Hartshorne's modal argument, which is an S5 formalization of Norman Malcolm's original reinterpretation of Proslogion II, is clearly deficient. Plantinga's argument is superior although it too fails, as I note in detail at my blog.
Meta: Neither argument fails. Every move Plantinga makes he got from Hartshorne. You are right that Malcom comes in there between Barth and Hartshorne. But you can't include everybody. None of them fail because none of them argue that the argument proves the existence of God. All of those thinks fit the argument into a larger system, as do I, where it is not the sole reason to believe but is an important piece of the puzzle.
We see this clearly at which Hartshorne (and by extension, Malcolm) argue that since God cannot be produced or cease to exist, He cannot be a contingent being. This is clearly fallacious. The fact that God cannot be caused to exist or be destroyed does not mean that He is modally necessary - all that entails is that all possible worlds at which God exists, He is neither produced nor destroyed hence the proposition "God exists" is true for all times t and at worlds at which God does not exist, He is not produced, hence the proposition "God exists" is false for all times t. It does not entail that God is logically/metaphysically necessary.
Meta: Yes it does! But that's not what they argue. Hartshorne does not argue that God is necessary because he does not cease or fail. That's my version that I got from Garrett Soalt. More to the point, it's an answer that came out on message boards, but by me. Hartshorne argues that if God exists, his existence must be necessary as a matter of the nature of the concept of God. He is not trying to do empirical analysis from data, he's not conducting an experment. He's arguing deductively from a concept. The concept is that of eteranl necessary being. Nevertheless, as a matter of fact, if God did not cease or fail God would be eternal. There two ways that could be. Either God is eteranl independently of anything else, or God is eteranl because he is eternally contingent upon some other eteranl necessity. There many reasons to decline the latter option, not the least of which is Occam. So we have eteranl God not contingent upon anything. If necessity is cannot or cannot fail then obviously God is necessary. If God creates all things he is ontologically necessary.
When you say:
and at worlds at which God does not exist, He is not produced, hence the proposition "God exists" is false for all times t.
that is clealry false becasue Plantinga's possible world's arguents shows that there cannot be a world in which God does not exist. God must exist in all possible worlds. In additon to that I would argue from my own view point that if God is the ground being then God must exist in all possible worlds. Far from being an added burden that the theist can't bear, this is a great argument that God has to exist qed.
It just means that if we have some possible world segment S that includes God, then any possible complement S* will likewise include God - and vice versa that if there is a possible world segment S' that precludes God, then any possible complement S'* will preclude God. It does not, of course, mean that either S or S' is necessary.
Meta: Yes it does. God cannot exist in some worlds and not others. God must exist in all possible worlds or not exist at all in any world. anything that is not impossible or contingent is necessary by definition. Unless you show why it is impossible for God to exist in some world, then you have not shown anything and God must exist in all possible worlds.
HRG on CARM used to argue that because he could concieve of a three particle universe, a universal contanining only three particals of sub atomic nature, then this proves can't exist because God could not have created such a world. I disproved this argument in many ways, not the least of which is that if God is being itself, any aspect of Being, even one particle universe shows that God msut be. So this is not a disproof anything, all it would prove, if it existed, is that God is an underachiever. But there's no reason to even see the three partical universe as a possible world.
The argument does not derive its specious plausibilty from God simpliciter, but purely from the property of eternity. An eternal universe or an eternal unicorn likewise cannot be produced or destroyed and both are possible - hence, both are necessary. This commits the same fallacy as the above. Hartshorne and Malcolm made the mistake of thinking that if God exists at a world, then He exists in all of them and if God fails to exist at a world, He fails to exist in all of them. This is clearly fallacious since what obtains is that if God fails to exist at a world, then He fails to exist (obviously enough!) at worlds at which He fails to exist and vice versa. Or more substantially, as I said above, the argument is committed to that (S v S') which clearly is unargued for.
Meta: That still leaves you in the position you were in at square one, you must show that is impossible or you have not demonstrated that he can't exist in some possible world.
Moreover you are just plain wrong about the nature of necessity. Anything that is not contingent or impossible is necessary. Those are the only choices. It could also be fictional, but that doesn't help your case any. To prove that God is merely fictional you still have to prove that God is impossible. I don't see a reason you give for God not to exist in a given possible world. If God exists at all he has to exist in all possible worlds.
The argument does not derive its specious plausibilty from God simpliciter, but purely from the property of eternity. An eternal universe or an eternal unicorn likewise cannot be produced or destroyed and both are possible - hence, both are necessary. This commits the same fallacy as the above.
It's your fallacy. By default an eternal existant would be necessary because it is neither impossible nor contingent. Except, in the case of an eternal contingency (Aquinas) which I've already explianed. The best analogy for that is the eternal flute player. The music from the flute player is eternal, but it is also contingent upon the player continuing to play. But you have not come up with any reason to pin God's existence upon some higher thing. In fact, if you did that we would not be talking about "God" but the higher thing would be God so you would just wind up provoing there is a God. But there is no reason to mulitply entities beyond necesstiy.
Moeover, if God is eternal and everything else is contingent we kind of have to figure God created it all, because otherwise there's no just logical reason to assume it all pops out of nothing or is created by the violation of Occam from the preceeding paragraph. That means that by defition God has to be ontologically necessary since the being of all things is pinned upon God's existence (or Being).
Let's break down your last statment some more:
and if God fails to exist at a world, He fails to exist in all of them. This is clearly fallacious since what obtains is that if God fails to exist at a world, then He fails to exist (obviously enough!) at worlds at which He fails to exist and vice versa.
Why would God fail to exist at any world? You must show this. Failing to show the impossiblity of God we can assume God must exist in all possible worlds. Otherwise why are calling him "God?" How can he create "all things" If he can't be in the places where all things are? What would be a reason for excluding him form any possible worlds? If God is the ground of being then he has to exist anywhere where the beings exist (that my answer not Plantingas). Moreover,
There are worthwhile ontological arguments out there, among them, Plantinga and Robert Maydole's. This ain't one of them.
Meta: I am glad you said that. Because as long you feel the need to make personal gabs, I doubt that you have read Hartshorne. If you have done so you should see that almost everything Plantinga says comes out of Hartshorne in some way. Now that is not put down Plantinga. He is brilliant, he has contrbuted tot he feild in ways I can't dream of doing. I'm sure he will be rememebered and I will not be. He deserves to be lauded as one of the great thinkers of our time, but I think he would be the first to praise Hartshorne for paving the way.
I am truely doubtful that you have read any of these people. You don't seem to understand the basic concepts.
show me a printed version of Plantinga's modal argument, and then one of Hartshorne's so we can all see the differences?