I misunderstood you as saying that it was a true account of reality (and not merely useful in practice). I guess I am missing your point if that is not the case?
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Yes! Rationality works, when it does, because somehow inferences within the mathematical system turn out to be true-enough in the real world.
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This is tricky, because rational inference preserves absolute truth, but not mostly-truth. For mostly-truth, you have to constantly keep your eye on how, concretely, the system is relating to reality: which can never be “accurately reflects absolute truths.”
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I should say by definition that what takes true inputs to true outputs is "logic", not "rationality", the latter of which many textbooks will agree is about decision under uncertainty. If you thought "rationality" meant what I'd call "logic", no wonder there is confusion.
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I’m using “rationality” in a quite broad sense as including all of math (including logic and decision theory) and a fair amount else besides.
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That said, doesn’t decision theory take true inputs to true outputs? If you set up a situation as a decision theory problem, decision theory yields a deductively correct answers.
End of conversation
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