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

The development of mathematics towards 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.

Ninety percent of [contemporary philosophers] see their principle task as that of beating religion out of men's heads. ... We are far from being able to provide scientific basis for the theological world view.

The axiomatic method is very powerful

Nothing new had been done in Logic since Aristotle!

...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.

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