Friday, June 20, 2014

Kurt Godel's God Proof

The Austrian mathematician Kurt Godel is widely considered to be one of the most significant logicians of all time - finding peers only in the likes of Aristotle and Frege.  At the age of 25 he published his famous "Incompleteness Theorems" which demonstrated that most important mathematical axioms are essentially unprovable and that finding a complete and consistent set of axioms for all of mathematics is not possible.  Most of us don't really get this but feel comfortable saying that he's obviously no lightweight.

Though he began work on his Ontological Argument in the 40's he didn't share it with anyone until 1970 and wasn't formally published until 1987!  Apparently, Godel didn't want anyone mistakenly thinking that he "actually believed in God."  Right.  Heaven forfend he should upset the apple cart in the academic bubble of Princeton and risk losing his job (not much has changed).  Strangely, despite his supposed lack of belief he argued extensively in favor of an afterlife and told the sociologist Burke Grandjean that his "belief was theistic, not pantheistic, following Leibniz rather than Spinoza.  After his death, his wife Adele told Hao Wang that "he was religious and read the Bible in bed every Sunday morning."  So much for theists being weak-minded and brainwashed group-think victims.

Have a look at his proof:


\text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall x[\varphi(x) \to \psi(x)]\right\} \to P(\psi) \\

\text{Ax. 2.} & P(\neg \varphi) \leftrightarrow \neg P(\varphi) \\

\text{Th. 1.} & P(\varphi) \to \Diamond \; \exists x[\varphi(x)] \\

\text{Df. 1.} & G(x) \iff \forall \varphi [P(\varphi) \to \varphi(x)] \\

\text{Ax. 3.} & P(G) \\

\text{Th. 2.} & \Diamond \; \exists x \; G(x) \\

\text{Df. 2.} & \varphi \text{ ess } x \iff \varphi(x) \wedge \forall \psi \left\{\psi(x) \to \Box \; \forall y[\varphi(y) \to \psi(y)]\right\} \\

\text{Ax. 4.} & P(\varphi) \to \Box \; P(\varphi) \\

\text{Th. 3.} & G(x) \to G \text{ ess } x \\
\text{Df. 3.} & E(x) \iff \forall \varphi[\varphi \text{ ess } x \to \Box \; \exists y \; \varphi(y)] \\
\text{Ax. 5.} & P(E) \\
\text{Th. 4.} & \Box \; \exists x \; G(x)

Pretty straightforward no?  Nonetheless, I hear from materialists all the time who blithely wave it off with a "that was discredited a long time ago" attitude.  They don't get it but are perfectly happy to assert that there is "no evidence" that there's a God.  Right, no evidence besides for the thousands of pages penned on the subject by many of the world's (universally acknowledged) greatest thinkers.  I find that they often confuse a counter-argument with a refutation so that if anyone, anywhere has disagreed it has (in their minds) been invalidated.

Here's an article from Der Spiegel on the topic to consider: Scientists Use Computer to Mathematically Prove God Exists.  Hey wait, scientists?  Computers?  Logic?  Don't theists just have a bunch of absurd Bronze Age myths to prove their point?

Anyone who's open-minded enough to actually consider Godel's argument and others like it should have a look at Stanford's excellent website.



  1. Ontological argument is a dismal failure. I have a book on my shelf the 6 ways to Atheism by Geoffrey Berg with NEW logical disproofs of God. Did not do a census, but my guess is virtually every modern philosopher would discredit the ontological argument; maybe those of Berg as well. To the best of my knowledge the ontological argument is not any Jewish literature, but was invented by the Christians.

    1. Who is Geoffrey Berg and why should I care what he thinks? Presumably, you agree with my assessment of Godel as one of the greatest logicians of all time yes? I doubt that you understand what he was trying to say and yet you just brush it aside with an allusion to a book you have by someone I can't get any info on online?

      Maybe you could just explain in your own words how the argument fails...

  2. Sorry to be late to the party...

    Goffrey Berg's book, while perhaps not Googlable better than a year ago, is now cited on several pages. The summation, at least based on my 10 minute perusal of the first five or six reviews, is that even atheists appear not to support the six arguments made, and of course deists are less than impressed as well. What seems common to the arguments-- again albeit only based on my limited and second-hand exposure-- is Berg's presumption that the limits of this universe must necessarily apply to god or God. Given the first comment above and since I am always interested in what those who reach conclusions different than mine have to say, I was interested in purchasing the book; but now, based on every review I saw, there is little reason to do so.