On the Theory of Induction

Abstract

Induction serves three purposes. It discovers hypotheses, it offers evidential support for generalities, and it tells us something about the future. There are no doubt others; but we shall be concerned chiefly with these. The search for evidence involves a peculiar method in the choosing of axioms, while formal guesses about the future rely upon the estimation of chances. Carnap’s excellent book is one of the most suggestive that has yet appeared on the topic. However, he is concerned with its logical aspects. Here we shall be occupied chiefly with aspects considered inherent; we shall deal with sub-topics, such as the phenomenology of induction or the theory of applications, only as they contribute to the broader viewpoint. We shall not impose an explanation upon induction but seek the one implicit in inductive procedures. There is a further difference. Carnap distinguishes logical from empirical probability. The understanding in this article is that induction proper is to be distinguished from the two meanings of probability, on grounds which will presently be introduced. Induction, we shall assume, is the generic name covering three groups of operations: induction proper, confirmation and frequency. All three, however, involve both the logical and the empirical orders to some extent.