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 a prioricity, 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 (even basic arithmetical facts) 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 Bertrand Russell  Logicism  Coherence
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Reprint years 2011
DOI 10.15173/russell.v31i1.2206
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References found in this work BETA

Epistemology Naturalized.Willard Van Orman Quine - 1969 - In . Columbia University Press. pp. 69-90.
Mathematical Knowledge.Mark Steiner - 1975 - Cornell University Press.
Principia mathematica.A. N. Whitehead & B. Russell - 1911 - Revue de Métaphysique et de Morale 19 (2):19-19.
Infinite Regrees and Foundations of Mathematics.Imre Lakatos - 1962 - Aristotelian Society Supplementary Volume 36:155--84.

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Citations of this work BETA

Bertrand Russell.A. D. Irvine - 2008 - Stanford Encyclopedia of Philosophy.
Principia Mathematica.A. D. Irvine - 2008 - Stanford Encyclopedia of Philosophy.

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