William Ernest Johnson

Who was William Ernest Johnson?

William Ernest Johnson was a British logician mainly remembered for his Logic, in 3 volumes. In 1924, in volume III he introduced the important concept of exchangeability.

He taught at King's College, Cambridge for nearly thirty years. He wrote a bit on economics, and John Maynard Keynes was one of his students. Johnson was a colleague of Keynes's father, John Neville Keynes.

Logic was dated at the time of its publication, and 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" 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.

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".