Uncertain Inference

Rating:
Summary: JM Keynes,not Kyburg,founded the interval valued approach
Review: This is a very interesting book which is tarnished to some degree by the failure of the two authors to discuss all of the relevant accomplishments made by J M Keynes in the A Treatise on Probability(1921) and by Rudolf Carnap in the Logical Foundations of Probability(1950).These ommissions appear in practically all of H E Kyburg's work,starting with his Probability and the Logic of Rational Belief(1961),and continuing through The Logical Foundations of Statistical Inference(1974),Studies in Subjective Probability(1980,2nd edition),Epistemology and Inference(1983),Probability is the Very Guide to Life(2003),and Uncertain Inference(2001).The first error of ommission occurs with respect to the case of interval valued probability.Kyburg claims the following:"Keynes had little to offer by way of a systemization of his logical probability".(Kyburg,(2001),pp.80-81).Kyburg credits Smith,Good,Levi,Dempster,Shafer,Walley,and himself as the major contributors who have developed and/or refined the interval valued(imprecise)approach to probability over the last 40 odd years.Contrary to Kyburg,Keynes adapted Boole's 1854 approach into a systematic method for specifying interval valued probabilities in his A Treatise on Probability in chapter 15,pp.160-163 and in chapter 17,pp.186-194.Keynes states this very clearly:"Most of such comparisons(inexact numerical comparison)must be based on the principles of Chapter V.It is possible ,however,to develop a systematic method of approximation which may be occasionally useful."(Keynes,1921,p.161)Keynes then credits both G Boole and G Yule,although clearly Boole has priority. Kyburg makes the same error again in his discussion of interval estimates on pp.113-115.Keynes is not mentioned.The second ommission in this book is the failure to cover Keynes's index for weight of the evidence,w,which Keynes integrated into a decision rule which he called a conventional coefficient of weight and risk,c.There is no discussion of D.Ellsberg's very similar index to measure the ambiguity of the evidence,rho,which Ellsberg likewise integrated into a decision rule.The third ommission is Kyburg's failure to discuss the contribution of Carnap in the last chapter of his 1950 book, titled Estimation.Pages 554-559 of Carnap's book are important in that the reliability of an estimate of a probability ,in areas where statistical frequences are the only source of evidence,such as the atomic and subatomic particles of physics,the molecules of chemistry,and the cells,genes,and chromesomes of biology,is given by the standard error of the estimate,which is the same as Keynes's probable error of the estimate.Carnap's urn ball model and his discussion of it on pages 558-559 reaches practically the same conclusions as reached by Keynes and Ellsberg.Kyburg,unfortunately,restricts his discussion of Carnap only to Carnap's degree of confirmation c(h,e) and the theoretical state and structure descriptions listed by Carnap in the first half of his book