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As an offshoot of Anselm's proof of the existence of God:

Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel. It is in a line of development that goes back to Anselm of Canterbury, (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist." A more elaborate version was given by Gottfried Leibniz (1646 AD to 1716 AD); this is the version that Gödel studied and attempted to clarify with his ontological argument.

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Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive

Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B

Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified

Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive

Axiom 2: If a property is positive, then its negation is not positive.

Axiom 3: The property of being God-like is positive

Axiom 4: If a property is positive, then it is necessarily positive

Axiom 5: Necessary existence is positive

Axiom 6: For any property P, if P is positive, then being necessarily P is positive.

Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.

Corollary 1: The property of being God-like is consistent.

Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.

Theorem 3: Necessarily, the property of being God-like is exemplified.

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