J M Keynes and E. Borel’s Initial Skipping of Part II of the A Treatise on Probability in His 1924 Review: What Changed Borel’s Mind 15 Years Later?

Abstract

Emile Borel’s review of the A Treatise on Probability in 1924 is, in my opinion, quite above average. I would give it a grade of B/B+. Borel was also an intellectually honest researcher. Borel did not pretend to have read Parts II, III, IV, and V of Keynes’s A Treatise on Probability, as has been done repeatedly by psychologists, philosophers, historians, and economists, who have cited the A Treatise on Probability in their references when writing about Keynes’s logical theory of probability in his A Treatise on Probability.

Borel apologizes to Keynes (and Bertrand Russell,who Borel knew had assisted Keynes in writing the A Treatise on Probability) for not reading Part II of Keynes’s A Treatise on Probability because he realized that, for Keynes, Part II was the most important part of the A Treatise on Probability. Borel was correct. It was the most important and intellectually powerful part of the book. It was the most important and intellectually powerful part of the book because Keynes presented for the second time in history a theoretical, technically advanced approach to imprecise probability. The first attempt in history was Boole’s original achievement in The Laws of Thought in 1854. Adam Smith had presented the first non technically advanced imprecise theory of probability in 1776 in the Wealth of Nations, which was opposed by Jeremy Bentham’s precise theory of probability that was used in his 1787 The Principles of Morals and Legislation.

However, Borel bemoaned the fact that Maxwell, who was a graduate, just like Keynes himself, of Cambridge University, who had made contributions to physics using the limiting frequency interpretation of probability, which Borel thought that Keynes had given insufficient space and emphasis to in his book, had been overlooked by Keynes. This is correct with respect to Part I of the A Treatise on Probability. However,it is incorrect with respect to the totality of A Treatise on Probability because Keynes covered Maxwell on pp.172-174 of Chapter 16 in Part II. Maxwell is listed in the index to A Treatise on Probability on p.463. In Part V, in chapter 32, Keynes makes it clear that, if the only relevant evidence consists of statistical frequencies and there is no other relevant evidence, then the logical probability estimate of a probability is identical to the estimate made by the limiting frequency theory if the statistical frequency can be shown to be stable over time using the Lexis -Q test.

Another important result of this paper is that it appears that no academic has read Part II of the A Treatise on Probability since 1921. Otherwise, it should already have become common knowledge that Keynes had covered Maxwell in chapter 16 of Part II of the A Treatise on Probability.