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

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 in Part II of the TP. The only exception was for areas of application that involved his Principle of Indifference and relative frequencies that had passed an application of the Lexis-Q test for the stability of the frequency, an early version of exploratory data analysis and /or goodness of fit tests. Keynes’s inductive logic in Part III of the TP is built directly on the method of inexact measurement and approximation of Part II of the TP. This involves Keynes’s use of a modified version of Boole’s Problem X that he solved on pp.192-194 of the TP and used on pp. 233-238 and 254-257 of Part III. 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 TP, Keynes’s work in Part III of the TP is then a prerequisite for his work in Part V of the TP. We can now see that it is impossible to grasp Keynes’s work in Part III of the TP unless Part II of the TP is understood first, and it is not possible to grasp Part V unless Part III of the TP has been digested. Heterodox economists, in general, study only chapters I-III, IV and VI of Part I of the TP. No Heterodox economist has ever studied Part II of the TP where Keynes covers Boole’s contributions in the appendix to chapter XIV, XV, XVI and XVII. III. O n C arabelli’s A ssessment of K eynes’s V iews on L ogic as P resented in H is tp What is any reader to make of the following assessments of Keynes’s inexact/imprecise approach to mathematics and logic based on Boole made by Carabelli? “3.1.1. Keynes’s view of probability, whose basic aspects were considered in the previous chapter, was centred (sic) on some general key doctrines. As I have already noted, these doctrines were not always explicit and expressed in univocal and coherent form. Hence the necessity not only of a close reading of Keynes’s text, but also of a sort of systematic reconstruction of Keynes’s approach to key epistemological topics, together with an attempt to clarify his position within its historical intellectual context. Such a task, which will be attempted in the present section, will enable one, for instance, to grasp the fact overlooked in a superficial reading of the Treatise, that Keynes (as we will see in Chapter 8) did not usually adopt the term ‘logical’ in the sense of formal logic, but in the sense of ordinary language logic, that is, in a sense which was actually antithetical to it. This explains the above-mentioned uncritical ranking of Keynes within the so-called logicist approach to probability.” (Carabelli, 1988, p.23). Contrary to Carabelli, Keynes makes it clear that he is building on Boole in Part II of the TP. Her major conclusion is the following one: "...the logicist interpretation of Keynes's theory appears to be based on a hasty reading of Keynes's text. In various passages Keynes did indeed speak of the "logical “character of his notion of probability. But this fact does not mean that...it was a logic of the formal type. In fact, it was an ordinary discourse logic."(Carabelli, 1988, p.145). The only citation that Carabelli can offer is a complete misinterpretation and misunderstanding of what Keynes is doing in the TP, which is building on Boole’s relational, propositional logic. Keynes is not deploying an “ordinary discourse logic”: “In the ‘Treatise’ the priority of ordinary language over mathematical language was unquestioned. ‘I shall not cut myself [sic]’, Keynes wrote, ‘from the convenient’ but looser, expressions which have been habitually employed by previous writers and have the advantage of being. immediately intelligible to the reader’. In the footnote, he praised ordinary language, in terms of its semantical character, contrasting it to the pure syntactical one of artificial mathematical language (Keynes, 1921, pp. 18-19).” (Carabelli, 1985, p.166) Carabelli completely bypasses the rest of chapters I and II, which are directly based on chapters I, XI and XII of Boole’s The Laws of Thought. In fact, what Keynes is saying is that his exposition in the TP will not be based on the same rigor as Russell’s work and not what is claimed by Carabelli below: “Just for its organic characteristics, its open structure and the non-finite number of propositions, its compatibility with contradiction and its semantical character, ordinary language permitted one to deal with phenomena presenting [sic] the attribute of complexity”. (Carabelli, 1985, p.166) Carabelli has not changed her views in nearly 35 years. In her latest contribution in 2021, we find the same claims made in 1988 in her following statements made about Keynes’s approach in 2021: “He…prefers ordinary discourse…He is interested in exactness, not precision.” (Carabelli, 2021, p.8-the reader should note that exactness is precision)) and “My interpretation of Keynes’s method stresses his logical way of reasoning as a non -demonstrative logic, based on his concept of probability, persuasion and ordinary language.” (Carabelli, 2021, p.10) and “Keynes belongs to the tradition of Aristotelian practical reasoning and (justified) realistic common sense…using ordinary language.”(Carabelli, 2021, p.15). There is simply no support anywhere in Keynes’s TP for any of Carabelli’s claims, as Keynes’s non demonstrative logic is identical to Boole’s formal, mathematical, symbolic, relational, propositional logic Volume XXIII Issue VI Version I 2 ( ) Global Journal of Human Social Science - Year 2023 D © 2023 Global Journals Pace Carabelli and Dow, There is No Common Discourse Language Logic in Keynes’s A Treatise on Probability