If God is infinitely powerful, can he create a rock so big, he can't move it?
You think you're so clever, don't you? I know you ask your question as a jest. Forgive me for taking it seriously. I like to pretend I'm clever, too.
Let's start with this. Did you know that the Bible says God cannot lie?
[S]o that by two unchangeable things in which it is impossible for God to lie, we who would have taken refuge would have strong encouragement to take hold of the hope set before us. (Hebrews 6:18)
There are some other things we know God can't do.
If we are faithless, He remains faithful, for He cannot deny Himself. (2 Timothy 2:13)
Your eyes are too pure to approve evil, And You cannot look on wickedness with favor. (Habakkuk 1:13)
Now, what do these things have in common? God cannot lie. He cannot deny himself. He cannot approve wickedness. These are all ethical constraints on what God cannot do.
So then, why can't God do these things?
There are absolute laws of morality because there is a God whose very nature sets the standard. It is the nature of God that dictates the fact that its wrong to lie, wrong to murder, and wrong to steal. God cannot act in an immoral way because to do so would be completely contrary to His nature. God is not like man, changing His behavior on a whim. He cannot deny Himself. And that means He never does anything that contradicts His own nature of perfect goodness.
A similar thing can be said of the laws of logic. Why is it impossible to construct a four-cornered triangle, or one of those irksome cube drawings they use as optical illusions?* Why does the universe adhere completely to laws of rationality? It's not like you can travel to another region of the world where two and two equals twelve. You can't travel back in time to an age in which self-contradictions were possible. And if you embark on a spaceship to set off for some wild expoplanet, you will find that even there you are bound by the fact that every triangle's angles must add up to 180 degrees.
No, laws of logic are inescapable every time, every where. Where do they come from? Like morality, laws of logic stem from the nature of God. And we already know that God can't contradict Hiself. It is immoral to lie; God's nature sets the standard for what is moral or immoral; thus, God cannot lie. It is illogical for God to create a stone so big He couldn't move it; God's nature sets the standard for what is logical or illogical; thus, God can't create a stone so big He can't move it. He cannot contradict Himself; He is not irrational.
But let's look at this with the tables turned. You attempt to mock God's existence with a rational conundrum. You think you can use logic to show a belief in God is ridiculous and logically unfounded. But apart from God's existence, you have no reason to accept that logic even exists. A lack of a Higher Power leaves you with a materialistic universe in which physical matter is all that exists.
And guess what? Physical matter does not include logic, which is an abstract, non-physical concept.
So, you're trying to suggest logically that God doesn't exist. But without God, logic wouldn't exist. Ergo, you're left refuting yourself with a non sequiter that only shows God does exist because for some reason, you take logic's existence for granted.