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The Oxford Handbook of Philosophy of Mathematics and Logic$
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Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL

THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL

Chapter:
(p.129) THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL
Source:
The Oxford Handbook of Philosophy of Mathematics and Logic
Author(s):

William Demopoulos (Contributor Webpage)

Peter Clark (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0195148770.003.0005

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

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