What is conditionalisation?

Conditionalisation is the Bayesian rule for updating belief: on learning a piece of evidence, an agent's new credence in any proposition should equal their old credence in that proposition conditional on the evidence. It is the standard account of how rational confidence changes as one learns.

What is a Dutch book?

A Dutch book is a combination of bets, each of which an agent regards as fair given their credences, that together guarantee the agent a net loss. The Dutch-book argument shows that only agents whose credences obey the probability axioms are immune to such guaranteed-loss betting, supporting probabilism.

Bayesian Epistemology

Bayesian epistemology models belief as a matter of degree: a rational agent's confidences should obey the laws of probability and should be revised, on receiving evidence, by conditionalising — a framework with surprisingly powerful arguments in its favour.

Definition

Bayesian epistemology is the theory that rational belief consists in degrees of confidence (credences) that conform to the axioms of probability and are updated by conditionalisation on new evidence, with rationality assessed by coherence and accuracy.

Scope

This topic covers the core commitments of Bayesianism: probabilism, the thesis that rational credences obey the probability axioms; conditionalisation as the rule for updating on evidence; and the principal arguments for these norms, including Dutch-book and accuracy-dominance arguments. It also covers standing problems such as the choice of priors, the problem of old evidence, and logical omniscience. Confirmation and induction are treated in a companion topic.

Core questions

Why should rational degrees of belief satisfy the probability axioms?
Is conditionalisation the correct rule for updating credences?
Where do prior probabilities come from, and can any be irrational?
How should idealised Bayesian agents be related to limited human believers?

Key theories

Subjective probability and the Dutch-book argument: Ramsey and de Finetti identify degrees of belief with betting dispositions and show that an agent whose credences violate the probability axioms is vulnerable to a Dutch book — a set of bets guaranteeing a loss — giving a pragmatic argument for probabilism.
Accuracy-dominance argument for probabilism: Joyce offers a nonpragmatic vindication: taking accuracy as closeness of credences to the truth, he shows that any non-probabilistic credence function is accuracy-dominated by a probabilistic one, so probabilism follows from caring about accuracy alone.

History

Bayesian epistemology grows from the subjective interpretation of probability advanced independently by Ramsey in 1926 and de Finetti in the 1930s, who grounded credence in coherent betting and proved Dutch-book and representation theorems. In the late twentieth century the accuracy-first program, exemplified by Joyce's 1998 argument, sought to justify the same norms without appeal to betting, broadening the case for probabilism.

Debates

The problem of the priors: Subjective Bayesians allow any coherent prior credences, which critics say makes rationality too permissive, while objective Bayesians seek principles such as indifference or maximum entropy to constrain priors, facing their own difficulties; how far rationality fixes the priors remains unsettled.

Key figures

Frank Ramsey
Bruno de Finetti
James Joyce

Seminal works

ramsey1926
joyce1998

Frequently asked questions

What is conditionalisation?: Conditionalisation is the Bayesian rule for updating belief: on learning a piece of evidence, an agent's new credence in any proposition should equal their old credence in that proposition conditional on the evidence. It is the standard account of how rational confidence changes as one learns.
What is a Dutch book?: A Dutch book is a combination of bets, each of which an agent regards as fair given their credences, that together guarantee the agent a net loss. The Dutch-book argument shows that only agents whose credences obey the probability axioms are immune to such guaranteed-loss betting, supporting probabilism.