# On the Explicit Connections Between Keynes’s Chapter 15 of the A Treatise on Probability(1921) and Chapter Four of the General Theory(1936):Keynes’s Method in the General Theory is Inexact Measurement and Approximation using Imprecise Probability from the A Treatise on Probability

13 Pages Posted: 23 Jun 2020

Date Written: May 30, 2020

### Abstract

Keynes, as he had done in all of his major works either directly or indirectly, from the 1913 Indian Currency and Finance through the General Theory in 1936, always used his A Treatise on Probability method and methodology of inexact measurement and approximation when performing a technical analysis. This involves Keynes’s use of interval valued probability to deal with the problem of uncertainty.

Uncertainty involves non(sub ) additive probability that introduces the immense complications of non additivity and non linearity into an analysis of decision making. Uncertainty, U, itself is a function only of the Evidential weight of the argument,w,or U=g(w). It occurs if Keynes’s Evidential Weight of the Argument,V(a/h) =w ,where 0≤w≤1,is less than 1.A w<1 automatically creates some degree of uncertainty. In Keynes’s system of logical probability, there is no other way of modelling uncertainty except as an a)interval estimate or a b) decision weight, like his conventional coefficient of risk and weight,c.In the Keynes -Townshend correspondence on 1937-1938 in Vol. 29 of the CWJMK,Keynes emphasizes that Townshend was correct in his conclusion that the entire concept of the liquidity preference theory of the rate of interest rested on his weight of the evidence analysis.

Keynes told Townshend ,who was intellectually lost, to reread pages 148 and 240 of the General Theory. Of course, it is on these two pages that Keynes’s makes the connection between uncertainty and weight as an inverse function. Only in chapter 26 of the A treatise on probability, however,is V(a/h), from chapter 6, set equal to w,where 0≤w≤1,in chapter 26.

However,after some 84 years,it is now clear to me that this was not enough.Keynes also needed to have told Townshend to read page 160 of the A treatise on probability and pp.39-40 and 43 of chapter 4 of the General Theory, since no economist in the 20th century has been able to connect Keynes’s condition for uncertainty to exist,w<1, with interval valued or imprecise probability.

**Keywords:** Chapter 4 of the GT, Chapter 15 of thenTP, Inexact Measurement, Approximation, Imprecise Probability, Keynes’s Method

**JEL Classification:** B10, B12, B14, B16, B18, B20, B22

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