Abstract

Two themes are developed here: one, general, enters into the analysis of the notion of object, the other, more specific but also complex, takes up the rehabilitation of Hilbert’s Program, thus paying tribute to the great work of Mic Detlefsen. He shows how the destruction of this program by Gödel’s theorem is a delusion, despite the greatness and the importance of Gödel’s work in the History of Logic. The refocusing of Hilbert’s work then opens up perspectives on the analysis of the notion of object and on the idea of effectiveness to which mathematical practice invites us.