Faith vs. intelligence

I've been reading "The God Delusion" by Richard Dawkins and I must say that Dawkins makes quite a few good arguments. For me, the ultimate question is, should we trust faith or intelligence? The more I think about it, the deeper this question becomes. In fact, I would claim that this is, overall, one of the most fundamental questions of philosophy. After all, philosophy attempts to explain the world through logical arguments, and logic is by definition intelligence and thus the complement of faith. We begin to understand the gravity of this question when we realise that we are essentially using logic to determine if logic or faith is the better solution. It is therefore an intrisically self-referencing question (Gödel would like this, wouldn't he?). In other words, we are trying to use logic to find out if logic is applicable to all question.
From a logical point of view, my reference to Gödel is not at all arbitrary. The current question lies close to the issues Gödel considered. For example, one of Gödel's question was "Can we find a logical proof for all true arguments?", that is, is logic an answer to everything?
However, from a holistic view point this is not the right question. We cannot answer a question on the validity of logic with a logical argument. The implicit (or, actually, the rather obvious) self-reference might short circuit any argument. On the other hand, to dismis logic on the base of such a self-reference is similarly a flawed conclusion. Ultimately, I cannot see any way around this logical short circuit. Quite simply, without logic, we cannot argue that logic is the answer.
The only remaining option, for me, is to have faith in logic. I cannot but believe that logic is the only way to go. This is an inherently contradictory statement. To put it in a more obvious form, "I have faith in that faith is not the answer".
The arguments of Dawkins, that clearly must remain within logic, might thus not be applicable. Interesting. Any teoist arguing against Dawkins, would thus not be able to provide anything of significance, since he would be forced to either use logic in order to prove something or, express his faith which would not convince anyone who doesn't already share that same faith.
Now I seem to be going in circles. This is a clear indication of the logical short circuit.
Finally, I would argue that human culture is based on logic, languages are based on logic and the only way for us to intrepret reality is through logic. Therefore, I see now alternative but to trust logic. I have faith in logic.