The argument looks like this:
- A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
- A being has maximal greatness if it has maximal excellence in every possible world.
- It is possible that there is a being that has maximal greatness. (Premise)
- Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
- Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
- Therefore, an omniscient, omnipotent and perfectly good being exists.
(NB: if X is possibly necessary, then it is necessary in some possible world. Or, in some possible world W’ it is true that it exists in all possible worlds.
So, X “expands” into all the possible worlds from W’, as opposed to from the actual world. But it makes no difference. Hence X exists in all possible worlds or is necessary. You need the right system of modal logic to make this conclusion. S5 works.)
However, why must we assume that (3) is correct? If maximal greatness is impossible, then it is impossible that any being has maximal excellence in every possible world: ~◊□(God exists) = □~□(God exists) = □◊(God does not exist) = there is a possible world in which God does not exist = (since God’s existence is possible) God is contingent.
Thus, the modal ontological argument starts by attempting to prove that God is necessary and from that concludes that God exists in the actual world. Doesn’t this seem like an overkill? Denying the crucial premise (3) does not lead to any absurdity but to a seemingly modest conclusion that God is a contingent being. And why can’t God be contingent? If He is contingent, then it is unclear whether or not He exists in the actual world, because the actual world may happen to be a possible world in which God exists, or it may happen to be a possible world in which God does not exist. So Plantinga’s argument does not work. What’s more, I don’t see how the modal ontological argument is at all equivalent to the Anselm’s original version of the argument.
We might be tempted to say that (3) is contingent. But simple modal transformations show that that’s not possible: either (3) is necessarily true, or it is necessarily false. At best we can say that it’s conceivable that God is necessary, and it’s conceivable that God is contingent. But we can’t say: God is possibly necessary and is possibly contingent.