The primary uses of probability in epistemology are to measure degrees of belief and to formulate conditions for rational belief and rational change of belief. The degree of belief a person has in a proposition A is a measure of their willingness to act on A to obtain satisfaction of their preferences. According to probabilistic epistemology, sometimes called ‘Bayesian epistemology’, an ideally rational person’s degrees of belief satisfy the axioms of probability. For example, their degrees of belief in A and -A must sum to 1. The most important condition on changing degrees of belief given new evidence is called ‘conditionalization’. According to this, upon acquiring evidence E a rational person will change their degree of belief assigned to A to the conditional probability of A given E. Roughly, this rule says that the change should be minimal while accommodating the new evidence. There are arguments, ‘Dutch book arguments’, that are claimed to demonstrate that failure to satisfy these conditions makes a person who acts on their degrees of belief liable to perform actions that necessarily frustrate their preferences. Radical Bayesian epistemologists claim that rationality is completely characterized by these conditions. A more moderate view is that Bayesian conditions should be supplemented by other conditions specifying rational degrees of belief.
Support for Bayesian epistemology comes from the fact that various aspects of scientific method can be grounded in satisfaction of Bayesian conditions. Further, it can be shown that there is a close connection between having true belief as an instrumental goal and satisfaction of the Bayesian conditions.
Some critics of Bayesian epistemology reject the probabilistic conditions on rationality as unrealistic. They say that people do not have precise degrees of belief and even if they did it would not be possible in general to satisfy the conditions. Some go further and reject the conditions themselves. Others claim that the conditions are much too weak to capture rationality and that in fact almost any reasoning can be characterized so as to satisfy them. The extent to which Bayesian epistemology contributes to traditional epistemological concerns of characterizing knowledge and methods for obtaining knowledge is controversial.
Probabilistic justification logic
