Resumo
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 (if we consider set theory as a conceptual theory) or, alternatively, as true statements about abstract objects (considering ZFC as an objectual theory). I want to argue here that, in either case, set theory can be seen as a body of knowledge largely built on intuitive foundations (rather than an instrumental theory conceived mainly for pragmatic purposes, the needs of mathematics in particular). I call this inquiry “phenomenological” for it approaches its subject from the perspective of the intentional acts that originate sets as doubly dependent objects (of other objects – their elements – and of a subject – taken here simply as the abstract form of a real subject – who collects these elements into a set). 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 (or at least most of them) express.Referências
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