Proofs of God's Existence and Rational Thinking

Throughout history, a number of individuals have tried to prove the existence of God. Such attempts include the Ontological Argument, the Cosmological Argument and the Argument from Design. I will not review each of these arguments here; I will only say that many modern philosophers consider each of these "proofs" flawed.

I do not intend to prove the existence of God, as I do not think that such can be done by any simple argument devised by man or woman. Why not? Well, consider mathematics. Courtesy of Godel, mathematics cannot be shown to be both consistent and complete. As a result of this, certain mathematical statements cannot be proved true, nor can they be proved false. This demonstrates that logic itself is of limited usefulness; that is, there are some things it just can't handle. Surely, if there are elements of mathematics that logic cannot handle, there must be aspects of God that logic cannot handle. Consider, in Transfinite Set Theory there exist two numbers, aleph null and its power set, two^aleph null. Both are infinite numbers (aleph null being the smaller of the two). However, it can be proved neither true nor false that a number exists between them. God is said to be infinite in a number of different ways. If we cannot fully grasp the infinite as it relates to mathematics, then how can we hope to grasp the infinite as it relates to God? To put it bluntly, the human mind runs into problems when it tries to grapple with the notion of the infinite. And, according to most religions, God is infinite.

However, rather than focus on arguments for or against God, I wish to focus on the notion of what constitutes "rational thinking." In particular, I wish to ask the question "Is belief in God rational?" Alternatively, and perhaps, more importantly, "Is belief in God totally irrational?"