Article Title：Sets and classes as many
Abstract：
In this paper the view is developed that classes should not be understood as individuals, but, rather, as 'classes as many' of individuals. To correlate classes with individuals 'labelling' and 'colabelling' functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.
Keywords: set; class; individuals; label; colabel; nonwellfounded set theory
DOI: 10.1023/A:1026564222011
Source：JOURNAL OF PHILOSOPHICAL LOGIC
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