Bayesian Confirmation Theory
Bayesian confirmation theory analyses evidential support in terms of probabilities updated by Bayes' theorem.
Definition
Bayesian confirmation theory holds that an agent's degrees of belief should satisfy the probability axioms and be updated by conditionalization, so that evidence confirms a hypothesis just in case it raises that hypothesis's probability.
Scope
This topic covers the probabilistic explication of confirmation as probability-raising, the role of priors and likelihoods, updating by conditionalization, Dutch-book and convergence arguments, and standing problems such as the choice of priors, the problem of old evidence, and disagreement among measures of confirmation.
Core questions
- What does it mean for evidence to confirm a hypothesis probabilistically?
- How should prior probabilities be assigned and constrained?
- Do Dutch-book and convergence arguments justify the Bayesian norms?
- How can already-known evidence confirm a theory (the old-evidence problem)?
Key concepts
- prior probability
- likelihood
- posterior probability
- conditionalization
- Dutch book
- convergence of opinion
- problem of old evidence
Key theories
- Probabilistic confirmation
- Evidence E confirms hypothesis H when the posterior probability of H given E exceeds its prior, computed via Bayes' theorem from likelihoods and priors.
- Subjective Bayesianism
- Probabilities are interpreted as coherent degrees of belief, with rationality requiring conformity to the probability calculus and updating by conditionalization.
History
Building on Carnap's logical probability and de Finetti's subjective probability, Bayesian confirmation theory matured from the 1960s into the dominant probabilistic framework. Howson and Urbach's textbook codified the subjective approach; Earman's 1992 study set out its successes and unresolved difficulties.
Debates
- The problem of priors
- Critics object that subjective priors make confirmation arbitrary, while Bayesians appeal to convergence theorems and coherence constraints to argue that priors wash out with evidence.
Key figures
- Rudolf Carnap
- Colin Howson
- Peter Urbach
- John Earman
- Bruno de Finetti
Related topics
Seminal works
- carnap1950
- howsonurbach2006
- earman1992
Frequently asked questions
- What is the old-evidence problem?
- If evidence is already known, its probability is 1, so conditionalizing on it cannot raise a hypothesis's probability. Yet known facts (like the perihelion of Mercury for general relativity) clearly confirm theories, which poses a challenge for the simplest Bayesian account.