Thursday, July 19, 2007
Godel's Theorem and Religious Assertions
If you are not a geek, you may be intimidated by this post, please don't be. What I am posting here may sound way above your head but hang on a bit, you may find this post interesting if not intriguing as it is related to Christianity in an indirect way.
You must have heard of Albert Einstein (you haven't? you must be gen X), but very likely you may have not heard of of Kurt Godel (see my picture? That's his photo). If Einstein is to Physics, then Godel is to Mathematics. Both of these figures discovered major results that revolutionized their fields. In one way or another, you must have heard of Einstein's Theory of Relativity, remember your high school physics? I doubt if you have heard of Godel while you were doing your high school algebra. You encounter him only if you are taking logic or number theory subjects, that is quite true but let me reduce in a nutshell the point I am about to make.
Godel is known for his Completeness and Incompleteness Theorems. Skip the first one, but let us focus on what his 1st Incompleteness Theorem because this has a relationship to theology.
In a nutshell, Godel's 1st Incompleteness Theorem may be stated this way on a popular level - there are some true things or statements that can not be proven. Remember this is my popularizing of it but technically what he stated was in the realm of arithmetic about arithmetic truths (about numbers and their properties). Since our language includes arithmetic (human language does) then simplistically, there are some true statements that have no proof in our world. This line of reasoning sounds reasonable but let us for the sake of argument, agree to this even though such popular notions is just an analogue of Godel's.
Now this has plenty of implications for the people of faith. For the one committed to sola scriptura, beliefs must be gathered from assertions made by Scripture. For those who are not committed to sola scriptura, then they may employ this theorem to their advantage. They can assert a statement of belief with nothing to back it up.
Let me give an example, take the RC belief in the bodily assumption of Mary. There is no direct support of this from Scripture and no matter how one tries, the Scripture just does not give even a suggestion that this has happened. Try as one may, it only winds up in frustration, making hard for Protestants to be convinced. Now to an RC apologist who is quite an expert when it comes to Philosophy ( they really are philosophically savvy and sophisticated), Godel's 1st Incompleteness Theorem may be appealed to for support - they can say "Mary was assumbed bodily into heaven" is one of these true statements that have no proof!. Let as call this statement - M.
There is a catch though, it won't work. The reason is that in order for them to say that M is true, they are still left with work to do, they still have to prove that M is a G Statement ie it satisfies the Theorem's properties. Hence, they must demonstrate that M is one of those statements that the 1st Theorem speaks about. Where do you go to prove M has the property of Godel's Incompleteness Theorem? You wind up showing a proof which is a type of question begging exercise.
(for amusement see here for weird reasonings based on the fact that since the Bible does not speak about all things we may derive many things)