# The Claim That the Diagram on Page 39 of Keynes’s a Treatise on Probability(1921) Represents ‘Keynes’s View of Probability’ (S. Bradley, 2019), Has No Support: It Represents a Very Brief Introduction to Part II of Keynes’s a Treatise on Probability On Non Additive Probability

26 Pages Posted: 5 Feb 2020

Date Written: January 13, 2020

### Abstract

A major error in analyzing how Keynes operationalized his logical theory of probability in 1921 is to assume that Keynes’s theoretical structure is presented by him at the end of Chapter III of the A Treatise on Probability on pp. 38-40, which contains a diagram on page 39 that Keynes himself characterized as being a “brief” illustration that would be supplemented later with a “detailed" analysis in Part II. Economists, who have written on Keynes’s A Treatise on Probability, such as G. Meeks, D. Moggridge, R. Skidelsky, R. O’donnell, A. Carabelli, A. Fitzgibbons, and many, many others, have erred by failing to cover Keynes’s non additive, non linear approach, using Boole’s interval valued probability, which is based on lower and upper probability bounds and represents a detailed approach to imprecise probability, in Parts II and III of the A Treatise on Probability. Instead, it is erroneously argued, on the basis of this diagram alone, that Keynes’s approach was an ordinal theory that could only be implemented some of the time.

No philosopher has ever made this error until the publication of an article in 2019 by S. Bradley in the Stanford Encyclopedia of Philosophy dealing with the origins of Imprecise Probability. The contributions of the founders of the imprecise approach (Boole and Keynes would use the word ‘indeterminate’) are simply either skipped over, as in the case of Boole, or completely misrepresented, as in the case of Keynes.

**Keywords:** Boole, Keynes, interval valued probability, upper-lower probability bounds, non additivity, imprecise probability

**JEL Classification:** B10, B12, B14, B18, B20, B22

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