Certain lexical and grammatical units encode aspects of intersubjective coordination. On the basis of discourse connectives, and especially of negation and complementation, linguistic communication is argued to be inherently ‘argumentative’, a matter of influencing other people’s attitudes and beliefs. Intersubjectivity is built into the very structure of grammar, and systematic properties of grammar show that mutual influencing, rather than just ‘sharing information’ or ‘joint attention’ is at the heart of human language. Because of that, language can on the one hand be seen as a special case of animal communication systems, which basically involve management and assessment of other organisms, notably conspecifics. On the other hand, an important difference is precisely that this management and assessment is indirect, presupposing shared knowledge, and aimed at other minds.