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.
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.
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