Cox's theorem

Cox's theorem is a fundamental result in probability theory that explains how to assign degrees of belief, or probabilities, to uncertain events. It shows that if you want to represent these beliefs consistently, you must follow certain logical rules. Specifically, it reveals that any way of combining beliefs should be based on how likely you think different outcomes are and must respect basic principles like coherence and consistency. Essentially, Cox's theorem lays a mathematical foundation for using probabilities to express and update our beliefs about the world in a rational way.