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A Quantum Structure Description of the Liar Diederik Aerts, Jan Broekaert and Sonja Smets

Summary: A Quantum Structure Description of the Liar
Diederik Aerts, Jan Broekaert and Sonja Smets
Center Leo Apostel (CLEA),
Brussels Free University,
Krijgskundestraat 33, 1160 Brussels
diraerts@vub.ac.be, jbroekae@vub.ac.be
In this article we propose an approach that models the truth behavior
of cognitive entities (i.e. sets of connected propositions) by taking into
account in a very explicit way the possible influence of the cognitive
person (the one that interacts with the considered cognitive entity).
Hereby we specifically apply the mathematical formalism of quantum
mechanics because of the fact that this formalism allows the descrip-
tion of real contextual influences, i.e. the influence of the measuring
apparatus on the physical entity. We concentrated on the typical situ-
ation of the liar paradox and have shown that (1) the truth-false state
of this liar paradox can be represented by a quantum vector of the non-
product type in a finite dimensional complex Hilbert space and the dif-


Source: Aerts, Diederik - Leo Apostel Centre, Vrije Universiteit Brussel


Collections: Multidisciplinary Databases and Resources; Physics