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A Quantum Structure Description of the Liar Paradox

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Abstract

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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REFERENCES

  • Aerts, D. (1992). Construction of reality and its influence on the understanding of quantum structures, Int.J.Theor.Phys. 31, 1813.

    Google Scholar 

  • Aerts, D. (1994). The biomousa: A new view of discovery and creation, in Perspectives on the World, Aerts, D., Apostel, L., et al., eds. VUB Press.

  • Aerts, D. (1998a). The creation discovery view and the layered structure of reality, in Worldviews and the Problem of Synthesis, the Yellow Book of Einstein meets Magritte, Aerts, D., Van

  • Belle, H., and Van der Veken, J., eds., Kluwer, Dordrecht. Aerts, D. (1998b). The entity and modern physics: The creation-discover y-view of reality, in Interpreting Bodies: Classical and Quantum Objects in Modern Physics, Castelani, E., ed., Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Aerts, D., and Aerts, S. (1994). Applications of quantum statistics in psychological studies of decision processes, Foundations of Science 1, 85.

    Google Scholar 

  • Aerts, D., and Aerts, S. (1997). Applications of quantum statistics in psychological studies of decision processes, in Foundations of Statistics, Van Fraassen, B., ed., Kluwer, Dordrecht.

    Google Scholar 

  • Aerts, D., Coecke B., and Smets, S. (1999). On the origin of probabilities in quantum mechanics: Creative and contextual aspects, in Metadebates, the Blue Book of Einstein meets Magritte

  • Cornelis, G., Smets, S., and Van Bendegem, J. P., eds., Kluwer, Dordrecht.

  • Clea Research Project. (1997—). Integrating Worldviews: Research on the Interdisciplinary Construction of a Model of Reality with Ethical and Practial Relevance, Ministry of the Flemish Community, Department of Science, Innovation and Media.

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Authors
  1. Diederik Aerts
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  2. Jan Broekaert
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  3. Sonja Smets
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Aerts, D., Broekaert, J. & Smets, S. A Quantum Structure Description of the Liar Paradox. International Journal of Theoretical Physics 38, 3231–3239 (1999). https://doi.org/10.1023/A:1026686316673

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  • DOI: https://doi.org/10.1023/A:1026686316673

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