Abstract

We try to point out how the integration of quantification and objects into the didactical analysis permits to question the "traditional" idea of a rupture between argumentation and proof in mathematics. We use a conceptual distinction described by Hintikka (1996) between indoor and outdoor games to assess the problem. Then we go to a description some examples of proof constructions and proof validation to provide some substance to our thesis. Our main claim is that the proof process is a dialectic one between actions on objects and syntactic (formal) work in proof construction. We think that claim to be inconsistent with the idea of a rupture between argumentation and proof