God contradicts logic, so I don't see how one would butress the other. Additionally this is the classic how do you know it exists if you can't see it, aka if you doubt god, why do you believe in love? The basic flaw is saying that god is an answer, instead of admitting that it is simply a gap in knowledge. In short this is a god of gaps arguement. (Atheists can't explain x, but theism can. Therefore atheism is false) It is the same as saying history doesn't teach you how to play the flute so history is false.This deserves a reply.
The Christian position is not that we simply refer to God to explain gaps in knowledge. To say that this is the Christian position is to argue against a straw man. Rather, the Christian position is that all knowledge presupposes the existence of God. The Christian position is that nothing whatsoever can be explained unless God exists. God is the God of the gaps and the non-gaps because He is the God of everything. Both the explained and unexplained cannot be account for unless God exists. That's the position the atheist will have to contend with if he wants to argue against Christianity (though we hope repentance and submission to Jesus Christ will be preferred -- and I don't say that lightly).
Let me add two clarifications. The Christian position is not that the atheist can't explain things or that he doesn't believe things which are true, rather, we say that the extent to which the atheist has any successes in his reasoning and explanation of things is only possible to the extent that he assumes the truth of the Christian worldview. The other clarification is this: there are no gaps in knowledge, not for God. There are gaps for human beings due to our finitude and the noetic effects of sin, but not for God.
Now that we've set forth the Christian position, let's turn our attention to Sam's position. In response to the previous post he admits that the atheist cannot arrive at a proper explanation of the laws of logic: "... it is simply a gap in knowledge." This is a devastating concession of cosmic proportions. One must eventually ask the atheist whether the laws of logic apply to that quote itself. How can laws of logic, which for the atheist are unexplainable, be applied to a gap in knowledge about the laws of logic which can't be explained by the atheist? Sam's position is self-defeating. In fact, Sam can't know whether anything he says whatsoever is true because it can't be known to him wether the laws of logic have been properly applied (since for him the laws of logic are a gap in knowledge.) Thus, Sam has no basis for saying, "God contradicts logic ... ."
He also wants us to think that the following is faulty reasoning: "Atheists can't explain x, but theism can. Therefore atheism is false." Well, it depends what you mean by "explain." I've said that atheists can explain things but only to the extent that they assume the truth of the Christian explanation of things. If the atheist doesn't assume the existence of God, he can't explain anything whatsoever. Therefore, because of that, atheism is false. Therefore, because of that, Christianity is true.
One final point about gaps in knowledge. The atheist believes that there are things unknown. This poses a problem of cosmic proportions for the atheist. If that which is not known can be known though it isn't yet, we have to wonder whether that unknown knowledge will affect the very process of knowing itself, in which case the atheist can't be certain whether he rightly knows anything now. And if that unknown is to become known, can we know it from our current method of knowing? These aren't silly philosophical games here, rather, it highlights the absurdity of the atheist position. The atheist is left not being able to know anything for certain because he can't eliminate the possibility that the unknown will change the very foundation or basis of knowing. But the Christian worldview can make sense out of knowledge and gaps in knowledge because everything is known by God. Everything is interpreted. Everything is analyzed. Everything is explained. Everything is accounted for because God is omniscient. Human beings can't know everything but they can have knowledge since God reveals knowledge through general and special revelation. In the Christian worldview, the human unknowns can't change the preconditions of knowing because God always is who He is. But for the atheist to admit there are gaps in knowledge is to admit his own defeat.