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The Generalised Liar Paradox: A Quantum Model and Interpretation

Summary: The Generalised Liar Paradox: A Quantum Model and
Diederik Aerts, Jan Broekaert and Bart D'Hooghe
Center Leo Apostel for Interdisciplinary Studies (CLEA)
Foundations of the Exact Sciences (FUND), Department of Mathematics
Vrije Universiteit Brussel, 1160 Brussels, Belgium
E-Mail: diraerts@vub.ac.be, jbroekae@vub.ac.be
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar
Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth prop-
erties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, &
Smets, 1999, 2000, Aerts, Broekaert, & Gabora 1999, 2000, 2002). Basically, the intrinsic con-
textuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted
quantum mechanical approach. The formal details of the model are explicited here for the
generalized case. We prove the possibility of constructing a quantum model of the m-sentence
generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar
Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m)m
mensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii)


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


Collections: Multidisciplinary Databases and Resources; Physics