Sunday, July 14, 2013

Moggridge on Keynes’s Theory of Probability

Keynes’s Treatise on Probability was published in 1921, but had grown out of the intellectual issues raised by G. E. Moore’s Principia Ethica. Probability theory had occupied a considerable part of Keynes’s time between 1906 and 1914. His first discussion of the subject can be dated to 23 January 1904, in a paper called “Ethics in Relation to Conduct” read before the Apostles (Skidelsky 1983: 151–152), and his work in probability was originally an attempt to refute one of Moore’s ideas in the Principia Ethica (Moggridge 1992: 118).

In fact, during Keynes’s work as a junior clerk in the Military Department of the India Office and the Revenue, Statistics and Commerce Department (from March 1907), he spent his spare time writing a thesis on probability theory (Skidelsky 1983: 177). On 12 December 1907, he handed in his dissertation on probability, and it was examined by W. E. Johnson and Alfred North Whitehead (Skidelsky 1983: 182).

On the strength of Alfred North Whitehead’s (1861–1947) opinion of a revised version of Keynes’s dissertation, Keynes was elected in March 1909 to a prize fellowship at King’s College, Cambridge (Skidelsky 1983: 204; Moggridge 1992: 185). However, the First World War and post-war issues intervened and it was not until 1921 that Keynes published a book on the subject.

Moggridge (1992: 143–166) gives a brief account of Keynes’s theory of probability.

Keynes held that science was concerned not only with certain knowledge but limited knowledge (Moggridge 1992: 145). The latter was concerned with the probability of inferences not absolutely certain, but the knowledge obtained Keynes did not regard as subjective (Moggridge 1992: 145).

Keynes held that probability was a property of propositions, and that an inferred proposition is probable only in relation to other propositions that function as premises. The logic of probability was the logic of rational belief (Moggridge 1992: 145–146).

Moggridge (1992: 146–147) sees Keynes doctrine of probability as having five elements:
(1) his conception of knowledge;
(2) the notion of probability as indefinable;
(3) the often non-numerical non-comparable nature of probabilities;
(4) the way in which preference, judgement, indifference, relevance or irrelevance in determining the preferability of one of a set of probabilities is the basis for belief, and
(5) the idea of the weight of argument.
In Chapter 3 of the Treatise on Probability, Keynes was clear that numerical values cannot be given to every proposition in an inductive argument (Moggridge 1992: 149).

In Chapter 4, discussed the “principle of indifference” (his term for the “the principle of non-sufficient reason”) limited domain of mathematical probabilities where numerical values can be given.

In Chapter 6, Keynes turned to what he called “weight of arguments,” which depended on the absolute amount of evidence available.

Part III of the Treatise (Chapters XVIII–XXIII) was devoted to induction and analogy, and Keynes also attempted to solve Hume’s problem of induction (Moggridge 1992: 157).

The last seven chapters of the Treatise (Part V) were devoted to statistical inference.

Moggridge, D. E. 1992. Maynard Keynes: An Economist’s Biography. Routledge, London.

Skidelsky, R. J. A. 1983. John Maynard Keynes: Hopes Betrayed 1883–1920 (vol. 1). Macmillan, London.


  1. Have you read any of the reviews that were published within a few years after A Treatise on Probability was published? You might want to take a look at Bertrand Russell's review, C.D. Broad's review, Sir R.A. Fisher's review, and E.B. Wilson's review.

    1. I have not read them, but might add them to the bibliography on Keynes and probability as a note to do so sometime!