Fressellian logic and why anything exists

We start our journey here where Bill Vallicella, aka Maverick Philosopher, characterizes seven possible responses to Leibniz's question why does anything exist rather than nothing? A very interesting post in its own right and highly recommended. Then he followed up on that post with another regarding one of the positions, rejectionism, which is the view that the question is nonsensical. The main question of that post is whether Wittgenstein, who "was struck with wonder at the sheer existence of things" was paradoxically a rejectionist. Embedded in that post, however, was a challenge: "translate 'Something exists' into standard logical notion [I think he means notation]. You will discover that it cannot be done." The standard logic Vallicella's talking about is the combination of Frege and Russell which he calls Fressellian logic, standard first-order predicate logic with identity. According to this logic, existence = instantiation. His argument -- his challenge rather -- is to ask, what exactly is the property being instantiated when something exists?

The challenge was then accepted by David Brightly at Tilly and Lola. Here is his reply:

And as a Fressellian I accept the challenge. That property is Individual aka Object, the concept at the root of the Porphyrean tree. We can say 'Something exists' with ∃x.Object(x), ie, there is at least one object. Likewise ∀x.Object(x) (which is always true, even when the box is empty) says 'Everything exists' and its negation (which is always false) says 'Some thing is not an object'. But both these last are unenlightening---because always true and always false, respectively, they convey no information, make no distinction, are powerless to change us.

Then Vallicella responds again in yet another post summarizing his objection wonderfully, and then going over Brightly's response, and his counter-response. He demonstrates, to my (untrained, non-Fressellian) satisfaction that "Something identical with itself is a man" does not mean the same thing as "A man exists", and substituting Brightly's "Individual aka Object" for "Something identical with itself" does not seem to solve the problem. However, this is not my field so I'll just conclude by saying I think something exists.

(cross-posted at Quodlibeta)