In this paper the view is developed that classes should not be understood a
s individuals, but, rather, as 'classes as many' of individuals. To correla
te classes with individuals 'labelling' and 'colabelling' functions are int
roduced and sets identified with a certain subdomain of the classes on whic
h the labelling and colabelling functions are mutually inverse. A minimal a
xiomatization of the resulting system is formulated and some of its extensi
ons are related to various systems of set theory, including nonwellfounded
set theories.