The Assessment of Keynes's a Treatise on Probability from the Point of View of a PhD Student in Statistics from Harvard University's Department of Statistics in 2006: The Impact of the Failure to Read Part II of Keynes's a Treatise on Probability

Abstract

Historical, as well as practically all current, assessments of J M Keynes’s A Treatise on Probability suffer immensely due to the failure of the readers of that book to cover Part II of the Treatise. As acknowledged by Emile Borel in his 1924 review of the A Treatise on Probability, this part of the book is extremely difficult and daunting. Borel’s solution to this problem was to simply skip Part II entirely and base his review only on the other four parts of the book. This eventually lead to only Part I of the A Treatise on Probability being covered as future readers also skipped Part II. Unfortunately, in skipping this part of the book, Borel completely overlooked Keynes’s explicit discussions about additivity being a special case while non(sub) additivity was the general case. Keynes then followed this analysis with his interval valued approach to estimating probabilities using Boole’s lower and upper bounds approach that Keynes called approximation. Skipping Part II was also the solution chosen by F Y Edgeworth, by Edwin Bidell Wilson initially, and by Bruno de Finetti. It is highly likely that this same choice, to skip Part II and read only Part I, was made by the “Fundamentalist Keynesians” centered around the economics and philosophy departments at Cambridge University, England in the last quarter of the 20th century. It should not be surprising that this same approach would be taken toward Keynes’s A Treatise on Probability at American universities, such as Harvard, as well. The idea that Keynes just had some suggestions,or intuitions, or hints, or ideas about non measurable probabilities (interval valued probabilities) has no support once Part II is fully integrated into an assessment of what it was that Keynes accomplished in 1921 in his A Treatise on Probability. Keynes’s contribution to interval valued probability ,both indeterminate (chapters 15-17,20,22 of the TP) and imprecise(chapter 29) probabilities, far, far exceeds the small one paragraph discussions on pages 30 and 34 of chapter III.