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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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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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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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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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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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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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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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.
End of conversation
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