# Comparing Edgeworth’s, Russell’s, and Broad’s 1922 Assessments of Keynes’s Weight of the Evidence, Based on Chapters 6 and 26 of the A Treatise on Probability, With Levi’s, Runde’s, Weatherson’s, Joyce’s, Feduzi-Runde’s, Kasser’s and Peden’s Assessments of Keynes’s Weight of the Evidence Based on Chapter 6 of a Treatise on Probability Alone: Skipping Chapter 26 of the A Treatise on Probability Leads to a Number of Errors of Omission

34 Pages Posted: 19 Nov 2018

Date Written: October 28, 2018

### Abstract

Edgeworth, Russell, and Broad studied Keynes’s weight of the evidence concept, as presented in chapters 6 and 26 of the A Treatise on Probability, in their reviews of the A Treatise on Probability in 1922. They found no problems with Keynes’s conceptualization of weight or treatment of it that presented confusions or errors as related to the claim that Keynes’s concept was restricted to an absolute, or gross, measure of weight. A reading of chapter 26, sections 7 and 8, of the A Treatise on Probability show that Keynes presented a relative concept of weight measures in degrees as is the probability concept.

On the other hand, Levi, Runde, Weatherson, Joyce, Feduzi-Runde, Kasser and Peden either ignore chapter 26 completely or present a superficial treatment of it that ignores the designation of w as measuring weight in degrees. Levi, Runde, Weatherson, Joyce, Feduzi-Runde, Kasser and Peden concentrate only on chapter 6 of the A Treatise on Probability. It is straightforward to show that skipping chapter 26 of the A Treatise on Probability leads to the omission of the chapter where Keynes decided to place his mathematical modeling of the weight of the evidence concept in the form of degrees. The diametrically different results obtained by Edgeworth-Russell - Broad, who make no mention about the claim that weight is an absolute, or gross, concept only, clashes directly with the Levi-Runde-Weatherson-Joyce-Feduzi-Runde-Kasser-Peden conclusion that weight is an absolute, or gross, concept only.

A comparison – contrast shows that Keynes treated weight of the evidence, w, overall, as a relative concept when measuring it for inclusion with the concept of probability to model expectations. The misbelief, that weight is only a gross, or absolute, concept, comes from Keynes’s comments about the balance of absolute knowledge and absolute ignorance made in chapter 6. Readers concentrate only on the first concept, absolute knowledge. It is mathematically impossible to treat the balance between absolute knowledge and absolute ignorance in absolute terms if one desires to incorporate a simultaneous treatment of probability and weight together to model expectations. Weight of evidence must be treated in relative terms as done by Keynes in his c coefficient in chapter 26 A Treatise on Probability.

Current assessments of Keynes’s weight concept in the A Treatise on Probability are erroneously based on a metaphor on page 77 of chapter 6 that Keynes used before he presented the mathematical analysis in chapter 26 of the A Treatise on Probability. Keynes’s chapter 26 is the omega while chapter 6 is the alpha. It is impossible to fully grasp Keynes’s weight of the evidence concept without a detailed study of chapter 26 of the TP and the c coefficient, where V does not appear at all because V(a/h)=w ,0 ≤w ≤1, so that w=K/(K I). V is now formally consistent with P(a/h) =α,where 0 ≤ α ≤ 1 ,allowing Keynes to combine both probability and weight relations in his decision theoretic c coefficient.

**Keywords:** Weight, Interval Valued Probability, the C Coefficient, Logical Relations, P, V, Imprecise Probability, Indeterminate Probability

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

**Suggested Citation:**
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