Thursday, October 27, 2011


Frege says somewhere that, if a single contradiction were to be discovered in mathematics, "the whole building would collapse like a House of Cards". Please, why? This claim seems largely an artefact of the wrong metaphor. Mathematics is not a house with foundations which have to bear the whole weight. It is rather a planetary system of different theories entering into various relationships, and happily spinning together in logical space. Damage one, and the system will continue, maybe with some debris orbiting here and there. Or, here is another metaphor for mathematics, equally attractive, due to Chaim Perelman: it is a wonderful tapestry of many strands woven together by the great mathematicians. Pull out one strand, and the tapestry may be weaker by an epsilon, but tears can mended. And this brings me to my most central objection: we know from the history of mathematics and the sciences that contradictions are never the end of a story.

Johan van Benthem in Philosophy of Mathematics: 5 Questions, Hendricks & Leitgeb, eds., Automatic Press (2008) p. 38

No comments:

Post a Comment

Please understand that this weblog runs on a third-party comment system, not on Blogger's comment system. If you have come by way of a mobile device and can see this message, you may have landed on the Blogger comment page, or the third party commenting system has not yet completely loaded; your comments will only be shown on this page and not on the page most people will see, and it is much more likely that your comment will be missed.