A cognitive version of semiotics has to reopen the discussion of how to understand language in general and the possibility of a theory of language. L. Hjelmslev and his current French semio-linguistic followers, inspired by the great pioneer of structural semantics A.-J. Greimas, anchor their inquiry exclusively in text and discourse. By contrast, cognitive linguistics from Langacker and Talmy to Croft and Evans anchors language in the embodied mind, but has no perspective on text and discourse other than claiming that culture in general shapes what is not shaped by mind and perception. In one frame(Hjelmslev-Greimas), language is everything, and in the other(Langacker-Croft), it is almost nothing(in itself). Could we instead conceive language as ‘something’, as forming a substantial, structured, particular link between culture and the mind-brain, essential to both culture and mind-brain? Could we build a theoretical and analytical study of language in all forms, in order to describe it as a structured architecture of instances that connect culture and mind? In that case, we will have to revisit the models of both semio-linguistics and cognitive linguistics and examine the semiotic functions in language that allow the sharing of meaning to which other animals have no access, the sophisticated connection of communication and thinking that makes human culture possible. This paper shortly presents a few core suggestions concerning three involved issues: the linear wording of language(linearization); the role of syntax as a reconstruction of thought that simulates its composition; and the complex semiotic functions that connect its ‘immanent’ core operations and its ‘transcendent’ enunciational and pragmatic operations.