One of Godel's Theorem which affect arithmetic is that (in lay man's terms) there are things that are true, or there are statements that are true but there is no proof of it. There are true statements in a system that have no proofs in that system. So how does it apply to Christianity?
Well this applies to the idea of God. Think about it for the moment. That means faith in God is plausible, to say the least. In fact, Godel had a mathematical proof for the existence of God but it only got published posthumously. He knew he would be persecuted if he came out of the closet as a Christian believer (incidentally his biographers say he was Lutheran). He knew other issues would cloud his mathematical involvement and he would be carried out to other debates had he made noises.
At any rate, one of the things that came around his theorems is the matter of consistency.
Many people think that if a system of belief is consistent, that means it is true! Not so in mathematics. So when I hear Islamic apologists criticize the Bible for alleged inconsistencies and they claim that the Qu'ran has not got them, who are they trying to impress? One does not have to have divine intervention to have a system that is consistent. Mathematicians are doing that for centuries now. I think the Calvinists should listen to this too. Consistency does not imply truth necessarily. However, truth implies consistency.
Hence, I dare say, the Word of God is true and therefore consistent. Jesus says so. Think about that once again.
Then there is also the RC apologists who is able to prove many things from Catholic dogma, as if this is a tower of strength. This is false notion too. For in mathematics, if your system is able to prove any statement under the sun, something is wrong, it is inconsistent. For a system to be consistent, there must be statements it cannot prove or pry on. The sophist motto is ex falso quod libet. From a contradiction prove anything. If you are operating on this mode, watch out your system of belief has a contradiction and that will compound more confusion.
Concordian thinking, at times, pleads ignorance, which is a good thing and a correct thing to do. Go only so far as Scripture. Because, fools rush in where angels fear to thread.
On the other hand, if we plead ignorance in all things, well... I think this not Christian either.