An Introduction to the Philosophy of Science

In the first of two chapters on probability in scientific inquiry, the basic ideas of probability theory are introduced through examples involving games of chance. The chapter then focuses on the Bayesian approach to probability, which adopts the stance that probabilities should be understood as expressions about the degrees of belief. The Bayesian approach as a general framework for probability is explained through examples involving betting that extend beyond games of chance, which also allows the introduction of the idea of probabilistic coherence as a condition of rational partial belief. We are then finally ready for Bayes’s theorem, a theorem of the probability calculus that plays a central role in the Bayesian account of learning from evidence. That account is illustrated with a historically motivated example from the history of paleontology. The chapter considers objections to the Bayesian approach and the resources Bayesians may draw on for answering those objections.