A Discussion on Finite Quasi-cardinals in Quasi-set Theory

Foundations of Physics 41 (8):1338-1354 (2011)
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Abstract

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general

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Jonas R. B. Arenhart
Universidade Federal de Santa Catarina

References found in this work

Possibility of Metaphysics: Substance, Identity, and Time.E. J. Lowe - 1998 - Oxford, GB: Oxford University Press UK.
Identity in physics: a historical, philosophical, and formal analysis.Steven French & Décio Krause - 2006 - New York: Oxford University Press. Edited by Decio Krause.
Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.

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