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Contextual Semantics in Quantum Mechanics from a Categorical Point of View

Karakostas, Vassilios and Zafiris, Elias (2017) Contextual Semantics in Quantum Mechanics from a Categorical Point of View. Synthese, 194 (3). pp. 847-886. ISSN 0039-7857

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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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Karakostas, Vassilioskarakost@phs.uoa.gr
Zafiris, Eliasezafiris@math.uoa.gr
Keywords: Quantum Mechanics, Kochen–Specker Theorem, Category Theory, Categorical Adjunction, Subobject Classifier, Correspondence Truth, Contextual Semantics
Subjects: Specific Sciences > Computation/Information > Quantum
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
General Issues > Structure of Theories
Depositing User: Prof. Vassilios Karakostas
Date Deposited: 20 Aug 2017 16:35
Last Modified: 20 Aug 2017 16:35
Item ID: 13336
Journal or Publication Title: Synthese
Publisher: Springer
Official URL: https://link.springer.com/article/10.1007/s11229-0...
DOI or Unique Handle: https://doi.org/10.1007/s11229-015-0970-3
Subjects: Specific Sciences > Computation/Information > Quantum
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
General Issues > Structure of Theories
Date: 2017
Page Range: pp. 847-886
Volume: 194
Number: 3
ISSN: 0039-7857
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13336

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