Probability

Since the late twentieth century, some subjectivists have canvased further desiderata on credences. For example, we might evaluate credences according to how closely they match the corresponding relative frequencies, according to how well "calibrated" they are. Also under consideration are "scoring rules" that refine calibration. Various subjectivists believe that rational credences are guided by objective chances (perhaps thought of as propensities), so that if a rational agent knows the objective chance of a given outcome, her degree of belief will be the same as the objective chance. There has been important research on the aggregation of opinions and the preferences of multiple agents. This problem is well known to readers of the risk-assessment literature. Moreover, in light of work in economics and psychology on bounded rationality, there have been various attempts to "humanize" Bayesianism, for example, in the study of "degrees of incoherence," and of vague probability and decision theory (in which credences need not assume precise values).

Since the late twentieth century there have also been attempts to rehabilitate the classical and logical interpretations, and in particular the principle of indifference. Some objective Bayesians appeal to information theory, arguing that prior probabilities should maximize entropy (a measure of how flat a probability distribution is), subject to the constraints of a given problem. Probability theory has also been influenced by advances in theories of randomness and in complexity theory (see Fine; Li and Vitanyi), and by approaches to the "curve-fitting" problem—familiar in the computer science, artificial intelligence, and philosophy of science literature—that attempt to measure the simplicity of theories.

While Kolmogorov's theory remains the orthodoxy, a host of alternative theories of probability have been developed (see Fine; Mückenheim et al.). For instance, there has been increased interest in nonadditive theories, and the status of countable additivity is a subject of lively debate. Some authors have proposed theories of primitive conditional-probability functions, in which conditional probability replaces unconditional probability as the fundamental concept. Fertile connections between probability and logic have been explored under the rubrics of "probabilistic semantics" and "probability logic."