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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Replying to @ESYudkowsky @Meaningness and
...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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Oh! After brushing my teeth and before I forget :) maybe this is helpful: When designing an airplane wing, use finite element analysis, not DT. Implementing a network protocol, use a parser, not DT. In hydrology, use percolation theory, not DT.
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Replying to @Meaningness @ArtirKel and
I don’t think any of these are “approximations of DT” in any interesting sense. If you declare by fiat that DT is the Theory of Everything, then you could try to force-fit it… but that’s going to come out awkward and unconvincing.
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If you don't see DT's laws as governing these cases, or if you think it's a critique of the use of DT that some option space is too large to be practically approximated; then I have the sense of pointing to a thing and a use that's still not in your ontology.
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Replying to @ESYudkowsky @Meaningness and
This is like saying "When building a car engine, use the Handbook of Chemistry and Physics, thermodynamics may not tell you the tensile strength of steel". It's a type error. Like thermodynamics, DT holds true everywhere, whether or not it's useful to think about it right now.
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So I think what you said here does express the crux of our disagreement (as I suggested earlier in the conversation). It seems that you think (1) DT has a special status among mathematical systems, and (2) that it is actually *true* of the macroscopic physical world.
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Replying to @Meaningness @ESYudkowsky and
If we wanted to continue the discussion, and if you agree, we could see (1) in what way DT is special, and (2) in what way it is “true everywhere.”
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Replying to @Meaningness @ESYudkowsky and
Thermodynamics is physics, not just math, and it is (presumably) true everywhere in space, by virtue of accurately representing physical phenomena. The Chomsky Hierarchy, relating parsers & language types, is “true everywhere” in the sense that physical space is irrelevant to it
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