Mathematician Kurt Gödel formalized an ontological proof of God's existence
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« The proof is based on the following definitions and axioms:
- Definition 1: x is divine (a property noted as G(x)) if and only if x contains as essential properties all properties that are positive and only these.
- Definition 2: A is an essence of x if and only if, for each property B, if x contains B, then A implies B.
- Definition 3: x necessarily exists if and only if each essence of x is necessarily exemplified.
- Axiom 1: Any property strictly implied by a positive property is positive.
- Axiom 2: A property is positive if and only if its negation is not positive.
- Axiom 3: The property of being divine is positive.
- Axiom 4: If a property is positive, then it is necessarily positive.
- Axiom 5: Necessary existence is positive.
From these and the axioms of modal logic, we deduce, in order:
- Theorem 1: If a property is positive, then it is possibly exemplified.
- Theorem 2: The property of being divine is possibly exemplified.
- Theorem 3: If x is divine, then the property of being divine is an essence of x.
- Theorem 4: The property of being divine is necessarily exemplified. »
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