Inductive Logic and Statistics

This chapter concerns inductive logic in relation to mathematical statistics. I start by introducing a general notion of probabilistic induc- tive inference. Then I introduce Carnapian inductive logic, and I show that it can be related to Bayesian statistical inference via de Finetti's representation theorem. This in turn suggests how Carnapian induc- tive logic can be extended to include inferences over statistical hy- potheses. With this extension inductive logic becomes more easily applicable to statistics. I consider two classical statistical procedures, maximum likelihood estimation and Neyman-Pearson hypothesis test- ing, and I discuss how they can be accommodated in an inductive logic with hypotheses.