What implications does the paper “A Counter Example to Theorems of Cox and Fine” by J. Y. Halpern have for Cox’s theorem and probability theory as extended logic? This is the description of the paper:

“Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same counterexample is used to disprove a result of Fine on comparative conditional probability.”

Edit: You can access the paper here - https://arxiv.org/abs/1105.5450

A similar question seems have been posted (but not answered) here:

- https://stats.stackexchange.com/q/190187/297721
- https://stats.stackexchange.com/q/190184/297721
- https://stats.stackexchange.com/q/189757/297721

Why is Cox’s theorem being disputed? Are there any non-sequiturs in the proof that Professor Jaynes give for it in his book? If not, then how can it be disputed?

Thanks for the reply!

This stuff is

wayover my head. What is the tldr version? Is the interpretation of probability that Professor Jaynes expounded in his book correct? Can I use the results that he derives in his book along with the interpretation of probability as extended logic?Any references on bits of randomness, MDL, and the purely epistemic interpretation of probability?

If the purely epistemic interpretation of probability has these weaknesses, are there any other interpretations of probability which are more applicable in practice?