Abstract

Logicism is the thesis that all or, at least parts, of mathematics is reducible to deductive logic in at least two senses: (A) that mathematical lexis can be defined by sole recourse to logical constants [a definition thesis]; and, (B) that mathematical theorems are derivable from solely logical axioms [a derivation thesis]. The principal proponents of this thesis are: Frege, Dedekind, and Russell. The central question that I raise in this paper is the following: ‘How did Russell construe the philosophical worth of logicism?’ The argument that I build in response to this is that Russell perceived an inverse proportion between a logical reduction of mathematics and the certitude of non-novel mathematical theorems—such that the more we reduce mathematics to logic, the more certain we become of our mathematical theorems; this was portrayed through a presentation of mathematical knowledge as coherent. Therefore, I set out to sketch Russell’s coherence theory and appraise it in relation to the presence discourse: i.e., in relation to logicism and mathematical certainty.