In a previous article, I had written about why any empirical arguments seeking to either prove or disprove God are necessarily faith-based arguments. Today, I seek to defend logical arguments for God from the same issues of requiring faith to come to a proof. An objection I've heard from Theists is that a strictly logical proof of God still requires some sort of faith. More specifically, it requires faith in a logical universe, since if illogical universes could exist, we have no reason to assume that our universe is logical.
This is a great objection because it makes us think deeply about any proofs. If an illogical universe can exist, and our universe could be illogical, then we cannot prove anything at all. An illogical universe implies that contradictions can exist, and if contradictions exist, then knowledge is impossible. Any proposition and it's negation can be true at the same time or false at the same time effectively making everything meaningless. It can be tempting to say that faith is required to "make sense" of the universe, which reason cannot do alone.
I don't think the objection holds, but before I get to that, it's worth mentioning that the argument for faith is one with little to no merit. If faith really is required to make sense of the universe, adherents of faith are only grasping in the dark for any semblance of truth, with no actual ability to ever establish it. There would be no basis on which to classify faiths are better or worse than each other because even faiths with contradictions are "possible" in an illogical universe. This isn't a worldview worth adopting for anyone.
The reason logic doesn't require faith is that logic is a necessary presupposition to make any claim, argument or proposition. For any proposition to exist, it must have a determinate meaning. So it cannot be self-referential and must say something specific. This is important because a proposition having determinate meaning requires the laws of logic. The law of identity is required to have a determinate meaning as otherwise the terms of a proposition would be meaningless. The LNC is required for a determinate status for anything, while the LEM is required to affirm or deny any determinate meaning. Logic is a necessary presupposition for any proposition.
So far, I expect many to be unconvinced because none of this matters if logical contradictions exist. However, it is precisely from this insight that we realize why they cannot. For us to be able to state that contradictions exist, we must presuppose logic in order to make that statement. Since we know that logic is a necessary presupposition, we know that contradictions cannot exist. Asserting the existence of contradictions is self-defeating because we must presume they are false to prove they are true. Thus, contradictions cannot exist, and logic is saved.
I consider this problem to be the most important philosophical issue ever because it addresses our ability to know anything at all. All of philosophy itself hinges upon this. I am myself a proponent of the Transcendental Argument for God (TAG) which goes further than what I've spoken about here and states that our necessary presuppositions also necessitate God. Due to the nature of presuppositions, all attempted logical proofs of God implicitly require the Transcendental Proof for God to be true. I plan to bring up the TAG at a future time after proofing out my thoughts, but this should serve as a good introduction to the structure of the argument.