Michael Emmett Brady
Bateman’s claim (2016, History of Political Economy) that “Keynes had postulated that probability is an objective logical relation between two propositions.” appears nowhere in Keynes’s A Treatise on Probability. His claim is similar to those made by C.Misak in her 2020 biography of Ramsey. Bateman just assumed that what the supposed 18 year old boy genius had claimed was correct and that whatever Ramsey said/wrote had to be true because he was a genius .Actually, Ramsey’s two reviews are incomprehensible , utterly preposterous, gobbledygook that Ramsey had simply manufactured out of the thin air or in his own imagination.
Keynes’s logical theory of probability postulated that there was a rational degree of probable belief,α,based on an objective, logical, relation of similarity that held between multiple a and h propositions(not two propositions) .These propositions had to be related ,linked or associated with each other ,where the h proposition(s) supplied evidence and the a proposition(s) was a conclusion that had to be based on the evidence provided by the h propositions.
Ramsey’s failure to correctly define Keynes’s propositional logic is carried out through both reviews so that all of the points he claimed to be making are wrong .All of his example problems are wrong because he fails to grasp that the a and h propositions must be related. Otherwise, there can be no similarity between them, which means that there is no objective probability relation connecting them and no α can be defined.
The entire Ramsey critique of Keynes’s logical theory of probability is based on a large number of empty claims and errors made by Ramsey that have no textual support in any part of the A treatise on Probability or in anything written by Keynes in his lifetime.
Ramsey’s three page review is filled with obvious errors and mistaken claims such as “First, he (author’s note-Keynes) thinks that between any two non-self-contradictory propositions there holds a probability relation (Axiom I), for example between 'My carpet is blue' and 'Napoleon was a great general'; it is easily seen that it leads to contradictions to assign the probability 1/2 to such cases, and Mr. Keynes would conclude that the probability is not numerical. But it would seem that in such cases there is no probability; that, for a logical relation, other than a truth function, to hold between two propositions, there must be some connection between them. If this be so, there is no such probability as the probability that 'my carpet is blue' given only that 'Napoleon was a great general', and there is therefore no question of assigning a numerical value.”(Ramsey, 1922; 1989).
Nowhere in the A Treatise on Probability or anything written by Keynes in his lifetime did Keynes state”… that between any two non-self-contradictory propositions there holds a probability relation…”(Ramsey, 1922).
Second, there is no such axiom one “…Axiom I…” in Keynes’s A treatise on Probability (Ramsey, 1922)that was asserted by Keynes in the A Treatise on Probability or anything written by Keynes in his lifetime.
Ramsey’s “…'My carpet is blue';' Napoleon was a great general'…” (Ramsey, 1922) example is directly ruled out by Keynes’s argument form, first specified on p.4 of A Treatise on Probability, specifying that the h proposition(s), that form the premises of the argument, must contain relevant evidence that is related /associated to the proposition(s) upon which to base a conclusion, a, so that P(a/h)=α,0≤α ≤1, where α is a degree of rational belief .The a and h propositions must be related so that the evidence supporting the conclusion is connected ,where P stands for the logical, objective, probability relation (the similarity exhibited between the h and a propositions) that holds between h and a. Given the fact that nothing Ramsey is talking and writing about on p.3 of his note has anything to do with Keynes’s A treatise on Probability, the claim, that Ramsey destroyed and demolished Keynes’s logical theory in 1922, is a claim that most likely can only be found among economists and philosophers who write about Keynes’s views on probability despite never having actually read anything in the A Treatise on Probability except bits and pieces cobbled together in a bizarre fashion.