Mathematician Kurt Gödel provided a formal argument for God's existence. The argument was constructed by Gödel but not published until long after his death. He provided an argument based on modal logic; he uses the conception of properties, ultimately concluding with God's existence.

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: If a property is positive, then its negation is not positive

Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is 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