Extensionality, Proper Classes, and Quantum Non-Individuality
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510.6+530.12:531.1 (1)
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GREENBERG, William. Extensionality, Proper Classes, and Quantum Non-Individuality. In: Computer Science Journal of Moldova, 2015, nr. 3(69), pp. 329-342. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 3(69) / 2015 / ISSN 1561-4042 /ISSNe 2587-4330

Extensionality, Proper Classes, and Quantum Non-Individuality
CZU: 510.6+530.12:531.1

Pag. 329-342

Greenberg William
 
Necunoscută, SUA
 
Disponibil în IBN: 26 noiembrie 2015


Rezumat

In this paper I address two questions: (1) What distinguishes proper classes from sets? (2) Are proper classes and quantum particles individuals? Against the familiar response to (1) that proper classes are too big to be sets, I propose that it is not a difference in size that distinguishes such collections but a difference in individuation. The linchpin of my proposal and centerpiece of an NBG-like fragment of class and set theory (“NBG”: von Neumann-Bernays-G¨odel), is an Axiom of Restricted Extensionality according to which sets are individuated by their members but proper classes are not. This setting (I call it NBG−) I show to be equi-consistent with its NBG counterpart. I answer (2) by exhibiting a parallelism in NBG− between proper classes and quantum particles, the former unindividuated by their members and the latter unindividuated by their relational properties. Since both violate the (weak) principle of the identity of indiscernibles as well as the principle of reflexive identity, in NBG− neither proper classes nor quantum particles are individuals.