I shall, in this post, take atheism to be the belief that there is (probably) no God, where God will be defined to be an omniscient and omnipotent being that is also totally good (much as Richard defines Him), and I shall argue (as I did briefly in a comment on this post of Richard's) that such a God is (probably) impossible. There are of course other definitions, e.g. atheism is sometimes regarded as the absence of a belief in God, so that it would include both atheism (as defined above) and agnosticism (the absence of a belief either way, which includes the belief that knowledge either way is impossible, which is another definition of agnosticism), and God is sometimes defined to be the Creator of this Universe.
......Such a Creator would know (more or less) all that could be known about this Universe, just as an author would know all about her story, or a painter all about his painting; and similarly, such a Creator would have (more or less) complete power over this Universe. So, it may have been that God was originally defined to be the Creator, and that it was then deduced that such a God would be all knowing and all powerful in that sense (which is, after all, the sense that concerns us, as beings within this Universe), and that such properties only then became definitive, e.g. through their apparent utility—certainly many arguments (as in that linked post) do begin by defining God to be infinitely perfect (rather than the Creator). So, I’ll now argue that such a God, which I’ll refer to as ‘He,’ is (probably) impossible.
......My argument is primarily concerned with omniscience, with God knowing absolutely everything. Not only does He know everything about His Creation (as any Creator would), He also knows whether or not there are, for example, other Gods. If there are any, He knows everything that they know, including precisely what it is like to be them (which might imply that there is only one God), and if not then He knows how he knows that there are not. But it is quite inconceivable how he could know that there are not any other Gods (either at all, or beyond those that He does know all about). The problem is not so much with the “omni,” but with the “science.” It would of course not follow, from some conjectured infinitude having inconceivable properties, that it did not exist; but the concept of knowledge is the concept of true beliefs that are in some way tied down to (or that in some reliable way arise from) the things known about, and we are here considering one being’s knowledge of the non-existence of other similar beings, where there might well be absolutely no connection between them.
......Ironically this problem (for this fairly common kind of theism) resembles a fairly common reply to atheists, who are told that while they might obtain a justified belief that there was a God by His revealing Himself to them, they could hardly obtain scientific knowledge that there was not a God (not even in Heaven) just by failing to have had such a revelation. Imagine (for an analogy) completely separate spacetimes with absolutely no causal connections between them—how could any being, in one of them, know anything about what was going on in the others, or even whether or not there were any others? Similarly, even were there only one spacetime, and a being within it had that true belief, how could that belief be justified?
......By hypothesis God would know that He knew everything, and He would also know how he knew that there were no other Gods (beyond any He might know about more directly, via informative connections), but how could that be? Could He have deduced that fact from His knowledge of His own omniscience? But how could He not then know that such circular justification would not make His belief (that there were no other Gods) knowledge? It is all very well for us to define God to be omniscient, because we can then ask whether or not God exists, but God could hardly do that! In short, the concept of omniscience (in this strict, absolute sense) seems to be self-contradictory. It seems to be, but it may not be, but as there seems to be little logical room for manoeuvre, I regard that conclusion as at least very likely (and not necessarily inconvenient for the theist, as I mentioned here).
......Regarding omnipotence, if God has the power to do absolutely anything, then could He make 2 plus 2 equal 5? If not then it again seems that we cannot interpret His definition in such a strict way after all. And of course, God would not get any less implausible were combinations considered, such as omniscience and (via free will) responsibility, together with omnipotence and (via this Universe existing, whether or not God created it) evil. After all, if God knows what we are going to do, and if He could have stopped us but did not, then, given that He is good, it seems that whatever we do must also be good, or at least (since we are only human) good enough (in what might have to be the best of all possible worlds), which seems unlikely.