Old evidence and new theories

Conclusion The discussion above indicates that there is some reason for optimism with regard to the project of incorporating logical-mathematical learning within Bayesianism, though it is obvious that there are many difficulties to be overcome. The biggest obstacle in this regard is overcoming the tension that exists between considerations of formal tractability and the desire to avoid demanding too much of rational agents. Jeffrey's solution seems more flexible in this regard than Garber's, but that may very well be because the general mechanisms underlying Jeffrey's rule of reparation have not been specified. In any case, in my view the verdict we should draw with regard to the problem of old evidence is a bit more pessimistic. Jeffrey's and Garber's solutions only address certain aspects of the problem, and thus can only provide partial solutions at best. The basic strategy of using logical-mathematical learning to induce a confirmation event does not completely evade the problem, which reemerges when the required logical-mathematical knowledge becomes old news. Thus, despite the solutions that have been offered to date, the problem of old evidence remains a fundamental challenge to the Bayesian point of view.This paper has benefited greatly due to valuable input from Bas van Fraassen, Richard Jeffrey, Alan Hájek, Gil Harman, Mike Thau, and Ned Hall.