[See Update and Update II]
Graham Oppy was kind enough to draw my attention to The Nature of Necessity (1974), in which Plantinga puts forward his modal ontological argument (MOA). Plantinga considers an objection very much like my own (pp. 218-219): "consider the property of no-maximality, the property of being such that there is no maximally great being. If this property is possible, then maximal greatness is not. But, so claims the objector, [this property is] every bit as plausibly possible as maximal greatness." Thus, Plantinga imagines the following modal counter-argument to MOA:
1) No-maximality is possibly exemplified.
2) If no-maximality is possibly exemplified, then maximal greatness is impossible.
3) Maximal greatness is impossible.
Plantinga concludes that either MOA or this counter-argument is sound. Clearly both cannot be. I question whether either is sound, since I question the coherence of the notion of maximal greatness. But, for the sake of argument, let's suppose that one or the other is sound. Plantinga's claim is that it is rational to accept the premise that maximal greatness is possible, and thus to believe that God exists. His argument for the acceptance of this premise is thus (p. 221):
Were we to believe only what is uncontested or for which there are incontestable arguments from uncontested premises, we should find ourselves with a pretty slim and pretty dull philosophy. Perhaps we should have Modus Ponens; certainly not much more. The policy of accepting only the incontestable promises security but little else.
So if we carefully ponder Leibniz's Law and the alleged objections, if we consider its connections with other propositions we accept or reject and still find it compelling, we are within our rights in accepting it--and this whether or not we can convince others. But then the same goes for [the possibility of maximal greatness]. Hence our verdict on these reformulated versions of St. Anselm's argument must be as follows. They cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion. And perhaps that is all that can be expected of any such argument.Plantinga has not given any reason to think that his premise is acceptable. He has only argued that, if careful consideration of the premise does not lead people to reject it, then it is acceptable, even if it remains contested. We must still wonder what makes it rational to accept the premise. With such a justification as Plantinga offers, any premise would have to be considered acceptable so long as somebody (or some group) carefully considered it and still decided to accept it. That's a rather weak justification for the premise, in my view. In any case, this is not my objection to the argument. As I've pointed out in a bit more detail, it is only rational to accept Plantinga's possible maximality premise if it is rational to reject the possible no-maximality premise. This means it is only rational to accept his premise if it is rational to assume that God exists. Thus, MOA begs the question.
Plantinga denies that his argument is question-begging (p. 218): "It is by no means obvious that anyone who accepts its main premise does so only because he infers it from the conclusion. If anyone did do that, then for him the argument is dialectically deficient . . ." Yet, once we realize that the main premise (that maximal greatness is possibly exemplified) is logically incompatible with the possibility of no maximality, then it seems quite obvious that his main premise can only be accepted by inference from the conclusion of the argument. Anybody who accepts the main premise of MOA without inferring it from the conclusion of MOA has failed to fully understand the premise.
Graham Oppy makes the same point in his entry on ontological arguments for the SEP, though without sufficient explanation:
But it is at least plausible to claim that, in each case, any even minimally rational person who has doubts about the claimed status of the conclusion of the argument will have exactly the same doubts about the claimed status of the premise. . . . anyone with even minimal rationality who understands the premise and the conclusion of the argument, and who has doubts about the claim that there is an entity which possesses maximal greatness, will have exactly the same doubts about the claim that there is a possible world in which there is an entity which possesses maximal greatness.I think this is exactly right. Unfortunately, Oppy does not explain why. The reason why Plantinga's premise is just as dubious as the conclusion is that the premise can only be accepted at the cost of rejecting the possibility of no-maximality. Given the logic Plantinga is working with, both premises cannot be accepted in the same argument.
Unfortunately, Oppy's section on Plantinga's argument has another flaw. [Not necessarily. See update below.] He claims that only a theist would prefer MOA to the following anti-ontological argument:
There is no entity which possesses maximal greatness.
(Hence) There is no possible world in which there is an entity which possesses maximal greatness.
He writes: "Plainly enough, if you do not already accept the claim that there is an entity which possesses maximal greatness, then you won't agree that [MOA] is more acceptable than the second." This is not convincing for the simple reason that many people are agnostic about the existence of God, and claim that belief in the possibility of God's existence or non-existence is more rational than belief in God's existence or non-existence. Oppy's anti-ontological argument may therefore seem less plausible to agnostics as well as theists. What Oppy should have observed is that only a theist would prefer MOA to the possible no-existence argument. This is why MOA begs the question.
Update: Oppy has raised some interesting points via email.
First, he agreed that maybe his SEP entry doesn't explain as much as it could, and he indicated some other places where he addresses the issue in more detail: Ontological Arguments and Belief in God (CUP, 1996); Arguing about Gods (CUP, 2006); and "Über die Aussichten erfolgreicher Beweise für Theismus oder Atheismus" in J. Bromand and G. Kreis (eds.) Gottesbeweise von Anselm bis Gödel Berlin: Suhrkamp, 599-642. Also, though he didn't mention it, charity compels me to observe that the SEP entry is about ontological arguments in general, and therefore a thorough examination of MOA isn't necessarily called for. Still, if there ever is an update to the SEP, I'd be happy to see a little more said on the topic.
Second, and more interestingly, Oppy takes issue with my criticism about agnostics. He points out that everything hinges on whether or not we accept a suitable modal logic and Plantinga's definitions. A rational agnostic, accepting those conditions, would not believe that God's existence and God's non-existence were both possible. Such an agnostic would not suppose that "it is possible that God exists" is more acceptable than "God does not exist." He has a point, and it indicates the question-begging nature of MOA. The possibility premise, properly understood, is not an agnostic premise at all. So, when he says that only a theist would find MOA more acceptable than his atheistic argument, he is right. A properly informed and rational agnostic would recognize MOA as begging the question in favor of theism, and so would not accept it any more than they would accept an argument that begged the question in favor of atheism.
Update II: I'm not sure how I could do it, but I wonder if it is possible to show that the MOA's possibility premise really is an agnostic premise. My anti-MOA argument does not require that we take the MOA's premise as a theistic premise. It only requires that we take my anti-MOA premise as equally plausible as the MOA premise. I'm about convinced that both the MOA and anti-MOA premises are not agnostic premises. But part of me resists, and so I suspect there might be a way of countering Oppy's point about agnostics. I just don't know how. Perhaps it might start with something like this: Agnostics believe that we do not know if God exists or not. Therefore, according to agnostics, it is possible that God exists and it is possible that God does not exist. Now, either the sort of possibility expressed here is not the one employed by MOA and anti-MOA, in which case it is not clear what sort of possibility is being employed in those arguments (see Van Inwagen, "Modal Epistemology," for a motivation for this view), or it is the same sort of possibility, in which case the MOA and anti-MOA premises should be properly considered agnostic premises. In any case, Oppy and I agree that MOA begs the question against anti-MOA (and anti-MOA begs the question against MOA). It's worth noting, at least, that one cannot dismiss my anti-MOA argument merely by showing that the MOA's premise is really agnostic about the existence of God. It has to be shown that the MOA's premise is more plausible than the anti-MOA's premise.