Very good. Then it seems that logic does not necessarily refer to reality. I think this because, as you say, set theory saved itself from the paradoxes of logic by fiat (I'm thinking of Zeno here). How could Zermelo and Fraenkel actually discover that "nothing is everything" or did they just realize that it is logically essential that that be so?
Although many solutions have been proposed to this paradox--of
which one resulted in today's canonical set theory by Zermelo and
Fraenkel--no proposed solution could let a set contain itself, which
would possibly reproduce the paradox. However, the concept of everything
must be a set, and a set containing itself--otherwise it is no longer
the set of everything. So avoiding the paradox requires everything to be
nothing, by which being and nothingness are the same.