William Ernest Johnson

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William Ernest Johnson (23 June 1858 – 14 January 1931), usually cited as W. E. Johnson, was a British philosopher and logician mainly remembered for his Logic (1921–1924), in 3 volumes. In 1924, in volume III he introduced the important concept of exchangeability.[1]

Life and career[edit]

Johnson was born in Cambridge on 23 June 1858 to William Henry Farthing Johnson and his wife, Harriet (nee Brimley). He was their fifth child. The family were baptists and political liberals.[2]

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.[3] At the age of around eight he became seriously ill and he developed severe asthma and lifelong ill health. Due to this his education was frequently disrupted.[4]

In 1879 he entered King's College, Cambridge to read mathematics having won a scholarship and he was 11th Wrangler in 1882. He stayed on to study for the Moral Sciences Tripos from which graduated in 1883 with a First Class degree.[5]

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

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. In 1896 thanks to Henry Sidgwick's efforts he was appointed as University lecturer at the University of Cambridge. In 1902 he was elected a Fellow of King's College, and Sidgwick Lecturer in Moral Sciences,.[6] His students included John Maynard Keynes, Frank Ramsey, Ludwig Wittgenstein, C.D. Broad and Dorothy Wrinch. He held these positions for nearly thirty years until his death in 1931.[7]

In 1923 he was elected a Fellow of the British Academy.

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


Johnson had ill health and was a famous procrastinator and he therefore published little. His major publication was a three volume work Logic (1921–1924) 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). Naomi 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".[8]

Logic ensured his election to the British Academy but by his death it appeared dated. Johnson can be seen as a member of the British logic "old guard" pushed aside by the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Yet an article entitled "The Logical Calculus" (Johnson 1892) reveals that he had nontrivial technical capabilities in his youth, 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.[9]

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, 1917, p.346)

Johnson also wrote three papers on economics (1891; 1894; 1913). ‘The Pure Theory of Utility Curves’ (1913)[10] was an important paper, representing "a considerable advance in the development of utility theory".[11] Johnson was an influence on his student, John Maynard Keynes. Johnson was a colleague of Keynes's father, John Neville Keynes. He was a Cambridge Apostle.

Selected publications[edit]

See also[edit]


  1. ^ Zabell (1992)
  2. ^ Broad, C.D. (1952). "William Ernest Johnson". In Broad, C. D. Ethics and the History of Philosophy. London: Routledge & K. Paul. pp. 94–95.
  3. ^ Braithwaite, R. B. "Johnson, William Ernest (1858–1931)". Oxford Dictionary of National Biography. Retrieved 20 June 2017.
  4. ^ Broad, C.D. (1952). "William Ernest Johnson". In Broad, C. D. Ethics and the History of Philosophy. London: Routledge & K. Paul. p. 99.
  5. ^ "Johnson, William Ernest (JHN878WE)". A Cambridge Alumni Database. University of Cambridge.
  6. ^ "University intelligence". The Times (36717). London. 17 March 1902. p. 11.
  7. ^ "Johnson, William Ernest (JHN878WE)". A Cambridge Alumni Database. University of Cambridge.
  8. ^ Johnson, W. E. (1921). Logic. Cambridge University Press.
  9. ^ Prior, A. N. (1949). "Determinables, Determinates and Determinants". Mind. 58: 1–20. doi:10.1093/mind/lviii.229.1. JSTOR 2254522.
  10. ^ Johnson, W. E. (1913). "The Pure Theory of Utility Curves". The Economic Journal. 23: 483–513. doi:10.2307/2221661. JSTOR 2221661.
  11. ^ Baumol, W. J.; Goldfeld, S.N., eds. (1968). Precursors in Mathematical Economics: An Anthology. London School of Economics and Political Science. p. 96.

Further reading[edit]