Keynes on Ramsey on Probability: What does it Prove?

This passage from Keynes’ short article “Ramsey as a Philosopher” (Keynes 1931) has caused a mountain of writing and controversy:

“Thus he [sc. Ramsey] was led to consider ‘human logic’ as distinguished from ‘formal logic.’ Formal logic is concerned with nothing but the rules of consistent thought. But in addition to this we have certain ‘useful mental habits’ for handling the material with which we are supplied by our perceptions and by our memory and perhaps in other ways, and so arriving at or towards truth; and the analysis of such habits is also a sort of logic. The application of these ideas to the logic of probability is very fruitful. Ramsey argues, as against the view which I had put forward, that probability is concerned not with objective relations between propositions but (in some sense) with degrees of belief, and he succeeds in showing that the calculus of probabilities simply amounts to a set of rules for ensuring that the system of degrees of belief which we hold shall be a consistent system. Thus the calculus of probabilities belongs to formal logic. But the basis of our degrees of belief—or the a priori probabilities, as they used to be called—is part of our human outfit, perhaps given us merely by natural selection, analogous to our perceptions and our memories rather than to formal logic. So far I yield to Ramsey—I think he is right. But in attempting to distinguish ‘rational’ degrees of belief from belief in general he was not yet, I think, quite successful. It is not getting to the bottom of the principle of induction merely to say that it is a useful mental habit. Yet in attempting to distinguish a ‘human’ logic from formal logic on the one hand and descriptive psychology on the other, Ramsey may have been pointing the way to the next field of study when formal logic has been put into good order and its highly limited scope properly defined.” (Keynes 1963: 243–244).

Just what was Keynes conceding here, by the words “So far I yield to Ramsey—I think he is right”?

It is not at all clear, and some have argued that Keynes was effectively repudiating his earlier logical theory of probability.

In essence, Keynes was responding to Ramsey’s criticisms of A Treatise on Probability in Ramsey (1922) and Ramsey (1931).

At the very least, it seems that Keynes in this passage was conceding that probability defined as an “objective relation between propositions” as perceived by human intuition was unsatisfactory: instead, probability was a “degree of belief.”

The crucial problem is possibly the way in which Keynes had attempted to justify the objective nature of the probability relation by means of a neo-Platonist ontology, a philosophical position which was questionable. According to Fioretti (2003: 135), Keynes himself seems to have grasped the problems of neo-Platonism and abandoned it later in life. One would assume that Keynes’ “recantation” (if it can be called that) was related to this.

But, at the same time, it is difficult to see how the passage constitutes a total capitulation to Ramsey and endorsement of Ramsey’s subjectivist theory of probability.

Keynes states that

“But in attempting to distinguish ‘rational’ degrees of belief from belief in general he was not yet, I think, quite successful. It is not getting to the bottom of the principle of induction merely to say that it is a useful mental habit. Yet in attempting to distinguish a ‘human’ logic from formal logic on the one hand and descriptive psychology on the other, Ramsey may have been pointing the way to the next field of study when formal logic has been put into good order and its highly limited scope properly defined.”

For Keynes, induction remains something more than a “useful mental habit”: that is, induction still belongs to some aspect of logic.

BIBLIOGRAPHY
Fioretti, G. 2003. “No Faith, No Conversion: The Evolution of Keynes’s Ideas on Uncertainty under the Influence of Johannes von Kries,” in Jochen Runde and Sohei Mizuhara (eds.), The Philosophy of Keynes’ Economics: Probability, Uncertainty and Convention. Routledge, London and New York. 130–139.

Keynes, John Maynard. 1931. “Ramsey as a Philosopher,” The New Statesman and Nation, 3 October.

Keynes, John Maynard. 1963. “F. P. Ramsey 1903–1930,” in John Maynard Keynes, Essays in Biography (new edn.). Norton, New York. 239–254.

McCann, Charles R. 1994. Probability Foundations of Economic Theory. Routledge, London.

Ramsey, Frank. P. 1922. “Mr. Keynes on Probability,” Cambridge Magazine 11.1: 3–5. [Reprinted in Ramsey 1989.]

Ramsey, Frank. P. 1931. “Truth and Probability,” in Frank. P. Ramsey, The Foundations of Mathematics and Other Logical Essays (ed. by R. B. Braithwaite). Kegan Paul & Co., London. 58–100.

Ramsey, Frank. P. 1989 [1922]. “Mr Keynes on Probability,” British Journal for the Philosophy of Science 40.2: 219–222.