“But it was PT:TLOS that did the trick. Here was probability theory, laid out not as a clever tool, but as The Rules, inviolable on pain of paradox”
I am unaware of a statement of Cox’s theorem where the full technical statement of the theorem comes even close to this informal characterization. I’m not saying it doesn’t exist, but PT:TLOS certainly doesn’t do it.
I found the first two chapters of PT:TLOS to be absolutely, wretchedly awful. It’s full of technical mistakes, crazy mischaracterizations of other people’s opinions, hidden assumptions and skipped steps (that he tries to justify with handwaving nonsense), and even a discussion of Godel’s theorems that mixes meta levels and completly misses the point.
“But it was PT:TLOS that did the trick. Here was probability theory, laid out not as a clever tool, but as The Rules, inviolable on pain of paradox”
I am unaware of a statement of Cox’s theorem where the full technical statement of the theorem comes even close to this informal characterization. I’m not saying it doesn’t exist, but PT:TLOS certainly doesn’t do it.
I found the first two chapters of PT:TLOS to be absolutely, wretchedly awful. It’s full of technical mistakes, crazy mischaracterizations of other people’s opinions, hidden assumptions and skipped steps (that he tries to justify with handwaving nonsense), and even a discussion of Godel’s theorems that mixes meta levels and completly misses the point.