# Why the Edgeworth and Russell Reviews of the a Treatise on Probability Are So Vastly Superior to the Two F.P. Ramsey Reviews: Edgeworth and Russell Both Recognized Keynes's Interval Valued Concept of Probability While F. P. Ramsey Completely Failed to Comprehend the Most Basic Concepts of Interval Valued Probability

56 Pages Posted: 21 Dec 2017

Date Written: December 18, 2017

### Abstract

Both F. P. Ramsey reviews of J M Keynes’s A Treatise on Probability demonstrate an abysmal lack of understanding on Ramsey’s part of Keynes’s Boolean concept of upper and lower probabilities. Ramsey had absolutely no idea about what an interval valued concept of probability was or how an axiomatic treatment of such a probability concept would have to proceed. Ramsey had no idea about what an imprecise and/or indeterminate probability was. The same problem arises with respect to the two articles by Richard Braithwaite on Keynes’s A Treatise on Probability. Even more lacking was Braithwaite’s Foreword to Volume 8 of the CWJMK version of the A Treatise on Probability published in 1973. Braithwaite commentary in this foreword simply shows that he does not have a clue about what an interval valued probability would be. Both Braithwaite and Ramsey could only understand what an ordinal and a cardinal (numerical) probability was. On the other hand, both Edgeworth and Russell dealt explicitly in their reviews of the A Treatise on Probability with Keynes’s concept of interval valued probability. Unfortunately, none of the heterodox Post Keynesians or “Fundamentalist” Keynesians and Institutionalists (Skidelsky, O’Donnell, Carabelli, Fitzgibbons, Lawson, Meeks, Runde, S.Dow, T. Raffaelli, Gillies, Mellor, etc.) ever read Edgeworth’s or Russell’s reviews of the A Treatise on Probability. What they read, instead, was Ramsey’s and Braithwaite’s works, which never mentioned interval valued probability because they had no idea about what an interval valued probability concept was. Keynes, as expected, wasted none of his very valuable time in replying to such individuals, since all they had to do was read Russell and Edgeworth.

This would explain why such individuals, heavily concentrated in the Economics and Philosophy Departments at Cambridge University, England, are unable to deal with Keynes’s concept of interval valued probability and constantly confused ordinal probability with interval valued probability.

Entire books have been written on Keynes, probability, uncertainty, and decision making where no mention is made of Keynes’s interval valued approach to probability,Boole ,upper and lower probabilities, and Keynes’s indeterminate or imprecise probabilities because Ramsey was totally ignorant of even a concept of interval valued probability.

One example is the 2003 book, titled “The Philosophy of Keynes’ Economics”, by Runde and Mizuhara. It will soon become apparent to the reader of this book that the reviews by Ramsey play an inordinate role in the assessment of Keynes’s TP. Over half of the 19 articles published in the Runde–Mizuhara book place the Ramsey reviews at the center of their evaluation of Keynes’s logical theory of probability. Correspondingly, there is no mention of the Edgeworth, Broad, or Russell reviews that DID discuss Keynes’s interval valued approach to probability or Boole. Interval valued Probability, in both the imprecise form and indeterminate form, are the major accomplishment of the TP. Edgeworth, Russell, and Broad succeeded in pointing this out in their reviews. Ramsey and Braithwaite completely failed to correctly assess Keynes’s interval valued approach.

**Keywords:** ramsey, Keynes, Broad, Russell interval valued probability, indeterminate prob., imprecise prob.

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

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