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Quantum superposition justified in a new non-Aristotelian finitary logic

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
      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: Radhakrishnan Srinivasan
      Date Deposited: 04 May 2002
      Last Modified: 07 Oct 2010 11:10
      Item ID: 635
      URI: http://philsci-archive.pitt.edu/id/eprint/635

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