Inductive Logic and Statistics

Abstract

Publisher Summary An inductive logic refers to a system of inference that describes the relation between propositions on data and propositions that extend beyond the data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. Inductive logic is largely dominated by the Carnapian programme, but the statisticians generally do not recognize Carnapian inductive logic as a discipline. This chapter shows that Carnapian inductive logic can be developed to encompass inference over statistical hypotheses and that the resulting inductive logic can partly capture statistical procedures. It presents a unified picture of inductive inference to which both inductive logic and statistics, past or present, can be related. It introduces a general notion of probabilistic inductive inference. The chapter also illustrates Carnapian inductive logic and relates it to Bayesian statistical inference via de Finetti's representation theorem. It provides a description of two classical statistical procedures—namely, maximum likelihood estimation and Neyman–Pearson hypothesis testing, and explores the ways these methods can be accommodated in extended inductive logic.