Foundations of Science

, Volume 11, Issue 4, pp 399–418

The Generalised Liar Paradox: A Quantum Model and Interpretation

Article

Abstract

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 properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality 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-dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Jan Broekaert
    • 1
  • Diederik Aerts
    • 1
  • Bart D’Hooghe
    • 1
  1. 1.Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of MathematicsVrije Universiteit BrusselBrusselsBelgium

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