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. 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." A memorial in
Mind also proffered a charitable partial explanation of his reluctance to publish. 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." 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, 1922, and 1924. This work may never have been published if it had not been for the efforts of
Newnham student Naomi Bentwich (1891–1988). A fourth volume on probability was never finished, but parts of it would be published posthumously as articles in
Mind. 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. 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. 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." 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.
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) He is also credited with coining the term '
redundancy theory of truth'. 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. and 1894's "On Certain Questions Connected with Demand" (the latter being co-written with C. P. Langer). Of ‘The Pure Theory of Utility Curves’ (1913)
Baumol &
Goldfeld (who reprinted all three papers with brief commentary) said it was "a considerable advance in the development of utility theory".
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”. 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. and had been a colleague of his father
John Neville Keynes. ==Select publications==