Between rationalism and subjeetivism
In an analysis of the inductive theory of C. D. Broad in 1959, Von Wright remarked that the most important contributions to inductive logic between the world wars were made by Keynes, Nicod, Johnson, Broad, Ramsey and Fisher, and noted that they were all Cambridge men, and constituted a "Cambridge tradition in modern inductive logic") To this Cambridge list in the period up to 1950 should of course be added Von Wright himself, and R. B. Braithwaite and Harold Jeffreys.
All these were concerned in one way or another with the application of probability to induction. Between them they represented the three major types of probability theory recognized at the time: Fisher and Braithwaite are frequentists, Keynes, Nicod, Johnson, Broad and Jcffreys are logicists, and Ramsey effectively founded the personalist school by his proposal to measure degrees of rational belief by rationally acceptable betting quotients. In view of the large majority vote for logicism, it is surprising to note the almost total demise of the logicist school after Carnap's Logical Foundations of Probability in 1950. This work both
Irreducible probability relations
Keynes believed that probability is a logical relation