1. If it’s not possible that a supreme being exists, then supreme beings must have the property of “not being supreme”
Support:: If no one can be supreme, then even supreme beings must have the property of not being supreme. Seems like an absurd proposition on the face of it (“if it is not possible that supreme beings exist, then supreme beings can’t have any properties at all”), but it is in fact logical. If this proposition were false, then it would say “If it’s not possible that a supreme being exists, then supreme beings can still be supreme”. Clearly, this is not the case.
2. A property that supreme beings must have is a perfection
Support:: This is from the axiom that if a property is a necessary condition for being supreme, then that property is a perfection.
Objection: If a supreme being is impossible, then there are no properties that are required for being a perfection. So this premise requires you to already agree with the conclusion (that it is possible that a supreme being exists). The argument is guilty of begging the question.
3. ”Not being supreme” is not a perfection
Support:: This is from the axiom that if something is a perfection, then its negation is not a perfection.
Objection: But if a supreme being is impossible, then every property is a perfection. Thus, accepting this premise seems to require you to already accept the conclusion (that it is possible that a supreme being exists), and hence the argument is guilty of begging the question.
4. Therefore, it is possible that a supreme being exists
Support:: From 1,2,3
1. It’s possible that a supreme being exists
Support:: From the previous argument
2. Therefore, there actually exists a being for whom it is possible that it is impossible for someone else to be greater than
Support:: From 1 and from the logical axiom called Barcan. This axiom states: “if everything is necessarily P, then necessarily, everything is P.” The logical equivalent of this axiom (used in this argument) is: “If it’s possible that there is something that is P, then there actually is something that is possibly P.” This is a logical axiom that can be derived from other principles of logic.
Objection: The Barcan formula is widely accepted, but still controversial. It means that if it is possible that I had a sibling, then there actually is a being who is possibly my sibling. Seems crazy on the face of it, but it is derivable from other logical axioms. So the Barcan formula is a weak spot in the argument, but per Oppy the above objection about question-begging is much stronger.
3. Therefore, there is a being for whom it is impossible for someone to be greater than
Support:: From the logical axiom that if something is possibly impossible, then it is impossible.
4. Therefore, a supreme being exists
Support:: From 3.
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