed 200 pounds a year to a research fund for Johnson.[16] He was also kind to Johnson during his ill-health.[17]

He died in St Andrew's Hospital, Northampton, on 14 January 1931 and is buried at Grantchester, Cambridgeshire.[5]

Work

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Members of the Moral Science Club circa 1913, with W. E. Johnson sat in the middle of the front row (to the right of Bertrand Russell)

Johnson, who suffered poor health, published little. That, though "very able", he was "lacking in vigour" and had "published almost nothing" is a matter Bertrand Russell commented upon unsympathetically in a letter to Ottoline Morrell of 23 February 1913.[18] Johnson's obituary in The Times, penned by J. M. Keynes, more kindly reports that "his critical intellect did not readily lend itself to authorship."[19] A memorial in Mind also proffered a charitable partial explanation of his reluctance to publish.[20] In plainer terms, C. D. Broad wrote that Johnson "wrote much, but owing to ill-health and excessive diffidence and self-criticism he published very little."[21]

Johnson's major publication was a three volume work Logic which was based on his lectures, Its volumes appeared, along with favourable reviews in the journal Mind, in 1921,[22] 1922,[23] and 1924.[24][25]

This work may never have been published if it had not been for the efforts of Newnham student Naomi Bentwich (1891–1988).[6] Bentwich persuaded him to publish, typed and co-edited the manuscript and encouraged him to finish the project. The preface to the first volume carries the acknowledgement: "I have to express my great obligations to my former pupil, Miss Naomi Bentwich, without whose encouragement and valuable assistance in the composition and arrangement of the work, it would not have been produced in its present form."[26] A fourth volume on probability was never finished, but parts of it would be published posthumously as articles in Mind.[27][6]

Logic ensured his election to the British Academy and won him honorary degrees from the universities of Manchester and Aberdeen.[28] Though conceding that Logic was "dated", even at publication, Sébastien Gandon argues that it would be unfair, given "the richness of his thought", to see Johnson "only as a member of the British logic 'old guard' pushed aside by the Principia Mathematica" of Alfred North Whitehead and Bertrand Russell.[29] Gandon contends that "many of Johnson's insights are today an integral part of philosophy" and that this is so especially of Johnson's doctrine of determinable and determinate.[29] Johnson's work and influence in this latter regard is discussed in the Stanford Encyclopedia of Philosophy entry on Determinables and Determinates by Jessica Wilson.[30][31]

In his early work "The Logical Calculus" (1892), as Baruch Brody notes, he "developed an elegant version of Boolean propositional and functional logic, using conjunction and negation as his primitive symbols."[27] It reveals the technical capabilities of Johnson's youth.[32] The article begins as follows:

"As a material machine economises the exertion of force, so a symbolic calculus economises the exertion of intelligence ... the more perfect the calculus, the smaller the intelligence compared to the results."

A. N. Prior's Formal Logic cites this article several times.[33]

John Passmore tells us:

"His neologisms, as rarely happens, have won wide acceptance: such phrases as "ostensive definition", such contrasts as those between ... "determinates" and "determinables", "continuants" and "occurrents", are now familiar in philosophical literature." (Passmore, 1957, p. 346)[34]

He is also credited with coining the term 'redundancy theory of truth'.[35][36] Of his discussion of it, as Sahlin writes:

W. E. Johnson in his Logic of 1921 discusses the eliminability of the predicate 'true'. According to Johnson, this predicate and its semantic import is best understood if it is compared with the functioning of the number '1' within arithmetic. Multiplying a number by 1 does not change anything, nor does adding 'it is true' to a sentence.[12]

Ramsey, as Sahlin notes, likely wrote his more substantial remarks on the topic thinking a reference to Johnson superfluous.[12] Of Johnson, Keynes writes:

If his influence on Cambridge thought is to be summed up briefly, it may be said that he was the first to exercise the epistemic side of logic, the links between logic and the psychology of thought. In a school of thought whose natural leanings were towards formal logic, he was exceptionally well equipped to write formal logic himself and to criticise everything which was being contributed to the subject along formal lines.[19]

Economics

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Johnson wrote three papers on economics. The first two, both published in the Cambridge Economic Club, being 1891's "Exchange and Distribution"[37] and 1894's "On Certain Questions Connected with Demand"[38] (the latter being co-written with C. P. Langer).[39] Of ‘The Pure Theory of Utility Curves’ (1913)[40] Baumol & Goldfeld (who reprinted all three papers with brief commentary) said it was "a considerable advance in the development of utility theory".[41] Joseph Schumpeter described it as an "important paper [that] contains several results that should secure for its author a place in any history of our science”.[42]

He wrote fourteen entries for the first edition of R. H. Inglis Palgrave's Dictionary of Political Economy (1894–1899), mostly on economic method. He also lectured on mathematical economics from 1905–1922.[39] He was of particular influence on John Maynard Keynes[27] and had been a colleague of his father John Neville Keynes.[6]

Select publications

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References

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  1. ^ "may have been taken in 1902, when Johnson became a Fellow of King's College" – Zabell, Sandy L. (1982) p. 1098
  2. ^ a b Zabell, S.L. (2008) "Johnson, William Ernest (1858–1931)" In: Durlauf S.N., Blume L.E. (eds) The New Palgrave Dictionary of Economics.(2nd ed, 2008.) Palgrave Macmillan, London doi:10.1007/978-1-349-58802-2_868
  3. ^ Zabell, S. L. (1992). "Predicting the Unpredictable" (PDF). Synthese. 90 (2 [pp. 205–232]): 229. doi:10.1007/BF00485351. ISSN 0039-7857. S2CID 9416747.
  4. ^ a b Zabell, Sandy L. (1982). "W. E. Johnson's "Sufficientness" Postulate". The Annals of Statistics. 10 (4 [pp.1090–1099]): 1097, 1099. doi:10.1214/aos/1176345975. ISSN 0090-5364.
  5. ^ a b c d e f g Braithwaite, R. B. (2004). "Johnson, William Ernest (1858–1931)". Oxford Dictionary of National Biography (online ed.). Oxford University Press. doi:10.1093/ref:odnb/34206. Archived from the original on 9 June 2019. (Subscription, Wikipedia Library access or UK public library membership required.)
  6. ^ a b c d e f g h Broad, C. D. (1931). "William Ernest Johnson" (PDF). Proceedings of the British Academy. 17: 94–114.
  7. ^ a b c d e "Johnson, William Ernest (JHN878WE)". A Cambridge Alumni Database. University of Cambridge.
  8. ^ First semester. (2017). In P. Bogaard & J. Bell (Eds.), The Harvard Lectures of Alfred North Whitehead, 1924–1925: Philosophical Presuppositions of Science (fn. 5. p. 493). Edinburgh University Press.
  9. ^ Russo, John Paul (2015). I. A. Richards: His Life and Work. London: Routledge. p. 46. ISBN 9781138842717. OCLC 898154256. Richards' supervisor in moral science for his "last two years, nearly" ... W. E. Johnson ... was important "not so much for any one thing, but in the general intellectual rigor and imagination brought to bear upon issues." He was a "quiet, gentle man" who suffered badly from asthma. When Richards went to King's for supervision he would often find him lying in bed and would take notes from a man "quietly delivering monologues." Compared with McTaggart ... Johnson was "more judicious, more balanced, more interested in trying to say and restate what others thought. McTaggart was ... always trying to push his theories..." ... Johnson's were "lessons in intellectual integrity.
  10. ^ Wisdom, John (1944). "L. Susan Stebbing, 1885–1943". Mind. 53 (211): 283–285. doi:10.1093/mind/LIII.211.283. ISSN 0026-4423. JSTOR 2250468.
  11. ^ Aldrich, John (February 2022). "W.E. Johnson and Cambridge thought on probability" (PDF). International Journal of Approximate Reasoning. 141: 155. doi:10.1016/j.ijar.2021.10.010.
  12. ^ a b c Sahlin, Nils-Eric (31 August 1990). The Philosophy of F. P. Ramsey. Cambridge University Press. pp. 56–57. ISBN 978-0-521-38543-5.
  13. ^ F. P. Ramsey, "Review of W. E. Johnson's Logic Part II" The New Statesman, 19 (July 1922), pp. 469–470.
  14. ^ Monk, Ray. (1991). Ludwig Wittgenstein: The Duty of Genius. London: Vintage. p. 42. ISBN 0099883708. OCLC 877368486. On 1 February 1912 Wittgenstein was admitted as a member of Trinity College, with Russell as his supervisor. Knowing that he had never received any formal tuition in logic, and feeling that he might benefit from it, Russell arranged for him to be 'coached' by the eminent logician and Fellow of King's College, W. E. Johnson. The arrangement lasted only a few weeks. Wittgenstein later told F. R. Leavis: 'I found in the first hour that he had nothing to teach me.' ... Leavis was also told by Johnson: 'At our first meeting he was teaching me.' ... The difference is that Johnson's remark was sardonic, Wittgenstein's completely in earnest. It was actually Johnson who put an end to the arrangement...
  15. ^ Britton, Karl (1967). "Portrait of a Philosopher". In Fann, K. T. (ed.). Ludwig Wittgenstein: the man and his philosophy. Internet Archive. [New York] [Dell Pub. Co.] p. 61. ISBN 978-0-391-00897-7. He said how much he liked and admired Johnson and how well they got on as soon as they had decided to give up the philosophical questions.
  16. ^ Wittgenstein, Ludwig (1974). von Wright, G. H. (ed.). Letters to Russell, Keynes, and Moore. Cornell University Press. pp. 108, 121.
  17. ^ Malcolm, Norman (19 November 1981). "Wittgenstein's Confessions". London Review of Books. Vol. 03, no. 21. ISSN 0260-9592. Retrieved 2 April 2026. Although Wittgenstein had a poor opinion of W.E. Johnson's three-volume work on logic, and Johnson in turn thought that Wittgenstein was arrogant and a disastrous influence in Cambridge, yet when Johnson's health began to deteriorate 'no one,' says Drury, 'could have shown more sympathetic solicitude than Wittgenstein did.' He went frequently to Johnson's home to play chess with him, and often was the audience while Johnson played Bach on the piano, since Wittgenstein knew that Johnson would not play unless he had a listener.
  18. ^ Russell, Bertrand (2002). The Selected Letters of Bertrand Russell. The Private Years, 1884-1914. Griffin, Nicholas. London: Routledge. pp. 433–434. ISBN 0415260140. OCLC 49594254. W. E. Johnson ... is very able, but lacking in vigour, and has published almost nothing. His family make a cult of him, and talk as if having the ideas were everything, and writing them out a mere vulgar mechanical labour. It vexes me, because anybody who has ever written knows the intolerable labour of getting one's ideas into proper shape, long after they have seemed all right as mere thoughts. Universities are full of people who ought to write and don't — I always feel annoyed with them, and with people who minimize the labour of actually producing something.
  19. ^ a b "W. E. JOHNSON," The Times, 15 January 1931. Reprinted in Delphi Collected Works of John Maynard Keynes (Illustrated). Delphi Classics. 2026. ISBN 978-1-80170-307-9. and The Collected Writings of John Maynard Keynes (1978) pp. 349–350 doi:10.1017/upo9781139524230.037
  20. ^ D., A. (1932). "W. E. Johnson (1858–1931): An Impression". Mind. 41 (161): 136–137. ISSN 0026-4423. JSTOR 2250151. he gave above all the impression of one steadily pursuing his own way, and of not caring very much whether his views became known or not, or whether anyone agreed with him. It was the pure intellectual desire to reach truth, rather than the desire to-spread it or the hope of acquiring reputation, which seemed to drive him on. And this perhaps partly explains that reluctance to publish, which was in the end so fortunately overcome.
  21. ^ Broad, C. D. (1957). "The Local Historical Background of Contemporary Cambridge". In Mace, C. A. (ed.). British Philosophy in the Mid-Century: A Cambridge Symposium. p. 23 – via Internet Archive. Johnson was a most acute thinker and a very hard and conscientious worker. He wrote much, but owing to ill-health and excessive diffidence and self-criticism he published very little. After contributing a series of three important articles, entitled "The Logical Calculus,' to the first three volumes of Mind in 1892 to 1894, he published nothing in philosophy until 1918, when he broke his long silence with two articles in Mind entitled "The Analysis of Thinking'.
  22. ^ Gibson, James (1921). "Review of Logic: Part I." Mind. 30 (120): 448–455. ISSN 0026-4423. JSTOR 2249513 – via Internet Archive.
  23. ^ Broad, C. D. (1922). "Review of Logic, Part II" (PDF). Mind. 31 (124): 496–510. ISSN 0026-4423. JSTOR 2249771.
  24. ^ Broad, C. D. (1924). "Mr. Johnson on the Logical Foundations of Science" (PDF). Mind. 33 (131): 242–261. ISSN 0026-4423. JSTOR 2249779.
  25. ^ Broad, C. D. (1924). "Mr. Johnson on the Logical Foundations of Science (II.)" (PDF). Mind. 33 (132): 369–384. ISSN 0026-4423. JSTOR 2249554.
  26. ^ Johnson, W. E. (1921). Logic. Cambridge University Press.
  27. ^ a b c Brody, Baruch. "Johnson, William Ernest | Encyclopedia.com". www.encyclopedia.com. Retrieved 30 October 2025.
  28. ^ "William Johnson (1858-1931)". www-history.mcs.st-andrews.ac.uk. Retrieved 21 June 2019.
  29. ^ a b Gandon, Sébastien (2016). "Wittgenstein's Color Exclusion and Johnson's Determinable". In Costreie, Sorin (ed.). Early Analytic Philosophy – New Perspectives on the Tradition. Springer International Publishing. p. 269. ISBN 9783319242149. OCLC 936040958. The book was already dated at the time of its publication. But seeing Johnson only as a member of the British logic 'old guard', pushed aside by the Principia Mathematica, would be unfair and would not give credit to the richness of his thought. Indeed, many of Johnson's insights are today an integral part of philosophy. ... This is especially the case with Johnson's doctrine of determinable and determinate...
  30. ^ Wilson, Jessica (2017), "Determinables and Determinates", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2017 ed.), Metaphysics Research Lab, Stanford University, retrieved 30 October 2025.
  31. ^ Having also been discussed in that article's precursor Determinates vs. Determinables by David H. Sanford.
  32. ^ Passmore, John (1957). "New Developments in Logic". A Hundred Years of Philosophy. Harmondsworth, Middlesex, England: Gerald Duckworth & Co. Ltd.
  33. ^ Prior, A. N. (1949). "Determinables, Determinates and Determinants". Mind. 58 (229): 1–20. doi:10.1093/mind/lviii.229.1. JSTOR 2254522. PMID 18113196.
  34. ^ Passmore, John (1957). "Some Cambridge Philosophers; and Wittgenstein's Tractatus". A Hundred Years of Philosophy. Harmondsworth, Middlesex, England: Gerald Duckworth & Co. Ltd.
  35. ^ Kunne, Wolfgang (5 June 2003). Conceptions of Truth. Oxford University Press. p. 36. ISBN 978-0-19-924131-6.
  36. ^ Baldwin, Thomas (2010). Moore. Arguments of the Philosophers. Routledge. p. 327. ISBN 978-1-136-95777-2.
  37. ^ Johnson, William Ernest (1891). Exchange and distribution. Cambridge, Eng. – via HathiTrust.{{cite book}}: CS1 maint: location missing publisher (link)
  38. ^ Johnson, William Ernest; Sanger, Charles Percy (1891). On certain questions connected with demand. Cambridge, Eng. – via HathiTrust.{{cite book}}: CS1 maint: location missing publisher (link)
  39. ^ a b Moscati, Ivan (2005). "W. E. Johnson's 1913 Paper and the Question of his Knowledge of Pareto" (PDF). Journal of the History of Economic Thought. 27 (3): 283–304. doi:10.1080/09557570500183553. ISSN 1469-9656. S2CID 142585583.
  40. ^ Johnson, W. E. (1913). "The Pure Theory of Utility Curves". The Economic Journal. 23 (92): 483–513. doi:10.2307/2221661. JSTOR 2221661.
  41. ^ Baumol, W. J.; Goldfeld, S. M., eds. (1968). Precursors in Mathematical Economics: An Anthology. London School of Economics and Political Science. p. 96.
  42. ^ Schumpeter, Joseph A. (1954). History of Economic Analysis. Psychology Press. p. 1063. ISBN 978-0-415-10892-8. W. E. Johnson, "The Pure Theory of Utility Curves, Economic Journal, December 1913. This important paper contains several results that should secure for its author a place in any history of our science. But, having apparently been written in ignorance of Pareto's work, it aroused not unnatural resentment on the part of Italian economists because of its failure to acknowledge Pareto's priority in most essentials. {{cite book}}: ISBN / Date incompatibility (help)
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