Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Extensionality, Proper Classes, and Quantum Non-Individuality
Authors: William J. Greenberg
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Abstract
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.USA
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Contents
- Convex graph covers
- Set-theoretic Analysis of Nominative Data
- Admissibility, compatibility, and deducibility in first-order sequent logics
- Small P Systems with Catalysts or Anti-Matter Simulating Generalized Register Machines and Generalized Counter Automata
- Extensionality, Proper Classes, and Quantum Non-Individuality
- Edge detection in digital images using Ant Colony Optimization
- Probability on groups and an application to cryptography
- Classification of Early Stages of NAFLD Based on Dual Diagnostic Methods
- Annotation on PhD Thesis
