Global Journal of Human Social Science, D: History, Archaeology and Anthroplogy, Volume 23 Issue 6

Pace Carabelli and Dow, There is No Common Discourse Language Logic in Keynes’s A Treatise on Probability Michael Emmett Brady Abstract- 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 20 th and 21 st centuries. Dow and Carabelli are not alone in their confusions. For another example, R. O’Donnell (See O’Donnell, 1989, 1990 a, b) is another economist who completely overlooked that all of the foundations of Keynes’s logical approach to probability are to be found in Boole’s The Laws of Thought (1854). Contrary to O’Donnell, it is Boole, not Keynes, who developed the first technically advanced, logical theory of probability in history. I. I ntroduction he paper will be organized in the following manner. Section Two will cover Keynes’s relational, propositional logic as introduced by him in chapters I and II of the A Treatise on Probability, while simultaneously demonstrating that Keynes is using Boole’s basic approach. Section Three will examine Carabelli’s claims that Keynes’s logic is NOT a mathematical one, but a common discourse logic (rhetoric). Section Four will examine Dow’s very similar claims. Section Five will cover Chick’s claims about Keynes’s common discourse logic. Section Six will conclude the paper. II. K eynes’s F ormal A pproach to L ogic in H is a T reatise on P robability Pace Carabelli and Dow, there is no common discourse logic in Keynes’s A Treatise on Probability (TP, 1921). All Post Keynesian, Institutionalist and Heterodox economists, as well as all orthodox economists, who have published work on Keynes in the 20 th and 21st centuries, have simply overlooked Boole’s contribution to the basic foundations of Keynes’s work. George Boole, and not J M Keynes in his 1921 A Treatise on Probability , put forth the first technically advanced, mathematical and logical treatment of a logical theory of probability in 1854 in his The Laws of Thought (LT,1854). It was based on a logic of propositions about events or outcomes and not the events or outcomes themselves. Boole’s logic is a mathematical logic and has absolutely nothing to do with an ordinary discourse human logic, which involves the use of commonsense language between humans or the intuitionism/Platonic, metaphysical speculation currently dominant in discussions in academia about Keynes. Given that Keynes built his A Treatise on Probability directly on the mathematical and logical approach and foundation of G Boole’s Boolean algebra and logic, it is simply impossible for Keynes’s approach in his A Treatise on Probability to have been based on a logic of ordinary language as claimed by Carabelli (1985, 1988, 2003), Chick (1998), and Chick and Dow (2001). Keynes is supposed to have had some kind of a unique, unclear and peculiar approach to logical analysis, which was supposed to have been based on an intuitive approach that can’t be discerned, according to Anna Carabelli (1985, 1988, 2003) and other heterodox economists. Carabelli argues that Keynes was anti-logicist, anti-empiricist, anti-positivist, anti- rationalist, and anti-formalist in his method, as well as being anti-mathematical. It is quite impossible for Keynes to have opposed all of these positions completely and still write Parts II, III and V of the A Treatise on Probability , which provide formal, T © 2023 Global Journals Volume XXIII Issue VI Version I 1 ( ) Global Journal of Human Social Science - Year 2023 D Author: Adjunct Lecturer, California State University, Dominguez Hills, College of Business Administration and Public Policy, Department of Operations Management, 1000 East Victoria St Carson, California USA. e-mail: mandmbrady@juno.com