Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments

SUMMARY The main purpose of this paper is to consider what explicata are possible for corroboration and explanatory power of a hypothesis. The work is intended to sharpen some previous work by Popper. It will be found, for example, that the only possible explicatum for explanatory power, satisfying the desiderata, is a monotonic function of amount of information (without expectations). Corroboration has a wider variety of explicata, one of them being “weight of evidence”. This, too, is essentially unique if probabilities of hypotheses are not to appear explicitly in the formula. In the choice of an experimental design we may have difficulty in judging the relevant utilities. In such cases it may be reasonable to base the choice on a knowledge of the probability distribution of some measure of corroboration, and especially on the expectation.