ABSTRACT
The best formal treatment of classes in existence is that of Peano. But in this treatment a number of distinctions of great philosophical importance are overlooked. A reason for distinguishing wholes from classes as many is that a class as one may be one of the terms of itself as many, as in “classes are one among classes”, whereas a complex whole can never be one of its own constituents. The consideration of classes which results from denoting concepts is more general than the extensional consideration, and that in two respects. A relation which, before Peano, was almost universally confounded with e, is the relation of inclusion between classes, as e.g. between men and mortals. All classes, whether finite or infinite, can be obtained as the objects denoted by the plurals of class-concepts—men, numbers and points.
