- For the Meinongian solution to negative existentials -- i.e., that there are nonexistent objects independent of thought -- is a very elegant one. It's usually accused of 'ontological extravagance', but I don't think most people have much of an idea what they mean by phrases like that.
I would accuse it of ontological extravagance for the following reason: it claims that "there are" nonexistent objects. But of course there aren't.
An 'ontological claim' is just a fancy expression that there are (or there aren't) things of a certain kind. There are no non-existent things, because to say that unicorns are non-existent is just another, clearly confusing to some, way of saying that there are no unicorns.