Pace Carabelli and Dow, There is No Common Discourse Language Logic in Keynes’s A Treatise on Probability

For 45 years both A Carabelli and S Dow have been arguing that Keynes s non demonstrative logic in the A Treatise on Probability is a common discourse logic rhetoric They provide no textual evidence anywhere in Keynes s A Treatise on Probability to support this claim They have never supported through the citation of specific pages or paragraphs in Keynes s book their claims that Keynes s logic is NOT a formal logic What is in the A Treatise on Probability is a version of Boole s relational propositional logic that Keynes combined with a first order predicate logic These are mathematical formal symbolic logics They have nothing to do with common discourse logics using the English language A simultaneous reading of chapters I and II of Keynes s book and chapters I XI and XII of Boole s The Laws of Thought lead to one and only one conclusion- Keynes s logic is a formal logic derived from G Boole The only conclusion that follows from Keynes s application of Boolean logics is that Carabelli and Dow have been severely confused for 45 years in what a formal logic is and what a common discourse logic is Given that Keynes s non-demonstrative logic is a formal mathematical symbolic logic the only conclusion possible is that Keynes is a formalist and a logicist who was and is vastly superior to any economist either orthodox or heterodox in the 20th and 21st centurie

Contrary to T. Hirai, Ramsey’s Critiques of Keynes in 1922 and 1926 Were Completely Wrong

This paper covers Harai’s analysis, contained in his section, titled “Keynes as a philosopher”, of Keynes’s logical theory of probability. Harai spends too much of his time repeating Ramsey’s claims about having uncovered serious errors in the structure of Keynes’s relational propositional theory. .For 100 years, Keynes’s logical theory has been interpreted and misevaluated through the eyes of an ignorant 18 year old teenager. The result has been the proliferation and spread of what can be called the “Ramsey myth”.The “Ramsey myth” is that an 18 year old teenager appeared at Cambridge University in 1921.This 18 year old teenager was a genius who wrote a three page review in the Jan., 1922 issue of Cambridge Magazine, which supposedly destroyed, devastated and demolished the logical foundations of Keynes’s A Treatise on Probability, which was his relational, propositional logic founded on Boole’s relational, propositional logic. Russell countered this in his review, but was ignored (See Brady, 2016a). In 1931, it is further supposed that Keynes then capitulated to Ramsey and repudiated his own logical theory of probability, accepting some version of Ramsey’s subjectivist theory. This myth is what Hirai’s paper is based on. It was false in 1921 and it is false today in 2022

Keynes’s Theory, Based on an Imprecise, Interval Valued Approach to Probability, Rejected Ramsey’s Emphasis on the Importance of the Use of Mathematical Expectations in Decision Theory

Keynes spent chapter 12 of the General Theory emphasizing two major points that were extremely important in long run decision making, confidence and expectations. Keynes saw that the technical analysis of the role of confidence in decision making had been overlooked in economics. Keynes corrected this lacuna in the General Theory. Confidence was defined as a function of Keynes’s evidential weight of the argument, V, where V=V (a/h) =w,0?w?1,just as the term “very uncertain”, used three times on p.148 of the General Theory, was defined as a function of a slight amount of information, a definition that is identical to Keynes’s definition of “very uncertain” on p.310 of his A Treatise on Probability. w equaled the degree of the completeness of the relevant information upon which the probabilities were based. Keynes’s definition of V can be found on p.315 of his A Treatise on Probability in chapter 26, titled “The application of probability to conduct”. His discussion of the completeness of the evidence can be found on pp.313-315.The second major point was Keynes’s completely overlooked discussion of the reasonable calculation of probabilities, based on approximate and inexact measures like interval valued probability and his decision weight, c, which he called a conventional coefficient of weight and risk, c, versus the unreasonable calculation of probabilities based on strict or exact mathematical expectations calculations as advocated by Frank Ramsey. The heart of Ramsey’s theory is a reliance on betting quotients and mathematical expectations based on precise probability

Keynes Never Assumed at Any Time in His Life… That All Statements or Proposition Stand in Logical Relation to each other (Misak, 2020, p. 114)

In a review of C.Misak’s2020 biography of F P Ramsey, a reviewer named F. E. Guerra-Pujol assumed that the material contained in Misak’s book on Keynes, as regards Ramsey’s claims about Keynes’s Logical Theory of Probability, on pp. 112-121 and pp.264-273,was true.The problem is that all of the material in Misak’s book dealing with Keynes is wrong, as it is based on claims made by F. P. Ramsey that directly conflicted with Keynes’s application of Boole’s relational, propositional logic