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Oligopsony comments on Only say 'rational' when you can't eliminate the word - Less Wrong
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When discussing these third-person as you are now, cognitive algorithms as algorithms are being invoked. But we all know that "p" and "Alice thinks that p" are hardly reducible to each other, it's first-person items like "I believe that p" that are deflationary. So while it is clearly the case that you can imagine situations where the sky is not blue but it would be epistemically rational to believe that it is, that does not demonstrate situations where one could justifiably claim only one of "the sky is blue" and "it is rational to believe that the sky is blue" (indeed the justifiability of the former just is the content of the latter.)
"I believe that 'P'." is only deflationary because it treats belief as if it were binary, but it isn't. "I have 0.8 belief in 'P'." is certainly not the same as "It is true that 'P'." Yes? One is a claim about the world, and one is a claim about my model of the world.
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.