Lewis's Triviality Theorem

Lewis's Triviality Theorem shows that combining a standard probability measure with certain belief-update functions, like Bayesian updating, can lead to logical contradictions. In essence, it suggests that assigning probabilities to all conditional beliefs (beliefs given specific conditions) consistently within classical probability rules is impossible. This reveals fundamental limitations in how we model conditional beliefs using traditional probability theory, highlighting that some intuitive assumptions about how beliefs and updating should work cannot all be true simultaneously without inconsistency.