How to Catch a Tortoise: Infinity
A.W. Moore, 18 December 2003
“According to the iterative conception, a set is something whose existence is parasitic on that of its members: the members exist ‘first’. Thus there are, to begin with, all those things that are not sets (planets, twins, positive integers etc). Then there are sets of these things. Then there are sets of these things. And so on, without end . . . But there never comes a set to which every set belongs. There is no set of all sets.”