# An Examination of the Very Severe Ignorance of Keynes’s A Treatise on Probability Among Heterodox Economists and Their Erroneous Beliefs About Logical and Subjective Probability

24 Pages Posted: 21 Oct 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: October 10, 2019

### Abstract

Heterodox economists have simply skipped the two most important parts of Keynes’s A Treatise on Probability (1921), Part II and Part V. They basically assess Keynes’s position on probability and uncertainty based on a reading primarily of Chapter III of Part I of the A Treatise on Probability.

This results in their failure to grasp Keynes’s inexact measurement – approximation approach to probability in Part II and Keynes’s inexact measurement – approximation approach to statistics in Part V of the TP. Both Part II and V form the basic foundation of Keynes’s approach to logical probability that Keynes built on Boole.

Specifically, heterodox economists are ignorant of (i) Keynes’s inexact approach to measurement, based on Boolean approximation that uses lower and upper bounds, when dealing with probability and (ii) Keynes’s inexact approach to measurement ,based on Boolean approximation that uses lower and upper bounds, when dealing with statistics.

This results in a belief that Keynes’s method involved an application of ordinal probability only some of the time, because there was supposed to be entities, called non-comparable, non-measureable and incommensurable probabilities, that can’t be analyzed. Heterodox confusions about Keynes’s discussion on pp. 31-36 of the TP concerning unknown probabilities and indeterminate probabilities, where indeterminate probabilities are Boolean in nature and have nothing to do with unknown probabilities, leads heterodox economists into an intellectual quagmire of quicksand that could have been easily avoided if they had covered Parts II and V of A Treatise on Probability.

The extensive, but unique, Keynes–Townshend correspondence over the connections between the GT and TP in 1937-38 showed why Keynes’s method of inexact measurement and approximation for both probability and statistics is what links the GT and TP. On questions of probability and expectations, only the TP and the GT are mentioned by Keynes and Townshend in their correspondence. There is no mention of the 1937 QJE article or of fundamental uncertainty or of Frank Ramsey or subjective probability.

An examination of both Rosser and Skidelsky reveals that they both simply have no basic understanding about what a logical theory of probability is or what a subjective theory of probability is. Both Rosser and Skidelsky, like Muth before them, confuse the two approaches.

An examination of Rosser and Skidelsky illustrates the astounding ignorance of Keynes’s A Treatise on Probability on the part of heterodox economists. Neither Rosser or Skidelsky demonstrate that they have even the slightest understanding of what an interval valued probability is, what Keynes’s method was-inexact measurement and approximation, how uncertainty is related to non additivity, that Keynes was not a subjectivist, that Savage rejected the frequency approach to probability, and that subjective probability distributions can’t possibly converge to an objective probability distribution because objective probability does not exist according to de Finetti.

Keywords: probability, objective, subjective, logical, approximation, inexact measurement, non additivity and uncertainty

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

Suggested Citation

Brady, Michael Emmett, An Examination of the Very Severe Ignorance of Keynes’s A Treatise on Probability Among Heterodox Economists and Their Erroneous Beliefs About Logical and Subjective Probability (October 10, 2019). Available at SSRN: https://ssrn.com/abstract=3467399 or http://dx.doi.org/10.2139/ssrn.3467399