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 |
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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 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 |

### Available Versions of this Item

- Quantum superposition justified in a new non-Aristotelian finitary logic. (deposited 04 May 2002)
- Quantum superposition principle justified in a new non-Aristotelian finitary logic. (deposited 01 Sep 2004)
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- Quantum superposition principle justified in a new non-Aristotelian finitary logic. (deposited 01 Sep 2004)

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