An Examination of the Fundamental Reasons Why Frank Ramsey Failed in His Reviews of J M Keynes's a Treatise on Probability

26 Pages Posted: 8 Mar 2017

See all articles by Michael Emmett Brady

Michael Emmett Brady

California State University, Dominguez Hills

Date Written: March 5, 2017


Frank P Ramsey did not consider the possibility of representing the concept of probability by an interval valued approach in his lifetime. Ramsey considered probability to be either ordinal or numerical. There was absolutely no room for interval estimates and interval probability in his approach. It is mentioned nowhere in any of his published or unpublished work. Ramsey was not familiar with the applied work done by George Boole on interval valued probability.

Ramsey believed only in the standard mathematical theory of probability. The crucial assumption for Ramsey was additivity. Of course, Keynes rejected additivity except as a special case. This is the major difference between Ramsey and Keynes. Keynes believed it obvious that there is missing relevant evidence or knowledge in many decisions made by human beings. Non addiitvity immediately leads to uncertainty. Uncertainty requires the existence of non additivity.

Keynes made it explicit in Part II of the A Treatise on Probability that additivity was a special case and not the general case. Unfortunately, Ramsey could not follow Keynes’s analysis in Part II of the TP. This, for instance, was a severe problem also for both F Y Edgeworth and E B Wilson. However, Edgeworth figured out that Keynes’s “non numerical” probabilities were interval valued by means of a very careful reading of Chapter III of the TP. It is very probable that Edgeworth also had the benefit of many private discussions with Keynes between 1909 and 1920 when both men were co-editors of the Economic Journal. Unfortunately, Ramsey’s conclusion was that Keynes’s “non numerical probabilities” were ordinal probabilities. Economists have mistakenly followed Ramsey’s assessment and ignored Edgeworth’s vastly superior assessment of the interval valued nature of Keynesian probability.

The major defect in the CWJMK version of the A Treatise on Probability is that the editorial foreword was written by a rabid proponent of Ramsey’s belief in additivity, Richard Braithwaite. Anyone reading this editorial foreword before he/she reads the A Treatise on Probability will be completely biased against Keynes’s technical analysis in the A Treatise on Probability. The only existing antidote to Braithwaite’s “review” is the two combined reviews of Edgeworth, who provided, overall, the best reviews ever written of the A Treatise on Probability and Bertrand Russell’s review. In fact, I had to use Edgeworth’s two reviews to buttress my case in support of my dissertation with one of my dissertation committee members.

Keywords: interval valued probability, approximation, interval versus comparative probability, Edgeworth, Russell

JEL Classification: B10, B12, B14, B16, B20, B22

Suggested Citation

Brady, Michael Emmett, An Examination of the Fundamental Reasons Why Frank Ramsey Failed in His Reviews of J M Keynes's a Treatise on Probability (March 5, 2017). Available at SSRN: or

Michael Emmett Brady (Contact Author)

California State University, Dominguez Hills ( email )

1000 E. Victoria Street, Carson, CA
Carson, CA 90747
United States

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