On Kyburg's assessments of Keynes's graphical, interval valued and lattice representations of probability in Chapter III on page 39 of his A Treatise on Probability

Kyburg’s periodic assessments of Keynes’s contributions to imprecise probability, interval valued probability, and decision making under uncertainty from 1959 till 2010 suffered from three major problems that Kyburg was never able to overcome in his lifetime. These three problems are the same three problems faced by all members of SIPTA, all papers published in the Journal of Approximate Reasoning that deal with and/or mention the work of JM Keynes since its inception, as well as all heterodox and orthodox economists, especially Post Keynesians like B. Bateman,J. B Davis , T. Lawson ,J. Runde  and R. Skidelsky.

The three reasons are

·         A complete and total ignorance of the work of G Boole in his The Laws of Thought (1854) concerning logical probability, interval valued, imprecise probability and the relational, propositional (sentential) logic developed by Boole

·         A complete and total ignorance of the Boole-Keynes connection. This can only be grasped through a reading of Parts II and III of Keynes’s A Treatise on Probability or grasping Keynes’s footnote 2 on p.5 of the A Treatise on Probability

·         A concentration on chapters III, IV and VI of Part I of Keynes’s A Treatise on Probability. Kyburg was not nearly as successful as F Y Edgeworth. Edgeworth, but not Kyburg, realized that Keynes’s theory was based on lower and upper probability intervals. Edgeworth was able to focus on Keynes’s emphasis on the word “between” in chapter III of his A Treatise on Probability in which Keynes spent a great deal of effort discussing his interval valued approach, where Keynes’s emphasis and focus was on the phrase” between two numbers (Keynes’s italics).” Once this emphasis by Keynes is grasped, then a reader of Keynes’s work is in a position to realize that Keynes is using interval valued probability.

Despite these deficiencies, Kyburg was able to reject practically all of Ramsey’s ludicrous claims that he made about Keynes’s logical theory of probability because Kyburg understood Keynes’s graphical presentation of interval probability in chapter III on page 39 of the A Treatise on Probability. Thus, although Kyburg’s assessment is not of the same quality and depth as Edgeworth’s, it is more than sufficient to lead to the rejection of the F P Ramsey critiques in 1922 in Cambridge Magazine and in “Truth and Probability “in 1926.

All past and current academic “interpretations” of Keynes’s diagram, with the exception of  Kyburg’s correct analysis , claim that the diagram on page 39 is a representation of ordinal probability. This makes no sense, as an ordinal approach allows one to conclude only that one probability is either > or < than another probability.

Kyburg presented his lattice structure analysis of Keynes’s diagram on p.39 four times -in 1995,1999, 2003, and 2010.All four papers are nearly identical. This paper thus relies on the 2010 paper exclusively.