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Will_Sawin comments on Dutch Books and Decision Theory: An Introduction to a Long Conversation - Less Wrong
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Your choice is either accepting that you will be sometimes inconsistent, or accepting that you will sometimes answer "I don't know" without providing a specific number, or both.
There's nothing wrong with "I don't know".
For Perfect Bayesian or for Subjective Bayesian?
Subjective Bayesian does believe many statements of kind P(simple math step) = 1, P(X|conjunction of simple math steps) = 1, and yet P(X) < 1.
The problem with "I don't know" is that sometimes you have to make decisions. How do you propose to make decisions if you don't know some relevant mathematical fact X?
For example, if you're considering some kind of computer security system that is intended to last a long time, you really need an estimate for how likely it is that P=NP.
Then you need to fully accept that you will be inconsistent sometimes. And compartmentalize your belief system accordingly, or otherwise find a way to deal with these inconsistencies.