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.
Almost all instances of the word "true" can be eliminated from the sentences in which they appear by applying Tarski's formula. For example, if you say, "I believe the sky is blue, and that's true!" then this can be rephrased as the statement, "I believe the sky is blue, and the sky is blue." For every "The sentence 'X' is true" you can just say X and convey the same information about what you believe - just talk about the territory the map allegedly corresponds to, instead of talking about the map.
When can't you eliminate the word "true"? When you're generalizing over map-territory correspondences, e.g., "True theories are more likely to make correct experimental predictions." There's no way to take the word 'true' out of that sentence because it's talking about a feature of map-territory correspondences in general.
Similarly, you can eliminate the sentence 'rational' from almost any sentence in which it appears. "It's rational to believe the sky is blue", "It's true that the sky is blue", and "The sky is blue", all convey exactly the same information about what color you think the sky is - no more, no less.
When can't you eliminate the word "rational" from a sentence?
When you're generalizing over cognitive algorithms for producing map-territory correspondences (epistemic rationality) or steering the future where you want it to go (instrumental rationality). So while you can eliminate the word 'rational' from "It's rational to believe the sky is blue", you can't eliminate the concept 'rational' from the sentence "It's epistemically rational to increase belief in hypotheses that make successful experimental predictions." You can Taboo the word, of course, but then the sentence just becomes, "To increase map-territory correspondences, follow the cognitive algorithm of increasing belief in hypotheses that make successful experimental predictions." You can eliminate the word, but you can't eliminate the concept without changing the meaning of the sentence, because the primary subject of discussion is, in fact, general cognitive algorithms with the property of producing map-territory correspondences.
The word 'rational' should never be used on any occasion except when it is necessary, i.e., when we are discussing cognitive algorithms as algorithms.
If you want to talk about how to buy a great car by applying rationality, but you're primarily talking about the car rather than considering the question of which cognitive algorithms are best, then title your post Optimal Car-Buying, not Rational Car-Buying.
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