This paper concentrates on Keynes’s solution to a version of Boole’s Challenge Problem of 1851. The problem is solved by Keynes mathematically at the end of Chapter 15 of the A Treatise on Probability, 1921. A study of this problem demonstrates Keynes’s understanding of Boole’s technique...

Frank P Ramsey did not consider the possibility of representing the concept of probability by an interval valued approach in his lifetime. Ramsey considered probability to be either ordinal or numerical. There was absolutely no room for interval estimates and interval probability in his...

The Townshend–Keynes exchanges over decision making, weight of the argument (evidence), non numerical probabilities (Keynes’s term for Boole’s constituent probabilities, used in The Laws of Thought in 1854, that appears on page 163 of the A Treatise on Probability in chapter 15 on inexact...

Starting with J. Muth’s unsupported and unsupportable claims, originally made in 1961, that “rational expectations” were subjective probability distributions that were distributed around a known, true, objective probability distribution, various economists have provided the same type of...

The operational definitions of uncertainty used by John M. Keynes and Frank H. Knight are based on missing information that will not be available to the decision maker at any time. The founder of this approach is George Boole. This leads to indeterminate interval probabilities. The definition of...

Smith, Keynes, and Knight, in that order, made seminal contributions to decision making which emphasized uncertainty and indeterminate probabilities, as opposed to mere imprecision. De Finetti’s views on uncertainty are diametrically opposed to those of Smith, Keynes, and Knight once the clear...