It would be irrational to believe "it will not come up 5 or 6" because P(P(5 or 6) = 0) = 0, so you know for certain that its false. As you said "Claims about the probability of a given claim being true, helpful as they may be in many cases, are distinct from the claim itself."
Before taking up any belief (if the situation demands taking up a belief, like in a bet, or living life), a Bayesian would calculate the likelihood of it being true vs the likelihood of it being false, and will favour the higher likelihood. In this case, the likelihood that "it will not come up... (read more)
It would be irrational to believe "it will not come up 5 or 6" because P(P(5 or 6) = 0) = 0, so you know for certain that its false. As you said "Claims about the probability of a given claim being true, helpful as they may be in many cases, are distinct from the claim itself." Before taking up any belief (if the situation demands taking up a belief, like in a bet, or living life), a Bayesian would calculate the likelihood of it being true vs the likelihood of it being false, and will favour the higher likelihood. In this case, the likelihood that "it will not come up... (read more)