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Quantum superposition principle justified in a new non-Aristotelian finitary logic

Srinivasan, Radhakrishnan (2004) Quantum superposition principle justified in a new non-Aristotelian finitary logic. [Preprint]

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        Abstract

        In the proposed non-Aristotelian finitary logic (NAFL), truths for formal propositions can exist only with respect to axiomatic theories, essentially as temporary axiomatic declarations in the human mind. An undecidable proposition $P$ in a consistent NAFL theory T is true/false with respect to T if and only if it has been axiomatically declared as true/false by virtue of its provability/refutability in an interpretation T* of T. In the absence of any such axiomatic declarations, $P$ is in a superposed state of "neither true nor false" and consistency of T requires the existence of a non-classical model for T in which $P \& \neg P$ is the case. Here T* is an axiomatic NAFL theory that, like T, resides in the human mind and acts as the "truth-maker" for (a model of) T. Quantum superposition is justified by identifying "axiomatic declarations" for the truth/falsity of $P$ (by virtue of its provability/refutability in T*) with "measurement" in the real world. NAFL also explains and de-mystifies the phenomenon of entanglement. NAFL severely restricts classical infinitary reasoning, but possibly provides sufficient machinery for a consistent axiomatization of quantum mechanics.


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        Item Type: Preprint
        Additional Information: This is an expanded version of a contributed paper accepted for publication in the International Journal of Quantum Information <http://www.worldscinet.com/ijqi/ijqi.shtml> as part of the proceedings of the meeting on "Foundations of Quantum Information", FQI04, University of Camerino, April 16-19, 2004 <http://web.unicam.it/FQI04/>. The publication is tentatively scheduled for December 2004.
        Keywords: Quantum superposition, entanglement, non-classical logic, finitary reasoning.
        Subjects: Specific Sciences > Mathematics
        Specific Sciences > Physics
        Specific Sciences > Physics > Quantum Mechanics
        Depositing User: Radhakrishnan Srinivasan
        Date Deposited: 01 Sep 2004
        Last Modified: 07 Oct 2010 11:12
        Item ID: 1923
        URI: http://philsci-archive.pitt.edu/id/eprint/1923

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