'As you've probably begun to see,' David Foster Wallace writes in Everything and More, 'Aristotle manages to be sort of grandly and breathtakingly wrong, always and everywhere, when it comes to infinity.' A much milder version of this antagonism towards Aristotle appears in both Brian Clegg's Brief History of Infinity and Robert and Ellen Kaplan's The Art of the Infinite. Clegg writes that Aristotle 'made a distinction on the matter of infinity that was to prove useful, but also was a fudge that made it possible to avoid the real issue for a couple of thousand years'. And the Kaplans describe how Georg Cantor won certain 'striking insights . . . by going against the authority' of Aristotle. All three books express what has become, nowadays, received wisdom: that Aristotle ('the bad guy') promulgated certain views about infinity that had the status of orthodoxy until the late 19th century, when Cantor ('the good guy') finally showed what was wrong with these views and how we should really think about the infinite. I do not myself subscribe to this standard account, and in due course shall explain why not.

LRB 18 December 2003 | PDF Download