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.
