ABSTRACT
Statistical and probabilistic reasoning plays an important role in scientific inference. It is sometimes thought that such reasoning provides an answer to the problem of induction. While induction cannot give us logical certainty, because we cannot logically rule out alternatives, it might be that it can lend a high probability to its conclusions. In this chapter, as well as describing some of the probabilistic-statistical techniques used in science, I shall examine in some detail the hope for an a priori probabilistic inductive method. Before starting, it should be clear that the prospects are not very good as regards a thoroughgoing response to Hume’s problem. In general, Hume’s problem asks: How can observations limited to a small region of space-time tell us what is happening throughout space-time? The conclusion of an inductive argument, whether it be an argument by naive induction or sophisticated statistical reasoning, will always reach out beyond the evidence. There will always be room for the Humean sceptic to respond that any method we employ rests upon some assumption to the effect that the observable portion of space-time is some sort of reflection of the universe as a whole. As the rest of reality might be utterly unlike the observed part, this principle is clearly empirical and so cannot be justified by any a priori (e.g. mathematical) reasoning.
