There are many attributes that are commonly attributed to God, or at least some versions of the Christian God, one of which is omniscience. I have my doubts that omniscience is a possible trait for any being to have because it seems to me to be a paradoxical trait. If God (or any being) knows everything that can be an object of knowledge can s/he know what it is like to not know everything that can be an object of knowledge? I say everything that can be an object of knowledge because there are obviously things that are unknowable like a round square or a married bachelor. However, I don't think that a being could know everything that was knowable and simultaneously know the experience of not knowing everything that it knowable (knowing the experience of not knowing everything that is knowable is something that is knowable because as humans that is how our experience is).
Just a minor addition to Mitch Green's astute observations: Some defenders of the coherence of omniscience (Richard Swinburne, for example), hold that omniscience does not include the knowledge of future free acts. Swinburne and R.M. Adams and others do so on the grounds that there is no truth or falsehood now about what a future free agent will do. Aristotle held this as well (or at least most commentators think so!). If this viewpoint is correct, "omniscience" would mean something like all that it is possible to know or all that can be known. If future free action is not knowable in principle then any being, even an omniscient being, would not know something and thus would know what it is like to be ignorant. For an excellent book on omniscience and other divine attributes, check out Richard Swinburne's The Coherence of Theism. Professor Green rightly notes that some philosophers have worried about the limits of knowledge that might be in play if a being is incorporeal. And I must agree...
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