A quantum structure description of the liar paradox

In this article we propose an approach that models the truth behavior of co gnitive entities (i.e., sets of connected propositions) by taking into acco unt in a very explicit way the possible influence of the cognitive person ( the one that interacts with the considered cognitive entity). Hereby we spe cifically apply the mathematical formalism of quantum mechanics because of the fact that this formalism allows the description of real contextual infl uences, i.e., the influence of the measuring apparatus on the physical enti ty. We concentrated on the typical situation df the liar paradox and have s hown that (1) the true-false state of this liar paradox can be represented by a quantum vector of the nonproduct type in a finite-dimensional complex Hilbert space and the different cognitive interactions by the actions of th e corresponding quantum projections, (2) the typical oscillations between f alse and true-the paradox-is now quantum dynamically described by a Schrodi nger equation. We analyze possible philosophical implications of this resul t.