# On Keynes's Realization That His Concept of Uncertainty in the General Theory, Defined as an Inverse Function of Weight from the 'A Treatise on Probability', Would Not Have Any Impact at All on Economists Thinking

31 Pages Posted: 4 Aug 2017

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: August 4, 2017

### Abstract

J M Keynes’s General Theory is a straightforward application of Keynes’s A Treatise on Probability. Keynes, in that book, based his logical theory of probability on Boole’s upper and lower probabilities. Practically all of Part II of the TP was devoted to developing non(sub) additivity and approximation into an interval valued approach to probability. This means that one is dealing with uncertainty. Uncertainty can’t exist without non (sub) additive probabilities. Keynes operationalized sub additivity in two ways. First, by using interval valued probability and second, by using his conventional coefficient of risk and weight, c, which incorporated the impact of the weight of the evidence, w, which was an index for measuring the completeness of the relevant evidence on the unit interval [0, 1].

The conventional coefficient, c, and indeterminate, interval valued probability are mirror images of each other. If w=1, then there are precise, determinate, additive probabilities. If w< 1, then there are indeterminate probabilities and imprecise probabilities. A w<1 means that non (sub) additivity is the general case.

Keynes brings all of this together in the General Theory in chapter 12 on page 148 with his definition of uncertainty being an inverse function of the weight of the evidence. Liquidity Preference is then defined by Keynes as a positive function of uncertainty. Confidence is defined as an inverse function of uncertainty. This means that uncertainty exists whenever w <1. However,uncertainty can be graded and measured with the same kind of interval valued approach Keynes applied to probability based on approximation in chapters 15-17 of the A Treatise on Probability. Keynes also applied his interval valued approach from the A Treatise on Probability in chapter 15 to chapter 4 in the General Theory when dealing with the price level and output as a whole.

Keynes builds his theory of the rate of interest on the LP(LM) curve of liquidity preference and the IS curve, based on his Y-multiplier model, which rests on the D-Z model of expected prices and expected profits. Keynes’s IS curve incorporated the weight of the evidence concept as it related to changes in the news over time in the form of confidence in the expectation the businessman calculated.

Keynes was fully aware when he wrote the General Theory that all economists of his time either subscribed to the limiting frequency interpretation of probability or the subjectivist theory of probability a la I Fisher, Poincare or Borel. Keynes never expected the economics profession, who were followers of the theory of decision making of Jeremy Bentham, to accept his version of IS –LM. That is precisely what happened. Other versions of IS-LM then were developed by Hicks, Lange, Modigliani, Tobin, etc., that were based on the subjectivist concept of risk with known probability distributions. The Post Keynesian and Institutionalist schools followed Shackle, where Keynes’s uncertainty concept was replaced by Shackle’s concept of making decisions without any evidence where the expectations were judged to be dream like apparitions.

Keynes was the only practitioner of the logical theory of probability in the 20th century and 21st century among economists.

Keywords: Harrod, Hicks, Keynes, IS-LM, Liquidity Preference, QJE 1937, Chapter 15, pp.180-182 of GT, Chapter 21

JEL Classification: B10, B12, B14, B16, B20, B22

Suggested Citation

Brady, Michael Emmett, On Keynes's Realization That His Concept of Uncertainty in the General Theory, Defined as an Inverse Function of Weight from the 'A Treatise on Probability', Would Not Have Any Impact at All on Economists Thinking (August 4, 2017). Available at SSRN: https://ssrn.com/abstract=3013497 or http://dx.doi.org/10.2139/ssrn.3013497