Why Did F. P. Ramsey Never Repeat the Claims He Had Made on the First Page of His Jan., 1922 Cambridge Magazine Three Page Note Concerning Keynes’s Logical Theory of Probability?: It Is Easy for a Reader To See That Ramsey’s Review Is Dead Wrong if That Reader Has Actually Read the 'A Treatise on Probability'

The first page of the 18 year old, F. P. Ramsey’s very short three page review, in the Cambridge Magazine issue of Jan., 1922, of Keynes’s A Treatise on Probability is comprised of claims about Keynes’s logical theory of probability that, to use L. J. Savage’s characterization of academics who tried to apply his Subjective Expected Utility model to Large Worlds (macro, intertemporal, long run decision making), as opposed to Small Worlds (micro ,short run decision making), was “utterly preposterous” and complete ”nonsense”. Ramsey’s very small review was obviously never refereed J. M. Keynes and/or Bertrand Russell could have made short work of the 18 year old Ramsey’s note in a few minutes, thereby permanently ending his academic career at Cambridge before it ever had a chance to get started. However, they decided not to do so, as they recognized that Ramsey had special intellectual gifts, although they were clearly undeveloped at the time. Keynes decided to take Ramsey under his wing and train him. The very, very severe problems with the first page consist of two claims made by Ramsey. The first claim made by F. P. Ramsey is that: “We have, then, numerous probability relations; these it is commonly supposed are all numerical, that is, correlated with the real numbers from 0 to 1 in such a way that the ordinary rules of the probability calculus hold, e.g., that the product of the numbers correlated with two probabilities is equal to the number correlated with the product (in Mr. Keynes' sense) of the two probabilities. Mr. Keynes denies this; he supposes not only that not all probabilities are numerical, but also that it is possible to have two probabilities which are unequal and such that neither is greater than the other. This view is based on the difficulty in so many cases of saying with any confidence which of two probabilities is the greater, or of assigning any numerical measures to them. But it would appear that the force of this objection to the ordinary view is exaggerated to Mr. Keynes for two reasons.” The second claim made by F.P. Ramsey is that: “First, he 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’s first claim is the result of his gross ignorance of Keynes’s imprecise, interval valued ,non additive approach to probability, as was illustrated by Keynes in the discussions of the beauty contest problem on pp.25-28, as well as by six other illustrations contained in Chapter III of the A Treatise on Probability. The mathematical analysis was presented in Part II of the book, a part that Ramsey never got around to ever reading in his lifetime. The second claim made by Ramsey has nothing to do with Keynes’s use of propositions, which must be stated in the form of an argument- one proposition must contain relevant evidence while the second proposition must be a conclusion with respect to the proposition containing the relevant evidence. Only then is a relation of logical probability present. Nowhere at any place in his A Treatise on Probability or any other work written in Keynes’s lifetime did Keynes state: “…that between any two non-self-contradictory propositions there holds a probability relation (Axiom I)…” There is no such Axiom I in Keynes’s A Treatise on Probability. Therefore, Ramsey’s”… 'My carpet is blue' and 'Napoleon was a great general…” example is an oxymoron because his two propositions do not form an argument. The current belief among academics, that has been a belief for 100 years, that Ramsey not only destroyed and demolished Keynes’s logical theory of probability, but that Keynes himself felt compelled by the overwhelming logical power of Ramsey’s critique to accept Ramsey’s critique and adopted a subjective theory of probability himself, calls into question the claims made by academics writing on Keynes that they are publishing scientific works that contribute to the growth of knowledge. All I see is utter and complete nonsense.