The Idea

Probability is not a property of the world; it is a measure of your uncertainty about it. The frequentist reading (“50% of infinite flips land heads”) only applies to repeatable physical processes. The Bayesian reading (a credence of 0.5 means maximal uncertainty between two outcomes) applies to anything you can be uncertain about: one-off events, historical claims, scientific hypotheses. “The probability Napoleon won at Waterloo” is a perfectly sensible number about your knowledge, not about 1815.

The normative core: hold beliefs as graded credences rather than binary verdicts, keep them coherent with the probability axioms, and update them by Bayes’ rule when evidence arrives. New belief is old belief weighted by how well the hypothesis predicted the evidence. Today’s posterior becomes tomorrow’s prior, so knowledge accumulates instead of restarting.

Why I Keep It

It is both my epistemology and my statistics. Bayesian inference answers the question I actually care about (what should I believe about this parameter, given this data) rather than what would happen across hypothetical repetitions. Practically: Bayesian mixed-effects models for multilingual data, explicit priors, and graded confidence in claims rather than significance verdicts. It also connects downward to cognition: predictive processing treats the brain itself as an approximate Bayesian updater.

Tensions

• Where do priors come from? “Previous inquiry” regresses; at some point priors are bedrock, and different bedrock means rational-looking disagreement.
• Exact inference is usually intractable, so real practice runs on approximations. The normative story is cleaner than the computational one.

Key Sources

• Ramsey, F. P. (1926). “Truth and Probability”
• Jaynes, E. T. (2003). Probability Theory: The Logic of Science
• Howson, C., & Urbach, P. (2006). Scientific Reasoning: The Bayesian Approach