  From our point of view, this is an interesting analysis, because on this account of set, we clearly ought to believe in an axiom of complementation for sets. If you think that a negation of a proposition is a proposition (so that in particular a negation of an atomic proposition is a proposition) then you also believe that a negation (or complement or whatever you want to call it) of a predicate is another predicate. Notice that this doesn’t tell you that your complementation has to be classical, but it does tell you that a complement of a set should be a set. This will turn out to be one of the axioms of NF.