Syntactic and Semantic Distribution in Quantum Measurement

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The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct nondistributivity relations in the derivation: one with a semantics governed by an empirical conjunctive syntax, the other composed of conjunctive primitives in the quantum mechanical probability calculus. We venture to speculate how the two come to be confused in the derivation of the theorem.