Problems in Lewis’s Theory of Induction

Abstract

My study of Peirce’s theory of induction has shown that Peirce has made two justifications of induction, the probabilistic and non-probabilistic. By the probabilistic justification of induction, induction is shown to be a valid inference which consists in having a logical leading principle and drawing conclusions with probability. This justification of induction, as stated in Peirce’s own terms, as we have seen, is inadequate. But I have suggested the way in which Peirce’s argument can be mended. There are two conclusions which we may draw from this probabilistic justification of induction. First, we may say that there is always a logical and a priori-determinable relation between premises, which assure us of the existence of a fair sample with a given composition, and the inductive conclusion drawn from such premises. This relation we express by saying that the inductive conclusion follows with probability from its premises in accordance with a logical leading principle. It is wherein the validity of inductive inference consists. In other words, the validity of inductive inference consists in a probability relation between its conclusion and its premises.