I often say that God is limitless, and thus undefinable, and that is why philosophers have so much trouble when they talk about Him. You can’t prove or disprove His existence because you cannot even define Him. You can’t actually say anything meaningful about Him.
But to say that He is limitless and undefinable is to limit and define Him.
Christianity solves this neatly. Of course He transcends even undefinability. He can be defined, and He did take on limits, in the Incarnation. He is somehow fully present in what appears to be a small piece of bread, and thus He defeats even our most noble attempt to understand Him with only our intellect.
So, I must reevaluate my earlier assumptions. Given that He can be defined, and thus can be understood in some way, can His divinity be proven or disproven? I don’t think so, because in what at first seems like a paradox but is actually quite necessary, His infinity appears to depend on His being limited, and vice versa.