Keynes’s Theory of Measurement is contained in Chapter III of Part I and in Chapter XV of Part II of the A Treatise on Probability (1921;1973 CWJMK Edition): Keynes Stated That the Exposition in Chapter III of the a Treatise on Probability Was 'Brief', While the Exposition in Chapter XV, Part II, Of the a Treatise on Probability, Was 'Detailed'

Professor Yasuhiro Sakai (see 2016; 2018) has argued that there is an mysterious problem in the A Treatise on Probability, 1921 in chapter 3 on page 39 (page 42 of the 1973 CWJMK edition). He argues that there is an unsolved mystery that involves this diagram that has remained unexplained in the literature. The mystery is that Keynes does not explain what he is doing in the analysis involving the diagram starting on the lower half of page 38 and ending on page 40 of chapter III. In fact, the mystery is solved for any reader of the A Treatise on Probability who reads page 37 and the upper half of page 38 carefully and closely. Keynes explicitly states on those pages that he will give only a brief discussion of the results of his approach to measurement on pages 38-40, but will provide a detailed discussion of his approach to measurement in Part II, after which the brief discussion of the results presented on pp.38-40 will be strengthened. The Post Keynesian (Joan Robinson, G L S Shackle, Sydney Weintraub, Paul Davidson) and Fundamentalist (Donald Moggridge, Robert Skidelsky, Gay Meeks, Anna Carabelli, Athol Fitzgibbons, Rod O’Donnell, Tony Lawson, Jochen Runde) schools of economics, as well as economists, in general, such as Jan Tinbergen and Lawrence Klein, have ignored chapter XV of the A Treatise on Probability. Keynes demonstrates on pp.161-163 of the A Treatise on Probability in chapter XV that his approach to measurement is an inexact approach to measurement using approximation to define interval valued probability, which is based on the upper-lower probabilities approach of George Boole, who discussed this approach in great detail in chapters 16-21 of his 1854 The Laws of Thought. Therefore, the only conclusion possible is that the “mysterious” diagram presented on page 39 of the A Treatise on Probability is an illustration of Keynes’s approximation technique using interval valued probability, since the problem on pages 162-163 of the A Treatise on Probability explicitly works with seven “non numerical” probabilities while the illustration of Keynes’s approach using the diagram on page 39 works with six “non numerical” probabilities and one numerical. It is impossible for the diagram on page 39 to support any claim, as has been done repeatedly for the last 45 years by the Post Keynesian and Keynesian. Fundamentalist schools, that Keynes’s theory was an ordinal theory that could only be applied some of the time. This leads precisely to the wrong conclusion that Keynes was arguing that macroeconomic measurement, in general, was impossible in economics, which was G L S Shackle’s conclusion. An understanding of chapter XV of the A Treatise on Probability explains the conflict that existed between J M Keynes and J Tinbergen on the pages of the Economic Journal of 1939 -1940.The major point of discussion, underlying all of Keynes’s major points, was that Tinbergen’s exact measurement approach, taken from macroscopic physics, using the Normal probability distribution’s precise, exact, definite, linear, additive, and independent probabilities, was not possible given the type of data available in macroeconomics. Only an inexact approach to measurement using imprecise and indeterminate interval valued probability was tenable. An understanding of chapter XV of Part II of the TP explains the fundamental point of disagreement between J M Keynes and J Tinbergen over the issue of measurement. Tinbergen brought his physic background with him to the study of economics. Tinbergen believed that the exact measurement approach that he had absorbed in his study of statistical physics, using additive, linear, exact, precise definite probability distributions like the Normal or log normal, could be used in the study of macroeconomics that would provide a precise and exact explanation of business cycles. Keynes, of course, given his great, overall experience in academia, industry, business, government, the stock markets, bond markets, money markets, banking, finance, and commodity futures markets, had vast experience that Tinbergen, an academic only, did not have. Keynes saw that Tinbergen’s application was the wrong one, although the technique would be applicable to studies of consumption and inventories.