Keynes, Boole and the interval approach to probability

This paper provides evidence on how Keynes devised a mathematical framework for his system of probability, which he called «approximation», in A Treatise on Probability, 1921. Keynes used standard conditional, mathematical probability to duplicate Boole’s results in the Challenge problem. He also showed how Boole’s approach would lead to the specification of interval estimates. It is also demonstrated that Keynes provided a solid mathematical structure for his nonlinear, non-additive decision theory. We suggest he should be recognized as the founder of the modern nonadditive, nonlinear approach to probability.