NDLI: Contextual semantics in quantum mechanics from a categorical point of view

Content Provider	Springer Nature Link
Author	Karakostas, Vassilios Zafiris, Elias
Copyright Year	2015
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 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.
Starting Page	847
Ending Page	886
Page Count	40
File Format	PDF
ISSN	00397857
Journal	Synthese
Volume Number	194
Issue Number	3
e-ISSN	15730964
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-11-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Kochen–Specker theorem Category theory Categorical adjunction Subobject classifier Correspondence truth Contextual semantics Philosophy of Science Epistemology Logic Philosophy of Language Metaphysics
Content Type	Text
Resource Type	Article
Subject	Philosophy Social Sciences

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