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

Boole’s discussion on pp.242, 272 in Boole’s The Laws of Thought (1854). Consider the following statement: “The reason that the investment decision relies on animal spirits is that rational quantitative calculation alone cannot justify action under uncertainty. This argument, building on Keynes’s Treatise on Probability, provides the basis for the broader interpretation of animal spirits in the Post Keynesian literature, one captured by Kregel (1987) in the term ‘rational spirits.” (Dow and Dow, 2011, p.6). Again, there is nothing in Keynes’s TP even remotely related to what Dow and Dow are claiming, which is why there are not any citations to any pages or paragraphs from the TP. Keynes follows G. Boole’s interval valued approach ,which Keynes covered in chapters 15 ,16,and 17 of the TP. Chapters I and II of the TP are Keynes’s versions of Boole’s chapters I ,XI, and XII . The investment decision DOES NOT rely on animal spirits. It is based on Keynes’s non numerical probabilities (Boole’s interval probabilities) and Keynes’s Evidential Weight of the Evidence. In cases of decision making under Ignorance, decisions makers put off making a decision and remain liquid. The broader “interpretation” of Keynes’s extremely brief coverage of animal spirits in the Post Keynesian literature has nothing to do with Keynes and has nothing to do with Keynes’s TP. “As Carabelli (1988: 237) puts it: ‘What he [Keynes] appeared to think was that different types of rationality, or rules of reasonableness, existed, according to the different cognitives [sic] domains, which characterized the different economic groups.’ Since animal spirits enter into the perception of uncertainty surrounding knowledge, they affect the process of judgement (Davis 2003).” (Dow and Dow, 2011, p.9) The claims of Dow and Dow, based on Carabelli, have nothing to do with Keynes’s use of Boole’s relational, propositional logic in his TP. This relational, propositional logic is a mathematical, formal, symbolic logic, which Dow and Dow have absolutely no understanding of. It is objective because the decision maker is able to assign a rational degree of belief based on the content of the h and the a propositions, where the h propositions supply the evidence to support the a proposition conclusion. It doesn’t matter whether the facts are different or perceived differently by different decision makers. Relative to their choice of what counts as evidence, they will be able to identify a rational degree of belief, expressed either an a numeral or an interval. This has nothing to do with some amorphous, ordinary language logic. V. T he D ow and C hick C laims about K eynes’s “ A nti- F ormalist” P osition C ompletely and T otally I gnores the B oole – K eynes C onnection This section will be divided into two subsections, (5a) and (5b).(5a) will cover Chick and Dow while (5b) will cover Chick . (5a) Chick and Dow (2001) The work of Chick(1998) and Chick and Dow (2001) is based directly on Carabelli (1988).Chick and Dow make exactly the same identical mistake made by Carabelli in 1985 and 1988 ,which is to skip the Boolean foundation of Keynes’s inexact method and substitute a claim that Keynes was engaged in some type of ordinary language logic. Such a “logic” appears nowhere in the TP and is not mentioned anywhere by any reviewer of the TP. Every reviewer of the TP who mentioned the word “logic” in the TP recognized it as a formal, mathematical logic, although they all failed to connect Keynes’s approach to Boole and incorrectly concluded that Keynes had developed some new type of logical analysis that depended on intuition. In the Treatise on Probability, Keynes sought a “…logic …to be applicable to everyday belief and action, as well as to ’scientific ‘knowledge and resulting policy recommendations. In the common sense tradition…based on(ordinary) logic…Ordinary logic in turn generates knowledge which is imperfect, partial or vague…Thus, an organicist understanding of the subject matter justifies the adoption of an ordinary (human) logic…” (Chick and Dow, 2001, p.711). Such an ordinary human logic exists nowhere in the TP or GT. It apparently is based on a misquotation and misunderstanding of Keynes’s initial, introductory statements made in chapter II of the TP on pp.18-19, which is what is cited by Carabelli. (5b) Chick (1998) Chick is completely unaware that Keynes, following Boole, had developed mathematical techniques to analyze “complex “systems long before Zadeh was born. Her ignorance of Keynes’s mathematical approach to probability and statistics, using imprecision, approximation and upper and lower bounds for probabilities that Keynes identifies in his TP as inexact measurement, can be seen in her next assessment of Keynes’s TP: “Keynes accepted the fact of irreducibly limited and imperfect knowledge, and warned against misplaced precision: Much economic theorizing to-day suffers, I think, because it attempts to apply highly precise and mathematical methods to material which is itself much too vague to support such treatment. (Keynes, CW XIV, p. 379.) Our precision will be a mock precision if we try to use such partly vague and non-quantitative concepts [net real output and the general price level] as the basis of a quantitative Volume XXIII Issue VI Version I 4 ( ) 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