Contextual semantics in quantum mechanics from a categorical point of view

Citation data:

Synthese, ISSN: 0039-7857, Vol: 194, Issue: 3, Page: 847-886

Publication Year:
Usage 106
Downloads 104
Abstract Views 2
Captures 1
Readers 1
Social Media 2
Tweets 2
Citations 1
Citation Indexes 1
Repository URL:
Vassilios Karakostas, Elias Zafiris
Springer Nature, Springer
Arts and Humanities, Social Sciences
Most Recent Tweet View All Tweets
article description
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 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 algebras. 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 inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications 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.

This article has 0 Wikipedia mention.