Abstract

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object of truth values, or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is in- herent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical im- plications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. In this light, the transcendence condition of the usual concep- tion of correspondence truth is superseded by a reflective-like transcendental reasoning of the proposed account of truth that is suitable to the quantum domain of discourse.