# J M Keynes’s Logical Theory of Probability in the A Treatise on Probability (1921) Is Based on the Interval Valued Approach of Boole and Not on the Principle of Indifference, Which Was of Minor Concern to Keynes, or Ordinal Probability or Rank Ordering

22 Pages Posted: 10 Jun 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: May 23, 2019

### Abstract

It was George Boole who published the first systematic exposition of a logical theory of probability in 1854 in The Laws of Thought. J M Keynes was the second scholar to publish a systematic, technical exposition of logical probability. This was all carefully presented by the American mathematician,Theodore Hailperin, in 1986. J M Keynes built on Boole using an improved version of Boole’s approach that he probably developed while working with Willian Ernest Johnson, who had also developed an unpublished, systematic approach to logical probability before Keynes.

Keynes made very significant improvements to the written materials that made up the subject matter of probability and statistics in the nineteenth century. One of these areas involved Laplace’s earlier Principle of Non-Sufficient Reason. Keynes did systematically improve the nature and range of application of the Principle of Non Sufficient Reason with his Principle of Indifference (POI), which was Keynes’s name for his improved version of Laplace’s Principle of Non Sufficient Reason.

However, Keynes NEVER attempted to build a systematic approach operationalizing probability on his POI. Keynes built his own approach on George Boole’s original interval valued approach that used upper and lower probabilities. Keynes called this Approximation or Inexact measurement.

The major reason for the failure of economists and philosophers to correctly grasp Keynes’s Inexact, approximation approach to measurement is their failure to comprehend the role played by Boole in Keynes’s A Treatise on Probability.

This lacuna is being remedied by Professor R. Arthmar.

Keywords: Keynes, Boole, Johnson, POI, Laplace, Interval Valued Probability, Non-numerical Probability

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

Suggested Citation

Brady, Michael Emmett, J M Keynes’s Logical Theory of Probability in the A Treatise on Probability (1921) Is Based on the Interval Valued Approach of Boole and Not on the Principle of Indifference, Which Was of Minor Concern to Keynes, or Ordinal Probability or Rank Ordering (May 23, 2019). Available at SSRN: https://ssrn.com/abstract=3392823 or http://dx.doi.org/10.2139/ssrn.3392823