In this note, I wish to draw attention to an objection to these arguments which has hitherto gone unnoticed. If a property is positive, then its negation is not positive. The property of being God-like is positive. If a property is positive, then it is necessarily positive.
Necessary existence is positive.
The property of being God-like is consistent. Necessarily, the property of being God-like is exemplified. Given a sufficiently generous conception of properties, and granted the acceptability of the underlying modal logic, the theorems listed to follow from the axioms. If a property is positive, then its negation is not positive. If a property is positive, then it is necessarily positive.