Induction , Rational Acceptance , and Minimally Inconsistent Sets

1. Introduction. The purpose of this paper is to present a theory of in-ductive inference and rational acceptance in scientific inquiry. A concept of relevant deduction is defined in which the truth of each and every premise of a deductive argument is essential to establishing the truth of the conclusion by deduction from the premises. This definition is based on the completely abstract notion of a minimally inconsistent set of statements. In terms of this same abstract logical concept and the relation of probability, we shall define a concept of inductive inference that is a principle of rationality. This concept of inductive inference is shown to form the basis of a principle of acceptance in which two important epistemic utilities are maximized. 2. Conditions of Relevant Deduction. Suppose we are engaged in reasoning concerning some scientific conclusion that is neither contradictory nor logically true. If we intend to establish the truth of the conclusion by deduction from the premises, then it is important that several conditions be met to ensure that the deductive argument is relevant to that end. First the premises of such a relevant deductive argument, RD, must be logically consistent: