Abstract

Can we say that the mathematical signs refer, beyond the mathematical sense, to ideal objects which would correspond to this sense and realize it? Parallel to this, if Husserl affirms that the intuition of essences and sensitive intuition participate in the same generic concept of intuition as a giving act, can we however affirm that mathematical evidence is giving ideal objects such as sensitive perception gives individual objects?We show that the notions of object and evidence have a different status and other modalities in mathematics than in other fields, and that the notion of categorical intuition must be replaced by that of categorical fulfilment, which designates the totality of theoretical procedures by which knowledge is validated. Against the temptation of the universalization of concepts, we advocate a regional phenomenology, practiced closely to the fields of thematized objects and their specific mode of access.