Logic & Fallacies

I found logic and fallacies very interesting. I made it a point reallt trying to learn them and understand them, because often when arguing eith someone, the debate stops at one point, though it didn't have to because I can't pouint out what is wrong with the argument. The logic fallacies are the tools which I can use to do that.
But it also makes me wonder about something Dr Long said in the very beginning of TOK. To what extent can logic help us? Is logic all there is to the world or is there something unreasonable that goes beyond everything that can be justified? Does logic really encompass the enitre world?
I would say that logic is a tool, just as the logic fallacies are to me. Humans can't live in a state of continuous uncertainty and we must have ways to explain all we percieve. It is almost like the allegory of the cave - what if there is world beyond not only what we perceive but also beyong all other limits of the mind?
One of the examples for the logic fallacies was the exsintence of God. If you can't prove that he doesn't exist it must mean that he does. I know that I have used this argument from time to time, but I won't be doing that again.
In our world of logic, couldn't the question be turned around? If you can't prove that he does exist it must mean he doesn't. This is the agrument most atheist people use, but wouldn't this be as much of a fallacy as the one I used to make?