# On Weckstein's 1959, Keynesian, Weight of the Evidence – Based Demolition of G L S Shackle's Attack on the Concept of Probability

32 Pages Posted: 2 Jun 2017 Last revised: 11 Jun 2017

Date Written: June 1, 2017

### Abstract

R. Weckstein’s 1959 article in the February,1959 Symposium in Metroeconomica on Shackle’s theory of possibility demonstrated that Shackle’s attack on the concept of probability, as an approach to be used by decision makers in the real world, due to the theory of probability’s requirements, such as objectivity, complete ordering, the additivity of objective probabilities, divisibility, repetition, and repeatability, was applicable mainly to the relative and limiting frequency interpretations of probability. Shackle’s attack also held against the subjective theory of probability, which also made the assumptions of complete ordering and additivity. However, Weckstein demonstrated that all of Shackle’s objections to probability per se totally failed when confronted by logical theories of probability, in general, and J M Keynes’s Logical Theory of Probability, in particular, which explicitly criticized classical, limiting frequency, relative frequency, and subjective theories of probability. Keynes explicitly pointed out that all of these other theories of probability were actually special cases, sound and valid in their specific fields of application, but not general in scope or application. Keynes argued that only his logical theory of probability could be a general theory of probability, applicable to single events, infrequent events, and frequent events in the form of Boole’s propositional logic and development of indeterminate/imprecise/determinate probabilities.

Specifically, it was the Keynesian concept of the weight of the evidence that leads to the complete refutation of Shackle’s attacks on probability per se. Shackle’s attacks on the concept of probability are sound when made against the Classical, Propensity, Subjective, Relative Frequency, and Limiting Frequency interpretations of probability, but are unsound when confronted with Keynes’s Theory of logical probability.

Shackle never responded to Weckstein’s criticisms based on Keynes or logical theories of probability. In fact, he deliberately chose to respond mainly to Weckstein’s mention of Reichenbach’s posit approach to singular events in his article. In fact, Shackle never dealt with Keynes’s logical theory of probability in his lifetime since he never got past page 14 of the A Treatise on Probability. Instead, Shackle attempted to completely bypass the A Treatise on Probability and The General Theory, which is built on Keynes’s weight of the evidence, by claiming that Keynes’s February,1937 article in the Quarterly Journal of Economics represented Keynes’s final view of decision making and probability. A recent article by Derbyshire represents a continuation of Shackle’s severe misrepresentation of probability and especially of Keynes’s work on uncertainty, decision making, and probability.

Keynes, building on the logical approach to probability of Boole, had already solved the problems that other theories of probability had in dealing with single, crucial decisions, additivity, and uncertainty. Keynes finished with his analysis in the 1908 Fellowship dissertation, which contained his interval valued, on linear, non-additive approach, when Shackle was five years old. This appears in the TP in Part II. Shackle never read the TP. He read little bits and pieces of it. He then wrote vague and ambiguous comments on the TP that made no sense when he wrote them and which still do not make any sense in 2017. Keynes’s approach would make a better foundation for scenario planning than Shackle’s, with his theory of possibility, if one assumes that academics are capable of actually reading the TP. However, it might be the case that academics are not capable of reading the TP. In that case, then, Shackles’s theory would be a second best choice.

**Keywords:** Weight, Interval Valued Probability, Upper and Lower Probabilities, Nonnumerical Probabilities, Liquidity Preference

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

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