A Quantum Structure Description of the Liar Paradox
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In this article we propose an approach thatmodels the truth behavior of cognitive entities (i.e.,sets of connected propositions) by taking into accountin a very explicit way the possible influence of the cognitive person (the one that interactswith the considered cognitive entity). Hereby wespecifically apply the mathematical formalism of quantummechanics because of the fact that this formalism allows the description of real contextual influences,i.e., the influence of the measuring apparatus on thephysical entity. We concentrated on the typicalsituation of the liar paradox and have shown that (1) the true-false state of this liar paradox canbe represented by a quantum vector of the nonproducttype in a finite-dimensional complex Hilbert space andthe different cognitive interactions by the actions of the corresponding quantum projections, (2)the typical oscillations between false and true —the paradox — is now quantum dynamically describedby a Schrodinger equation. We analyze possiblephilosophical implications of this result.
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