On J M Keynes's Clear Cut Discussion of Interval Valued Probability in Chapter III of the a Treatise on Probability

Abstract

In chapter III of the A Treatise on Probability, Keynes made it very clear that ordinal, qualitative probability did not apply in many cases. Further, ordinal probability was very weak as far as providing useful information upon which a decision maker could act. However, this did not mean that probabilities could not be analyzed technically if numerical and ordinal probability were inapplicable. In fact, Keynes’s argument was that, while numerical and ordinal probability could not be applied in many cases, interval valued probability could be used to make judgments about the choice of an option, given alternatives, that would be valuable to the decision maker. Of course, a problem would occur if the intervals were to overlap. Interval valued probabilities that overlapped would be ” non numerical”, “non comparable“, “non measurable” or “ incommensurable”. Keynes’s discussions on pp. 32-36 of chapter III of the A Treatise on Probability have been severely misinterpreted to mean that no probabilities could be provided because there was a category of “unknown” probabilities. T. Seidenfeld’s 2004 academic journal summary puts an end to the claims of the Keynesian Fundamentalists and their assertions about Keynes’s supposed unknown probabilities.