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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Décio Krause
Federal University of Santa Catarina

Citations of this work

Structures and Structural Realism.Décio Krause - 2003 - Logic Journal of the IGPL 13 (1):113-126.
Logical and Philosophical Remarks on Quasi-Set Theory.Newton Da Costa - 2007 - Logic Journal of the IGPL 15 (5-6):421-431.

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References found in this work

Parts: A Study in Ontology.Peter M. 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).
An introduction to the philosophy of science.Rudolf Carnap - 1974 - New York: Dover Publications. Edited by Martin Gardner.

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