Intentional objects and objective existence

Abstract

In this paper I show the possibility of an ontology of mathematics that keeps some points in common with platonism and constructivism while diverging from them in other essencial ones. I understand that mathematical objects are simply the referential focus of mathematical discourse, I also understand that their existence is merely intentional but none the less objective, in the sense of being shared by all those who are engaged in the mathematical activity. However, the objective existence of mathematical entities is not secured once and for all but only in so far as the mathematical discourse is consistent. This is the core of the criterium of objective existence put forward and that I believe should sustain a mathematical ontology without the presupposition of the independent existence of a domain of mathematical objects, and without the restrictions imposed on it by constructivism and formalism in their various versions.