So, maybe the crux here is “Once you define distance there is in fact a shortest path through the maze.” If you make a bunch of ontological assumptions, then probability theory applies—relative to those assumptions.
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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Writing this tweet, I have an unbounded number of possible things to say; an inconceivable set of possible outcomes; no clearly-defined goals; and any numerical probabilites would be meaningless. Do you know about aardvark cucumbers?
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That is, an epistemic, not ontological problem. One can hold that 1)DT is the best way of deciding, objectively 2)DT cannot be applied in its textbook form, just approximated As GA Cohen said, just because one cannot reach some tasty grapes doesn't mean they are less tasty
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