I'm aware you cant prove anything hence why I recommended weak atheism. To me it is the only logical position in regards to a god. There is no reason to believe such an entity exists.
There are different levels of faith, faith in something using empirical evidence is more logical then faith in something because an ancient books says it exists.
But you can't really base it on logic, as your limiting it to a set of axioms. So you can't really say logically it is a better position, all logical theories can be expressed mathematically, but then we have the problem of incompleteness. So the best position would actually be to Agnostic atheism.
"If a man has failed to find any good reason for believing that there is a God, it is perfectly natural and rational that he should not believe that there is a God; and if so, he is an atheist... if he goes farther, and, after an investigation into the nature and reach of human knowledge, ending in the conclusion that the existence of God is incapable of proof, cease to believe in it on the ground that he cannot know it to be true, he is an agnostic and also an atheist - an agnostic-atheist - an atheist because an agnostic... while, then, it is erroneous to identify agnosticism and atheism, it is equally erroneous so to separate them as if the one were exclusive of the other..."
- Robert Flint, in his Croall Lecture of 1887-1888 (published in 1903 under the title Agnosticism).