# Keynes’s Method in the A Treatise on Probability and the General Theory Is Inexact Measurement Involving Approximation, Imprecise Probability, and Indeterminate Probability Using Boolean Interval Valued Probability: There Is no Explicit Theory of Ordinal Measurement Developed, Used or Deployed Anywhere in Either the A Treatise on Probability or the General Theory

53 Pages Posted: 14 Mar 2019 Last revised: 26 Mar 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: February 23, 2019

### Abstract

Keynes was a lifelong proponent, advocate and user of the inexact measurement techniques that he had learned from reading Boole’s The Laws of Thought and been taught by William Ernest Johnson. Keynes called these techniques inexact measurement or approximation in the A Treatise on Probability. They involved the use of interval valued probability (upper-lower probability bounds) to deal with indeterminate probabilities and Chebyshev’s Inequality, which was used in order to provide a lower bound for imprecise probability estimates. Keynes extended his approximation techniques to encompass outcomes involving macroeconomic gross domestic product and other aggregate measures in Chapter Four of the General Theory.

Chapter III of the A Treatise on Probability in an introduction to the discussion of measurement. The discussion of measurement is continued in chapter five and finished in Part II in chapters 15-17 of the A Treatise on Probability. It is impossible to understand Keynes’s approximation approach to measurement unless the reader of the TP has understood Chapters 15-17. Keynes is very clear on this: “It will not be possible to explain in detail how and in what sense a meaning can sometimes be given to the numerical measurement of probabilities until Part II is reached. But this chapter will be more complete if I indicate briefly the conclusions at which we shall arrive later.” (Keynes,1921, p.37)

It is not possible for the Cambridge fundamentalists (Skidelsky, O’Donnell, Carabelli, Fitzgibbons, Runde) to understand Keynes’s views on measurement because they have not read or understood Part II of the A Treatise on Probability.

Keynes’s unchanging lifetime views on inexact measurement versus exact measurement and imprecise probability versus precise probability explain the Keynes-Tinbergen debate of 1939-40. Tinbergen’s background in Physics meant that he was an advocate of the Limiting Frequency interpretation of probability. Tinbergen was thus an advocate of precise and definite probability and exact measurement. Tinbergen brought this view with him when he started working in economics. Keynes was the exact opposite.

Tinbergen was used to analyzing inanimate phenomenon, like atoms, protons, electrons, particles, cells, molecules, genes, chromosomes, fair decks of cards, dice, coins, etc. Keynes was used to analyzing animate human behavior. Humans, unlike inanimate phenomenon, like atoms, protons, electrons, particles, cells, molecules, genes, chromosomes, fair decks of cards, dice, coins, can think and reason. Humans have memories, emotions, minds, and brains. While exact calculation and precision can be applied in many areas of the physical and life science, it is doubtful in most social sciences, liberal arts, behavioral sciences and especially in most areas of economics, finance and business. The exception would be studies of consumer consumption spending and business inventory demand, which are highly stable in the short run.

Keynes was not an ordinalist .Nowhere in the TP or GT does Keynes develop ,apply, or advocate an ordinal theory of probability. The Keynesian fundamentalists have misinterpreted pp.38-40 of the TP by ignoring Keynes’s clear statement on p.37 of the TP that his detailed analysis on measurement would take place in Part II, while only a brief introduction would take place on pp.38-40 of chapter III.

Keywords: Keynes inexact measurement, approximation, imprecise probability, exact measurement, precise probability, Tinbergen, ordinal probability

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

Suggested Citation

Brady, Michael Emmett, Keynes’s Method in the A Treatise on Probability and the General Theory Is Inexact Measurement Involving Approximation, Imprecise Probability, and Indeterminate Probability Using Boolean Interval Valued Probability: There Is no Explicit Theory of Ordinal Measurement Developed, Used or Deployed Anywhere in Either the A Treatise on Probability or the General Theory (February 23, 2019). Available at SSRN: https://ssrn.com/abstract=3340343 or http://dx.doi.org/10.2139/ssrn.3340343