Kurt Godel was a logician who lived from 1906 to 1978. He is best known for his two Incompleteness Theorems that show the inherent limitations of axiomatic systems. Pretty standard water-cooler-discussion material, I know. Godel is also the subject of one of my favourite books by Douglas Hofstadter:
Godel, Escher, Bach: An Eternal Golden Braid
I spent years in university trying to fully grasp Kurt Godel’s Incompleteness Theorem and its relation to the Liar’s Paradox.
The following, however, is something completely different. It’s a reproduction of an attempt by Godel to prove the existence of God, a proof that emerged around 1970. I found the proof in Clifford Pickover’s fantastic book, “Wonders of Numbers.” Very few people, even logicians, agree on what it means (let alone if it’s correct)
Proof
Axiom 1. (Dichotomy) A property is positive if and only if its negation is negative.
Axiom 2. (Closure) A property is positive if it necessarily contains a positive property.
Theorem 1. A positive property is logically consistent (i.e., possibly it has some instance.)
Definition. Something is God-like if and only if it possesses all positive properties.
Axiom 3. Being God-like is a positive property.
Axiom 4. Being a positive property is (logical, hence) necessary.
Definition. A property P is the essence of x if and only if x has P and P is necessarily minimal.
Theorem 2. If x is God-like, then being God-like is the essence of x.
Definition. NE(x) means x necessarily exists if it has an essential property.
Axiom 5. Being NE is God-like.
Theorem 3. Necessarily there is some x such that x is God-like.
qed