David Brightly asks whether we can avoid Meinong quite so easily. Meinong draws a distinction between being and existing. Thus some things which have Being may not exist - the golden mountain which I am thinking of, perhaps?
I already engaged with this objection in my second point here. The problem for the Meinongian thesis is that "Vallicella is thinking of a non-existent thing" is perfectly consistent with "no thing is non-existent", where scope of 'no thing' covers every object whatsoever, and is therefore inconsistent with "some non-existent thing has Being". So the Meinongian solution doesn't solve anything.
I suppose the Meinongian could object that the scope of 'no thing' may fail to cover those things that have Being but which are non-existent. But (a) I can still insist that I mean nothing whatsoever, not just nothing that is not a non-existent Being. And (b) as I argued here it would not be possible for the Meinongian and the anti-realist to have an argument at all unless they agreed on the meaning of categorical statements like 'no A is B' or 'some A is not B'. When the anti-realist says that there aren't any non-existent, he is denying exactly what the Meinongian asserts when he asserts that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.
David also comments on the curious fact we can reason about apparently non-existent objects. Indeed. The Square of Opposition seems to work for fictional characters. 'All the characters in Lord of the Rings are hobbits' implies 'some of the characters in Lord of the Rings are hobbits', is the contrary of 'none of the characters in Lord of the Rings are hobbits' and is the contradictory of 'some of the characters in Lord of the Rings are not hobbits'. More is needed.