Abstract

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized by representing categorically the global structure of a quantum algebra of events in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a contextualist account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to state the totality of facts of nature.