# Harold Jeffreys on J M Keynes's A Treatise on Probability: Overlooking George Boole is a Fatal Error

16 Pages Posted: 26 May 2016 Last revised: 8 Jun 2016

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: May 25, 2016

### Abstract

Harold Jeffreys’ overall assessment of J M Keynes’s A Treatise on Probability, 1921, requires a reader to consider, not only his official review in Nature, 1922, but also the comments in his books, Scientific Inference, 1931 and Theory of Probability, 1939, as well as the second edition of Theory of Probability, 1947.

Jeffreys’ problem was that his approach to measurement required that all probabilities had to be measured by a single, precise number .This is tantamount to assuming that Keynes’s weight of the evidence, w, or William Johnson’s worth of the evidence, also denoted by w, are always equal to one. Jefferys obviously did not pick up this concept from his interactions with Johnson, as opposed to Keynes, who not only picked it up, but then connected it to Boole’s earlier logical approach to probability. Boole expressed this concept in terms of interval valued probability. Only if the weight or the worth of the evidence is equal, approaching to, or approximated by 1 will precise numbers be able to measure the probability relation. Jefferys’ failure to connect Boole to Keynes means that Jeffreys never understood what Keynes was doing in his A Treatise on Probability at any time during his life.

Keywords: addition axiom, Principle of Indifference, Laplace, Keynes, Jeffreys

JEL Classification: B10, B12, B20, B22

Suggested Citation

Brady, Michael Emmett, Harold Jeffreys on J M Keynes's A Treatise on Probability: Overlooking George Boole is a Fatal Error (May 25, 2016). Available at SSRN: https://ssrn.com/abstract=2784115 or http://dx.doi.org/10.2139/ssrn.2784115