A.W. Moore

The world, according to Ted Sider, has a basic structure. An optimal description of the world must capture this structure. It must also consist of truths. But these are two distinct requirements. We can produce more and more truths about the world and still not come any closer to capturing its structure. To do the latter we need to produce not just truths, but truths of the right sort. Now it...

“There are fundamental reasons of principle that, when it comes to settling unanswered mathematical questions, we shall never be able to dispense with divination and inspiration in favour of a mechanical application of rules. But even if the holy grail had existed, and even if we had found it, it might have been of purely theoretical interest. Of what practical significance would an algorithm have been if it had enabled us to determine whether or not the Reimann Hypothesis is true, but only if we had been able to spend a trillion times as long on the problem as it will take for the earth to be swallowed up by the sun?”

“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.”