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H. E. Kyburg never read beyond chapter 6 of Keynes's A Treatise on Probability. From 1959 till his death in 2007, Kyburg continually based his assessment of Keynes's accomplishments on pp. 30 and 34 of Chapter III of the A Treatise on Probability. Edgeworth's careful and judicious reading of Keynes's chapter III allowed him to conclude that Keynes's theory was an interval valued theory of probability, as opposed to Kyburg's claims that Keynes merely had made some comments that would lead one to conclude that Keynes had made some interesting “suggestions, hints, notions,i ntuitions, ideas,” that would lead to an interval valued theory of probability if they were developed mathematically and logically.Wheeler 's evaluation of Keynes is simply a repetition of Kyburg's nearly 50 years of evaluations ,which are vastly inferior to Edgeworth's evaluation, which skipped Part II of Keynes's A Treatise on Probability.A study of Part II of A Treatise on Probability reveals that Keynes had a very advanced mathematical and logical theory of interval valued probability based on Boole's original presentation on pp.265-268 of The Laws of Thought that was presented in chapters 15,16, and 17 of Part II. This was accepted by the American mathematician E .B. Wilson, who acknowledged this grudgingly in his second, disguised review of the A Treatise on Probability that concentrated on chapter 17 of Part II, while ignoring the crucial chapter 15 in the September, 1934 issue of the Journal of the American Statistical Association. Wilson's 1934 paper has never been cited by any academic in any field in the 20th or 21st centuries. It also leads to a total rejection of Ramsey's two reviews of Keynes's A Treatise on Probability, as well as Wheeler's assessment about “... Ramsey's brilliant critique of Keynes's ideas about probability...” (Wheeler, 2012,p. 443).
With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, John Maynard Keynes (1883-1946) breathed new life into studies of both disciplines. Originally published in 1921, the famous economist's most important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the "logical-relationist" theory. In so doing, he explored the logical relationships between classifying a proposition as "highly probable" and as a "justifiable induction." A Treatise on Probability argues that probability is a matter of logic, which renders it objective: a statement involving probability relations possesses a truth value independent of opinion. Keynes demonstrates that if a hypothesis has even the smallest finite probability, it can be transformed into certainty by a sufficient number of observations. This is his attempt to overcome Humean skepticism by asserting that theoretically grounded hypotheses need only exhibit finite probability to form the basis of science and rational action. Another key idea discussed in A Treatise on Probability is that probability relations constitute only a partially ordered set in the sense that two probabilities cannot necessarily always be compared. Keynes further maintains that probability is a basic concept that cannot be reduced to other concepts
F. Y. Edgeworth made the only correct assessment of Keynes's Logical Theory of Probability in his A Treatise on Probability among philosophers in the 100 years between 1921 and 2020. The reason is that he actually read the entire book, with the exception of Part II, which he was able to assess through his very careful reading of Part I.The major problem confronting any philosopher, who wants to take into consideration the various different aspects of Keynes's A Treatise on Probability, is the unfortunate fact that there is no philosopher,with the one exception of Edgeworth (Bertrand Russell did not read Part V), who has read beyond chapters 1-4 plus some parts of chapter 6 of the A Treatise on Probability. This assessment includes every philosopher associated with SIPTA, as well as B. Koopman, I. J. Good, T. L. Fine, P. Suppes, H.E. Kyburg, I.Levi, S. Zabell, as well as younger philosophers, such as B. Weatherson, D. Rowbottom, R.Bradley, S. Bradley, J. Williamson, T. Siedenfeld, G. Wheeler, etc.The conclusion reached is that after 100 years there is only one sure path currently available to philosophers who want to know what it was that Keynes actually accomplished in the A Treatise on Probability-read and reread the two reviews made by Edgeworth. A reader is then in a good position to grasp what it was that Keynes had erected in 1921-the first mathematically and technically advanced interval valued approach to probability in history. Kyburg's claim, that he was the first to have put forth a detailed interval valued approach for a logical theory of probability, is simply a major oversight made by Kyburg.Edwin B. Wilson's conclusion, that Edgeworth was by the far the most qualified academic to review Keynes's A Treatise on Probability, still holds good 100 years after he published his reviews of Keynes's book.