Gödel's Proof: God's Existence

Kurt 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 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 and only if x has P and is necessarily minimal.

Theorem 2. If x is God-like, then being God-like is the essence of x.

Definition. NE(x): 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.

Source: Wang Hao (1987) Reflections on Kurt Goedel. MIT Press: Cambridge, Mass. (Page 195).