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:
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 give us no reason to think of one term as more basic than the other. Logically, they 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.
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.)
Suppose we try to define the existential 'is' in terms of the misnamed 'existential' quantifier. (The proper moniker is 'particular quantifier.') We try this:
y is =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. This thing, however, must exist. Thus
Quine exists =df Quine is identical to something that exists
and
Pegasus does not exist =df nothing that exists is such that Pegasus is identical to it.
The conclusion is obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist.
I have now supplied enough clues for the reader to advance to the insight that the ontological opposite of 'nothing,' is primary.
Mere logicians won't get this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.)
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