Abstraction and Additional Nature

Bob Hale, Crispin James Garth Wright

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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:
1.To get the character of this objection into sharper focus;
2.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
3.To advance the debate of the issues thereby raised.
Original languageEnglish
Pages (from-to)182-208
Number of pages27
JournalPhilosophia Mathematica
Volume16
Issue number2
Early online date4 Oct 2007
DOIs
Publication statusPublished - Jun 2008

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Set Theory
Abstraction
Nature
Character
Foundations of Mathematics
Mathematics

Cite this

Abstraction and Additional Nature. / Hale, Bob; Wright, Crispin James Garth.

In: Philosophia Mathematica, Vol. 16, No. 2, 06.2008, p. 182-208.

Research output: Contribution to journalArticle

Hale, B & Wright, CJG 2008, 'Abstraction and Additional Nature', Philosophia Mathematica, vol. 16, no. 2, pp. 182-208. https://doi.org/10.1093/philmat/nkm036
Hale, Bob ; Wright, Crispin James Garth. / Abstraction and Additional Nature. In: Philosophia Mathematica. 2008 ; Vol. 16, No. 2. pp. 182-208.
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