Probability

Abstract

It is already clear, from the discussion of the last chapter, how we are going to define probability: We shall say that the probability of a statement of the form ^┏x∈y^┓, relative to a strictly consistent body of knowledge w is the interval [p, q], whenever relative to the rational corpus w, x is a random member of z, with respect to membership in y’s and we know (in w) that the proportion of y’s among z’s lies in the interval [p, q]. Furthermore, again, in accordance with a remark made in the last chapter, we shall say that the probability of any statement s is [p, q], relative to w, just when s is connected by a biconditional chain in w to ^┏x∈n^┓, and the probability of ^┏x∈y^┓, relative to w, is [p, q]. Finally, we take account of more general (not necessarily strictly consistent) rational corpora by stipulating that the probability of a statement s, relative to the rational corpus w, is [p, q] just in case the probability of s, relative to every maximal consistent subset of w is [p, q].