This paper formally states all of the assumptions necessary in the proof of Cox’s theorem (R1-R5 in the paper) and notes where the controversies are before going on with the proof. R5 is obviously not well supported and the major dispute over R1 is whether plausibilities must be universally comparable. (R1 and R5 correspond to your two major objections above, in order).
As requested below, a top level post would be very interesting
I’m working on a post on this topic, but I don’t think I can really adequately address what I don’t like about how Jayne’s presents the foundations of probability theory without presenting it myself the way I think it ought to be. And to do that I need to actually learn some things I don’t know yet, so it’s going to be a bit of a project.
This paper formally states all of the assumptions necessary in the proof of Cox’s theorem (R1-R5 in the paper) and notes where the controversies are before going on with the proof. R5 is obviously not well supported and the major dispute over R1 is whether plausibilities must be universally comparable. (R1 and R5 correspond to your two major objections above, in order).
As requested below, a top level post would be very interesting
thanks! I haven’t seen that one before.
I’m working on a post on this topic, but I don’t think I can really adequately address what I don’t like about how Jayne’s presents the foundations of probability theory without presenting it myself the way I think it ought to be. And to do that I need to actually learn some things I don’t know yet, so it’s going to be a bit of a project.