Is it necessary to admit the thesis of semantic objectivism, which asserts that there is meaning in itself, endowed with absolute identity and ontologically independent of consciousness? Or should the thesis be maintained, within the domain of mathematical idealities, that every sense refers to a gift of sense by consciousness? Here we examine the question within the framework of axiomatic mathematics : are axiomatic systems not closed a priori by the position of the axioms? Therefore, what Derrida said about mathematical (...) objects (the fact that they are releasable to an adequate giveness and exhaust themselves in their phenomenality) does not apply to formal systems? We want to show that any act of aiming ideal objects has a surplus horizon structure and that it is to this that the being in itself of such objects can be reduced. The axiomatization of the theories reinforces the holistic status of the act of aiming mathematical idealities: object forms have only intratheoretical exis... (shrink)