1. Either God can create a stone that he cannot lift, or he cannot.
2. If he can, then, necessarily, there is at least one task that God cannot perform (namely, lifting the stone in question).
3. If he cannot, then, necessarily, there is at least one act that God cannot perform (namely, creating the stone in question).
4. There is at least one task or act that God cannot perform.
5. If God is omnipotent, then he can perform any task or act.
6. God is not omnipotent.
I do not find this argument persuasive, for two reasons. First, the standard response to this sort of argument is to distinguish between what is logically possible and what is not. Straightforwardly, any contradiction is not a logical possibility and if something is not a logical possibility it is not within any agent’s power to bring about (not even God’s). The very notion of an omnipotent being that can create (i.e. do) something he cannot do is incoherent – it is either meaningless (in which case there is no real contradiction, but also no contradiction with omnipotence) or it is a straightforward contradiction (in which case it is not a genuine logical possibility, and hence not within the scope of an omnipotent being’s power – and so no contradiction with omnipotence).
The second response is to distinguish between de dicto necessity and de re necessity. The ‘necessarily’ involved in premises 2 and 23 above are de dicto – they concern the logic of the propositions. These need not be stating anything about the necessity governing the agent – God – however, as that would involve de re necessity. This is a further spelling out of the first response. De re, God is able to do whatever is within God’s power to do. But even God cannot bring about (of necessity de re) what is either incoherent or impossible (of necessity de dicto). The point is that the necessity is not describing God but an incoherent or impossible state of affairs – and so does not describe a contradiction with divine omnipotence.