ABSTRACT
A long line of philosophers, from Zeno to M.Bergson, have based much of their metaphysics upon the supposed impossibility of infinite collections…. The definitive solution of the difficulties is due…to Georg Cantor. (Bertrand Russell)
Apart from an anti-Aristotelian backlash among the medievals, spearheaded by Gregory of Rimini and partly followed through by the rationalists (see above, Chapters 3 and 5), the time up until the early-mid nineteenth century saw nothing but hostility towards the actual mathematical infinite. Some of the hostility was towards the mathematical infinite per se. We saw something of this in Hegel. But some of it was emphatically not that. It was hostility specifically to the actual mathematical infinite. Here, of course, the key figure was Aristotle, for whom the infinite was certainly to be understood in mathematical terms; what had to be resisted was the idea that it could be given ‘all at once’. For over two thousand years this was the prevailing view.
