There's No Logical Proof of God

There are a few ways we can show this. Here's the most basic:

If a system of logic is created that does not have the existence of God as an axiom, it cannot show that God exists. This is because by definition, God is of an order of complexity beyond other axioms (else He would be subject to, and limited by, such axioms). If a system of logic is created that has the existence of God as an axiom, it cannot show that God exists either, since that existence is treated as axiomatic and hence not to be proven. If we use any kind of reasoning in which X and not-X covers all the possibilities (principle of bivalence), then God cannot be shown to exist by logic.

Here's a theological proof:

If God requires belief, then that belief must be volitional (free-willed). Otherwise, it has no significance. Therefore God cannot present a complete proof of His existence, because if such were to exist, then the option to not believe would be irrational. That would mean that belief would be the only rational choice, thus removing the option of free-willed rational belief. This also means that if anyone tells you that they can prove the existence of God, they are either lying, or they are advancing an argument that is sufficient for them to believe but does not necessarily compel belief in anyone else.

That said, I believe I have good grounds for belief in God, and I am not ashamed to say that I can give a good account of my faith.