In this paper, I address the dispute between normativism and descriptivism by focusing on the arbitration problem. For this, I propose to take into account the discussion on the collapse problem that has taken place recently in the philosophy of logic. My proposal maintains, on the one hand, that human reasoning, as a social practice, is an essentially regulated activity and, on the other hand, that formal systems of reference in the psychology of reasoning are the result of various processes of reflective equilibrium. This makes it possible to defend the normative role of formal systems as a standard for human reasoning. Furthermore, I argue that the adequacy of a formal system is marked by the specific contexts of reasoning. Thus, I defend normative pluralism regarding formal systems of inference within the framework of empirical studies on human reasoning.