Omnipotence is Not Disproven by Paradoxical Questions

Your arguments are very imaginative and well argued. However, I still believe (for the purpose of this debate, anyway) that they are fallible, as the first two rely on the idea that we 'can not' conceptualise these ideas in our minds. This is certainly true for a human understanding, and a human brain... But shouldn't an omnipotent being always be able to do, always 'can' and never 'can't'? To suggest that something is impossible to conceptualise is to suggest that for an omnipotent being, there is something not possible. Regardless of the idea that this makes no logical sense to us, total power has to overcome logic by brute force, or it wouldn't be total. One alternative is that an omnipotent being can make square triangles and yellow a scent, but he (or she, of course) chooses not to. If they had chosen to, we wouldn't question it, or consider it at all unusual. But this argument leads us to the thorny issue of how an omnipotent being makes choices, and the crux of my argument. If an omnipotent being is choosing to not break the rules of logic, even though they can (which is, I believe, the only explanation that leaves the concept of omnipotence intact) then they're an active, choosing, rational being. Essentially, they change. They contain within themselves the possibility for all changes and all actions, and in order to preserve this infinite potential, they can only make temporary choices - such as 'today squares and triangles are different, but somehow with my infinite power, I may make them the same tomorrow.' Otherwise, if they made an irreversible change, that would be equal to them not have the power to change something. This rationally allows the concept of omnipotence, and allows statements 1 and 2. (With both 3 and 4 I will happily concede that they show nothing about the existence of an omnipotent being.) .... But it implies, or rather, shows that an omnipotent being would have to exist within time. Otherwise, how could it use it's power in some things (such as making, say, the Universe or a cup of tea) but not in others - the very fact that an omnipotent being has the power and the potential to do everything shows that it has future possible actions it could take. And all things that have a future must therefore be within time. This leads you to the infinite difficulties of 'what has a beginning must have began', or the problem that something must have created infinite power. And, more significantly, the issue that omnipotence can't exist in the physical world, but also can't exist out of it. To sum up this argument, an omnipotent being must be able to create anything he wishes even if logically impossible. However, this would require him to make time-involved choices that he could only make if he existed within the frame of time. That would make him a physical concept, but omnipotence can't be physical because the physical world is never infinite or total. This is what I would call a true paradox. I hope it's clear how I have moved from your argument to mine, and why I believe your argument is good, but not water tight. I'm also trialling out these ideas, and just seeing where they take me.