credences

Credence, in epistemology and decision theory, refers to the degree of confidence an agent assigns to a proposition being true. It is usually expressed as a number between 0 and 1, with 1 meaning certainty and 0 meaning disbelief. In Bayesian contexts, credences are treated as subjective probabilities that guide belief revision and action.

Formally, a credence function assigns to each proposition p a value c(p) in [0,1], representing how strongly the agent endorses p. Coherence requires that the assignments obey the basic laws of probability: the credence of tautologies is 1, contradictions 0, and the values on a partition of possibilities sum to 1; in practice this means avoiding sure loss in betting scenarios.

Updating credences in light of new evidence is commonly done by conditionalization: c(A|E) = c(A ∧ E)/c(E) when c(E) > 0. When evidence is uncertain, Jeffrey conditioning or related methods may be used.

Credence is distinct from, though related to, belief. Belief is often taken as a binary or qualitative state, while credence is a quantitative measure of the strength of that belief. In some approaches, a single credence function describes an agent’s probabilistic mind; in others, people work with imprecise probabilities, where a credal set of possible functions expresses uncertainty about the exact numbers.

Historically, the idea traces to Ramsey and de Finetti and has become central in Bayesian epistemology and decision theory, with applications in science, law, and risk assessment.