Keynes’s Method Has Nothing to Do With a Common Discourse or Ordinary Language Logic: Keynes’s Method, Which Involved the Use of Inexact Measurement in Probability and Statistics, Based on Approximation, Was Based Directly on Boole’s Mathematical Logic and Algebra

Abstract

It is impossible to correctly grasp Keynes’s method of analysis in the A Treatise on Probability in 1921 if the work of G Boole is ignored. Unfortunately, all Post Keynesian, Institutionalist and Heterodox economists , who have published work on Keynes in the 20th and 21st centuries, have done just that. 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 that was based on a logic of propositions about events or outcomes and not the events or outcomes themselves. This logic is a mathematical logic and has absolutely nothing to do with an ordinary discourse human logic, which involves the use of a common sense language between humans.

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 unique, unclear and peculiar approach to analysis based on intuition 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 and still write Parts II and V of the A Treatise on Probability, which provide formal, mathematical, and logicist underpinnings to his approach of Inexact measurement and Approximation that leads directly to Keynes’s specification of lower and upper bounds on all probabilities and outcomes except for areas of application involving his Principle of Indifference and relative frequencies that have passed an application of the Lexis-Q test (exploratory data analysis and /or goodness of fit tests).

Keynes’s inductive logic of Part III of the A Treatise on Probability is built directly on the method of inexact measurement and approximation of Part II of the A Treatise on Probability. This involves Keynes’s use of a modified version of Boole’s Problem X that he solved on pp.192-194 of the A Treatise on Probability and used on pp.234-237 and 254-257. Keynes’s development of the concept of finite probability, applicable to both numerical and non numerical probabilities, was a necessary prerequisite for understanding Keynes’s work in Part III on induction and analogy. Given Keynes’s work on the relationship between probability and induction in Part III of the A Treatise on Probability it is impossible for Keynes to have been a rationalist, as claimed by R.O.Donnell.

Keynes’s work in Part III of the A Treatise on Probability is then a prerequisite for his work in Part V of the A Treatise on Probability.

We can now see that it is impossible to grasp Keynes’s work in Part III of the A Treatise on Probability unless Part II of the A Treatise on Probability is understood and it is not possible to grasp Part V unless Part III of the A Treatise on Probability has been digested. Heterodox economists, in general, study only chapter III of Part I of the A Treatise on Probability. No Heterodox economist has ever studied Part II of the A Treatise on Probability.