
doi: 10.2139/ssrn.3348201
Professor Sakai has intuitively and heuristically demonstrated correctly that Keynes’s introductory diagram on page 39 of the 1921 edition (Page 42 of the CWJMK 1973 edition), which Keynes intended to be only a brief introduction illustrating his theory of measurement in chapter III of the A Treatise on Probability, is meant to demonstrate interval valued probability graphically as an illustration to demonstrate the nonlinear and non-additive nature of interval valued probability. It is in chapter 15 on pp.162-163 of the A Treatise on Probability that Keynes deploys his improved and revised Boolean algebra approach, based on conditional probability, (see also chapter 17 for an alternative way in which Keynes solves another version of this problem), in order to show how such a problem would be solved mathematically. It is interesting to note that, despite Keynes’s clear-cut discussions in chapter III stating that this chapter was only an introduction to the topic of measurement, the Keynesian Fundamentalists have ignored Keynes’s many worked out problems in chapters 15, 16, and 17 of the A Treatise on Probability of problems that were originally done by Boole in his 1854 The Laws of Thought.
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