A third problem, one of Russell’s objections to Meinongianism (see [Russell 1905a, 1907]), turns on the fact that existence is, on Meinongianism, a property and hence figures into the base of the naive comprehension principle. So, consider the condition of being winged, being a horse, and existing. By the naive comprehension principle, there is an object with exactly these features. But then this object exists, as existing is one of its characterizing features. Intuitively, however, there is no existent winged horse. An existent object cannot so easily be thought into being. Indeed, for every intuitively nonexistent object that motivates Meinongianism—Zeus, Pegasus, Santa Clause, and Ronald McDonald—there is, by the naive abstraction principle, an object just like it but with the additional property of existing. But then there is an existing Zeus, an existing Pegasus, etc.. This is overpopulation not of being but of existence as well.
So suppose we use the encoding/exemplifying distinction. Shouldn't we be able to encode an object for the predicate exemplifies something, just like we can encode something per exists? If this is not enough to recapitulate Russell's objection, what about encoding an object as encodes exemplifying something? And then encodes encoding exemplifying something, etc.?
Or, then, can we show that any attempt to adjust our theory of predication to accommodate these pairs of existence-like predicates will fail once taken to its second- or maybe third-order? E.g., can we not stipulate that there is a Meinongian object for, "A cleverly disguised shrimp with a property that is both the bare existence property and a nuclear property"? The nuclear/extranuclear distinction is supposed to block that by making such a property into a contradiction, which is nullified from the system. However, for a (neo-)Meinongian, is it not possible that there is an impossible object with the property of being a violator of the nuclear/extranuclear distinction, or more classically-speaking being such that its nuclear properties are its extranuclear properties (c.f. Russell's paradox, and the motives behind his theory of types)?P
P: or take a naively/toy Platonic distinction between active and passive essential predication. One might also call this a fountain/mirror distinction, although historically, it is emphasized in the form of the participation terminology, wherein (at least some) Forms do self-participate (at one stage in Plato's thought, anyway, perhaps). At any rate, suppose the Form of Nonexistence was the set of things that don't exist. If it has no elements, then everything exists. However, if it is not an element of itself, then this Form does exist. But if the Forms self-participate, i.e. they are (by type) what they are reflected as, then the Form of Nonexistence should be the prototype of all its possible elements, to wit a nonexistent thing. Accordingly, if Plato doesn't have a Form of Nonexistence, here, then there's a Form for everything, including paradoxically (inconsistently) the very Form of Nonexistence, too. For if this Form doesn't exist, then the Form of Nonexistence is an element of itself. But if it does not exist, it has no elements. So if it didn't exist, it would be both an element and not an element of itself. So either way, it exists.
Or consider the Form of Imperfection, i.e. of imperfect participation, such as by physical exemplars. If it perfectly participates in itself, then it imperfectly participates in itself perfectly. But if it doesn't exist, then all participation is perfect and the supposedly most important distinction between Forms and exemplars is extinguished. (In fact, it seems as though Plato did wander through these woods already with his inchoate talk of a demiurge, or a demi-Form (supposing we take there to be a Form-operator F in our toy system, so that we can go to the demi-operator for F) perhaps; and of a world-soul, too, no less (and a world of Forms, which should be the Form of the World, except then it's also the Form of the Good (if the world is the sun and what it illuminates, so to say), and the Form of the Good is the Form of Forms and the Form of demi-Forms, after all; and so on and on).)