J M Keynes’s Range Definition of Uncertainty (Uncertainty Ranges From Complete Knowledge to Complete Ignorance) Versus the Post Keynesian (Joan Robinson, P. Davidson, G. Shackle) Binary-Dual Definition of Uncertainty: Confusing and Mixing Up the Contradictory and Conflicting Definitions of Keynes (Greenspan) and Shackle on Uncertainty

J M Keynes's definition of uncertainty directly contradicts the definition of uncertainty given by G L S Shackle, which is the same as that used by Joan Robinson, Paul Davidson, heterodox and Post Keynesian economists. Keynes defined uncertainty to be an inverse function of the weight of the argument in chapter 12 on page 148 in footnote 1. The weight of the argument is analyzed logically in chapter 6 of the A Treatise on Probability and mathematically in chapter 26 of the A Treatise on Probability, where Keynes incorporates it in a weighted decision rule which can be used as an alternative to the difficult interval valued approach Keynes created in Part II of the A Treatise on Probability that is based on the work of George Boole.This means that uncertainty is a range having different gradations from situations of complete knowledge to situations complete ignorance. Alan Greenspan has provided a similar type range in 2004 that he called a Continuum. The Greenspan Continuum ranges from complete knowledge to no knowledge. Shackle’s definition of uncertainty is a binary definition that has no ranges. Thus there is either complete and total uncertainty, which Shackle called fundamental uncertainty (fundamental uncertainty is also called radical uncertainty, unknowledge, or irreducible uncertainty by Heterodox and Post Keynesian economists) or there is Knowledge, which is complete, true, and has deductive certainty. Shackle’s definition is just the two extreme outcomes of Keynes’s range and Greenspan’s range. It completely eliminates what Keynes called probabilistic knowledge, which deals with intermediate situations of uncertainty, where the decision maker has some things he has knowledge of and some things he does not know. The University of Groningen’s online course, “Decision Making in a Complex and Uncertain World” has confused and mixed up these contradictory meanings of Keynes, Greenspan and Shackle on Uncertainty in their course by adopting Shackle’s definition and claiming that this is also Keynes’s definition. This can be amended by simply separating Keynes and Greenspan from Shackle and his followers, the Post Keynesians like Paul Davidson, S. Weintraub and Joan Robinson, when uncertainty is introduced. Keynes’s definition and views on uncertainty are explicitly linked to chapters 6 and 26 of the A treatise on Probability. What Keynes means by uncertainty in the General Theory is that the evidential weight of the argument, V(a/H), is equal to w, where w has been normalized on the unit interval from 0 to 1,so the 0≤w≤1, Keynes then states on p.148 that Uncertainty is an inverse function of the weight of the argument, w, which can range between 0 and 1. This can be written as U(Uncertainty)=f(w), so that Uncertainty is a range of different gradations from w=0, complete ignorance through w=1, complete knowledge. It is easily seen that heterodox economists have fixated on the extreme case where w=0, while orthodox neoclassical and new neoclassical economists proclaim the w=1, which is, of course, the rational expectations hypothesis. Greenspan’s Continuum completely solves this conflict by showing how he constantly maneuvered the American and World economy by using an approach to monetary policy from 1987 to 2005 that consistently considered the full range of possible outcomes, ranging from complete ignorance to complete knowledge. Alan Greenspan should already have been awarded either a Nobel (Memorial) prize in economics or a Nobel Prize in Literature for his accomplishment.