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Ramsey's criticism

Ramsey's main critique of Keynes's view of probability as set forth in the Treatise as it was finally published, as well as the development of his own views, appears in The Foundations of Mathematics as the long chapter on "Truth and Probability." Here Ramsey does take note of the fact that

Keynes holds that probabilities are not always expressible by numbers, but "only that there is a one-one correspondence between probability relations and the degrees of belief which they justify" (Ramsey, 1931, pp. 160-1). This renders the manifold of probabilities similar (in the technical sense) to the manifold of degrees of belief. This, remarks Ramsey, should have "provided quite as worthy material for his skepticism as did the numerical measurement of probability relations" (Ramsey, 1931, p. 161). This is an odd thing to say, since it is apparently Keynes's intuitions about rational belief that lead him to this view about probability, rather than vice versa. In any event, since the structure of this manifold of probabilities is very different from the structure of the reals between 0 and 1, to which Ramsey wished to reduce all degrees of belief and all probabilities, it is a pity that Ramsey did not provide more motivation for his drastic reduction of Keynes's rich manifold of probabilities to the simple (alleged) structure of degrees of belief.

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