Russell’s Early Logicism: What Was It About?

Abstract

‘The nineteenth century, which prided itself upon the invention of steam and evolution’, Bertrand Russell wrote in an early essay, ‘might have derived a more legitimate title to fame from the discovery of pure mathematics’ (1901a, 366). Russell believed — and he was not alone in thinking this — that the discovery of pure mathematics was essentially a matter of finding out what is involved in mathematical reasoning. It is eminently reasonable to think that mathematical reasoning should be a matter of logic. But it was far from self-evident at the time Russell composed the essay. In the forms in which it existed before the late nineteenth century, formal logic had very few, if any, genuine applications. Insofar as one was concerned with discovering what was involved in mathematical reasoning, one could therefore set traditional Aristotelian logic aside, for it was simply irrelevant.