Non-reflexive Logical Foundation for Quantum Mechanics

Foundations of Physics 44 (12):1369-1380 (2014)

Abstract
On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity
Keywords Identity  Non-reflexive logic  Interpretation of quantum mechanics
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DOI 10.1007/s10701-014-9848-3
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References found in this work BETA

Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.

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