# The Role of Ignorance About Keynes’s Inexact, Approximation Approach to Measurement in the A Treatise on Probability in the Keynes-Tinbergen Exchanges of 1938–1940

61 Pages Posted: 9 Apr 2019 Last revised: 19 Dec 2019

Date Written: March 16, 2019

### Abstract

There is no evidence that J. Tinbergen ever read the technical analysis provided by J. M. Keynes in Parts II and V of the A Treatise on Probability in the 1938-1940 time period or at any later time in his life. The same conclusion holds for econometricians in general. They simply do not understand what Keynes’s Inexact, Approximation Approach to Measurement in the A Treatise on Probability entails.

Tinbergen and Keynes held diametrically opposed positions on measurement. Tinbergen’s approach to measurement was guided by the Limiting Frequency interpretation of probability while Keynes’s approach followed the logical approach of George Boole. Tinbergen’s physics background led him to deploy an exact approach to measurement based on the specification of probability distributions, like the normal and lognormal, with exact and precisely defined measurements. All probabilities were assumed to be well defined, precise, exact, determinate, definite, additive, linear, independent single number of answers. Keynes’s approach was an inexact one to measurement based on his modification of Boole’s original approach in 1854 in The Laws of Thought in chapters 16-21. Probabilities for Keynes were, with a few exceptions, partially defined, imprecise, inexact, indefinite, indeterminate, nonadditive, nonlinear, and dependent. Probability estimates for Keynes required two numbers to specify the probability within a lower and upper bound(limit), and nor one like Tinbergen’s approach. Keynes called this approach Approximation. Keynesian probabilities are interval-valued. There are no more than a single handful of academics, worldwide today, who grasp the fact that Keynes’s approach to measurement in the A Treatise on Probability was an interval-valued approach that was covered by Keynes in chapters III and XV.

There was no economist alive in the late 1930’s-1940’s who understood Keynes’s approach in the A Treatise on Probability. An example of this ignorance is Lawrence Klein’s review in 1951 of Harrod’s biography of Keynes.

The assessments of the Keynes –Tinbergen exchanges in 1938-40 were practically identical to the assessment made of the A Treatise on Probability by Ronald Fisher in his 1923 Eugenics Review of the A Treatise on Probability, where Fisher completely overlooked the inexact approach to measurement that Keynes presented in Parts I –V of the A Treatise on Probability. He dismissed the A Treatise on Probability based on his belief that Keynes was arguing that probability could not be applied since it was, at best, ordinal in nature.

Only one economist in the 20th century understood exactly what it was that Keynes had done in the A Treatise on Probability. That economist was named F. Y. Edgeworth. However, Edgeworth died in 1926. His two 1922 book reviews of the A Treatise on Probability required a great deal of mathematical and statistical competence on the part of a reader. That mathematical competence was missing from the economics profession in the late 1930s and 1940s. The result was that Edgeworth’s two superb reviews were forgotten and never read by economists.

The problem, from Keynes’s perspective, was that Tinbergen was trying to apply to economic data techniques which were only sound in physics, where laboratory controlled environments with detailed experimental design could generate data and replicate/duplicate the experiments worldwide. Keynes had always argued that economics was not a physical or life science like physics, engineering, biology or chemistry and that it could never be like physics. A great abyss thus separated Tinbergen from Keynes from the very start of the private exchange of letters that began in 1938 to the final exchanges in the 1939-40 time period in the Economic Journal. Tinbergen’s complete and total ignorance of Keynes’s approach to inexact measurement meant that the possibility of some type of intellectual compromise was impossible from the very start.

The main reason for the completely divergent views expressed by Keynes and Tinbergen in their 1938-40 exchanges in the Economic Journal was due to their completely different technical backgrounds. Keynes’s background was logic, mathematics, and philosophy. Tinbergen’s background was physics. There simply was no common ground between the two academics.

**Keywords:** Keynes, Tinbergen, Econometrics, Exact Measurement, Inexact Measurement

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

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