William Ernest Johnson

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]

W. E. Johnson

William Ernest Johnson.jpg
W. E. Johnson (c.1902)[1]
William Ernest Johnson

(1858-06-23)23 June 1858
Died14 January 1931(1931-01-14) (aged 72)
Northampton, England, United Kingdom
Alma materKing's College, Cambridge
OccupationPhilosopher, logician and economist
Spouse(s)Barbara Keymer Heaton

Life and careerEdit

Johnson was born in Cambridge on 23 June 1858 to William Henry Farthing Johnson and his wife, Harriet (née 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 spent some time teaching 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 University Teacher of Theory of Education 1893-98 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 Lecturership, 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] John Maynard Keynes, Frank Ramsey, Dorothy Wrinch,[4] C. D. Broad,[2] R. B. Braithwaite[6] and Susan Stebbing.[10] In 1912 (at Bertrand Russell's request) Johnson also attempted to 'coach' Ludwig Wittgenstein in logic but this was an arrangement that was both brief and unsuccessful.[11]

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


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.[12] 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".[13]

Johnson's major publication was a three volume work Logic (1921,1922, 1924) which was based on his lectures. This may never have been published if it hadn't been for the efforts of Newnham student Naomi Bentwich (1891–1988).[6] Naomi persuaded him to publish, typed and co-edited the manuscript and encouraged him to finish the project.[6] 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".[14] A fourth volume on probability was never finished, but parts of it would be published posthumously as an article in Mind.[15][6]

Logic ensured his election to the British Academy and won him honorary degrees from the universities of Manchester and Aberdeen.[15] Though conceding that Logic was "dated", even at publication, Sébastien Gandon argues that it would be a 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.[16] 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.[16] 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.[17][18]

"The Logical Calculus" (1892) reveals the technical capabilities of Johnson's youth,[19] and that he was significantly influenced by the formal logical work of Charles Sanders Peirce. 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.[20]

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)[21]

Johnson also wrote three papers on economics. The first two, both published in the Cambridge Economic Club, being 1891's “Exchange and Distribution" and 1894's “On Certain Questions Connected with Demand” (the latter being co-written with C. P. Langer).[22] ‘The Pure Theory of Utility Curves’ (1913)[23] was an important paper, representing "a considerable advance in the development of utility theory".[24][2] Prior to the latter he would also write fourteen entries for the first edition of R. H. Inglis Palgrave's Dictionary of Political Economy (1894-1899).[22] He was also of particular influence on John Maynard Keynes[25][6] (and had been a colleague of his father John Neville Keynes).[6]

Selected publicationsEdit


  1. ^ "may have been taken in 1902, when Johnson became a Fellow of King's College" -Zabell, Sandy L. (1982) "W. E. Johnson's 'Sufficientness' Postulate" p.1098
  2. ^ a b c 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 also online
  3. ^ Zabell, S. L. (1992). "Predicting the unpredictable" (PDF). Synthese. 90 (2 [pp. 205–232]): 229. doi:10.1007/BF00485351. ISSN 0039-7857.
  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. doi:10.1093/ref:odnb/34206.
  6. ^ a b c d e f g h i j Broad, C.D. (1952). "William Ernest Johnson". In Broad, C. D. (ed.). Ethics and the History of Philosophy. London: Routledge & K. Paul. pp. 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. ISSN 0026-4423. JSTOR 2250468.
  11. ^ 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 ...
  12. ^ Russell, Bertrand, 1872-1970. (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.CS1 maint: multiple names: authors list (link)
  13. ^ W. E. JOHNSON, The Times, 15 January 1931. Reprinted in The Collected Writings of John Maynard Keynes (1978) pp. 349–350 doi:10.1017/upo9781139524230.037
  14. ^ Johnson, W. E. (1921). Logic. Cambridge University Press.
  15. ^ a b "William Johnson (1858-1931)". www-history.mcs.st-andrews.ac.uk. Retrieved 21 June 2019.
  16. ^ a b Gandon, Sébastien (2016). Wittgenstein's Color Exclusion and Johnson's Determinable. Early Analytic Philosophy - New Perspectives on the Tradition. Costreie, Sorin. 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 ..
  17. ^ 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 26 June 2019
  18. ^ Having also been discussed in that article's precursor Determinates vs. Determinables by David H. Sanford
  19. ^ Passmore, John (1957). "New Developments in Logic". A Hundred Years Of Philosophy. Harmondsworth, Middlesex, England: Gerald Duckworth & Co. Ltd.
  20. ^ Prior, A. N. (1949). "Determinables, Determinates and Determinants". Mind. 58 (229): 1–20. doi:10.1093/mind/lviii.229.1. JSTOR 2254522.
  21. ^ Passmore, John (1957). "Some Cambridge Philosophers; and Wittgenstein's Tractatus". A Hundred Years of Philosophy. Harmondsworth, Middlesex, England: Gerald Duckworth & Co. Ltd.
  22. ^ 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.
  23. ^ Johnson, W. E. (1913). "The Pure Theory of Utility Curves". The Economic Journal. 23 (92): 483–513. doi:10.2307/2221661. JSTOR 2221661.
  24. ^ Baumol, W. J.; Goldfeld, S.N., eds. (1968). Precursors in Mathematical Economics: An Anthology. London School of Economics and Political Science. p. 96.
  25. ^ "Johnson, William Ernest." Complete Dictionary of Scientific Biography. via Encyclopedia.com. 21 Jun. 2019
  26. ^ a b c d e *Free at Internet Archive (public domain)
  27. ^ *Free at Internet Archive (public domain), also: hypertext transcription
  28. ^ *Free at Internet Archive (public domain), also: hypertext transcription
  29. ^ *Free at Internet Archive (public domain), also: hypertext transcription

External linksEdit