Proof! that There Are Proofs for the Existence of God

An article on io9 caught my eye (ref), not because they were claiming a new proof for the existence of God, but because of the report that it was the great mathematician, Kurt Gödel, who offered that proof!

Gödel is most famous for his Incompleteness or Inconsistency Theorems (ref). Gödel worked during the middle of the twentieth century, when general relativity and quantum mechanics were offering a new relativistic, indeterminate view of the world. This view was over against the formerly classic Newtonian view. Gödel's theorems were part of that zeitgeist, in that he proved if you tried to build a system (or a computer!) that could develop a complete set of logical statements from scratch, there would necessarily be at least one which might be correct in that system, but whether it was correct or not could not be proven. For instance, if the system being developed were the English language, it could create the correct English sentence, “This is not an English sentence.” ... which is not capable of proof (although it sounds like something I would say.) And so you could never have an absolutely complete logical system. Ever. 

This brought the relativistic thought of that age to new heights, arguing that just as there was no absoluteness to the universe; neither could there ever be an absolute system of thought. But that the man in his free time was also doodling proofs for the existence of God was news to me (ref).

Gödel's Proof for the Existence of God

The io9 article starts out by inferring it was a modification of the proof offered by Anselm of Canterbury (1033-1109) in his best-selling Proslogion (ref). I am somewhat aware of Anselm’s proof and know that it was used in process theology and process philosophy in the 70s and 80s (a school of thought which was favored by some members of the Dominican religious order or “Dominicanes” in Latin. Tradition has it that their detractors said it with a pause, “Domini Canes” = Dogs of the Lord. Religious humor. Ha.)

Anselm’s proof is not adequately portrayed in such a short news article (nor I suspect is Gödel’s.) In fact, it seems to me that in the article text, there seems to be a flaw that occurs between the these two sentences:

1) If he doesn't exist, he necessarily doesn't exist in any possible worlds.
(insert flaw here)
2) It is not possible to say that God does not exist in any possible world.

The first sentence stands almost as a tautology:

If (God exists = FALSE), then necessarily (God exists = FALSE).

OK, got it, but there is no reason to think that the second sentence follows from the first, nor is any proof offered that the second sentence is true on its own. So, the first sentence is all that stands.

But the Wikipedia article referenced above does a more complete job, as when they reference Anselm's restatement of his proof in his third chapter of the Proslogion. This version states, in short form, if the God concept is “greater than which cannot be thought” yet doesn’t contain the necessity to exist, you haven’t thought hard enough. That's the version of the proof that was preferred by process philosophers following Charles Hartshorne (ref)

Gödel’s proof does seem to follow along Anselm's lines, but I wasn’t able to find a good statement of it in the article. I suspect Gödel’s proof (which I can’t read) doesn’t have that simple a problem wrong with it, but likely has some unprovable hypothetical that didn't take away from it's use as an exercise in logic. This article here (ref) does do a more complete job of explicating things. But it still comes to the same point; that without proof that God exists somewhere, there is no convincing argument anywhere.

Maybe God wanted it that way.