The mathematics of non-individuality

Abstract

Some of the forerunners of quantum theory regarded the basic entities of such theories as 'non-individuals'. One of the problems is to treat collections of such 'things', for they do not obey the axioms of standard set theories like Zermelo- Fraenkel. In this paper, collections of objects to which the standard concept of identity does not apply are termed 'quasi-sets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. At the end, it is shown how quantum statistics can be obtained within quasi-set thbeory.

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Author's Profile

Décio Krause
Federal University of Santa Catarina

References found in this work

The emperor’s new mind.Roger Penrose - 1989 - Oxford University Press.
Parts: a study in ontology.Peter M. Simons - 1987 - New York: Oxford University Press.
Parts: A Study in Ontology.Peter Simons - 1987 - Oxford, England: Clarendon Press.
Introduction to logic.Patrick Suppes - 1957 - Mineola, N.Y.: Dover Publications.
Representation and Invariance of Scientific Structures.Patrick Suppes - 2002 - CSLI Publications (distributed by Chicago University Press).

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