(Book Introduction) The Edgeworth-Wilson Correspondence in 1923 on the a Treatise on Probability (1921): What It Tells Us About Current, Academic Assessments of That Work

Abstract

The Edgeworth-Wilson exchanges in 1923 reveal that neither Francis Isidro Edgeworth, one of the top ten economists of all time in world history ,nor Edwin Wilson, one of the very top American applied mathematicians in the USA in the first half of the twentieth century, had any idea about how to deal with Part II of J.M. Keynes’s, A Treatise on Probability (1921). The same conclusion holds for Ronald Fisher, who Stephen Stigler claims was the greatest statistician of the twentieth century. Richard Dawkins claims he was also the greatest biologist since Darwin. In fact, it is Benoit Mandelbrot, by a longshot, who was the greatest statistician of the 20th century.

Part II of the, A Treatise on Probability includes Keynes’s formal analysis of his Boolean, non additive, nonlinear, indeterminate, interval valued approach approach to logical probability, based on the use of upper and lower limits or bounds.

This inability to deal with Part II of the A Treatise on Probability would explain why the Keynesian Fundamentalists (the Robinsons, R. Skidelsky, P. Davidson, G.L.S. Shackle, J. Runde, S. Dow, R. O’Donnell, A. Carabelli, T. Lawson, and hundreds of other Post Keynesian and Institutionalist economists) have completely failed to grasp the interval valued approach of Keynes. They simply lacked the necessary training in mathematical logic, probability, and statistics needed to comprehend what Keynes was doing. The result is a gigantic, intellectual mess based on (a) their misbelief that Keynes’s theory is an ordinal theory that can only be applied some of the time because of their confusion regarding unknown and indeterminate probabilities and (b) their inability to find the very large number of errors made in F. P. Ramsey’s two very poor reviews of Keynes’s A Treatise on Probability. Again, Ramsey was simply overwhelmed by Part II of the A Treatise on Probability and could not follow Keynes’s analysis of interval valued probability. Ramsey’s claims about Keynes’s “mysterious non numerical probabilities” not obeying the laws of the calculus of probability and the Stohs-Garner discussions about “what is a non numerical probability?” are the foundation for the Fundamentalist position of Skidelsky that Keynes’s approach was an ordinal approach that could only be applied some of the time. Nothing is further from the truth.

Keywords: Edgeworth-Wilson correspondence, Boole, interval valued probability, ordinal probability, mathematical logic

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