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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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Logicism in the Twenty‐first Century

Logicism in the Twenty‐first Century

(p.166) Logicism in the Twenty‐first Century
The Oxford Handbook of Philosophy of Mathematics and Logic

Bob Hale (Contributor Webpage)

Crispin Wright (Contributor Webpage)

Oxford University Press

According to Gottlob Frege, his logicism died when it was discovered that the underlying theory of extensions is inconsistent. The neo-logicist attempts to found mathematics on other abstraction principles, such as the so-called Hume’s principle that two concepts have the same number if and only if they are equinumerous. This chapter discusses the state of neo-logicism, responding to various objections that have been raised against it.

Keywords:   Frege, logicism, neo-logicism, mathematics, abstraction, Hume’s principle

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