One of Veatch's acquaintances, Reinhard Grossmann, in his 1992 book The Existence of the World thoroughly considers how to properly analyze what he calls "existence facts." He argues that existence does not belong to any of the categories (i.e., it's not an entity, an attribute, a quantity, an action, etc.). He further clarifies that it's not a ~property of a property~ or a "relational property." (I would think that existence and identity ~are~ relational properties, specifically when considering an existent and its characteristics in their reciprocal relations to one another, that's a different issue, for another time.)
Instead, Grossmann says, existence is a "feature" of the world. I.e., it is something about the world. This smells suspiciously like a ~basic fact~ about all of existence...er, um...I mean, the world.
Here is an extended excerpt where his reasoning, latching onto a few bits of modern logic along the way, ends up looking very similar to mine:
[Grossmann]I argued earlier that, contrary to Frege and Russell, it makes perfect sense to say of an individual like Caesar that he exists. But in the sentence 'Caesar exists,' the word 'exists' functions somewhat like a predicate. [OK, "somewhat like." Close enough for the present purpose!] I say 'somewhat,' because there is a difference, a difference which I find revealing: there is no indication of exemplification. 'Caesar exists' is in this regard quite different from 'Caesar is the conqueror of Gaul.' Of course, this fits in well with our contention that existence is not a property and, hence, cannot be exemplified. But the fact remains that in 'Caesar exists' existence is somehow connected with Caesar and we must now ask how this connection appears from our point of view that existence is the variable entity. I think that to say that Caesar exists is to say that he is an existent. Let us be somewhat pedantic and spell this out in detail. The sentence:
(6) 'Caesar exists'
represents the same fact as:
(7) 'Caesar is an existent.'
But here the 'is' does not signify exemplification, but represents identity:
(8) 'Some (at least one) existent is identical with Caesar.'
Or, written with the variable expression 'e':
(9) 'Some e is such that: e = Caesar.'
This is our most perspicuous way of representing the fact that Caesar exists. Let 'A' be the name of any entity whatsoever. The fact that A exists is of the form:
(10) Some e is such that: e = A.
or, for short, in English: A is an existent.
Now, skipping down a couple of paragraphs:
[Grossmann] Every thing is identical with an entity [he means: with an existent]; its existence consists in its being (identical with) an entity. But this means that every thing has its own existence, that every thing is a little piece of existence...Everything exists. If everything exists, then existence must exist. [He is arguing inductively for Rand's Existence axiom.] I fail to understand how anything could have this 'feature' of existence, whatever it may be, unless there is this 'feature' in the first place.
Translation: I fail to understand how it could be a fact that any existent is an existent, unless it is necessarily universally true of EVERY existent that it is an existent--i.e., that all existents exist, that Existence exists.
One more excerpt:
[Grossmann] To say of a particular thing a that it exists, as we have seen, is to say that a is identical with an existent. Similarly, to say that existence exists is to say that existents are identical with existents:
(11) Some e is such that: e = e.
But (11) states that some entity is self-identical. According to our view, therefore, to say that existence exists is to say nothing more nor less than that an existent is self-identical. Can this really be the meaning of the existence statement? I think that this view is forced upon us by the discovery that existence is the variable entity [i.e., existent], for I do not see how else one could analyze the fact that the variable exists.
Pretty heavy, abstract stuff. But it makes sense to me.
I'm glad that Grossmann's semantical gymnastics make sense to someone. 8-)
None of this stuff is necessary to understand the meaning of "X exists" or "X is an existent," nor does Grossmann's analysis clarify what we mean. Consider these remarks by Grossmann:
"To say of a particular thing a that it exists, as we have seen, is to say that a is identical with an existent." No. To say that X exists is to say that X exists, period. To say that X is identical with an existent is implicitly to compare two different things. X is not somehow identical to itself; it is itself. We need only say that X is an existent, or that X exists.
Grossman: "to say that existence exists is to say nothing more nor less than that an existent is self-identical." This inflation of philosophic verbiage is pointless and misleading. The weird expression "self-identical" is presumably meant to express identity, but this is not what Rand meant by "existence exists."
Here is my personal favorite: "(9) 'Some e is such that: e = Caesar.' This is our most perspicuous way of representing the fact that Caesar exists."
According to my dictionary, "perspicuous" means "Clearly expressed or presented; easy to understand." I therefore humbly suggest that "Caesar exists" is the most perspicuous way of representing the fact that Caesar exists. 8-)