Isn't it an axiom? I'm not exactly that familiar with Aristotle. But, from what I understand of formal propositional logic, it is an axiom.
The reason I asked you that is to illustrate something: We use it, yet we cannot prove it under emprical models. We not only use it, we need it - to make sense.
God is like that. Sometimes called the "uncaused cause", He provides a transcendental unifying origin for all of the axioms/trasncendentals that we take for granted. In unifying He provides a rational basis, a reason for reality as we know it. To my mind, He provides a logical basis for the pursuit of knowledge. No God leaves me without a reason (for reality, transcendental truth/axiom - in short anything not directly verifiable by the scientific method), and seems to me quite irrational.
I'm a student myself; this board is a good reality check. Most have been very patient and kind even in disagreement.