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We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.

We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we investigate what Herzberg means (...) by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non , and we ventilate our misgivings about Herzberg’s suggestion that the notion of solvability might help the foundationalist. (shrink)

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. (shrink)

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. (shrink)