For Tim M. who wants to discuss this topic with me. ComBox open.
Singular existence is the existence of particular individuals. It is the existence attributed by a use of a singular sentence such as 'Max exists,' where 'Max' is a proper name.
A standard way to conceptualize singular existence, deriving from Quine and endorsed by Peter van Inwagen, is in terms of the 'existential' -- I prefer to say 'particular' -- quantifier of standard predicate logic. Thus,
Max exists =df for some x, x = Max.
x exists =df for some y, x = y.
In the standard notation of modern predicate logic with identity,
x exists =df (∃y)(x = y).
What the latter two formulae express is that an individual exists if and only if it is identical to something. Assuming that there are no nonexistent objects in the domain of quantification, these biconditionals are undoubtedly true, and indeed necessarily true. Meinongians reject the assumption but it is quite reasonable, so let it stand. Even so, I cannot see that the biconditionals just listed sanction the reduction of existence to identity-to-something.
Those of a deflationary bent would welcome such a reduction. For it would allow the elimination of existence as a topic of metaphysical investigation in favor of the sober logic of 'exists.' You will notice that on the left-hand side of the biconditionals there is the apparently non-logical, content-rich word 'exists' whereas on the right-hand side all the symbols are logical. If we can get rid of the word 'exists,' then perhaps we can get rid of the temptation to ask about Existence and Being. Aquinas, for example, tells us that God is not an ens among entia, but esse, Being or To Be: Deus est ipsum esse subsistens. This presupposes that there is such a 'thing' as Being. If the deflationary account is correct, there isn't.
So my question is this: is the deflationary account adequate? Or is there more to existence than can be captured by the so-called 'existential' quantifier of modern predicate logic?
An Argument Against Reduction
If Max is identical to something, then this thing can only be Max. The upshot is that the existence of Max is his self-identity. But note that whereas my cat Max, being a contingent being, might not have existed, it is not the case that Max might not have been self-identical. It is true that Max might not have existed, but it is false that Max might not have been Max. So existence cannot be reduced to self-identity. This holds for all contingent beings. Only a necessary being such as God could be such that existence and self-identity are one and the same. The argument, then, is this:
P1. Every contingent existent is possibly nonexistent
P2. No contingent existent is possibly non-self-identical
C1. No contingent existent is such that its possible nonexistence = its possible non-self-identity
C2. No contingent existent is such that its existence = its self-identity.
It follows that there is more to existence than what is captured by our Quinean biconditionals.
Is the above argument decisive? A Quinean might respond by denying (P2) and running the argument in reverse. Insisting that to exist = to be self-identical, he argues that if a thing is contingent (possibly nonexistent), then it is possibly non-self-identical. If Max is contingent, then there is a possible world W in which he doesn't exist. Since Max does not exist in W, he has no properties there. Hence he is neither self-identical nor non-self-identical in W.
Is this objection any good?