Probability logic and probabilistic induction

This article reviews some philosophical aspects of probability; and describes how probability logic can give precise meanings to the concepts of inductive support, corroboration, reputation, and related notions, as well as provide a foundation for logically sound statistical inference. Probability logic also provides a basis for recognizing prior distributions as an integral component of statistical analysis, rather than the current misleading practice of pretending that statistics applied to observational data are objective. This basis is important, because the use of realistic priors in a statistical analysis can yield more stringent tests of hypotheses and more accurate estimates than conventional procedures.