C.I. Lewis, E.J. Nelson, and the Modern Origins of Connexive Logic

Abstract

Modern logic owes an important debt to C.I. Lewis and his students. In addition to Lewis's five modal logics, they are responsible for the creation (or discovery) of the logic of analytic implication and connexive logic. In this paper, we examine E.J. Nelson's connexive logic as an attempt to formalise the notion of entailment while avoiding the paradoxes of strict implication. We also look briefly at the reception of Nelson's logic and at Lewis's reply to it.