One-page proof of God’s existence

Sometime in 1970, Kurt Gödel’s mathematical proof of the existence of God began to circulate among his colleagues. The proof was less than a page long and caused quite a stir:

Gödel’s Mathematical Proof of God’s Existence

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 Godlike if and only if it possesses all positive properties.
Axiom 3. Being Godlike 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 Godlike, then being Godlike is the essence of x.
Definition. NE(x): x necessarily exists if it has an essential property.
Axiom 5. Being NE is Godlike.
Theorem 3. Necessarily there is some x such that x is Godlike.

I obtained this proof from Hao Wang, Reflections on Kurt Gödel (Cambridge, Mass.: MIT Press, 1987), page 195. How shall we judge such an abstract proof? How many people on Earth can really understand it? Is the proof a result of profound contemplation or the raving of a lunatic? Recall that Gödel’s academic credits were impressive. For example, he was a respected mathematician and a member of the faculty of the University of Vienna starting in 1930. He emigrated to the United States in 1940 and became a member of the Institute of Advanced Study in Princeton, New Jersey.

(Clifford A. Pickover, A passion for mathematics: numbers, puzzles, madness, religion, and the quest for reality, John Wiley & Sons, 2005, p. 285-286)

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