John Maynard Keynes’s Upper and Lower Valued Probabilities: A Study of How Statisticians, Philosophers, Logicians, Historians, and Economists Failed to Comprehend Keynes’s Breakthrough Application of G.Boole’s Interval Approach to Probability in the 20th Century
Michael Emmett Brady
California State University - Department of Operations Management
January 30, 2012
Over the course of their professional lives, Henry E. Kyburg, Isaac Levi, and Jochen Runde have maintained the claim that J M Keynes’s contributions to probability and decision theory were of a comparative, qualitative nature only. They maintained that J M Keynes had some interesting, but undeveloped ideas, hints, suggestions, and intuitions about the structure of his logical approach to probability. They assert that he made some progress in clearing the way for later researchers who would then create the interval estimate approach to probability that he did not. They claimed that Keynes himself had never provided any detailed, formal mathematical structure at any time in his life to support his intuitions and brilliant ideas.
It is a rather simple task to demonstrate that these claims are false by pointing out that there are 17 worked out problems provided by J M Keynes in chapters 15 and 17 of his A Treatise on Probability (1921,TP), as well as the applications of interval estimates used by Keynes in chapters 20, 22, and 26 of the TP, that show beyond any doubt that J M Keynes had created the first explicit interval estimate approach to probability in history. George Boole was the first to work out the mechanics of an interval estimate approach. However, Keynes was the first to emphasize the application and importance of such an approach in applied areas like decision theory.
I have chosen Kyburg, Runde ,and Levi because they are representative of how academics in the fields of philosophy and economics handle Keynes’s TP. It must be noted here that Kyburg , Levi, and Runde have an understanding of Keynes’s A Treatise on Probability that is superior to that of any statistician or mathematician with the exception of Hailperin (1986) .My disagreement with Kyburg, Levi, and Runde is that they have failed to adequately complete the job of correctly identifying Keynes’s theory because they restricted their analysis to basically one chapter of the TP, chapter III.
The worst treatment of the TP comes at the hands of statisticians. This is due to their commitment to the assertion that all probabilities must be precise, single number answers. NO statistician who reviewed the TP had any inkling of the case Keynes was making.
Number of Pages in PDF File: 24
Keywords: nonlinear and non additive probabilities, upper and lower bounds or limits, approximation
JEL Classification: B30, B16, C02, C10
Date posted: January 31, 2012 ; Last revised: February 7, 2012