Meeting of the Aristotelian Society, held in Senate House, University of London, on Monday, 8 November, 2004 at 4.15 p.m.
III —ON THE MEANING OF THE WORD ‘PLATONISM’ IN THE EXPRESSION ‘MATHEMATICAL PLATONISM’*
Version of Record online: 8 AUG 2005
Proceedings of the Aristotelian Society (Hardback)
Volume 105, Issue 1, pages 55–79, June 2005
How to Cite
Bouveresse, J. (2005), III —ON THE MEANING OF THE WORD ‘PLATONISM’ IN THE EXPRESSION ‘MATHEMATICAL PLATONISM’. Proceedings of the Aristotelian Society (Hardback), 105: 55–79. doi: 10.1111/j.0066-7373.2004.00102.x
- Issue online: 8 AUG 2005
- Version of Record online: 8 AUG 2005
- Cited By
ABSTRACT The expression ‘platonism in mathematics’ or ‘mathematical platonism’ is familiar in the philosophy of mathematics at least since the use Paul Bernays made of it in his paper of 1934, ‘Sur le Platonisme dans les Mathématiques’. But he was not the first to point out the similarities between the conception of the defenders of mathematical realism and the ideas of Plato. Poincaré had already stressed the ‘platonistic’ orientation of the mathematicians he called‘Cantorian’, as opposed to those who (like himself) were ‘pragmatist’ ones. I examine in this paper some very perplexing aspects of the use which is made at that time of a number of concepts, particularly ‘idealism’ (which generally designates what we would call ‘mathematical realism’) and ‘empiricism’ (which can designate almost any form of antirealism, even if, like for example intuitionism, it is not empiricist at all). There are, of course, historical reasons that may explain why it was for a time so easy and natural to use the words and the concepts in a way that may seem now very strange and to treat as if they were equivalent the two oppositions: realism/antirealism and idealism/empiricism.