 In the inductive logics of Keynes and Carnap, Bayes’ theorem, a straightforward theorem of probability theory, plays a central role in expressing how evidence comes to bear on hypotheses. Bayes’ theorem expresses how the probability of a hypothesis h on the evidence e, \(P[h \pmid e]\), depends on the probability that e should occur if h is true, \(P[e \pmid h]\), and on the probability of hypothesis h prior to taking the evidence into account, \(P[h]\) (called the prior probability of h). (Later we’ll examine Bayes’ theorem in detail.) So, such approaches might well be called Bayesian logicist inductive logics. Other prominent Bayesian logicist attempts to develop a probabilistic inductive logic include the works of Jeffreys (1939), Jaynes (1968), and Rosenkrantz (1981).