And Gödel not only stated this theorem; he proved it (see the article for details).
I'm going to make an analogy between Gödel's mathematicalcal thinking and my theological thinking--bearing in mind Ellenberg's cautionary statementent: "Any scientific result that can be approximated by an aphorism is ripe for misappropriation." The similarity between Gödel and myself is that my rational study of the Bible has led me to the same irrational place (There's only one irrational place, right?) that his rational study of logic led him. In Gödel's terms, here is the result of my theological thinking:
Given any system of dogmata that produces no paradoxes, there exist statements about God which are true, but which cannot be proved using the given dogmata.
What led me to this conclusion was Jesus claim to be the truth. If this is the case then any system of statments about Him (or doctrine) will never reveal truth in its entirety, because truth can only be fully known by knowing (having a relationship with) the Person who is truth, Jesus.
So what now? Do I give up on rational enquiry of my faith? Forget my Greek and Hebrew? Throw out my theological books because their words cannot reveal their fullest meaning? Perhaps even leave behind the Bible in my quest for spiritual enlightenment?
I believe I overstate my case, as would someone who thinks Gödel's theorem proves mathematics to be a meaningless exercise. Did I mention that the title of that article was "Does Gödel Matter? The romantic's favorite mathematician didn't prove what you think he did." Ellenberg explains why:
...what's most startling about Gödel's theorem, given its conceptual importance, is not how much it's changed mathematics, but how little. No theoretical physicist could start a career today without a thorough understanding of Einstein's and Heisenberg's contributions. But most pure mathematicians can easily go through life with only a vague acquaintance with Gödel's work. So far, I've done it myself. How can this be, when Gödel cuts the very definition of "number" out from under us? Well, don't forget that ...there are some statements that are true under any definition of "number"--for instance, "2 + 2 = 4."...Gödel's theorem, for most working mathematicians, is like a sign warning us away from logical terrain we'd never visit anyway.
I guess we don't have to give up on rationality, and I don't have to quit my blog. After all, there are statments that hold up under any Biblical understanding of God (e.g. "God is love.") All a statment like "Jesus is the truth" does is show us the boundaries of rational inquirey, not remove its usefulness altogether. Logic and reason are simply a tools we use to describe and comprehend truth, not the beginning and end of it.
So, I guess that means I can still parse the Greek, account for context, critique theological arguments, and use the Crosswalk.com Bible Study Tools I just added to apokalupto [shamless plug]. But now I'll be a little more humble as I do it and a little more lenient with those who don't see things exactly my way. And, hopefully, I'll always have in mind the reason why I study--to understand a good Friend a little better.