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Vaniver comments on 5 Axioms of Decision Making - Less Wrong
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I'm pretty sure that a Dutch Book is only a Dutch Book if it's pure arbitrage- that is, you beat someone using only the odds they publish. If you know more than someone else and win a bet against them, that seems different.
Quite possibly. I'm not a good judge of mathematical truth- I tend to be more trusting than I should be. It looks to me like if you can prove "every prime can be expressed as the output of algorithm X", where X is some version of the Collatz conjecture in reverse, then you're done. (Heck, that might even map onto the Sieve of Eratosthenes.) That it isn't solved already drops my credence down from ~.95 to ~.8.
Yes. Crudely speaking they have to be stupid, not just ignorant!
Not being able to decide upon the Collatz conjecture is stupidity, not ignorance. A very widespread sort of stupidy, but still.
Grandparent is self contained and entirely Collatz-independent.
They publish probability of axioms of arithmetics being roughly 1 and probability of Collatz conjecture being 0.8, you see that the conjecture is logically equivalent to the axioms and thus that their odds are mutually inconsistent. You don't "know" more in the sense of having observed more evidence. (I'd agree that this is a tortured interpretation of Dutch booking, but it's probably what you get if you systematically distinguish external evidence from own reasoning.)