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  • For the expression of structure, 2-valued logic (2VL) is a necessary and sufficient criterion. In any structured (syndiffeonic) system, everything finally comes down to 2VL. We can come at this fact from below and from above. From below, we merely observe that because 0VL and 1VL do not permit nontrivial distinctions to be made among syntactic components, they do not admit of nontrivial, nonunary expressive syntax and have no power to differentially express structure. From above, on the other hand, we note that any many-valued logic, including infinite-valued logic, is a 2-valued theory - it must be for its formal ingredients and their referents to be distinguished from their complements and from each other - and thus boils down to 2VL. So 2VL is a necessary and sufficient element of logical syntax for systems with distributed internal structure. Infinite-valued logics can add nothing in the way of scope, but can only increase statistical resolution within the range of 2VL itself (and not individual resolution except in a probabilistically inductive sense).

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