Grazer Philosophische Studien

Volume 12/13, 1981

Keith Lehrer
Pages 131-141

The Evaluation of Method
A Hierarchy of Probabilities Among Probabilities

A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same is true of higher order probabilities. However, when higher order probabilities are normalized to obtain weights that are used to average the probabilities of the next lower level, the averaging process will yield convergence towards a single first order probability condensing higher order information. An infinite averaging process can be finitely calculated to obtain a coherent assignment. Hence there is no vicious regress of probabilities. Memory beliefs illustrate the convergence of an infinite hierarchy