Logician Kurt Gödel's ontological proof for the existence of God. (This should keep salyavin808 busy for a while.) 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 http://en.wikipedia.org/wiki/Logical_consequence 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 a positive property From these axioms and definitions and a few other axioms from modal logic, the following theorems can be proved:
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. Symbolically:
