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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Yes, boo to twitter threading!
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OK, another attempt at finding a crux. For you, decision theory is THE TRUE framework, according to which any practical method must be judged. For me, it’s just one bit of math among many, with no special value.
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I'm not sure what you mean by "THE TRUE" here. I'm tempted to reply with https://arbital.com/p/expected_utility_formalism/?l=7hh … to explain what makes this math so specially relevant to decision-making and belief, but I have a dark presentiment that's not what you mean.
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I’ve just now read the first bit of that, which is the Dutch Book Argument, so we’re back to where we started… maybe twitter needs a circular thread mechanism :)
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I didn't think DBA appeared there until later? Anyway, from the end: "We have multiple spotlights all shining on the same core mathematical structure, saying dozens of different variants on, 'If you aren't running around in circles or stepping on your own feet or...
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...wantonly giving up things you say you want, we can see your behavior as corresponding to this shape. Conversely, if we can't see your behavior as corresponding to this shape, you must be visibly shooting yourself in the foot.'"
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So, my rephrasing would be something like: if a situation behaves in a way such that probability/decision theory works well when you apply it to that situation, then you should definitely do so. Which I agree with! It’s great when it works! In most situations, it doesn’t apply.
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But when is it that you can't apply it?(By applying it I mean approximating it). What heuristics or methods are there that are superior to DT sometimes that are not approximations of it?
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DT simply doesn’t apply unless there’s a global metric of goodness (and there isn’t one). When there is a large space of actions and outcomes, it can’t even be “approximated” by any physical agent. And, there is no general theory even of what it *means* to approximate DT.
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A mathematician wouldn't necessarily choose PA as the unique best formalization of what we really mean when we do arithmetic...
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