Do you have a specific example in mind?
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Well, to get decision theory to apply, you have to characterize the situation in terms of a set of well-defined actions, well-defined outcomes, well-defined goodnesses, and you need some meaningful way of estimating probabilities. None of those are objectively given.
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This example isn't analogous but I'm curious how you'd reply to a student saying, "The notion of 'objectively true sentences' is wrong and can't be rescued, because words don't have culturally independent meanings and there's no Objective Teacher to grade answers as correct."
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This has several moving parts, so it’s a bit complicated. First, there is no clear definition of “objective” or “objectively true,” as far as I have been able to discover. There are several pretty different uses that are all quite vague.
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Replying to @Meaningness @ESYudkowsky and
Under some reasonable interpretations of “objectively true,” there aren’t any outside math and possibly QFT. Under some other reasonable interpretations, lots of things are objectively true. Lots of arguments founder on this contrast.
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Suppose I suggested you can have a distinguishable solid subsystem of a fuzzy system. Distinguishing objects in the environment is fuzzy, assigning meaning to "three" is fuzzy, but once counting and naming is done, the arithmetic subsystem is locally quite solid.
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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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Replying to @Meaningness @ESYudkowsky and
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.
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