Two Notes on Probability

There is a fairly widespread view that, at least in one important sense of the term, probability is most properly attributed to statements: and that what is being asserted when it is said that a statement is probable, in this sense, is that it bears a certain relation to another statement, or set of statements, which may also be described as confirming, or supporting, or providing evidence for it. There are some, indeed, who maintain that this is the only sense in which it is correct to speak of probability; that what we ‘really mean’ when we assert anything to be probable is always that some statement bears the requisite relation to such and such a piece of evidence. Thus Keynes 1 assumes that every significant probability statement can be fitted into his formula ‘a/h=p’, where a is the proposition which is said to be probable, h is the evidence on which it is probable, and p is the degree of probability that h confers on a, a quantity which may or may not be numerically measurable. And Kneale 2 takes it for granted that probability is relative to evidence: if this is often overlooked, it is because in talking about probability we seldom bother to specify the evidence on which we are relying: ‘our probability statements are commonly elliptical’.3