J M Keynes’s 1931 Comment, “…I Yield to Ramsey, I Think He Is Right” Refers to Ramsey’s Work on Precise Probability and Degrees of Belief, Not to Imprecise Probability and Degrees of Rational Belief: 20th and 21st Century Philosophers and Economists Simply Are Ignorant About Keynes’s Imprecise Theory of Probability Contained in Part II of the A Treatise on Probability

Abstract

A major error ,committed by all philosophers and economists in the 20th and 21st century who have written on the 1931 comment of Keynes on Ramsey about “…I yield to Ramsey, I think he is right”, is their failure to recognize that Keynes’s logical theory of probability is an imprecise theory of non additive probability based on intervals and dealing with rational degrees of belief, whereas Ramsey’s theory is a precise theory of additive probability that deals with degrees of belief only. The two theories merge only in the every special case where Keynes’s weight of the argument, V(a/h) =w,0≤w≤1, has a value of w=1 and all probability preferences are linear. Nowhere in any of Ramsey’s publications during his life is there ANY recognition on his part that the two theories are diametrically opposed except in the special case where w=1 and probability preferences are linear. It should have been obvious to Ramsey, if he had indeed read the book that he claimed he had read, that Keynes’s probabilities MUST be non additive if, as Ramsey also failed to recognized, only a partial order can be defined on the probability space.