# Keynes Always Adhered to His Logical, Objective Probability Relation, Defined As P(a/H) Equals a Rational Degree of Belief, α: Logical Probability Always Remained the Guide to Life for J M Keynes

23 Pages Posted: 28 Aug 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: August 23, 2019

### Abstract

Keynes’s 1931 acknowledgement, that Ramsey’s theory of subjective degree of belief, based on numerically precise probability, was acceptable to him in the special case where w=1, has been constantly misinterpreted. This misinterpretation follows from the lack of understanding of Keynes's weight of the argument relation. This required that Keynes’s second logical relation of the A Treatise on Probability, the evidential weight of the argument, V(a/H)=w,0≤w≤1, where w=K/(K+I) and K defined the amount of relevant knowledge and I defined the amount of relevant ignorance, was defined and explicitly taken into account. It has been completely overlooked by all commentators that Keynes also stated in the same comment in 1931 that Ramsey’s theory did not deal with Keynes’s rational degrees of belief, P(a/h)=α,where 0≤α≤1. Only in the special case where w=1 does Keynes accept Ramsey’s approach because then the lower probability also equals the upper probability, which means that you now have additive, precise numerically definite probabilities.

Keynes conceded to Ramsey what he had always agree about, that the purely mathematical laws of the probability calculus can be interpreted as coherence constraints requiring that the probabilities of rational decision makers must be consistent with the assumption of additivity if, and only if, w=1.

The literature on Keynes’s logical probability relation, P, has failed to grasp Keynes’s very clear statements supporting it.

Keywords: logical probability, logical relation between h and a, imprecise, Ramsey, precise, interval valued probability

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

Suggested Citation

Brady, Michael Emmett, Keynes Always Adhered to His Logical, Objective Probability Relation, Defined As P(a/H) Equals a Rational Degree of Belief, α: Logical Probability Always Remained the Guide to Life for J M Keynes (August 23, 2019). Available at SSRN: https://ssrn.com/abstract=3442033 or http://dx.doi.org/10.2139/ssrn.3442033