Russell on Logicism and Coherence


Authors
Conor Mayo-Wilson
University of Washington
Abstract
According to Quine, Charles Parsons, Mark Steiner, and others, Russell’s logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as aprioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell’s explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems by showing mathematical knowledge to be coherently organized. The paper outlines Russell’s theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics.
Keywords Logicism  Bertrand Russell  Coherence
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