Abstract This chapter discusses the existence of linguistic norms (defined as socially determined and commonly shared criteria for correctness of action specific to language). It considers linguistic structure and semantic compositionality, lexical semantics, speech acts, and implicit communication and concludes that there are no linguistic norms stricto sensu at any of these levels. However, social norms constraining communication in the intimate societies in which language evolved have left traces in contemporary languages, notably in the universal existence of implicit communication. Key words: linguistic norm, linguistic structure, semantic compositionality, lexical semantics, speech act, implicit communication, Grice, principle of cooperation, society of intimates, evolution of language.