# Keynes (Boole), Knight, (and Ellsberg) Against Ramsey, De Finetti, and Savage: It Had Nothing to Do with 'Radical Uncertainty', But Involved the Issue of Inexact, Indeterminate, Imprecise, Interval Valued (Weak Evidence) Probability Versus Exact, Determinate, Precise (Strong Evidence) Mathematical Probability

22 Pages Posted: 13 Jun 2018

Date Written: May 27, 2018

### Abstract

Recent articles in July, 2016 by P. Krugman and J. Fels reviewing Mervyn King's The End of Alchemy: Money, Banking, and the Future of the Global Economy, demonstrate a confusion by all three regarding what the issue was in the intellectual conflict between Keynes and Ramsey, between Ellsberg and de Finetti-Savage, and between Keynes (Boole), Knight, (and Ellsberg) and Ramsey, de Finetti, and Savage. The major issue had nothing to do with the alleged unmeasurability of so called non quantitative probability, but with the issue of strong evidence versus weak evidence. Keynes argued in both the A treatise on Probability and the General Theory that exact, precise numerical probabilities could rarely be used in the real world of economic, business, and financial decision making because of the paucity and/or flimsiness of relevant evidence available. Instead, "non numerical" probabilities had be used which incorporated the fact of what Keynes called major "weight of the evidence" deficiencies in the data, information, knowledge or evidence. This lead to Keynes's indeterminate, imprecise "non numerical", interval valued probabilities or his conventional coefficient of risk and weight decision, c.

Keynes's definition of uncertainty in the General Theory has absolutely nothing to do with radical uncertainty, but is defined on page 148 of the General Theory to be an inverse function of the weight of the evidence, w, where V(a/h)=w. V(a/h) is the evidential weight of the argument from evidence h to conclusion a and 0≤w≤1. Radical uncertainty can occur only if w=0. That means that h=0 and there is no V relation that holds for conclusion a. It is Joan Robinson, GLS Shackle and Paul Davidson, not Keynes and Knight, who make this argument. King, Krugman and Fels are basing their "analysis" of uncertainty, not on what Knight and Keynes said, but on the false claims made by Robinson, Shackle and Davidson about Keynes and Knight.

Knight's third category, "estimates", is an inferior version of Keynes's c coefficient, which incorporated w, the weight of the evidence. Deficiencies in w lead to distorted or slanted non additive, non linear "non numerical", decision weights or c coefficients. Knight was not able to integrate a concept of weight of the evidence into his "estimates" category. However, he clearly demonstrated that a probability of ½, based on strong evidence, is to be preferred to an "estimate" of 1/2, which has the same form as a probability, but is based on weak evidence. This, of course, is clearly brought out in the first Ellsberg urn thought experiment and by Keynes in chapter 6 of the TP on pages 75-76. The Keynes-Townshend correspondence of 1937-38 proves beyond a shadow of a doubt that Keynes's General Theory is based on his non numerical probabilities and weights of the evidence.

Ellsberg's conflict with de Finetti and Savage dealt with the same issues that separated Keynes from Ramsey. Ramsey never grasped the fact that interval valued probability CAN NEVER satisfy the additivity and linearity axioms of the mathematical calculus of probability.

**Keywords:** Keynes, Knight, Ellsberg, Ramsey, Savage, de Finetti, Fels, Krugman

**JEL Classification:** B10, B12, B14, B16, B20, B22

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