ABSTRACT
Keynes’s Treatise on Probability (1921) sets out a theory which is, in a sense, the antithesis of the frequency theory. He holds that the relation used in deduction, namely “p implies q”, is the extreme form of a relation which might be called “p more or less implies q”. “If a knowledge of h”, he says, “justifies a rational belief in a of degree α, we say there is a probability relation of degree α between a and h”. We write this: “a/h = α”. “Between two sets of propositions there exists a relation, in virtue of which, if we know the first, we can attach to the latter some degree of rational belief.” Probability is essentially a relation: “It is as useless to say ‘b is probable’ as ‘b is equal’ or ‘b is greater than’.” From “a” and “a implies b”, we can conclude “b”, that is to say, we can drop all mention of the premiss and simply assert the conclusion. But if a is so related to b that a knowledge of a renders a probable belief in b rational, we cannot conclude anything whatever about b which has not reference to a; there is nothing corresponding to the dropping of a true premiss in demonstrative inference.
