I am pretty sure that p and “it is rational to believe that p” can come apart even from a first-person perspective. At least, they can come apart if belief is cashed out in terms of inclination to action in a single case.
Let me illustrate. Suppose there are five live hypotheses to account for some evidence, and suppose that I assign credences as follows:
Further suppose that I am in a situation where I need to take some action, and each of the five hypotheses recommends a different action in the circumstances.
Assuming that by “belief” one means something like “what one proposes to act on in forced situations,” then it is rational to believe h2. It is rational to act as if h2 were true. But one need not think that h2 is true. It is more likely to be true than any of the other options, but given the credences above, one ought to think that h2 is false. That is, it is much more likely on the evidence that h2 is false than that it is true.
“It’s rational to believe that #32 will win” and “It’s rational to bet on #32″ are not the same thing. In fact, they’re using different senses of “rational”, as we usually carve things up.
Thus in your example, “it’s rational to believe h2” and “h2″ are still equivalent, but “act as though h2” is not.
I am pretty sure that p and “it is rational to believe that p” can come apart even from a first-person perspective. At least, they can come apart if belief is cashed out in terms of inclination to action in a single case.
Let me illustrate. Suppose there are five live hypotheses to account for some evidence, and suppose that I assign credences as follows:
C(h1) = 0.1; C(h2) = 0.35; C(h3) = 0.25; C(h4) = 0.15; C(h5) = 0.1; and C(other) = 0.05.
Further suppose that I am in a situation where I need to take some action, and each of the five hypotheses recommends a different action in the circumstances.
Assuming that by “belief” one means something like “what one proposes to act on in forced situations,” then it is rational to believe h2. It is rational to act as if h2 were true. But one need not think that h2 is true. It is more likely to be true than any of the other options, but given the credences above, one ought to think that h2 is false. That is, it is much more likely on the evidence that h2 is false than that it is true.
“It’s rational to believe that #32 will win” and “It’s rational to bet on #32″ are not the same thing. In fact, they’re using different senses of “rational”, as we usually carve things up.
Thus in your example, “it’s rational to believe h2” and “h2″ are still equivalent, but “act as though h2” is not.
Could you elaborate on the mistake you think I’m making? I’m not seeing it, yet.