Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics

Jonas R. B. Arenhart
Universidade Federal de Santa Catarina
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non- classical logic termed nonreflexive logic. In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may be absolutely indistinguishable. The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible. Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical motivations and consequences of it.
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References found in this work BETA

On the Identity and Diversity of Objects in a Structure.James Ladyman - 2007 - Proceedings of the Aristotelian Society 81 (1):23--43.
Semantic Analysis of Non-Reflexive Logics.J. R. B. Arenhart - 2014 - Logic Journal of the IGPL 22 (4):565-584.
Quantifiers and the Foundations of Quasi-Set Theory.Jonas R. Becker Arenhart & Décio Krause - 2009 - Principia: An International Journal of Epistemology 13 (3):251-268.

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