David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Foundations of Science 11 (4):399-418 (2006)
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.
|Keywords||Philosophy Philosophy of Science Mathematical Logic and Foundations Methodology of the Social Sciences|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Dirk Aerts (1982). Description of Many Separated Physical Entities Without the Paradoxes Encountered in Quantum Mechanics. Foundations of Physics 12 (12):1131-1170.
Diederik Aerts (1994). Quantum Structures, Separated Physical Entities and Probability. Foundations of Physics 24 (9):1227-1259.
D. Aerts, J. Broekaert & Liane Gabora (2002). Intrinsic Contextuality as the Crux of Consciousness. In Kunio Yasue, Marj Jibu & Tarcisio Della Senta (eds.), No Matter, Never Mind: Proceedings of Toward a Science of Consciousness: Fundamental Approaches (Tokyo '99). John Benjamins
Citations of this work BETA
No citations found.
Similar books and articles
J. C. Beall (ed.) (2007). Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Lon Berk (2003). Why the Liar Does Not Matter. Journal of Philosophical Logic 32 (3):323-341.
Robert L. Martin (ed.) (1984). Recent Essays on Truth and the Liar Paradox. Oxford University Press.
Richard Heck (2012). A Liar Paradox. Thought: A Journal of Philosophy 1 (1):36-40.
Bradley Dowden, Liar Paradox. Internet Encyclopedia of Philosophy.
Shahid Rahman, Tero Tulenheimo & Emmanuel Genot (eds.) (2008). Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox. Springer.
Jeff Snapper (2012). The Liar Paradox in New Clothes. Analysis 72 (2):319-322.
Dale Jacquette (2007). Denying The Liar. Polish Journal of Philosophy 1 (2):91-98.
Diederik Aerts, Jan Broekaert & Sonja Smets (1999). The Liar-Paradox in a Quantum Mechanical Perspective. Foundations of Science 4 (2):115-132.
Added to index2009-01-28
Total downloads31 ( #124,661 of 1,792,217 )
Recent downloads (6 months)1 ( #464,595 of 1,792,217 )
How can I increase my downloads?