David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Foundations of Physics 37 (6):855-878 (2007)
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept
|Keywords||quasisets particle number quasicardinality quantum indistinguishability|
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Citations of this work BETA
Steven French & Décio Krause (2010). Remarks on the Theory of Quasi-Sets. Studia Logica 95 (1/2):101 - 124.
Benjamin C. Jantzen (2011). No Two Entities Without Identity. Synthese 181 (3):433-450.
Jonas Rafael Becker Arenhart (2013). Weak Discernibility in Quantum Mechanics: Does It Save PII? Axiomathes 23 (3):461-484.
Jonas R. Becker Arenhart (2012). Many Entities, No Identity. Synthese 187 (2):801-812.
Jonas R. Becker Arenhart (2012). Finite Cardinals in Quasi-Set Theory. Studia Logica 100 (3):437-452.
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