Non-Atomic Systems of Individuals Revisited

Abstract

Recently, various attempts have been made to generalize Goodman's well-known principle of individuation' so as to render it appropriate to non-atomic systems of individuals with respect to the of membership. As Schuldenfrei points out2, my own efforts in this direction3 were flawed in two respects: (1) by my previous criteria all atomic individuals were identified, and (2) contrary to Goodman's demands, the atoms of set theory failed to be identified with their singletons. The easiest correction of these errors would seem to be this: throughout the former Definition (8) of ancestral base, let the word ancestor refer to the improper with respect to membership (which is reflective) rather than to the proper (which is irreflexive). The revised definition reads as follows: