Old Evidence and Logical Omniscience in Bayesian Confirmation Theory

The Bayesian framework is intended, at least in part, as a formalization and systematization of the sorts of reasoning that we all carry on at an intuitive level. One of the most attractive features of the Bayesian approach is the apparent ease and elegance with which it can deal with typical strategies for the confirmation of hypotheses in science. Using the apparatus of the mathematical theory of probability, the Bayesian can show how the acquisition of evidence can result in increased confidence in hypotheses, in accord with our best intuitions. Despite the obvious attractiveness of the Bayesian account of confirmation, though, some philosophers of science have resisted its manifest charms and raised serious objections to the Bayesian framework. Most of the objections have centered on the unrealistic nature of the assumptions required to establish the appropriateness of modeling an individual's beliefs by way of a pointvalued, additive function. But one recent attack is of a different sort. In a recent book on confirmation theory, Clark Glymour has presented an argument intended to show that the Bayesian account of confirmation fails at what it was thought to do best. Glymour claims that there is an important class of scientific arguments, cases in which we are dealing with the apparent confirmation of new hypotheses by old evidence, for which the Bayesian account of confirmation seems hopelessly inadequate. In this essay I shall examine this difficulty, what I call the problem of old evidence. I shall argue that the problem of old evidence is generated by the