Chapter

THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL

William Demopoulos and Peter Clark

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print March 2005 | ISBN: 9780195148770
Published online July 2005 | e-ISBN: 9780199835560 | DOI: http://dx.doi.org/10.1093/0195148770.003.0005

Series: Oxford Handbooks in Philosophy

THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL

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The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our critical exposition of the view proceeds by tracing its answers to three fundamental questions: (1) What is the basis for our knowledge of the infinity of the numbers? (2) How is arithmetic applicable to reality? (3) Why is reasoning by induction justified?

Keywords: logicism; Frege; Dedekind; Russell; Kant; intuition; infinity; arithmetic; applicability; induction

Chapter.  15937 words. 

Subjects: Philosophy of Mathematics and Logic

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