How J M Keynes's Logical Theory of Probability Totally Refutes All Attacks on the Concept of Probability

Abstract

J Derbyshire has recently repeated G L S Shackle’s original attack on the concept of probability in a number of recent articles. He adds nothing new to Shackle’s arguments of forty to eighty years ago that were completely refuted in 1959 by R. Weckstein, who based his refutation of Shackle on a relatively limited understanding of chapters 1-3 and 6 of Keynes’s A Treatise on Probability (1921). Shackle never replied to Weckstein’s repeated demonstrations in 1959 that Keynes’s approach refuted his arguments, which held only against the limiting frequency, relative frequency, propensity and subjective interpretations of probability. Shackle’s arguments failed completely when confronted with Keynes’s theory of logical probability. J M Keynes’s theory of probability is a logical, objective, epistemological approach that is based on partial ordering and not complete orderings. This results in non additive, non linear interval valued probabilities, specified and operationalized in terms of logical propositions about any kind of event. It can easily deal with unique events, single events, crucial events, infrequent events, frequent events, non repeatable events, irreversible events, path dependence, sensitivity to initial conditions, emergence, complex causation, attractor states, partial uncertainty, complete and total uncertainty, fundamental uncertainty, irreducible uncertainty, by means of Keynes’s weight of the evidence analysis, which, when combined with his interval valued probability, can demonstrate that Shackle’s theory is a very special theory that applies only to situations of complete and total uncertainty, which Keynes categorized as ignorance. There is not a single one of Derbyshire’s objections to the concept of probability left standing if Keynes’s logical approach to probability is used.