This concept of "population" doesn't really seem to be consistent with my understanding of a set.
Set A is the set of all widgets that have a frozz. The existence of Set A doesn't imply that there exists a widget that has a frozz. Perhaps the existence of such a widget is an open question. But the set is perfectly well defined.
If I don’t know what frozz is, is the set well defined? Maybe in form, but not in essences. Lisper’s example in sibling comment is indeed well formed, but I know that if I get a counter-example to the conjecture it will pass the population interface and become part of the set. Therefore, I don’t see how we differ comparing simple membership with population and query. My feeling is we disagree over an ex nihilo vs procedural emergence of sets.
Right. The set of all integers which are both even and odd is a well-defined set. It just happens to be empty. The set of all counter-examples to the Goldbach conjecture is a well-defined set. We don't know if it's empty or not.
Set A is the set of all widgets that have a frozz. The existence of Set A doesn't imply that there exists a widget that has a frozz. Perhaps the existence of such a widget is an open question. But the set is perfectly well defined.