Journal Article

Abstraction and Additional Nature†

Bob Hale and Crispin Wright

in Philosophia Mathematica

Volume 16, issue 2, pages 182-208
Published in print June 2008 | ISSN: 0031-8019
Published online October 2007 | e-ISSN: 1744-6406 | DOI:
Abstraction and Additional Nature†

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In ‘What is wrong with abstraction’, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their ‘Hale on Caesar’ and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are:

To get the character of this objection into sharper focus;

To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and about the effects of impredicativity in abstraction principles—which underlie it; and

To advance the debate of the issues thereby raised.

Journal Article.  12011 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic ; Mathematics

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