It is not possible to be all-knowing. No such being can exist, not even it such a being happened to be creator of the universe. Firstly, there is no reason to presume that a creator god would be all-knowing. Just because something was created (i.e., electric charge creating lightning), doesn't make the cause of it (a) godly, or (b) omniscient. So, the mere belief that there is a creator god shouldn't imply that such a god would be all-knowing (such a thing is an unfounded assumption of theism). In short, it isn't necessary that god would be all-knowing. But there is another issue to do with epistemology (theory of knowledge):
If you knew everything, then you should know that you know everything. If you do not know if you know everything, then you don't know everything. So, would a god know everything? How would it know? There are some questions that even a god could not answer. One proceeds from a possible being that God could create. God could create a solipsistic being and make that being so that it thinks it created the universe. It could give such a being all knowledge except knowledge that it itself was created. Such a being would have no idea that it was, in fact, a created being and that there was another, higher, creator. If God wanted to create such a deluded being, it could do so. The problem is, our theorized God itself does not know if it exists in such a state of ignorance. In short, God cannot know if it does actually know everything.
All intelligent sentient beings must realize that without verification from other beings than itself or from science, it cannot know if it is correct in its world view. It doesn't matter how intelligent or knowledgeable a being is - if that being wants to verify its knowledge to make sure that it is correct then it needs to look to something more intelligent than itself, or to science. But what if you are the creator of science? You couldn't then use your own construct to test if your own construct was true, it would be an invalid test. If god attempted to find out if it did indeed know everything, it would realize that it has no way to know. How does it know it knows everything? It merely thinks it does. The God has no test, method or possibility of finding out if it does indeed know everything. It could be the created-being theorized in the first paragraph, and it wouldn't know. In short, it does not and cannot know if this is true. God does not know everything and is not omniscient. In fact, no being can know everything because no being, however creative or perfect, can verify its own knowledge is complete.
Assume that God does know everything. For some reason god chooses not to know something. It erases something from its own knowledge, and, makes it so that it hasn't known about it for all of time so it can't simply look into a different time when it did know. It then removes its own memory of having intentionally forgotten something. I argue in "The Four Dimensions and the Immutability of God" (Vexen Crabtree, 2007) that God can't do such things. But I might be wrong, so here's the clincher:
How would god know now if it had intentionally chosen not to know something? It wouldn't be able to contradict its own will in chosing not to know, but if it destroyed the memory of making such a choice, it also wouldn't know if it had actually forgotten anything. This is another (tenuous) class of self-knowledge that any being lacks and can never know. Strike two against omniscience!
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Vexen Crabtree 2002 Apr 14