Srinivasan, Radhakrishnan (2002) Quantum superposition justified in a new non-Aristotelian finitary logic. [Preprint]

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Abstract

A new non-Aristotelian finitary logic (NAFL) is proposed in which it is postulated that the truth or falseness of an undecidable proposition in a theory T is meaningful only when asserted axiomatically; there is no truth other than axiomatic truth. It is shown that under this hypothesis, the law of the excluded middle and the law of non-contradiction for such undecidable propositions must fail to be theorems of T. The phenomenon of quantum superposition is thus explained in NAFL. It is also shown that infinite sets cannot exist in any consistent theory of NAFL, which makes it a very restrictive logic. Implications for some modern mathematical and physical theories are analyzed from the point of view of NAFL.

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Item Type:	Preprint
Creators:	Creators Email ORCID Srinivasan, Radhakrishnan
Keywords:	non-Aristotelian finitary logic, anti-realism, quantum superposition, undecidability, consistency, model theory, set theory, law of the excluded middle, law of non-contradiction
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Mechanics
Depositing User:	Dr. Radhakrishnan Srinivasan
Date Deposited:	04 May 2002
Last Modified:	07 Oct 2010 15:10
Item ID:	635
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Mechanics
Date:	March 2002
URI:	https://philsci-archive.pitt.edu/id/eprint/635

Available Versions of this Item

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

Commentary/Response Threads

• Srinivasan, Radhakrishnan Quantum superposition justified in a new non-Aristotelian finitary logic. (deposited 04 May 2002) [Currently Displayed]
  • Srinivasan, Radhakrishnan Platonism in classical logic versus formalism in the proposed non-Aristotelian finitary logic. (deposited 21 May 2003)
  • Srinivasan, Radhakrishnan Inertial frames, special relativity and consistency. (deposited 27 Jun 2002)

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