A Bayesian Proof of a Humean Principle

Abstract

This is of course an informal principle, but it will be shown that, if the terms are formally explicated in a certain plausible way, then the resulting formal version of the principle can be proved rigorously given Bayesian assumptions. As is often the case, however, the formal explication is not unique, and in fact an alternative explication of one of the terms (due to Philip Dawid) will be given which prevents the proof going through. Still the fact that at least one plausible formal explication of Hume's principle can be proved rigorously seems not uninteresting. Let M state that a particular miracle has taken place, and let t stand for the testimony in favour of M. t will be regarded as sufficient to establish the miracle