# Keynes Had No ‘Hidden Method’ in the A Treatise on Probability (1921): Keynes's Method Is an Explicit Inductive Logic Built on Inexact Measurement and Approximation, Which Was Openly Based on Boole’s Non Linear, Non Additive Approach Using Interval Values Probability

22 Pages Posted: 1 Nov 2019

See all articles by Michael Emmett Brady

California State University, Dominguez Hills

Date Written: October 22, 2019

### Abstract

J M Keynes’s method was explicitly introduced and used in the A Treatise on Probability in Parts II, III and V. Keynes’s method is an inductive logic built on the mathematical logic and algebra of George Boole. Boole introduced non linearity and non additivity into his approach using interval valued probability that used lower and upper bounds. Boole’s approach, like Keynes’s, deals explicitly with problems like non comparability, non measurability and incommensurability that can’t be dealt with by additive and linear probability representations. Keynes initially introduced a brief discussion of these problems in chapter III of the A Treatise on Probability and Chapter 4 of the General Theory.

Keynes called this method inexact measurement and approximation in chapter 15 of the A Treatise on Probability. It is impossible for Keynes to be anti-mathematical,anti-formalist, anti logicist, or a rationalist, given that, building on Boole, he created an inductive logic. Rationalists, by definition, do not accept the concept of induction, which is why they are called deductivists and not inductivists. Keynes, of course, took certain elements of the rationalist perspective and combined these elements (a priori thought, intuition, etc.) with certain elements of empiricism to create an early version of logical empiricism. Similarly, it is impossible for Keynes to have been anti logicist, anti formalist and anti mathematical because his work in Parts II and V of the A Treatise on Probability is logical,formal,and mathematical analysis built directly on the mathematical logic and algebra of George Boole.

The belief that Keynes was a rationalist and/or anti logicist, anti formalist and anti mathematical is maintained by economists, such as A. Carabelli and R. O’Donnell, who never read or understood Parts II, III and V of the A Treatise on Probability or chapters 16-21 of G Boole’s 1854 The Laws of Thought. It is impossible for Keynes to be a rationalist and proclaim at the end of chapter 26 of the A Treatise on Probability that probability is the guide to life since all rationalists reject inductive logic.

Keywords: probability, inductive logic, deduction, inexact measurement, approximation, Carnap, Keynes

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

Suggested Citation

Brady, Michael Emmett, Keynes Had No ‘Hidden Method’ in the A Treatise on Probability (1921): Keynes's Method Is an Explicit Inductive Logic Built on Inexact Measurement and Approximation, Which Was Openly Based on Boole’s Non Linear, Non Additive Approach Using Interval Values Probability (October 22, 2019). Available at SSRN: https://ssrn.com/abstract=3474080 or http://dx.doi.org/10.2139/ssrn.3474080

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