Here's a good essay that points out the flaws in claiming God is beyond logic/can't be known/etc:
God is Not Beyond Logic
It’s a widespread practice among believers to defend God from criticisms with some variation of “God is beyond comprehension,” “your logic is not God’s logic,” or “God it beyond the limitations of our logic.” Even many non-believers seem to be willing that these are fair points and that critiques of God can’t really survive this rebuttal.
But if we scratch below the surface on this kind of talk, we can see that it really doesn’t make any sense; it’s a muddle headed evasion. There is no “our” logic that is separate from God’s logic, or lack thereof. A lot of people who haven’t reflected on what they are saying will throw claims around like these, but they haven’t recognized that what they are suggesting is unintelligible. There are several problems with it. First, they don’t really want to go there. If they try to assert that God is beyond logic, beyond comprehension, or that God’s goodness (and evil) are things that we can’t fathom, then they have effectively disqualified themselves from making any assertions about him. If we can’t understand God’s goodness, or power, or nature, then we certainly aren’t entitled to assert that it is true that God exists or that God is good. If they want to say that belief is reasonable, intelligible, supported by the evidence, rational, or epistemically inculpable, then they can’t also insist that God is beyond comprehension. You can’t have it both ways. On what grounds would you stand where you could assert anything about God if you have categorically denied that we can have any vantage on God? Even worse, on what grounds could you possibly insist that belief in something like this is reasonable when it cannot, by definition, be accessed by us.
Second, there’s a long history on this issue and it’s not just atheists who are holding God to the bounds of logic. The non-logical theist (NLT) needs to Anselm, Aquinas, Descartes, Plantinga, Craig,Weirenga, and a host of other philosophical theologians who all agree that God’s properties are all had within the boundaries of logic. Without logic, there won’t be any way to say it is true that God is X, because logic is what allows us to demarcate between true and false. Logic and reason are not things you simply discard when the fancy strikes you. Without them, you’ve got no way to even make an assertion. Without them, human speech acts are just gibberish. To make an assertion, even one like, “God is beyond logic,” is to assert that there is some state of affairs that obtains in the world. A sentence of the form, “X is . . . . “ says that something—X—is one way and not another. People like to say that our logic is limited and there could be things beyond it, but if something is not a thing and if it doesn’t have properties, then it isn’t a something at all. To be, to have a property, or to exist is to be one way and not another. The claims “God exists,” or “God is beyond logic,” assert that it is not the case that there is no God, and that it is not the case that God is subject to logic. The irony, and the profound paradox, of the last claim is that the speaker employs the logic of the assertion to try to liberate God from logic. But there’s no escaping that making an assertion is making a claim about the way the world is, and it is denying claims about what the world is not. What rules of assertion are you going to employ to argue for or claim that “logic is limited”? Logic? Then it’s not limited. Something else? How do we discern truth from nonsense, and falsehood in claims about logic itself if not by employing it? Or should we just accept all claims about the limits of logic without any argument or reasons?
If someone tells you that God is beyond the law of non-contradiction, then they’ve just left the realm of any intelligible discourse. There’s nothing to talk about when the fabric of logic that makes assertions possible itself has been rejected. Within the philosophical community, it’s pretty much accepted across the board that the Stone Paradox creates a problem for an unrestricted account of omnipotence. No one who has thought about it seriously thinks that being omnipotent, where “omnipotent” means the unrestricted power to do anything, even logically impossible feats, is even intelligible.
http://www.provingthenegative.com/2008/07/god-is-not-beyond-logic.html?m=1
And they always try to turn the argument around to put the burden of proof on atheists - except we don't need to prove gods don't exist, we're not the ones making a positive claim.
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