Russellʼs conception of logic as a key to understanding the relationship between logic and metaphysics

Abstract

Although Bertrand Russell is now widely recognized as a founder of modern mathematical logic, his work on logic suggests that he himself had a totally different conception of logic from that of modern mathematical logic. Many commentators have tried to give an account of this difference by explaining logic for him as a universal language, a formal language that captures ʻthe logical furniture of the universeʼ. This explanation, however, turns out to be misleading, when we focus upon his view of language as a ʻtransparent medium.ʼ It seems to be more correct to think that Russell conceived of logic as concerned with the logical furniture of the world, or more precisely, with the forms that govern the way the world is, while he took a formal language merely as a medium to describe these forms. I will call such a view of logic ʻthe metaphysical conception of logic.ʼ The aim of this paper is to show that, by attributing this conception of logic to Russell, we can reach a better understanding of the difference between logic as Russell conceived it and modern mathematical logic. To illustrate his metaphysical conception of logic I will focus upon two features of Russellʼs philosophy, which in turn suggest that he shared the metaphysical conception of logic with his predecessors. Although I cannot develop this point fully,this would be another advantage of the above account of Russellʼs logic.