A common argument: Suppose God is all-powerful. Now, let God create a rock so heavy that God cannot lift it. Common conclusions: 1) But if God cannot lift it, then God is not all-powerful. 2) The rock cannot exist since it creates a contradiction. Thus, God is not all-powerful since God cannot create a rock that cannot be lifted. I know that arguments such as these are not considered sound. In philosophy, we defined "all-powerful" as able to do all that is logically possible. In that case, the whole discussion is moot since it isn't a question that our logic system can handle. However, suppose one does not subscribe to that definition of "all-powerful". Then, do we say that the question is not well-posed? Can someone pick at this very common argument more formally? If possible, I'd like a more concrete example that shows the fallacies involved in such an argument. Thanks.