Introduction

Abstract

The present work concerns Bertrand Russell and the conception of logic that underlies the early version of his logicist philosophy of mathematics. The views examined here are those that are found in The Principles of Mathematics (1903a; PoM for short), a work which, as John Passmore put it, ‘first made it perfectly clear that a new force had entered British philosophy’ (1966, 216). Russell had been working on the foundations of mathematics for several years, and although his entire philosophical outlook had changed in the intervening years, the single most important event was his participation in the International Congress of Philosophy in Paris in early August 1900. It was there that he met Giuseppe Peano, an Italian mathematician, and first learned about mathematical logic in any serious sense of the term. PoM is an exposition of Russell’s initial vision of logicism, which he formulated as a result of reflecting on the arithmetization of analysis and geometry — ‘modern mathematics’ as he used to call it — and the methodological consequences of the new logic.