The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.

I don't believe in empirical science. I only believe in a priori truth.

All generalisations - perhaps except this one - are false.

I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife

Said to physicist John Bahcall. I don't believe in natural science.

I don't believe in natural science.

The more I think about language, the more it amazes me that people ever understand each other at all.