On the Very Severe Contradictions, Inconsistencies, and Confusions in the Assessment of Keynes’s Logical Theory of Probability in the A Treatise on Probability by Heterodox Economists: J.M. Keynes Showed That Incommensurability Is Dealt with by Interval Valued Probability

Very severe contradictions, inconsistencies, and confusions exist in the exchanges between two Heterodox economists, who are considered to be the top Heterodox experts on Keynes’s A Treatise on Probability, logical theory of probability, and of the connections between the A Treatise on Probability and Keynes’s General Theory.

The exchanges between Sheila Dow and Anna Carabelli in 2015 show that they had no coherent understanding about the meaning of incommensurability (non comparability, nonmeasurability, incomparability) as was discussed by Keynes on pp. 30-34 of the A Treatise on Probability in 1921.

The standard assessment ,accepted by SIPTA and all philosophers who have written on Keynes’s contributions since 1921, with the exceptions of F Y Edgeworth, Bertrand Russell, and C D Broad, was made in 1999 by H E Kyburg in the initial SIPTA conference volume in 1999. He stressed that Keynes’s discussions imply a partial order, which means comparability based on measurement by a single precise probability is impossible in many cases. However, imprecise (interval valued probabilities with upper and lower bounds) probability can be used to deal with both cases where there is partial and/or conflicting evidence.

However, while acknowledging that Keynes had a number of valuable “notions ,intuitions, ideas, suggestions, hints or insights” about imprecise probability that were represented by Keynes’s term, ”non numerical probabilities”, Kyburg and SIPTA members argue that Keynes never provided any mathematical or logical modeling of any type in the A Treatise on Probability at all that would allow a decision maker to specify interval valued probabilities.

I have argued continuously since 1979 that Keynes did provide a clear cut mathematical structure for his ‘non numerical‘ probabilities in Parts II, III, IV, and V of the A Treatise on Probability. A study of the Dow and Carabelli exchanges (1) of 2015 show that Dow and Carabelli do not even accept the Kyburg-SIPTA position.

(1) I want to thank a student at Cambridge University,England,for making the Dow-Carabelli exchange available to me. I could not have written the paper without this information.