Carnap and the Logic of Inductive Inference

Publisher Summary This chapter discusses Carnap's work on probability and induction, using the notation and terminology of modern mathematical probability, from the perspective of the modern Bayesian or subjective school of probability. Carnap used logical probability as a tool in understanding the quantitative confirmation of a hypothesis based on evidence and in rational decision making. The resulting analysis of induction involved a two step process. The first step included a broad class of possible confirmation functions, commonly called the “regular c-functions,” along with a unique function in that class (early Carnap) or a parametric family (later Carnap) of specific confirmation functions. The first step in the process essentially placed Carnap in substantial agreement with subjectivists. The second step, however, limits the class of probabilities that distinguishes Carnap from the subjectivist brethren. Carnap largely shaped the way current philosophy views the nature and role of probability, in particular its widespread acceptance of the Bayesian paradigm.