Logicism in the Twenty‐first Century

Bob Hale and Crispin Wright

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print June 2007 | ISBN: 9780195325928
Published online September 2009 | e-ISBN: 9780199892082 | DOI:

Series: Oxford Handbooks

Logicism in the Twenty‐first Century

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This article focuses on issues which neo-Fregeanism must address, even if the scope of its leading claims is restricted to elementary arithmetic. Many of these concern the capacity of abstraction principles—centrally, but not only, Hume's Principle itself—to discharge the implicitly definitional role in which the neo-Fregean casts them, and thereby to subserve a satisfactory apriorist epistemology for (at least part of) mathematics. Others concern the other main assumption that undergirds the specifically logicist aspect of the neo-Fregean project (and equally, of course, Frege's original project): that the logic to which abstraction principles are to be adjoined may legitimately be taken to include higher-order—at the very least, second-order—logic without compromise of the epistemological purposes of the project.

Keywords: logicism; neo-Fregeanism; elementary arithmetic; epistemology; abstraction principles; Hume's Principle; twenty-first century

Article.  16574 words. 

Subjects: Philosophy of Mathematics and Logic

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