Chapter

Postscript

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: http://dx.doi.org/10.1093/0198236395.003.0017
Postscript

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This postscript outlines 18 outstanding issues for the neo‐Fregean programme, which are divided into three categories. The first of these concerns the nature and philosophical significance of the abstraction principles on which the foundational neo‐logicist programme is based. The second section concerns the underlying (second order) logic in terms of which Hume's Principle and similar abstractions are framed. The final set of challenges concern extensions of the neo‐Fregean approach beyond arithmetic. Some of the problems raised in the postscript are considered in papers included in this volume, others sketch new directions for research.

Keywords: abstraction principle; Hume's Principle; logic; logicism; neo‐Fregean

Chapter.  7861 words. 

Subjects: Philosophy of Mathematics and Logic

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