Logic, Modality, and Metaphysics in Early Analytic Philosophy

Abstract

This chapter treats C. I. Lewis' criticism of Bertrand Russell's material implication. This chapter gives an overview of the differences between Russell's conception of logic and contemporary ones. Lewis's criticism is often taken to rest on the divergence between material implication and our intuitive conception of logical consequence. The chapter argues that a more fundamental criticism Lewis makes is internal to Russell's conception: for Russell a system of logic must not merely enable correct inferences to be made; it must state correct implications. Lewis came to hold that a primitive notion of possibility is required if the laws of logic are to capture the facts of inferential practice. But Lewis's incorporation of modality is meant to revise Principia to make its axioms properly logical. The chapter concludes the chapter by sketching some other aspects of this history, from Wittgenstein through Carnap, Quine and the full re-emergence of modal notions in analytic philosophy.