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 June 2007 | ISBN: 9780195325928
Published online September 2009 | e-ISBN: 9780198614128 | DOI:

Series: Oxford Handbooks

The Logicism of Frege, Dedekind, and Russell

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This article is organized around logicism's answers to the following questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified? Although there are, as is seen in this article, important differences, the common thread that runs through all three of the authors discussed in this article their opposition to the Kantian thesis that reflection on reasoning with mere concepts (i.e., without attention to intuitions formed a priori) can never succeed in providing satisfactory answers to these three questions. This description of the core of the view differs from more usual formulations which represent the opposition to Kant as an opposition to the contention that mathematics in general, and arithmetic in particular, are synthetic a priori rather than analytic.

Keywords: logicism; infinity of the numbers; arithmetic; Kantian thesis; mathematics; Russell

Article.  15312 words. 

Subjects: Philosophy of Mathematics and Logic ; History of Western Philosophy

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