# Professor Sakai’s Conjecture About the Diagram on Page 39 (Page 42 of the 1973 CWJMK Edition) of the 1921 Edition Illustrating Keynes’s Interval Probability: His Heuristically Correct Analysis of Keynes’s Probability Intervals Is Supported by Keynes’s Worked Out Problem on pp.162–163 of the A Treatise on Probability and Footnote on p.161

32 Pages Posted: 1 Apr 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: March 7, 2019

### Abstract

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.

Keywords: Interval Valued Probability, a Treatise on Probability, Chapter III, Chapter 15, Approximation, Inexact Measurement

JEL Classification: B10, B12, B14, B16, B20, B22

Suggested Citation

Brady, Michael Emmett, Professor Sakai’s Conjecture About the Diagram on Page 39 (Page 42 of the 1973 CWJMK Edition) of the 1921 Edition Illustrating Keynes’s Interval Probability: His Heuristically Correct Analysis of Keynes’s Probability Intervals Is Supported by Keynes’s Worked Out Problem on pp.162–163 of the A Treatise on Probability and Footnote on p.161 (March 7, 2019). Available at SSRN: https://ssrn.com/abstract=3348201 or http://dx.doi.org/10.2139/ssrn.3348201