2015/10/25 by Décio Krause, Krause, Decio, Jonas R. Becker Arenhart +1
Computer Science · Physics and Astronomy · #03E10 #81P05 #81P70 #Advanced Algebra and Logic #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Logic, Reasoning, and Knowledge #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1510.07297
openalex publication_date 2015/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \itanonreflexive logic (a.k.a. `non-reflexive'). 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 \itanon-individuals in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). 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 (when they are not: all objects that obey classical logic are \itaindividuals in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical (mainly metaphysical) motivations and consequences of it.