Critics often defend that radical enactivism (REC) cannot scale up to explain more sophisticated cognitive activities as in logic and mathematics, which are often held to be constituted by representations. The naturalization of cognition proposed by this theory is then taken to be limited in scope. In order to offer a solution to the scope objection against it, I investigate how REC might be related to a broader pragmatist approach to examine the normativity of logic in the context of the existence of a great plurality of alternative logics. To tackle this problem, I aim at defending a comprehensive enactivist philosophical proposal based on the normativity of our ruled inferential practices. Accordingly, I defend an account of some important connections between logic and normativity, which refuses traditional representationalist, individualist, internalist and intellectualist views of logic and focuses on dynamic and embodied ruled interactions among cognitive agents with their environment. The interpretation to be developed here is that rational obligation should be taken as a normative obligation that binds us together and, in particular, that logical necessity should be taken as a kind of normative coercion, based on normative notions such as rules, authorizations, prohibitions and commitments. If logic, with several different non-classical systems, is mainly normative, and not descriptive, it is possible to naturalize it, meaning that logic is not a real challenge to REC.