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Vladimir_Nesov comments on Outlawing Anthropics: An Updateless Dilemma - Less Wrong
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Logic is already in some sense about uncertainty (e.g. you could interpret predicates as states of knowledge). When you add one more "uncertainty" of some breed, it leads to perversion of logic, usually of applied character and barren meaning.
The concept of "probability" is suspect, I don't expect it to have foundational significance.
So what would you call a field that deals with how one ought to make bets involving P!=NP (i.e., mathematical statements that we can't prove to be true or false), if not "logical uncertainty"? Just "logic"? Wouldn't that cause confusion in others, since today it's usually understood that such questions are outside the realm of logic?
I don't understand how to make such bets, except in a way it's one of the kinds of human decision-making that can be explicated in terms of priors and utilities. The logic of this problem is in the process that works with the statement, which is in the domain of proof theory.