After 100 Years, the Time Has Come to Acknowledge That Boole and Keynes Founded a Mathematically, Technically, and Logically Advanced Approach to Imprecise Probability

Abstract

Keynes’s and Boole’s contributions to the theory of imprecise probability are not just “notions” or “suggestions” or “intuitions”. Keynes and Boole actually worked out problems in great detail in which they derive lower and upper probability bounds based on their foundation of Boolean algebra and logic. Their work is very advanced and compares very favorably to work done up to the mid 1980’s, when T. Hailperin made major advances in the generalization of the Boole-Keynes approach.

Unfortunately,it appears that these contributions are not known,have been ignored,or are of a technical nature that is too difficult for present day researchers to master. Only Emil Borel in 1924 gave an answer, which was that it was too difficult for him to cover.