Can God create a stone that is so heavy that He cannot lift it Himself? If so, can God then lift that stone?

This, and similar variants, have been proposed to be a a paradox with omnipotence that would mean God cannot exist, but it's actually a misunderstanding of what we mean when we say that God is omnipotent, or more commonly, almighty. What we actually mean when calling God almighty, is that God has absolute power over everyone and everything, not that there is nothing that God cannot do. The Bible even mentions things that God cannot do. Lie, for example, as it goes against God's character.

But for that matter, if the claim would have been that God can do anything, even things that are not logically possible, then using a logical paradox to debunk that claim would have fallen flat anyway. It would have gone something like this...

- Can God create a stone that is so heavy that He cannot lift it Himself?

- Yes.

- Can God then lift that stone?

- Yes.

That makes no sense! But it wouldn't have to, if God can break the laws of logic. For this supposed paradox to work, one has to change the definition of omnipotence mid-way. One has to both assume that omnipotence means to be able to break the laws of logic, and assume that it doesn't mean that. And thus, this supposed paradox falls flat. It's not a paradox at all. It's a strawman argument that fails to defeat even the strawman it puts up.