What Was E. Borel Referring to in His 1939 Book when He Describes '…the Beautiful Work of Mr. J.m. Keynes…' in the A Treatise on Probability? The Answer Is the Belated Recognition on Borel’s Part of the Extremely Important Part Ii of the A Treatise on Probability on Imprecision and Inexact Measurement

E. Borel, in his 1924 review of the A Treatise on Probability, did not read Part II. He skipped Part II, although he did apologize to Keynes and Russell for doing so in his review, acknowledging that this was the most important part of Keynes’s A Treatise on Probability .Borel was certainly correct .He does not use the word “beautiful” to describe Keynes’s work at any place in his 1924 review. Now Parts I, III, IV, and V of the A Treatise on Probability are well done and make some breakthroughs, as acknowledged by Edgeworth in 1922 in his two reviews. However, statistics is not the type of mathematics where one mathematician would use the highest form of compliment possible among mathematicians, ”beautiful”, to describe the work of another mathematician. Borel recognized that Keynes was certainly a mathematician. By a process of elimination a la Sherlock Holmes, Borel can only be talking about Part II of the A Treatise on Probability. Part II is the part that Borel skipped in his review in 1924.Fifteen years later, Borel had to have finally been able to figure out what Keynes was doing ,with the help of Bertrand Russell and William Ernest Johnson, in Part II, much like Edwin Bidwell Wilson had finally been able to grasp Keynes’s points in Part II in 1934, some eleven years after his 1923 review of the A Treatise on Probability, although Wilson argued that uncertainty ,in Keynes’s sense, is really not important for a statistician. Borel must have been referring implicitly to Keynes’s truly impressive work on non additivity and interval valued probability in Part II of the A Treatise on Probability, which Keynes had based on G. Boole’s 1854 The Laws of Thought, in his footnotes in Chapter Two of his 1939 French book,the title of which is translated variously into English as Probability:Its Philosophy and Practical Value or Practical and Philosophical Value of Probabilities or Practical Value and Philosophy of Probabilities. Unfortunately, B. de Finetti ‘s review of Keynes’s A Treatise on Probability took place in 1938 and so he could not make use of Borel’s revised opinion of A Treatise on Probability that appeared in 1939 in Borel’s Practical and Philosophical Value of probabilities. The strange and incomprehensible failure of, especially ,philosophers and economists, but ,in fact ,all academics who have written on Keynes’s A Treatise on Probability, to cover Part II of the A Treatise on Probability means that theories of imprecise probability had to be created from scratch all over again, using Koopman’s 1940 works as a foundation, instead of building on Adam Smith, George Boole and J M Keynes with one,and only one, exception-the American mathematician, Theodore Hailperin. A careful reader of the contributions made by Adam Smith, G.Boole,J. M. Keynes, and T. Hailperin to imprecise probability ,with their emphasis on interval valued probability,non additivity and partial ordering, has no need to spend an inordinate amount of time reading the Koopman, C A B Smith ,Dempster, I J Good, H. Kyburg, I.Levi, i.e. SIPTA,etc. literature on imprecise probability because the latter literature is simply grossly ignorant about the former, which is basically involved in an exercise in reinventing the wheel . Borel needed to have made an explicit reference to Part II of the A Treatise on Probability in chapter 2 of his 1939 book. If he had, then, possibly, the history of decision science would have been very different and Ramsey’s error filled reviews in 1922 and 1926 would have been ignored.