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Keynes's Philosophical Development

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Davis bases his view of Keynes's philosophical development primarily on two error filled reviews of the A Treatise on Probability, written by Frank Ramsey in 1922 and 1926 ,plus Keynes's brief 4 page review of Ramsey's work in the New Statesman in 1931.Davis's ignorance of Keynes's logical theory of probability is best illustrated by his unclear,vague and dubious understanding of Keynes's views on induction(Davis,pp.142-146).Here is what Davis should have written.First,for Keynes there are two types of probabilities,imprecise interval(set)estimates that are"nonnumerical" and"nonmeasurable" because they require TWO numbers,not ONE number,to estimate the probability relationship and precise point estimates that require positive symmetrical evidence based on an application of Keynes's principle of indifference(and not the principle of nonsufficient reason).In Part II of the TP,Keynes introduces his theory of approximation in chapter 15 and extends the applications into chapter 17.Keynes gave the readers of his book ample warning by inserting references to chapter 15 in chapters 3,5 and 10.The theory of approximation represents Keynes's formal technique of specifying interval estimates.It is based on the work of George Boole in chapters 16-21 of The Laws of Thought(1854).Keynes then builds on one of Boole's problems by changing one of the assumptions.This modified problem allows Keynes to derive the major result of Part III for induction on pp.235-238 and 253-257 of the TP.This result holds for both precise and imprecise probabilities due to Keynes's definition of "finite probabilities".Now none of this appears in either Ramsey or Davis,who apes Ramsey.This is because Ramsey completely overlooked Keynes's definitions of nonmeasurable and nonnumerical in chapter III of the TP.In fact,Ramsey only read the first 4 chapters of the TP plus another 10-15 pages taken haphazardly from Parts II,III,and V.Ditto for Davis.For instance,Ramsey did not take the time to see that Keynes's axioms for addition and multiplication are defined on sets of propositions and were meant to apply to both precise and imprecise probabilities.Nor did Ramsey look at the extensions in chapters 8 and 15 of the TP.Ditto for Davis.In his review of Ramsey,Keynes completely rejected Ramsey's approach as a foundation for analogy and induction.This slips by Davis.Keynes "yields"to Ramsey what is already implicit in the TP-a rational decision maker will obey the laws of probability when they are strictly applicable and a single unique probability density function is known for certain.Of course, this means that Ramsey's theory is a special case of Keynes's.Davis's claim that Keynes rejected his general logical theory of probability to accept Ramsey's special theory of precise, numerical, subjective probabilities, and then implicitly formulated something called an intersubjective theory ,has no factual support in any of Keynes's writings.