Omniscience vs. Goodness
Omniscience vs. Humanity
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Defenses of omniscience make a persistent effort to gut the concept without appearing to do so. All along we find arguments to the effect that a god's omniscience is of some "limited" sort, as if a "limited omniscience" made any sense. But in the process an interesting fact has appeared: humans having extensive knowledge of matter which a god could have absolutely no knowledge of whatsoever. It is a curious state of affairs when people claim belief in an "omniscient" god which is supposed to be all-knowing, but which in fact knows a great deal less than they do. For this reason, it is reasonable to think that an omniscient god cannot exist.
Perhaps this god's factual knowledge is supposed to make it seem really important and powerful, but I'd be willing to put up against it the very human knowledge which can only result from our limited, physical nature any day of the week and twice on Sundays. I certainly wouldn't give up the ability to know the touch of a loved one or to know taste of a fine beer for the sake of knowing more facts, like in math.
Omniscience vs. Truth
Oddly enough, even that trade-off might not be possible - because it could be argued that a god could not logically know even all facts which would be included in the first category of knowledge, propositional knowledge. Even if there is a set of all truths, that set would have to be infinite and a god could never know that it knows all truths. To verify such a state would take an infinite amount of time - and although an infinite god might have such time to spare, it would never achieve its goal. But more interestingly, it has been argued by some like Patrick Grim, that there cannot logically be such a thing as "a set of all truths." If this is true, then a basic premise of omniscience is fatally flawed and it is reasonable to think that an omniscient god cannot exist.
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