1) Didn’t Immanuel Kant refute the ontological argument once and for all since existence is not a property? Response: Some earlier versions may have assumed that existence is a property and so would be subject to Immanuel Kant’s criticism that existence is not a property, as you remind us. But from that it doesn’t follow that existing necessarily is not a property. In any case, Plantinga’s version doesn’t assume that even necessary existence is a property. It assumes merely that a being is greater if it exists necessarily rather than contingently. That strikes me as pretty evidently true. The idea of a being which is omniscient, omnipotent, and morally perfect in every possible world seems perfectly coherent. By contrast, if this objection were correct that it’s impossible for anything to exist necessarily, then you’d have an ontological disproof of numbers, sets, propositions, properties, and so on, which is surely as stunning a result as the ontological argument. 2) Doesn’t Plantinga’s ontological argument infer something existence from a definition? Response: No, Plantinga’s version of the ontological argument is based upon a crucial modal premiss that it is possible that a maximally great being exists. One doesn’t simply infer the existence of such a being from its definition. One infers its existence from the possibility that such a being exists. 3) Why does premise 3 follow? Response: The definition of maximal greatness means that a maximally great being exists in every possible world so that if in some world there is a being that is maximally great, then that being must exist in every possible world including the actual world otherwise that being isn’t maximally great. So, premise 3 isn’t the controversial premise, premise 1 is the controversial premise. In fact, steps 2-6 follow by definition, so premise 1 is the crucial premise. 4) There isn’t anything logically incoherent about the statement, “God does not exist.” As for the atheist’s retort that it’s not self-contradictory to say, “God does not exist,” this is irrelevant because the argument is framed in terms of broadly logical possibility/necessity, not narrowly or strictly logical possibility/necessity. There’s no contradiction in asserting “The Prime Minister is a prime number,” but that hardly shows that such a statement is possibly true in the relevant sense (that there is a possible world in which that statement is true). The atheist has to maintain that the idea of maximal greatness is broadly logically incoherent, like the idea of a something being green all over and red all over. But the idea of maximal greatness seems perfectly coherent and therefore possible—which entails that maximal greatness is exemplified! It's crucial that we keep clear on the difference between metaphysical and merelyepistemic possibility. The assertion "It's possible that God exists, and it's possible that He doesn't exist!" is true only in the sense of epistemic possibility: "for all we know," God may exist or He may not exist. On the other hand, if God is conceived as a maximally great being (that is, a being which is maximally excellent in every possible world), then His existence is either necessary or impossible, regardless of our epistemic uncertainty. To illustrate: imagine seeing some extraordinarily difficult mathematical equation written on the blackboard. If it's beyond our ability to grasp, we may say that it's possible that the equation is true and it's possible that it is false. But we thereby merely confess our epistemic uncertainty concerning the equation's truth value. As a piece of mathematics, the equation itself is either necessarily true or necessarily false. We just don't know which. But if it is true, it's necessarily true, and therefore it's not possible for it to be false. And if it is false, then it's necessarily false, and therefore it's not possible for it to be true. In the same way, the epistemic entertainability of (1) or (1′) doesn't imply that both are metaphysically possible. Only one of the two can be true, and it's up to us to decide which one we think it is. The atheist has to maintain that the concept of a maximally great being is incoherent, like the concept of a married bachelor. The concept of a married bachelor is not a strictly self-contradictory concept (as is the concept of a married unmarried man), and yet it's obvious, once one understands the meaning of the words "married" and "bachelor," that nothing corresponding to that concept can exist. By contrast, the concept of a maximally great being does not seem even remotely incoherent. On the contrary, the concept of a maximally great being seems to be intuitively a coherent notion and, hence, possibly instantiated. 5) Why can’t there exist a maximally great lion, or maximally great island, or maximally great pizza. Now as you note, some of the parodies, like arguments for an unsurpassingly great island or a necessarily existent lion, are not well-thought out. We have good grounds for thinking that such concoctions are impossible, in contrast to the apparently coherent idea of a maximally great being. For example, a lion cannot exist in every possible world since it couldn’t exist in worlds that are only composed of abstract objects, and an island could always have more hula girls added to it, or hotels, or what have you. However, the notion of a maximally great being has intrinsic great making properties such as omniscience, omnipotence, omnibenevolence, etc. 6) Could a quasi-maximally great being exist? More difficult to assess is the notion of what I called a quasi-maximally great being: a being which is just like a maximally great being except that it lacks, for example, complete omniscience (like the God of so-called Open Theism, Who lacks knowledge of future free acts of men). My argument against such a parody is that any reason for thinking a quasi-maximally great being is possible also warrants belief in the possibility of a maximally great being, but if we think that a maximally great being is possible, then we must say that a quasi-maximally great being is impossible after all, since it’s impossible for the two to co-exist in the same world. My answer here is that there’s an asymmetry between our intuitions about the possibility of such beings. Any intuition for thinking a quasi-maximally great being to be possible also warrants belief in the possibility of a maximally great being; indeed, the way we came to form the idea of the former was by diminution of the idea of the latter. But our intuition of the possibility of a maximally great being, once we understand its implications, tends to undermine our intuition of the possibility of a quasi-maximally great being. We begin to suspect that despite appearances, it’s not really possible after all. Moreover, if it is possible that a maximally great being exists, then in virtue of its omnipotence and necessity, there can be worlds in which it exists, but a quasi-maximally being doesn’t because a quasi-maximally being does not exist in every possible world, and in at least one of those worlds, a maximally great being refrains from creating a quasi-maximally being. Thus, there is a causal asymmetry between a maximally great being and a quasi-maximally great being in which case a quasi-maximal being can only exist if a maximally great being chooses to create it. Notice that all this is said solely on the basis of appeal to modal intuitions alone (i.e., our intuitions about what is possible or necessary). But one of the significant new wrinkles in discussions of the ontological argument is support for (OA1) which goes beyond mere modal intuitions. Here considerations of simplicity may indeed have a role to play. By appealing to such factors, one is not altering the form of the ontological argument but marshalling reasons in addition to modal intuitions for the truth of (OA1).