# J M Keynes's Evidential Weight of the Argument, V(A/H),Which Applies to Arguments, is Different from the Weight of the Evidence, W, Which is a Measure of the Completeness of the Information, Data, Evidence, or Knowledge in the Premises, H

25 Pages Posted: 24 Aug 2017

Date Written: August 22, 2017

### Abstract

Keynes’s V(a/h) relation, first presented on p.72 of chapter 6 of the A Treatise on Probability (1921), represents the Evidential Weight of the Argument from h to a. H and a are related to each other and can’t be separated. V relates two sets of propositions, a and h. H is the premises and a is the conclusion. It is not possible to talk about h separately from a or a separately from h when using V.

Keynes introduced w, the weight of the evidence, in Chapter 26 of the A Treatise on Probability in preparation for the construction of his conventional coefficient of weight and risk, c. C is not a probability. C is a decision weight. It represents the first use of and creation of a decision weight in history. W is defined by Keynes as a measure of the completeness of the relevant evidence, knowledge or data that is contained in the premises, h. It is a measure of the completeness of the evidence contained in the premises. It has nothing to do with V(a/h). It was introduced in the first paragraph of chapter 6 on p.71, before Keynes introduced his V(a/h) relation on p.72. The first paragraph deals exclusively with the premises containing the evidence. It does not deal with V.

It is impossible to substitute V for w since they are different. V and w can’t be compared because V represents the logical relation between h and a, while w is a mathematical variable, normalized on the unit interval [0,1], that represents the completeness of the amount of available evidence, data, or knowledge, represented by h. Keynes never normalized V on the unit interval [0,1]. Keynes only normalized w on the unit interval [0,1].

The failure to understand the differences between V(a/h) and w, which is a measure of the strength of h, leads to confusion and error among heterodox economists, Post Keynesians, and economists associated with Cambridge University, England.

**Keywords:** weight, interval vaued probability, upper and lower probabilities, nonnumerical probabilites, c coefficient

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

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