Paradox of the Stone
One of the delightful ways atheists have of tormenting believers is through the logical puzzle known as the Paradox of the Stone.
Paraphrased, it goes something like this: If God exists, he is omnipotent. If God is omnipotent, he can create a stone he cannot lift. But if he cannot lift it, then he isn't omnipotent. And if he can't create it, he isn't omnipotent, either. Thus, God isn't omnipotent, and therefore doesn't exist.
Before vanishing in an Douglas Adams puff of logic, God could offer the Standard Solution to the paradox (see Mavrodes (1963) for one presentation), which has been widely accepted by theists for decades. It argues that since God is omnipotent, 'A stone he cannot lift' makes about as much sense as a 'square circle', a thing which is impossible.
This is not a valid rebuttal, since it starts by assuming that God is indeed omnipotent – the very point the paradox is trying to invalidate.
Enter Brown and Nagasawa (2005), who go about it differently. The standard solution says the paradox is fallacious because it contains a false premise; they argue that it is fallacious because it is question-begging. The details are in their paper, but they end with a delightful illustration:
Suppose that Lisa can hold her own child in her arms but that Nick cannot hold his child in his arms. In such circumstances, Lisa might claim: "Nick, I have an ability that you lack – that is, the ability to hold one's own child." On the face of it her claim is correct. However, if one examines it carefully by focusing on the word 'one', then one finds that Lisa is misleadingly comparing two different abilities. The one is Lisa's ability to hold, say, her one-year-old baby, and the other is Nick's ability to hold, say, his forty-seven-year-old son. It is misleading to compare those two different abilities as if they are the same.
nothing more to see. please move along.