The Aggregate of Qualities Argument

"...also, I can juggle!"

The Aggregate of Qualities Argument tries to claim that if there is a God, then He must have a certain combination of supernatural qualities, such as omnipotence, omniscience, omni-benevolence, etc. It is impossible for these qualities to exist in one  being, therefore God is impossible.

Here it is:

1. If God exists, God must necessarily possess all of several remarkable qualities (including supreme goodness, omnipotence, immortality, omniscience, ultimate creator, purpose giver).
2. Every one of these qualities may not exist in any one entity and if any such quality does exist it exists in few entities or in some cases (e.g. omnipotence, ultimate creator) in at most one entity.
3. Therefore it is highly unlikely any entity would possess even one of these qualities.
4. There is an infinitesimal chance that any one entity (given the almost infinite number of entities in the Universe) might possess the combination of even some two of these qualities, let alone all of them.
5. In statistical analysis a merely hypothetical infinitesimal chance can in effect be treated as the no chance to which it approximates so very closely.
6. Therefore as there is statistically such an infinitesimal chance of any entity possessing, as God would have to do, all God’s essential qualities in combination it can be said for all practical and statistical purposes that God just does not exist.

The argument hinges on the idea that these supernatural qualities cannot all exist in the same entity, but there is no evidence for this. Why can't the same being be both omnipotent and omniscient? Is there a single pair of godly attributes which directly contradict each other?

Some attributes seem to be self-contradictory, such as the Omnipotence Paradox or the Omniscience/Free Will Paradox, but these are easily resolved.

The only instance I know of more than one godly attribute in conflict is the Problem of Evil, but even that has many plausible refutations.

If all of there is no reason why these qualities cannot exist in the same being, then the argument falls apart.

The statistical portion is not only irrelevant to the rest of the argument, but also irrelevant to the question of God. Theists admit that in all of creation, there is only one. Of course the odds are infinitesimal.

But even if there was nothing in creation that possessed any of these qualities, it would still have no bearing on whether or not there was a God. A creator is not obligated to be like the creation.