There are a lot of slightly different formulations of the ontological argument for God, but I'm going to use William Lane Craig's phrasing of Plantinga's, because that's the version I first heard. His argument goes:
- It is possible that a maximally great being exists.
- If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
- If a maximally great being exists in some possible world, then it exists in every possible world.
- If a maximally great being exists in every possible world, then it exists in the actual world.
- If a maximally great being exists in the actual world, then a maximally great being exists.
- Therefore, a maximally great being exists.
My question is about premise 3. My background leans towards mathematics more than philosophy, but I read the premise as a definition - being an MGB is defined by an entity's existence in every possible world, and anything that does not so exist is not an MGB. I'm not entirely clear on the notion of how a single entity is identified across possible worlds, but I'll assume to it's possible to do that for the sake of argument.
The converse of P3 is that should any possible world fail to contain a purported MGB, then the entity cannot actually be an MGB. As an extension, if we can prove that at least one of a set of worlds fails to contain an object, that object cannot be a maximally great being.
I'm aware that the exact mechanics of "possible worlds" are controversial, but I have not found anything indicating that we cannot imagine two possible worlds such that they have no entities in common between them. (Whether those worlds are "real" or not doesn't matter) We could, for instance, compare the actual world with one defined by completely different laws of physics containing entities that cannot actually exist. The latter might still be internally consistent and so "possible" without issue. To dodge the obvious counterargument, we might specifically imagine these possible worlds as "lacking God" or similar - it is not evident why that is not, at least, a possibility.
If we have two possible worlds with nothing in common between them, then we have the construct mentioned earlier - a set of worlds, at least one of which fails to contain anything not in their "intersection." (To use the set-theory term.) But we have chosen the worlds specifically to make the intersection empty, and so all objects do not exist in at least one of the two worlds.
This in turn seems to imply that no entity can even possibly fufill premise 3, and if P3 is read as a definition as mentioned, that P1 is necessarily false.
My question is, is this correct reasoning? Are there any flaws or misinterpretations of the terms I've overlooked?