William Ernest Johnson

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Born: 23 June 1858 in Cambridge, Cambridgeshire, England
Died: 14 Jan 1931 in Northampton, England

William Johnson was a pupil at a school in Cambridge where his father was the headmaster. In 1879 he entered King's College Cambridge becoming 11th wrangler in the mathematical tripos of 1882. Johnson held various temporary positions around Cambridge for the 19 years.

During this time he published three papers on Boolean logic and one on probability. In 1902 he obtained a Fellowship at Kings and taught there. He was a shy, sickly man but a popular and respected teacher. One of his students persuaded him to publish Logic.

Logic, Johnson's most important work, is in three volumes, the fourth on probability was never finished but the parts which were written were published as Mind after his death. Logic won him considerable fame and honorary degrees.

Johnson viewed probability as expressing logical relations between evidence propositions and hypothesis propositions. He was opposed to the frequency interpretation of probability. His views on the foundations of probability theory influenced Keynes and others.

In [2] some aspects of his work is discussed:-

How do Bayesians justify using conjugate priors on grounds other than mathematical convenience? In the 1920s the Cambridge philosopher William Ernest Johnson in effect characterized symmetric Dirichlet priors for multinomial sampling in terms of a natural and easily assessed subjective condition. Johnson's proof can be generalized to include asymmetric Dirichlet priors and those finitely exchangeable sequences with linear posterior expectation of success. Some interesting open problems that Johnson's result raises, and its historical and philosophical background, are also discussed.