Richard: Cox’s theorem is an example of a particular kind of result in math, where you have some particular object in mind to represent something, and you come up with very plausible, very general axioms that you want this representation to satisfy, and then prove this object is unique in satisfying these. There are equivalent results for entropy in information theory. The problem with these results, they are almost always based on hindsight, so a lot of the times you sneak in an axiom that only SEEMS plausible in hindsight. For instance, Cox’s theorem states that plausibility is a real number. Why should it be a real number?
Richard: Cox’s theorem is an example of a particular kind of result in math, where you have some particular object in mind to represent something, and you come up with very plausible, very general axioms that you want this representation to satisfy, and then prove this object is unique in satisfying these. There are equivalent results for entropy in information theory. The problem with these results, they are almost always based on hindsight, so a lot of the times you sneak in an axiom that only SEEMS plausible in hindsight. For instance, Cox’s theorem states that plausibility is a real number. Why should it be a real number?