Logicism in the Twenty‐first Century

Bob Hale and Crispin Wright

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:

Series: Oxford Handbooks in Philosophy

Logicism in the Twenty‐first Century

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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

Chapter.  17041 words. 

Subjects: Philosophy of Mathematics and Logic

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