Variable Sharing and Mathematical Practice

Abstract The relationship between relevant logic and mathematical practice has often been twofold: while some relevant logicians have focused on the descriptive project of capturing (in some sense) informal mathematical reasoning better than classical logic does, others have engaged in the normative project of suggesting how mathematics should be done as opposed to how it is done now. Both projects have received heavy criticism. In this paper, I argue that the intuitive idea of variable sharing does point to a real aspect of mainstream mathematical practices, and this fact can be used to make sense of both relevantist projects: on one hand, relevant logics may be used to provide a more accurate model of this particular aspect of current practices, while on the other, they can suggest new practices which deviate from the standard precisely in their approach to variable sharing.