Meinongianism and Platonism

I have recently been reflecting on an objection to Meinongianism that I have encountered on occasion (cf. David Lewis 'Noneism or Allism?' for just one example), and that is the notion that the Meinongian is trying to have his cake and eat it too. In effect, the objection here states that the Meinongian is quantifying over and making theoretical use of a plenitude of objects, but avoids the requisite ontological commitment to these objects by holding that they do not exist. In effect, the Meinongian is doing nothing more than playing a word game.

If we wholeheartedly accept the current Quinean dogma in contemporary Meta-Ontology, then this would certainly be a natural objection. But what I would like to do is to turn this objection on its head and demonstrate how we can raise the very same sort of worry with regard to the Platonist.

The Platonist, for those who don't know, believes that, in addition to the singular concrete objects of the everyday world, there exist untold infinities of 'abstract objects' (such objects might include Numbers, Universals, Propositions, States of Affairs, etc.). What distinguishes these abstract objects from the aforementioned concrete objects is that, while concrete objects are always spatio-temporally locatable, abstract objects exist beyond space and time. 

This view is certainly well-established within the history of Philosophy, but it does appear rather strange sounding at first glance. For if someone were to inform us that an object such as Bigfoot exists, we might very sensibly want to ask 'Where does Bigfoot exist?' If we were told that Bigfoot does not exist anywhere in the universe, we might feel that our interlocutor was using the word 'exist' to mean 'timeless existence.' Realizing this, we might then ask him 'Well then, at what time does Bigfoot exist?' If he responds by saying that 'Bigfoot does not exist at any point in time, for he is an abstract object!' we would most likely feel that the wool has been pulled over our eyes.  Surely to claim that an object exists nowhere and never is the same thing as to say that it does not exist at all. And since the Platonist makes the exact same claim regarding all the endless abstracta, should we not then conclude that the abstracta also do not exist in any way?

(For clarification's sake, let us call the Platonist view of Ontological Commitment the Quantificational View, and let us call the view we have just adumbrated the Spatio-Temporal View, for obvious reasons).

Of course, a standard reply that the Platonist might make at this point is to say that "While abstract objects surely do not exist in our physical universe, they nevertheless do exist in the Realm of the Forms." But this can't be right, for to say that these objects exist 'in' the Realm of the Forms is already to imply that they are spatially located somewhere.

So is it not already apparent how we can apply the same sort of reasoning to attack the Platonist? For at least according to one plausible way of looking at things, the Platonist is doing nothing more than playing a word game. The Platonist has denied both of the factors that are used in determining existence (at least according to the Spatio-Temporal View). So we can very easily say that he has actually denied the existence of abstract objects, but in order to hold on to his pristine Platonic Heaven, he has inexplicably claimed that these abstract objects still somehow exist. Quite literally (to adapt a phrase from David Lewis) he has 'affirmed existence without affirming existence.'

In closing, what I would like to get across with my observations is that the objection that the Meinongian is playing a word game holds no water as of yet, because as has just been demonstrated, the same sort of remark can be made towards the Platonist. What is actually needed is a solid argument in favor of the Quantificational View and also a demonstration that something like the Spatio-Temporal View is incorrect. Modern classics like 'On What There Is' and 'Noneism and Allism' contain only dogmatic assertions, and thus are not fruitful places to look for the requisite arguments.