J M Keynes's Logical Theory of Probability Is Based on Interval Valued Probability, Not Ordinal Probability: How the Keynesian Fundamentalists Runde, Skidelsky, Carabelli, OODonnell, Meeks Got It All Wrong

Abstract

The misbelief that Keynes’s logical theory of probability was based on a foundation of ordinal probability can be traced back to Frank Ramsey’s query about Keynes’s “mysterious non numerical probabilities.” Ramsey’ s flawed analysis was then passed on to a host of other philosophers and economists. Two of these were Robert Skidelsky and Gay Meeks. Their work, based on Ramsey, was then passed on to a host of economists. Neither Skidelsky not Meeks had any formal training in mathematics, logic, statistics, or probability. They simply read into certain parts of one chapter of Keynes’s A Treatise on Probability (1921), chapter 3, a gross misinterpretation based on the erroneous work of Ramsey. They confused unknown probabilities with indeterminate (interval valued) probabilities. A Huge amount of academic work, numbering in the thousands of articles and hundreds of books, has been published based on this confusion. The intellectual foundation for their flawed analysis rests on the uncritical acceptance of two extremely poor book reviews of the A Treatise on Probability made by F P Ramsey in 1922 and 1926 when he was 18 and 22 years old, respectively. The vastly superior reviews of Keynes’s book, made, for instance, by Francis Y Edgeworth, C. D Broad, and Bertrand Russell, were simply ignored. This paper shows how this error occurred and why.