Exapologist was kind enough to inform me that my objection to Plantinga's modal ontological argument (MOA) is similar to one made by Peter Van Inwagen. I've just read Van Inwagen's argument, which can be found in the sixth chapter of his celebrated Metaphysics. I don't think his argument is strong enough, as I will explain.
The MOA aims to show that belief in God is just as rational as believing that God is possible. This would be an interesting result, since belief in God is widely regarded as less rational than belief in the mere possibility of God. So if the MOA is valid, it would be very interesting. What I have shown is that the argument is not valid. It begs the question. I show this by drawing attention to the premise that God's non-existence is possible. That premise is just as plausible as the premise of the MOA, and yet it contradicts the conclusion of the MOA. The defeat is therefore profound. All the MOA really shows is that it would be rational to believe that God existed if one first had rational ground for denying the possibility of God's non-existence. Yet, if you had that ground to begin with, you would not need the MOA. Thus, the MOA begs the question.
Given the logic and definitions Plantinga is working with, either God's existence is possible or God's non-existence is possible. Both premises cannot be true. What, then, to make of the competing premises? We might suppose that one of them is true, and we just need a reason to believe in one of them. Or we might suppose that neither is true, because neither is well-defined. I'm inclined to take the latter position.
Van Inwagen's argument is similar. Where I have constructed a modal argument that directly argues for the non-existence of God, Van Inwagen's modal argument approaches the conclusion indirectly, via the concept of a knowno. He writes (pp. 134-135):
consider the concept of a “knowno”: the concept of a being who knows that there is no perfect being. There would seem to be no reason, on the face of it, to suppose that there being a knowno is an intrinsically impossible state of affairs, like there being a liquid wine bottle. But consider. If a knowno is not intrinsically impossible, there is a knowno in some possible world. But then there is a possible world in which there is no perfect being, since, if someone knows something, then what that person knows is true. And, as we have seen, if a perfect being is possible, then there exists a perfect being in every possible world. It follows that if a knowno is possible, a perfect being is impossible and that if a perfect being is possible, a knowno is impossible. (The two statements ‘If a knowno is possible, a perfect being is impossible’ and ‘If a perfect being is possible, a knowno is impossible’ are logically equivalent.)
The possibility of a knowno entails not only the possibility of God's non-existence, but also the possibility of knowing about God's non-existence. Van Inwagen claims that neither the possibility of God nor the possibility of a knowno has rational support, and so neither the MOA nor his knowno argument can get off the ground. (This relates to his more general criticism of modal epistemology, according to which philosophers are too willing to trust such inscrutable "possibility arguments.")
Still, there may be a significant difference between the possibility of God's existence and the possibility of knowing of God's non-existence. That there is such an intuitive difference is evidenced by the fact that many people prefer agnosticism over atheism because they suppose atheists claim to know that which cannot be known. Some agnostics take God's existence to be just as possible as God's non-existence, and suppose that it is not knowable one way or the other. Thus, one might object to Van Inwagen on the grounds that, if God did not exist, it would not be knowable. The MOA might thus seem more plausible than Van Inwagen's counter-argument. My argument therefore seems a bit stronger. I do not make any suppositions or presuppositions about the knowability of God's existence or non-existence.
Also, there is one important point which Van Inwagen seems to have overlooked. He says that, unless we have an argument for the possibility of God's existence (or the impossibility of a knowno), we have no reason to think the ontological argument is sound. That is the wrong conclusion to draw. As I've shown, the MOA is incapable of serving the function it was designed to serve. You cannot sufficiently motivate the MOA without first denying that God's non-existence is possible, and you cannot do that without arguing for the conclusion of the MOA. The only way the MOA gets off the ground is with an antecedent argument against the possibility of God's non-existence, which would essentially be an argument for God's existence. Since the MOA is an argument for God's existence, the MOA begs the question. Its premises are not weaker than its conclusion, and in fact can only be motivated by an argument for its conclusion.
I'll close by returning to the point about agnostics and the ordinary belief in the possibility of God's existence. Agnostics about God may still be uncomfortable with the situation, because it looks like the possibility of God's existence is incompatible with the possibility of God's non-existence (assuming the validity of modal logic and the coherence of Plantinga's definition of "God," neither of which I require for my argument to work--I only claim that my anti-ontological argument is as valid and as coherent as the MOA. If my anti-ontological argument is incoherent or invalid, then so is the MOA. I'm fine with that.) Agnostics, however, believe that God's existence is just as possible as God's non-existence--both seem to be possible at the same time. If both cannot be possible, then agnostics hold a self-contradictory point of view.
This should remind us that the logical possibility we are dealing with in modal arguments is not the everyday sort of possibility people normally talk about. (See Van Inwagen's paper, "Modal Epistemology," which I linked to earlier, for a discussion of this issue.) Perhaps we should be suspicious of the very notion of logical possibility. My criticism of the MOA does not rest on any such suspicion, but, if we wanted to press the point, we could use it against Plantinga. Plantinga wants to show that belief in God is just as rational as belief in the possibility of God's existence. Yet, if the MOA does not deal with the ordinary notion of possibility, then it does not clearly draw Plantinga's desired conclusion. It only shows that belief in God is just as rational as belief in some philosophically sophisticated sort of possibility, and it's not so clear how rational that is. (What my anti-ontological argument might suggest is that belief in the sort of possibility that Plantinga requires is no more rational than believing that God's non-existence is impossible.) The MOA does not show that the ordinary belief in the possibility of God leads to any interesting conclusions about God's existence whatsoever.