The aim of this article is to see whether we can account for the normativity of law within the framework of legal positivism and whether the idea of a social convention could be of help in this endeavour. I argue, inter alia, that we should distinguish between (alpha) the problem of accounting for the normativity of law, conceived as a necessary property of law, and (beta) the problem of accounting for the use of normative legal language on the part of legal actors; that the debate about the normativity of law, which mainly concerns (alpha), is more or less identical to the debate between legal positivists and non-positivists; that one cannot account for the normativity of law, conceived along the lines of (alpha), within the framework of l...