Bayesian Epistemology Explained: Why Belief Isn’t All-or-Nothing

You'd bet your life that your coffee isn't poisoned, but would you bet your life that it'll freeze tonight? You believe both, but not equally. That difference is the starting point for Bayesian epistemology.

Traditional epistemology treats belief and knowledge as all-or-nothing: you have them or you don't. Bayesian epistemology adds nuance by studying degrees of belief, or credences. In this video, I cover the basics: what credences are, how conditional credences work, and how Bayes' Theorem tells us to update our confidence when new evidence comes in.

We work through an example: I'm 70% confident it'll freeze tonight, and then I see a weather report predicting a freeze. Where should my confidence end up? (Spoiler: about 91%, and where you start matters a lot.)

Then we tour the big questions Bayesian epistemologists work on:

• Kolmogorov's axioms as rationality constraints on credences
• Updating by conditionalization
• The problem of the priors (uniqueness vs. permissivism, convergence theorems)
• Peer disagreement
• Meta-credences: can I be 70% confident and 50% confident I'm wrong to be?
• Dutch Book arguments and decision theory
• Why all of this matters for AI: rationalist circles, Newcomb's Problem, and Bayesian approaches to defining AI rationality

I plan to turn many of these into their own videos. Which should come first? Let me know in the comments!