From an abstract of a lecture by Gregory Chaitin:

In other words, God not only plays dice in physics, but even in pure mathematics, in logic, in the world of pure reason. Sometimes mathematical truth is completely random and has no structure or pattern that we will ever be able to understand. It is NOT the case that simple clear questions have simple clear answers, not even in the world of pure ideas, and much less so in the messy real world of everyday life.

This is such a relief for me. Nevermind the god stuff, that's not really relevant to me. What gets me, what excites me, is that logic tells us that logic will never be completely logical. I love that. For me it encourages more play, more exploration, more interest. I don't understand why it gets some people down.