Using A. Greenspan’s Continuum to Generalize J.M. Keynes’s Evidential Weight of the Argument (Evidence), W, Where W Was Defined on the Interval 0 ≤ W ≤ 1, so that 0 Denotes Complete Ignorance and 1 Denotes Complete Knowledge

Abstract

J. M. Keynes made the concept of uncertainty a fundamental part of his rate of the interest theory of liquidity preference. Uncertainty was defined by Keynes on page 148 of the General Theory as an inverse function of the weight of the argument (evidence), where “argument” refers to logical considerations based on propositional logic and evidence refers to an analysis of a mathematical function and the variables that define the function. Thus, Uncertainty, U, is defined as a function of w, so that U =h(w). The weight of the argument was discussed in chapter 6 of the A Treatise on Probability, 1921. The weight of the evidence was discussed in chapter 26 using the term w to measure the completeness of the relevant evidence. Formally, the evidential weight of the evidence, V(a/h), =w, where w is defined on the interval 0 ≤ w ≤ 1. It is only in chapter 26 that Keynes formally defines V(a/h) =w.

Keynes’s logical and mathematical constructions are, however, very difficult for economists to grasp, since an economist must first grasp that chapter 6 of the A Treatise on Probability, 1921 provides only a purely, formal, symbolic, logical treatment that only a single handful of economists has been able to grasp correctly since 1921. Keynes does not integrate the concept of weight into a decision theory combined with probability that deals with expectations. Keynes does integrate probability and weight into a decision theory, however, in chapter 26 of the A Treatise on Probability, 1921 Keynes called this specific, simplified version of his overall interval valued approach a “conventional” coefficient of risk and weight. Only F Y Edgeworth and Bertrand Russell recognized the fundamental of chapter 26 of the A Treatise on Probability, 1921. Keynes uses this chapter for the theoretical foundation for his discussions of investment expectations about the mec and D2 in chapters 3, 12, 20 and 21 of the General Theory (1936).

Greenspan’s concept of a Continuum allows an economist to bypass Keynes’s correct, but very difficult and involved logical and mathematical discussions of the concept of weight, and simply define a Continuum that exists that spans continuously situations involving a complete lack of knowledge (ignorance) to a situation where the decision maker has complete knowledge and can assign precise, exact numerical probabilities. The decision maker must then decide for himself whether he is facing a situation of uncertainty, a situation of risk, or some mixture of the two. One could assume that in this intermediate situation that risk and uncertainty could be regarded as some linear combination of the two different types of situations. It was Greenspan’s unique ability to be able to apply his intuition and correctly judge what type of uncertainty he was facing at particular time. If one is facing uncertainty, then a proactive approach is required. Greenspan’s understanding of uncertainty was why Greenspan was proactive while Bernanke, who believed that there was no such thing as uncertainty, only risk assessments, was reactive in the face of the mounting uncertainty generated by the Northern Rock failure in Britain in August of 2007.