帰納論理学と確率

Abstract

This paper is a critical exposition of Carnap's and Hintikka's systems of inductive logic. First, Carnap's system of inductive logic is examined in detail, and despite its great virtue with respect to the confirmation of singular predictions, we conclude that it is unsatisfactory as a model of our informal inductive reasoning. The reason is that according to his inductive logic, no nontrivial universal statements are confirmable in an infinite universe. On our diagnosis, this feature stems from Carnap's partition of the set of all possible universes (state-descriptions) by the structure-descriptions and his probability assignment based on it; structure-descriptions can achieve only statistical generalities. Although Carnap defends his inductive logic by introducing the notion of the "instance confirmation" of a law, his argument is rejected on several epistemological grounds. Next we examine Hintikka's inductive logic which is an ingenious extension of the Carnapian logic. The essential difference of Hintikka's logic from Carnap's stems from Hintikka's partition of the set of all possible universes by means of the constituents, each of which is the strongest generalization in a possible universe. Starting from this partition, Hintikka then relativizes the Carnapian logic to each constituent. This determines inductive logic according to which not only singular predictions but also universal statements can be confirmed. In Hintikka's inductive logic, a certain sort of simplicity consideration also works. In this connection, Popper's view that the simplicity of a hypothesis can be explicated in terms of the logical strength or the amount of empirical content is briefly criticized. The application of simplicity consideration to hypotheses presupposes that these hypotheses are incompatible; hence the logical strength of a hypothesis cannot give a measure of its simplicity. Finally, several important directions for a further development of inductive logic are briefly indicated, including the author's own contribution in the field.