A Treatise on Probability, Ch 4

In this chapter, Keynes critiques the Principle of Indifference (abbreviated P.I.) which is his own name for what Bernoulli called ‘The Principle of Non-Sufficient Reason.’ The principle states that when several alternatives are possible—and yet there is no information whatsoever to prefer one over another—each alternative should be given equal probabilities. Suppose you are picking up a friend at the airport and don’t know which gate they will arrive at. What is the probability of arrival at gate A versus not-A? The P.I. calls for assigning P(A) a value of 1/2, or more generally 1/n where n is the number of known alternatives. Unfortunately, this principle quickly leads to paradoxes, which Keynes demonstrates in this chapter.  His goal is not to demolish the P.I., but instead refine it.