# How Keynes Solved the ‘Mystery’ of the Diagram on Page 39 (Page 42 of the 1973 CWJMK Edition) of the A Treatise on Probability in Part II in Chapter 15 on pp.161–163 Just As He Had Foretold on pp. 37–38 of Chapter III

34 Pages Posted: 2 Apr 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: March 9, 2019

### Abstract

On pp.37-38 of the A Treatise on Probability ,Keynes was very clear that he was only going to present a 'brief' analysis of non numerical probability graphically as an illustration. However, in Part II, he stated he would present a 'detailed' analysis. This detailed mathematical and logical analysis involved the application of his modified approach to inexact measurement using the method of approximation that had first been used by Boole in 1854. Keynes demonstrated and presented a simple, illustrated version of his interval valued approach in Chapter III of the A Treatise on Probability.

In Chapter 15, he provided the detailed mathematical application of his logical theory of probability. Keynes followed through on his promise to demonstrate a purely mathematical treatment of non numerical probabilities.The real mystery is the complete and total failure of the Post Keynesians and Keynesian Fundamentalists to grasp Keynes’s completely clear analysis 98 YEARS after the publication of the A Treatise on Probability in 1921.

So Keynes actually did precisely what he said he would do. The only real remaining mystery is why no philosopher, mathematician, or economist in the 20th or 21st centuries ever read chapters 15, 16, and 17 of the A Treatise on Probability. It has been 98 years since Keynes published his book in 1921. The time has come for serious scholars to move beyond Keynes’s introduction to measurement in chapter III of the A Treatise on Probability, using diagrams, to Keynes’s full scale mathematical and logical application of his inexact measurement approach that he called approximation based on Boole’s upper and lower, interval valued, estimate approach to probability and decision making.

Keywords: Keynes, Chapter III, Chapter XV, A Treatise on Probability, Keynesian Fundamentalists, Post Keynesians

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

Suggested Citation

Brady, Michael Emmett, How Keynes Solved the ‘Mystery’ of the Diagram on Page 39 (Page 42 of the 1973 CWJMK Edition) of the A Treatise on Probability in Part II in Chapter 15 on pp.161–163 Just As He Had Foretold on pp. 37–38 of Chapter III (March 9, 2019). Available at SSRN: https://ssrn.com/abstract=3349602 or http://dx.doi.org/10.2139/ssrn.3349602