Abstract

The main concern of this paper is the justification of the axioms of Zermelo-Fraenkel set theory, either as true statements about a concept of set or, alternatively, as true statements about abstract objects . I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations . I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent objects . Such an inquiry, I believe, brings to light the essential characters of sets as objects or, alternatively, the concept of set, which the axioms of the theory express