Knowledge from Probability

We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a theory of knowledge and belief formulated in terms of relations of comparative normality with a probabilistic reduction of those relations. It predicts that only highly probable propositions are believed, and that many widely held principles of belief-revision fail. How can we have knowledge that goes beyond what we have observed - knowledge about the future, or about lawful regularities, or about the distal causes of the readings of our scientific instruments? Many philosophers think we can't. Nelson Goodman, for example, disparagingly writes that "obviously the genuine problem [of induction] cannot be one of attaining unattainable knowledge or of accounting for knowledge that we do not in fact have" [20, p. 62]. Such philosophers typically hold that the best we can do when it comes to inductive hypotheses is to assign them high probabilities. Here we argue that such pessimism is misplaced.