Bob Hale and Crispin Wright

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI:

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The introduction to The Reason's Proper Study outlines how the essays collected in this volume fit into the broader neo‐Fregean philosophical programme. The notion of an ’abstraction principle’ is introduced and the basic neo‐Fregean account of arithmetic is outlined. Central theses here include the idea that platonism can be underwritten by a proper syntactical analysis of the notion of 'singular term’ (the ’context principle for reference’), and the logicist claim that abstraction principles can give rise to a priori knowledge of the abstracta they introduce. Some of the central challenges facing these proposals are outlined, and possible extensions of the programme beyond arithmetic are canvassed.

Keywords: abstraction principle; context principle; Frege; logicism; platonism; singular terms

Chapter.  14720 words. 

Subjects: Philosophy of Mathematics and Logic

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