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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Replying to @Meaningness @ESYudkowsky and
I take it that by “DT is true everywhere” you mean it is the correct analysis of all physical events (of a certain type, maybe), rather than just that it is a consistent branch of math. I don’t think that’s true.
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Replying to @Meaningness @ESYudkowsky and
As for the specialness, I am guessing that you believe all rational methods can be viewed as applications of DT, and that DT is unique in having this property. If “rational” is defined as “applications of DT” (which you came close to doing earlier) then this is correct.
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Replying to @Meaningness @ESYudkowsky and
However, I would say that context-free parsing with a pushdown automaton is a rational method. (We may disagree just as a matter of definition! Which is fine of course.)
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Offhand, I doubt parsing can be viewed in a DT framework at all (but maybe I’m wrong, and there’s some non-obvious mathematical reduction). If it can, it seems like it would very rarely if ever be meaningful or useful to view it that way.
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Replying to @Meaningness @ESYudkowsky and
Predicate calculus does have the property of universality: any formal method can be reduced to fopc. Thinking this way leads to logicism, which is (we agree?) a bad dead-end. I would expect that reducing everything to DT, if it were possible, would have the same bad consequences.
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