I used to take it for granted that it’s reasonable to make epistemic utilities be continuous functions of credences. But this is not so clear to me right now. Consider a proposition really central to a person’s worldview, such as:
life has (or does not have) a meaning
God does (or does not) exist
we live (or do not live) in a simulation
morality is (or is not) objective.
I think a case can be made that if a proposition like that is in fact true, then there is a discontinuous upward jump in epistemic utility as one goes from assigning a credence less than 1/2 to assigning a credence more than 1/2.
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