Keynes's conclusion, based on his Axiom (i), is that "…We can only be interested in our final results when they deal with actually existent and intelligible probabilities…" Ramsey's attack on Keynes completely collapses

Keynes’s main axiom in his A Treatise on Probability is his axiom (i), which appears on page 135.It states that “(i.) Provided that and h are propositions or conjunctions of propositions or disjunctions of propositions, and that h is not an inconsistent conjunction, there exists one and only one relation of probability P between a as conclusion and h as premise. Thus any conclusion a bears to any consistent premises h one and only one relation of probability.” (Keynes, 1921, p.135) It is dependent on definitions (I-VIII) on page 134 and an assumption dealing with Implication made in the top three lines of page 135.Keynes’s analysis on pp.135-137 then leads to the following conclusion on pp.137-138: “We can only be interested in our final results when they deal with actually existent and intelligible probabilities for our object is, always, to compare one probability with another…” (Keynes, 1921, pp.137-138). This statement by Keynes completely refutes Ramsey’s claims in 1922 and 1926.