This article elaborates upon many studies that stress the ability of the French indefinite pronoun ON (one, you, we, they) to anonymize what ON refers to. While this function can be verified in various contexts, there has been a tendency to focus on it and generalize it, leading to the consolidation of a “substitutive” approach to ON: if ON anonymizes, the reason is to be found in the fact that any another verbal unit whose meaning is more precise would fit in order to make reference to the same entity. This paper critically summarizes such a substitutive approach and shows by an enunciative and multimodal analysis of various extracts of public and televised debates that ON can be used to maintain the utterance at a general level of validity (i.e. orientation towards decontextualization), without preventing the simultaneous pointing, by other semiotic resources, of one or more specimens of the category bounded by ON (i.e. orientation towards contextualization).