Bayesian Inductive Logic, Verisimilitude, and Statistics

Below we will consider the relations between inductive logic and statistics. More specifically, we will show that some concepts and methods of inductive logic may be applied in the rational reconstruction of several statistical notions and procedures and that, in addition, inductive logic suggests some new methods which can be used for different kinds of statistical inference. Although there are several approaches to inductive logic and statistics, here we will focus on some versions of the Bayesian approach and, thereby, on the relations between Bayesian inductive logic and Bayesian statistics. The paper is organized as follows. The subjects of inductive logic and statistics will be shortly illustrated in Section 1, where it will be suggested that statistics can be seen as a special field of inductive logic. Two important theories developed within Bayesian inductive logic are the theory of inductive probabilities, started by Rudolf Carnap in the forties of the past century, and the theory of confirmation: the conceptual relations between such theories and statistics will be considered in Section 2. A recent version of Bayesian inductive logic, proposed by Ilkka Niiniluoto and others, has been developed by using the notion of verisimilitude, introduced in philosophy of science by Karl Popper; the key ideas of the verisimilitudinarian version of Bayesian inductive logic will be illustrated in Section 3, where it will be argued that it provides useful conceptual tools for the analysis of some important kinds of statistical inference.