Srinivasan, Radhakrishnan (2004) Quantum superposition principle justified in a new nonAristotelian finitary logic. [Preprint]
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Abstract
In the proposed nonAristotelian 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 nonclassical 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 "truthmaker" 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 demystifies 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  

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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 1619, 2004 <http://web.unicam.it/FQI04/>. The publication is tentatively scheduled for December 2004.  
Keywords:  Quantum superposition, entanglement, nonclassical 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 15:12  
Item ID:  1923  
URI:  http://philsciarchive.pitt.edu/id/eprint/1923 
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Quantum superposition justified in a new nonAristotelian finitary logic. (deposited 04 May 2002)
 Quantum superposition principle justified in a new nonAristotelian finitary logic. (deposited 01 Sep 2004) [Currently Displayed]
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