J M Keynes’s Theory of Evidential weight can only be expressed in a formal manner as V=V(a/h) =V(a/h1, h2, h3, h4……hn, hn+1….) =w, 0≤w≤1, where w=K/[K+I] and 1-w=I/[K+I] when K=knowledge and I =Ignorance.The erroneous Heterodox , Post Keynesian version is V(a/h)=V = K/(K+I),0≤V≤1.

Abstract

In 1990,J. Runde presented a formal, mathematical representation of Keynes’s theory of evidential weight, as presented in chapters 6 and 26 of Keynes’s A Treatise on Probability ,as V(a/h)=V = K/(K+I).In 1999,A. Vercelli revised this to read as V =V(a/h) = K/(K+I), 0≤V≤1.We can identify this as the Post Keynesian – Heterodox formulation of what they thought Keynes was supposed to have meant .We will abbreviate this as PK-H. The problem with the PK-H formulation is that it does not make any sense .It involves a basic ,fundamental error in conflating and confusing two separate fields, logic and mathematics,as Keynes’s V is a logical relation and not a mathematical variable. Keynes correctly transforms his logical relation ,V,into a mathematical variable ,on p.315 of the A Treatise on Probability in the following manner : “….where w measures the ‘weight,’(sic)…”(Keynes,1921,p.315). Now Keynes had already properly discussed w as being “….the degree of completeness of information upon which a probability is based…”(Keynes,1921,p.313) where Keynes had already done the necessary and sufficient normalization to the unit interval [0,1] needed to define a measure of weight ,so that w comes in degrees as 0≤w≤1. Keynes thus finishes what he started in the first paragraph of chapter VI on p.71 of the A Treatise on Probability,where ,instead of the balance being between the favorable and unfavorable evidence,which is given by the concept of probability ,where P is the probability relation ,so that one obtains the following: P(a/h)=α,0≤α≤1,where α=p/(p+q) and 1-α=q/(p+q),where p+q =1.(Keynes,1921,p.315). One obtains the other balance ,which is now a balance between the absolute amounts of relevant knowledge and of relevant ignorance ,respectively ,as V(a/h)=w, 0≤w≤1,where w=K/(K+I) and 1-w=I/(K+I),where K is ,obviously ,relevant Knowledge and I is, just as obviously,relevant ignorance,so that K+I=1. Only after this has been recognized can one understand Keynes’s conventional coefficient of weight and risk c. Unfortunately,no academic philosopher,economist,historian or decision theorist was ever able to grasp Keynes’s mathematical analysis underling the c coefficient of p.315 of the A Treatise on Probability in either the 20th or 21st century except Edgeworth. We will examine one out of the hundreds of erroneous papers which have incorporated Runde’s mathematical errors about V by examining a paper by Crocco (2006).