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Quantum Logic and the Question of the Empirical Nature of Logic

Quantum theory posses numerous challenges to philosophy. Instead of physics being asked by philosophy, e.g. about the reference of its terms, the interrogation changes direction: it is philosophy and not physics that ought to reflect on the logico-ontological foundations of quantum mechanics. A "case study" of Wittgenstein's Tractatus shows how radical the revisions might be after the reflection. According to Tractatus, atomic states of affairs are mutually independent, molecular states of affairs emerge only from "conjunctive composition" of atomic ones, and it possible for a language to give a complete description of reality. Neither of these postulates is consistent with quantum theory: observable atomic states of affairs are not mutually independent due to the uncertainty principle, unobservable molecular states of affairs can emerge also from "disjunctive composition" that corresponds to the physical superposition of states, consequently a complete description of the reality is not possible since it will either be indeterminate if it is observable or indefinite if unobservable. The revision affects logic which seems to be forced to distinguish between quantum-logic operators used in describing unobservable from those used in describing observable reality. Taking the type of disjunctive operators as an example, its quantum- logic definition does not make the classical expendable (Maudlin). Rather, as recent dynamic turn in quantum logic (Baltag, Smets) shows, both types of logic ought be reconciled within a common framework: quantum logic as the one that is sensitive to the empirical considerations of physical theory, and ``classical'' as the one imposed by the structure of language in use.

quantum logic; disjunction

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