Can God create a rock so heavy that he can't lift it?
The paradoxical question, "Can God create a rock so heavy that he can't lift it?" is a rather silly conundrum designed to show that the term omnipotent is actually meaningless.
Omnipotent means "all-powerful", which is typically understood to mean "able to do anything". If God can do anything, then he should be able to create such a rock. But once the rock is created, he should also be able to lift it, which contradicts the first claim.
This is reminiscent of a story about a medieval arms salesman who boasted that his sword was so sharp that it could penetrate any armor, and his shield was so tough that it could withstand any attack. A member of the crowd called out, "What happens when you strike your sword against your own shield?" The salesman was stumped.
The answer is that the salesman was lying about one of his products. Or to put it another way, a perfect sword and a perfect shield cannot exist simultaneously. If there exists any sword that can penetrate all shields, then by definition there does not exist any shield that can withstand all attacks.
Similarly, there cannot exist a rock that cannot be lifted in a universe that also contains a God who can lift anything. Yet this proves that there is something that God cannot create.
How do we get out of the paradox? An atheist would answer that the very idea of being "all-powerful" is meaningless and not worthy of consideration in the real world. However, apologists often respond that "all-powerful" means "God can do everything... that is logically possible."
- "His omnipotence includes power to do all that is intrinsically possible, not to do the intrinsically impossible. You may attribute miracles to Him, but not nonsense."
This raises the question of what exactly a miracle is, if not doing the impossible. Of course, the qualifier intrinsically is an important one. Still, this seems to paint a picture of God as simply the most powerful being in the universe, instead of an all-powerful one.
This subject is further explored in the article about the omnipotence paradox.