Jeffreys(J)does an excellent job in laying down a foundation for statistical inference based on a logical theory of probability.However,(J)appears not to have carefully read Keynes's A Treatise on Probability(1921),especially chapters 8,29,30,31 and 32.J appears not to have understood the generality of Keynes's approach.In the physical and life sciences,where one is dealing with evidence which is homogeneous and where every particle,electron,cell,molecule,gene or chromesome,etc.,is identical or practically identical to every other particle,electron,etc.,the only relevant evidence is statistical or frequency evidence.In such cases,Keynes's logical approach will give the same answer as Jeffreys would give.Keynes gave two other useful suggestions that were overlooked by J.The first was that the data pass a Lexis Q test for stability(satisfy the law of large numbers strictly).The second was Keynes's recommendation about using the Chebyshev Inequality as a lower bound on statistical estimates if the required assumptions necessary to assume a normal probability distribution were not met.J never understood that the very general axiomatic foundation that Keynes laid out in Chapter 12 of the TP applied to both precise and imprecise(partially ordered )probabilities.Keynes never claimed that the probabilities of scientific endeavor were partially ordered.Keynes did recognize,however, that the probabilities of the social sciences,liberal arts,economics,business,education and every day practical decision making were,in general,partially ordered.Finally ,J's claim ,in his introduction ,that Keynes withdrew his claim that most probabilities are inexact and indefinite,requiring two real numbers to specify the probability relation instead of one,in a 1931 New Statesman and Nation article reviewing Ramsey's collected essays,does not have a shred of evidence to support it.This type of offhand comment makes no sense as it would require Keynes to give up his general logical theory of probability in order to accept Ramsey's very special and narrow theory of probability.
