In that case, we’re done. Standard probability theory/Cox Theorem/de Finette would give us a ready made criticism of any conjecture that wasn’t isomorphic to probability theory, so we’d have isomorphism, which is all we need. Once we have functional equivalence, we can prove results in probability theory, apply Bayes theorem, etc., and then at the end translate back into Popperesque.
(Also, IIRC, Jaynes only claimed to have proven that rational reasoning must be isomorphic to probability theory)
I don't quite get your point. You are saying that if you bring up betting (a real life scenario where probability is highly relevant), then given your explanations that help you come up with priors (background knowledge needed to be able to do any math about it), you shouldn't act on those explanations in ways that violates math. OK, so what? probability math is useful in some limited cases, given some explanatory knowledge to get set up. no one said otherwise.
http://vimeo.com/22099396
What do people think of this, from a Bayesian perspective?
It is a talk given to the Oxford Transhumanists. Their previous speaker was Eliezer Yudkowsky. Audio version and past talks here: http://groupspaces.com/oxfordtranshumanists/pages/past-talks