Journal Article

Conservativeness, Stability, and Abstraction

Roy T. Cook

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 63, issue 3, pages 673-696
Published in print September 2012 | ISSN: 0007-0882
Published online April 2012 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axr047
Conservativeness, Stability, and Abstraction

More Like This

Show all results sharing these subjects:

  • Philosophy of Science
  • Science and Mathematics

GO

Show Summary Details

Preview

One of the main problems plaguing neo-logicism is the Bad Company challenge: the need for a well-motivated account of which abstraction principles provide legitimate definitions of mathematical concepts. In this article a solution to the Bad Company challenge is provided, based on the idea that definitions ought to be conservative. Although the standard formulation of conservativeness is not sufficient for acceptability, since there are conservative but pairwise incompatible abstraction principles, a stronger conservativeness condition is sufficient: that the class of acceptable abstraction principles be strictly logically symmetrically class conservative. The article concludes with an examination of which classes of abstraction principles meet this criteria.

1Introduction

2The Technical State of the Art

3Abstraction and Conservativeness

4Abstraction Stabilized

5Characterizing SLSC-Conservativeness

6Conclusion

Journal Article.  7423 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.