Finite Cardinals in Quasi-set Theory

Studia Logica 100 (3):437-452 (2012)
Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. According to some authors, this is the best way to understand quantum objects. The fact that identity is not defined for m-atoms raises a technical difficulty: it seems impossible to follow the usual procedures to define the cardinal of collections involving these items. In this paper we propose a definition of finite cardinals in quasi-set theory which works for collections involving m-atoms
Keywords Finite cardinals  Quasi-set theory  Identity
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DOI 10.1007/s11225-012-9406-y
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References found in this work BETA
Remarks on the Theory of Quasi-Sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1-2):101 - 124.

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Citations of this work BETA
From Primitive Identity to the Non-Individuality of Quantum Objects.Jonas Arenhart & Décio Krause - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2):273-282.
Semantic Analysis of Non-Reflexive Logics.J. R. B. Arenhart - 2014 - Logic Journal of the IGPL 22 (4):565-584.

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