Bayesian See BAYESIAN RATIONALITY, CONFIRMA -. TIO. Bayesian rationality, minimally, a property a system of beliefs (or the believer) has in virtue of the system’s ‘conforming to the probability calculus.’ ‘Bayesians’ differ on what ‘rationality’ requires, but most agree that (i) beliefs come in degrees (of firmness); (ii) these ‘degrees of belief’ are (theoretically or ideally) quantifiable; (iii) such quantification can be understood in terms of person-relative, time-indexed ‘credence functions’ from appropriate sets of objects of belief (propositions or sentences) – each set closed under (at least) finite truth-functional combinations – into the set of real numbers; (iv) at any given time t, a person’s credence function at t ought to be (usually: ‘on pain of a Dutch book argument’) a probability function; that is, a mapping from the given set into the real numbers in such a way that the ‘probability’ (the value) assigned to any given object A in the set is greater than or equal to zero, and is equal to unity (% 1) if A is a necessary truth, and, for any given objects A and B in the set, if A and B are incompatible (the negation of their conjunction is a necessary truth) then the probability assigned to their disjunction is equal to the sum of the probabilities assigned to each; so that the usual propositional probability axioms impose a sort of logic on degrees of belief. If a credence function is a probability function, then it (or the believer at the given time) is ‘coherent.’ On these matters, on conditional degrees of belief, and on the further constraint on rationality many Bayesians impose (that change of belief ought to accord with ‘conditionalization’), the reader should consult John Earman, Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory (1992); Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach (1989); and Richard Jeffrey, The Logic of Decision (1965). See also BAYES’S THEOREM , DECISION THE- ORY, DUTCH BOOK ARGUMENT, PROBABILITY, RATIONALITY. D.A.J.