Logic in accounts of the potential and actual infinite

This dissertation presents a new defense of logical pluralism, the view that there are many equally good accounts of logical consequence. The defense is composed of two parts: (i) an account of choice between alternative theories of logic, where each theory is judged based on its ability to satisfy several theoretical virtues, much like in scientific theory choice; and (ii) a historical component that connects debates over acceptable uses and formulations of the infinite to views of logic through these virtues, covering ancient, medieval, early modern, and modern positions in philosophy, science, and mathematics. It then argues that charitable interpretations of the historical positions on the infinite should lead one to endorse a logical pluralism.