Published February 13, 2024 | Version v1
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Keynes, a Connoisseur of Boolean uncertainty and the limits of precise numbers


Unfortunately, Jackson Lears’ June, 2023 article and 2023 book on Keynes’s applications  and assessment of uncertainty and animal spirits, respectively, are based on the  erroneous  work of the Post Keynesian school of economics  on uncertainty and animal spirits ,the foundation of which is the severely deficient work of F P Ramsey, I J  Good ,R .Skidelsky ,G L S Shackle and Terrence Hutchison’s  Pseudo Keynesians(Joan Robinson ,Austin Robinson, Richard  Kahn, Roy Harrod). The many, many errors in Ramsey’s two reviews of 1922 and 1926 or in  I J Good’s published work on Keynes between 1950-1990, concerning Keynes’ s logical theory of probability ,or in any article published by a Post Keynesian or heterodox economist , on Keynes’s 1921 A Treatise on Probability, are easily identified by any reader  of Keynes’s A Treatise on Probability .Of course, this requires the reader to have been familiar with Keynes’s use of (a) Boole’s formal, mathematical, symbolic , relational ,propositional logic, introduced in chapters I and II of the A Treatise on Probability ,and which  permeates Keynes’s A Treatise on Probability,(b) Keynes’s imprecise view of probability ,based on Boole’s lower and upper ,interval valued probability ,and (c) Keynes’s views on animal spirits ,which follow directly from Keynes’s understanding of Boole’s treatment of this topic in his The Laws of Thought.

The main problem with all heterodox accounts of Keynes’s approach in his A Treatise on Probability /General Theory is their complete and total ignorance of Keynes’s Boolean based approach that Boole put forth in 1854 in his The Laws of Thought. Keynes always, in general, rejected mathematical expectations as unreasonable ,but he never ,ever propounded the Post Keynesian and Heterodox claims about basing decision making on  comparative or ordinal probability. Keynes’s emphasis was on inexact measurement and approximation through the use of interval valued probability and/or decision weights, such as his conventional  coefficient ,c. We can call Keynes’s approach to expectations “Logical “ or “Boolean “ expectations. Until this fundamental, basis fact is acknowledged by Post Keynesians and Heterodox economists, it will impossible for them  be able to grasp what Hishiyama termed ,in 1969,Keynes’s “new logic of uncertainty.” ,which has nothing to do with the Carabelli-Dow dual of an ordinary ,common, discourse logic and the Skidelsky-Moggridge-Lawson-Carabelli-O’Donnell clams about ordinal probability .Keynes’s logical expectations  has everything to do with Boole’s formal, mathematical, symbolic relational, propositional logic and interval valued probabilities. Of course , this will not happen ,given the failure of Heterodox -Post Keynesian economists  to read The Laws of Thought and  A Treatise on Probability.



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