"Atheists attempt to use this question to prove that the concept of omnipotence is self-contradictory. But the problem here is a contradiction in terms. This issue becomes even more clear when we examine a related question: "Can God create an uncreated being?" The problem here is that the questioner has already defined the being to be uncreated and then proceeds to ask for something that contradicts that definition. The problem is in the questioner's terms, not any lack in God's potential. The same is true when asking God to make a circle with four sides. Having already provided a definition of a circle that could never include a four-sided figure, such a question is absurd. Something is certainly self-contradictory here, but it is the questioner's terminology and not the omnipotence of God.
The same is true when we come to the case of create a stone which cannot be lifted. Aside from the problem that we are placing an infinite unrestricted being under the finite restricted laws of our universe, the concept of the stone is self-contradictory. Basically, such a stone could not exist because it is conceptually incoherent. When one asks if God could create such a stone, one would normally identify the properties of such a stone. But here we haven't been given absolute properties, but instead we've been given properties of the stone relative to God's properties. The questioner has identified the potential stone as something so big that God couldn't lift, so even though we already know that there is nothing God cannot lift, they have used that as an attribute for the stone. Automatically, the concept of such a stone is nullified. Now, when they ask could God create such a stone, the answer is no, but that doesn't imply a lack of potential on the part of God. Instead, it reflects the fact that the concept of such a stone is illogical, unreal, inadmissible. It is very similar to asking if God can die. Well, death isn't an ability, its the inability to live. The immortal cannot die because that defies His attribute of immortality. Similarly, the omnipotent cannot create a task that He can't complete because such a task is merely a figment of one's imagination and could not exist.
You're basically asking, if God can do anything, can He make it impossible for himself to do something? The question is illogical and self-contradictory because the argument contradicts the premise. Once you have already established that God can do anything, then that's a set attribute and part of His nature. Therefore, He can do anything that is consistent with His nature, anything that is absolute.
Can God make 1=2? Well if 1=2, then it wouldn't be 1! So the idea is self-contradictory, not God.
The question also reminds me of the idea of what happens when an immovable rock meets an unstoppable force? The two things cannot exist in the same universe. Likewise, if God exists then all things which contradict His attributes are imaginary, non-existant and impossible. They are forever bound to the realm of imagination and cannot be brought into existence.
Shaykh Ibn Abil-'Izz (d. 1389CE) also answered this question in Sharhul Aqeedah Tahaawiyyah (p.137), in his discussion of the following verse:
And Allah, over each thing, is omnipotent; all-powerful [al-Baqarah 2:284]
This includes all that is possible. As for what is in intrinsically impossible - such as there being a thing that exists and does not exist at one and the same time - then, this has no reality, nor is its existence conceivable, nor is it termed 'a thing' by agreement of those with intelligence. Included in this category is: [Allah] creating the likes of Himself, making Himself non-existent, and other impossibilites.
This also serves as a reply to the question posed by some: 'Can Allah create a stone that He is unable to lift?' The argument being that if Allah cannot create such a stone, He is not all-powerful; but if He can, then likewise He is not all-powerful. The fallacy of this argument lies in the fact that such an affair is, in itself, impossible and exists only in the minds of certain people. And not all that the mind conjures-up has an existence that is possible, nor is it always termed 'a thing.'
Hopefully that makes the issue clear.
