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

that he used throughout the A Treatise on Probability. Keynes’s non -demonstrative logic is NOT a common discourse logic associated with Aristotle. Carabelli’s erroneous understanding of Keynes can be traced back at least to 1985: "…this mixture of anti-empiricism and anti-rationalism was the core of Keynes's peculiar epistemological position and makes it difficult to describe his position in simple terms “(Carabelli, 1985, pp. 151). It is actually quite easy to describe Keynes’s position-it is very similar to Boole’s position, which emphasized inexact measurement, approximation, interval valued probability and a relational, propositional logic. Carabelli’s position is restated in every published contribution she has made in the literature since 1985. On page 145 of Carabelli (1988, p.145), we find the cause of her misclassification of Keynes as being anti-mathematical (Carabeli, 1988, p.140), anti – logicist (Carabelli, 1988, p.10, pp.145-46, 280 and p.134- “What, therefore, was Keynes’s peculiar view on logic…”), anti-formalist (Carabelli, 1988, p.139) and anti-empiricist (Carabelli, 1988, p.94). She completely misrepresents the nature of the Keynes-Boole connection, which underlies the entire TP. She severely misreads paragraph 5 in chapter I of LT and some claimed, unspecified reading from chapter 21 of LT, which actually appears on pages 422-423 in the last chapter of LT, chapter 22. Carabelli severely misinterprets Boole’s linking of mathematical reasoning with correct reasoning as being an anti- Keynes mathematical view, which Carabelli implicitly contrasts with her misbelief that Keynes was anti mathematical. For Boole, logic always came first, and mathematical modeling only came after the nature of the variables being considered was fully understood. This is identical to the position taken by Keynes. In fact, the entire TP is built on Boole’s original logic and algebra. It is no wonder that Carabelli is unable to identify Keynes’s method or views on logic, mathematics and formal exposition correctly, as she is unable to identify what a formal, mathematical, symbolic logic is. IV. S . D ow Consider the following statements by Dow: “… much recent Keynes scholarship has been devoted to outlining the particular, alternative logic that Keynes developed in the Treatise on Probability (Keynes, 1973b). This "human logic" or "ordinary logic" was required to apply to a (nonergodic) world of which most knowledge is held with uncertainty . the economic system is nonergodic. Keynes argued that, in practice (in ordinary life, as in science ), we need to establish reasonable grounds for belief in propositions as the basis for action, in spite of uncertainty. According to his "ordinary logic," we do this by using judgment to combine direct knowledge, indirect (theoretical) knowledge, conventional knowledge, and animal spirits or intuition .” (Dow, 2005, p.387; italics added) and “It is also compatible with Keynes's ordinary logic that combines different sources of knowledge in order to increase confidence in propositions . In modem terminology, it is compatible. with pluralism. Indeed, Keynes was at pains to develop a different logic that was more rigorous in having more direct application to the real world than classical logic. (Dow, 2005, p.388; italics added). Nowhere in Keynes’s A Treatise on Probability is there an ordinary or human logic presented or applied as claimed by Dow. Dow fails to provide a single citation to any page or chapter of Keynes’s book that would demonstrate any support for her contentions. The logic Keynes applied (he never developed any logic) was Boole’s original, relational, propositional logic that he presented in 1854 in The Laws of Thought. Note that in order to discuss and apply the concepts of ergodicity and non -ergodicity, one must accept the limiting frequency interpretation of probability, which was rejected by Keynes except as a special case. Finally, Keynes’s A Treatise on Probability has nothing to do with pluralism or methodological pluralism. The italicized materials in her statements above have nothing to do with Keynes’s Boolean, relational, propositional logic. Dow has simply made all of her claims up, which is why there are no footnotes to any parts or pages of the TP. Let us move on to another article. Consider the following statement: “While closed systems are the province of classical logic, open systems are the province of a broader system of logic – ordinary logic, or human logic, as exemplified by Keynes (1973). While including classical logic as a special case for application under conditions of certainty, ordinary logic can also be applied to conditions of uncertainty, as pertain in open systems.” (Dow 2012, p.1). Again, Keynes’s logic in the TP has nothing to do with some “…broader system of logic – ordinary logic, or human logic, as exemplified by Keynes (1973).” Consider the following statement: “…and referring back to the Treatise on Probability which laid the philosophical foundations for Keynes’s use of the concept. There we argued that animal spirits were a critical element of a framework for decision making under uncertainty which was rational in a broader sense, an argument by which we continue to stand …” (Dow and Dow, 2011, p.1). There is no foundation or mention in Keynes’s TP for animal spirits. Keynes’s two paragraphs, on pp.161-162 of the General Theory (GT), are his attempt to incorporate what he had left out of the TP, as it was strictly of secondary importance and relevance. Keynes’s discussion of animal spirits is equivalent to © 2023 Global Journals Volume XXIII Issue VI Version I 3 ( ) Global Journal of Human Social Science - Year 2023 D Pace Carabelli and Dow, There is No Common Discourse Language Logic in Keynes’s A Treatise on Probability