Back to Search
Start Over
Strict Finitism Refuted?
- Source :
- Proceedings of the Aristotelian Society (Paperback); Sep2007, Vol. 107 Issue 3, p403-411, 9p
- Publication Year :
- 2007
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICS
NATURAL numbers
RATIONAL numbers
LOGIC
Subjects
Details
- Language :
- English
- ISSN :
- 00667374
- Volume :
- 107
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Proceedings of the Aristotelian Society (Paperback)
- Publication Type :
- Academic Journal
- Accession number :
- 27230275
- Full Text :
- https://doi.org/10.1111/j.1467-9264.2007.00230.x