This paper questions the premises of the theory of grammaticalization which claims that “abstract” grammatical morphemes derive from “concrete” lexical items through a process of phonetic and semantic attrition. This theory generally assumes that language is grounded in iconicity. Thus, questioning the latter also puts the former to a test. The first section presents arguments against the notion of lexical “concreteness”. The second raises the issue of whether the “abstractness” of grammar is an artifact of pedagogical discourse or truly reflects the nature of grammatical relations. The third part proposes to frame the problems that gave rise to the notion of grammaticalization in an utterance-based perspective inspired by the cognitivist approach to language. The conclusion attempts to explain why contemporary linguistics has taken the form of a mosaic of theories that are often difficult to reconcile.