'But to assign some probability to the wrong answer is logically equivalent to assigning probability to 0=1.'

Huh? This doesn't make sense to me. First of all, it seems like a basic category-mistake: acts of assigning probabilities don't seem to be the sorts of things that can bear logical relations like equivalence to each other.

Perhaps that's just pedantry and there's a simple rephrasing that says what you really want to say, but I have a feeling I would take issue with the rephrased version too. Does it trade on the idea that all false mathematical propositions are logically equivalent to each other? (If so, I'd say that's a problem, because that idea is very controversial, and hardly intuitive.)