The Mathematical Principles of Natural Philosophy.

Hempel and Oppenheim, in their paper 'The Logic of Explanation', have offered an analysis of the notion of scientific explanation. The present paper advances considerations in the light of which their analysis seems inadequate. In particular, several theorems are proved with roughly the following content: between almost any theory and almost any singular sentence, certain relations of explainability hold.

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring in covering laws (...) can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization. (shrink)