Strict Finitism Refuted?
Article first published online: 26 OCT 2007
Proceedings of the Aristotelian Society (Hardback)
Volume 107, Issue 1pt3, pages 403–411, October 2007
How to Cite
Magidor, O. (2007), Strict Finitism Refuted?. Proceedings of the Aristotelian Society (Hardback), 107: 403–411. doi: 10.1111/j.1467-9264.2007.00230.x
- Issue published online: 26 OCT 2007
- Article first published online: 26 OCT 2007
In his paper ‘Wang's Paradox’, Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett's argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there are sets of natural numbers which are closed under the successor operation but nonetheless have an upper bound; (2) Such a commitment is inconsistent, even by finitistic standards.
In this paper I claim that Dummett's argument fails. I question both parts of Dummett's argument, but most importantly I claim that Dummett's argument in favour of the second claim crucially relies on an implicit assumption that Dummett does not acknowledge and that the strict finitist need not accept.