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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
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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
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Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
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Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
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Axiom 2: A property is positive if and only if its negation is not positive
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Axiom 3: The property of being God-like is positive
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Axiom 4: If a property is positive, then it is necessarily positive
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Axiom 5: Necessary existence is a positive property
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Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
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Theorem 2: The property of being God-like is consistent.
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Theorem 3: If something is God-like, then the property of being God-like is an essence of that thing.
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Theorem 4: Necessarily, the property of being God-like is exemplified.
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