When Saint Anselm argues that “God is a being that of which nothing greater can be conceived" it seems like he's expressing the following relation:
∀x (¬MorePerfectThan(x,God))
or "for all x, x is not more perfect than God." (And presumably God is not more perfect than himself.) Where x is quantifying over everything. But if x is quantifying over everything, isn't Anselm quantifying over the universal set, which renders the argument incoherent? But if he's not, how can the argument establish that genuinely nothing is greater than God? Or does this difficulty somehow disappear when we translate the argument into modal logic rather than FOL?
(I know this question sounds like it might fit better on philosophy stack exchange. I asked it here because honestly I've found that answers to logic-related questions are always better on this site.)