It is interesting that 'nothing' has two opposites. One is 'something.' Call it the logical opposite. The other is 'being.' Call it the ontological opposite. Logically, 'nothing' and 'something' are interdefinable quantifiers:
D1. Nothing is F =df It is not the case that something is F.
D2. Something is F =df it is not the case that nothing is F.
These definitions, which are part of the articulation of the Discursive Framework (DF), give us no reason to think of one term as more basic than the other. Logically, 'nothing' and 'something' are on a par. Logically, they are polar opposites. Anything you can say with the one you can say with the other, and vice versa.
We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.
So far I have said nothing controversial.
Ontologically, however, being and nothing are not on a par. They are not polar opposites. Being is primary, and nothing is derivative. (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.' The second is meant.)
Now we enter the arena of controversy. For it might be maintained that there are no ontological uses of 'being,' and 'nothing,' that talk of being and nothing is replaceable without remainder by use of the quantifiers defined in (D1) and (D2).
Quine said that "Existence is what existential quantification expresses." I deny it: there is more to existence than what the existential quantifier expresses. Quine's is a thin theory of existence; mine is a thick theory. Metaphorically, existence possesses an ontological thickness. This is very important for metaphysics if true.
I won't be able to prove my point because nothing in philosophy can be proven. But I can argue for my point in a fallacy-free manner.
Suppose we try to define the existential 'is' in terms of the misnamed because question-begging 'existential' quantifier. (The proper moniker is 'particular quantifier.') This is standardly done as follows.
D3. y is/exists =df for some x, y = x.
In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something. In general, to be is to be identical to something, not some one thing of course, but something or other. This thing, however, must exist, and in a sense not captured by (D3). Thus
Quine exists =df Quine is identical to something that exists
Pegasus does not exist =df nothing that exists is such that Pegasus is identical to it
Pegasus is diverse from everything that exists.
The point, which many find elusive, is that the items in the domain of quantification must be there to be quantified over, where 'there' has not a locative but an existential sense. For if the domain includes nonexistent objects, then, contrary to fact, Pegasus would exist in virtue of being identical to an item in this widened domain.
The conclusion is obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).
Mere logicians won't accept or perhaps even understand this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) You have to have metaphysical aptitude to understand it. (But now I am tending toward the tendentious.)
Intellectual honesty requires that I admit that I am basing myself on an intuition, what J. Maritain calls the intuition of Being. I find it self-evident that the existence of a concrete individual is an intrinsic determination that makes it be as opposed to not be. This implies a real distinction between x and the existence of x. Accordingly, the existence of an individual cannot be reduced to its self-identity: the existence of Quine does not reduce to Quine's being (identical to) Quine, as on the thin theory. And the nonexistence of Pegasus does not reduce to its being diverse from everything. (If to be is to be identical to something, then not to be is to be diverse from everything.)
The Opponent does not share my intuition. In the past I have berated him for being 'existence-blind' but he might plausibly return the 'compliment' by accusing me of double vision: I see Socrates but I also 'see' the existence of Socrates when there is no such 'thing.'
So far, not good: I can't refute the Opponent but he can't refute me. Stand-off. Impasse, a-poria.
Let me try a different tack. Does the Opponent accept
ENN. Ex nihilo nihil fit?
Out of nothing nothing comes. Note that 'nothing' is used here in two different ways, ontologically and logically/quantificationally. For what the hallowed dictum states is that it is not the case that something arises from nothing/Nothingness.
Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.' If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propsitional negation, and then the thin theory bites the dust.
But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.