All of it, and if God isn't consistent, then you can't assume that the rest of the universe is consistent either. I'll explain why this is a bad thing in a moment.
I had this discussion with Meow Mix, and it didn't go very well. Have a look
here from post #70 onwards. It's true that logic is a human system, but a logically inconsistent God/universe is both incoherent and impossible. (Because, among other things, you can prove that God/universe doesn't exist.
) The whole idea of "truth" hands in its resignation, and you're left with... well, nothing.