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An Examination of Some Possible Explanations for the Existence of the ‘Mystery’ Concerning the Only Diagram in the A Treatise on Probability on Page 39 (Page 42 of the 1973 CWJMK Edition)

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Abstract: Professor Yasuhiro Sakai’s important 2016 contribution concerning the nature of Keynes’s contribution in his 1921 A Treatise on Probability summarized the general academic view that there was a great mystery about the nature of Keynes’s illustration, about his non-numerical probabilities in his diagram on page 39 in chapter III of A Treatise on Probability, concerning the operational capabilities of Keynes’s analysis of probability.In fact, Keynes had made it very clear on pp.37-38 of chapter III of A Treatise on Probability that a "detailed " analysis would be presented only in Part II of the A Treatise on Probability. What he presented in the diagram on page 39 was only a “brief” summary of conclusions that would be supported in a technical manner in Part II. The particular chapter that incorporates Keynes technical, detailed analysis was chapter XV of the A Treatise on Probability. Keynes explains exactly what his system of analysis involves on pp.159-160 and then provides a detailed analysis on pp.161-163. Keynes’s analysis demonstrated that his system of analysis is primarily an interval-valued one. It is not an ordinal system. For example, Carabelli (1988, 2003), Fitzgibbons (2003), and O’Donnell (2012, 2014) all rely completely on the “mysterious” diagram on page 39 of the A Treatise on Probability to support their main conclusion, which was that Keynes’s theory of probability was an ordinal one, at best. There is no support or discussion anywhere in the A Treatise on Probability for their conclusion, which directly conflicts with the analysis provided by Keynes in chapter 15 of the A Treatise on Probability, as well as Keynes’s explicit statements on pp.37-38 that no detailed analysis of his theory of measurement will be provided in chapter III of the A Treatise on Probability.This paper examines a number of possible explanations for this erroneous conclusion. Explanations range from mathematical confusion on the part of the Post Keynesian school and the Keynesian Fundamentalists to the acceptance of Ramsey’s very poor book reviews to an ignorance of the 1922 book reviews of F.Y. Edgeworth, Bertrand Russell, and C D Broad, as well as the failure to grasp Emile Borel’s review of 1923, in which he apologizes to Keynes (and Russell) at the very beginning of his review about his decision to ignore Part II of the A Treatise on Probability, which Borel acknowledged was the most important part of the book.Keynes’s interval-valued approach has never, ever been grasped, except by a very, tiny, handful of academics. The reason is that the vast majority of readers can’t follow Keynes in chapter 15 of the TP, in particular, or Part II, in general. It has been 98 years since Keynes published the TP and 111 years since he submitted his 1908 Fellowship Dissertation to Cambridge University, which has the same Part II analysis in it as the TP in 1921. There simply is no textual support in the TP for the belief that Keynes’s theory was an ordinal one. All of the evidence demonstrates that it was an interval one.

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