Abstract
If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the other by Dedekind. We argue that both face problems.
Original language | English |
---|---|
Pages (from-to) | 267-283 |
Number of pages | 17 |
Journal | Philosophical Quarterly |
Volume | 64 |
Issue number | 255 |
Early online date | 7 Feb 2014 |
DOIs | |
Publication status | Published - Apr 2014 |
Research Groups and Themes
- Centre for Science and Philosophy
Keywords
- structuralism
- abstraction
- Dedekind
- Frege