The set-or-class of things that don't exist

Question

If it could be determinate, how many things don't exist, i.e. if there could be a set of nonexistent things, would the existence of other things follow "mechanically"?

1. If it's not determinate that k-many things don't exist, then there is a proper class of nonexistent things, and there is not a proper such set.
2. If there weren't a proper set of nonexistent things, then nothing would not exist (supposing that we don't properly quantify over things except by considering them to be in the range of a proper set; as if it's such that if they're in the range of a proper class, they're not quantification-determinate).
3. If there is proper set of nonexistent things, then it must be of some size k.
4. The set-sized existential complement of the set of size k is the rest of some superset of k as such.
5. So the number of things that exist must be equal to or larger than the number of things that don't.
6. So "there must be something rather than only nothing." QED^∀

Historically, à la Fregeanism or the proposition V = WF, the empty set is styled as the set of things that don't exist in the theory (true contradictions for Fregeanism, unwell-founded sets for the exclusivistic axiom of foundation). However, if that is what was being meant in (1) through (6), the implication would be that the set of things that don't exist is empty, and so still everything somehow exists. And yet on another hand, if we are trying to answer, "Why is there something rather than nothing?" (at least for concrete somethings, if abstracta are necessarily existent) then have we yet left, "Why is there a set of nonexistent things instead of not there being such a set?" unanswered? (Note that, if there must be a proper set of nonexistent things, and a proper set of existent things, then the remaining proper class (the rest of the upward/outward expanse of sets) is such as neither exists nor doesn't exist, which conclusion might bring us some pause.)

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^∀Or, then, "If nothing is nontrivially absolutely true, then, 'Nothing exists,' is not nontrivially absolutely true, i.e. there is a substantive exception to, 'Nothing exists.' If there is a substantive exception to, 'Nothing exists,' then a substantive something exists. Ergo..." Perhaps my sense of these questions has been poisoned by the ontological neutralism of analytic philosophy of logic, but that (the preceding argument) sounds like trickery, however.

Answer 1

Classes can have infinite members, including classes which are parts of other classes including proper classes. Consider the real numbers and the surreal numbers.