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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:

  1. It is possible that a maximally great being exists.
  2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
  3. If a maximally great being exists in some possible world, then it exists in every possible world.
  4. If a maximally great being exists in every possible world, then it exists in the actual world.
  5. If a maximally great being exists in the actual world, then a maximally great being exists.
  6. 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?

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  • We can imagine time traveling and killing our parents, although possible it is not, not even logically. Imaginability does not imply possibility, especially metaphysical possibility that Plantinga works with. But there is a bigger problem: the definition of maximally great being is viciously circular on the model of the set of all sets. One has to characterize individuals first, and then set up possible worlds that feature them. The characterization can not jump ahead and get dependent on how they will be distributed over the totality of those possible worlds the way MGB's does.
    – Conifold
    Oct 2, 2020 at 20:31
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    @Conifold I'm not confident that we can reject the grandfather paradox as "logically impossible" when there might be, e.g. branching timelines. Also, I am not sure I agree that Plantinga's definition is circular, so long as we don't try to define PWs by whether they contain an MGB or similar predicates. I read it more as categorization - God would still be God in worlds where it exists, we just can't "label" it as an MGB if it doesn't also exist in other PWs. (i.e. being an MGB is not an "intrinsic" attribute of God)
    – redroid
    Oct 2, 2020 at 21:10
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    Is the 1st premise generally accepted? It seems like it's almost assuming what it's supposed to prove.
    – D. Halsey
    Oct 2, 2020 at 22:29
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    Surely, a maximally great seeing would be believed in by everybody. Having someone believe you exist is clearly a great quality, and having even one person not believing in the being would be a limitation of its greatness. I, for one, don't believe there exists a maximally great being, therefore it does not exist.
    – armand
    Oct 2, 2020 at 23:13
  • Branching timelines are parallel worlds, so that's not time travel, and we need not imagine them in grandfather's paradox, whether they are there or not. In any case, imagination is too feeble a device to judge what is possible. If God is not MGB in this circular sense then the argument is moot to establishing his existence, and if concepts of this sort are allowed one can derive any desired conclusions for them by the law of explosion, as in set theory paradoxes.
    – Conifold
    Oct 3, 2020 at 7:26

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This illustrates the limits of stipulative definition. On the one hand, possible worlds should have all possible entities in at least one of them. So if it is possible for a being to exist in all worlds, then it seems as if there must be a possible world that overlaps all other possible worlds. But this just shows that according to the "language game" of possible worlds, you can't describe things as possibilia ranging over different worlds. Things are only possible in a world; or, if there is also transworld possibility, then God pertains to that; but it no longer would follow that God existed "in" any possible world, and His possibility is not a function from being "in" a world.

Tl;dr version: theistic modality requires more than possible-worlds talk, so Plantinga is effectively equivocating in his argument.

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We probably have to accept that it is possible that a maximally great being (MGB) exists, since we know of no fact that would make this impossible. It sounds even rather plausible. That is, the opposite possibility seems implausible even if itself possible.

A MGB would have to be unique, if we don't equivocate on "maximally" and "great", given that two or more MGBs would together make a being greater than each of the assumed MGBs, which is a contradiction.

Suppose now there is just one world and nothing else, then, trivially, this world is an MGB. And given what we have already said, it would be the only MGB. I guess we already call this MGB "reality" and nobody makes a fuss about it.

Assume now that an MGB is not a world, then the sentence "a maximally great being exists in some possible world" is contradictory on the standard interpretation of the vocabulary whereby the MGB "exists in some world" and so the world in question would be at least as great or even greater than the MGB, both possibilities having already been dismissed.

This falsifies the second premise "If it is possible that a maximally great being exists, then a maximally great being exists in some possible world" (the first clause is accepted as true and the second clause is proven false).

This makes the whole argument nonsensical.

Nota -- It should be said, however, that in mathematical logic at least, the argument is valid precisely because the conjunction of its premises is false.

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  • That is, if we were to admit that the concept of MGB even makes sense.
    – armand
    Oct 3, 2020 at 23:29
  • @armand There is no doubt in my mind that any ontological argument to prove God can only rely on equivocation. We can make the notion of MGB logically consistent simply by equating it with reality, but then this only falsifies the ontological argument to prove God. The only possible MGB is reality itself. The argument couldn't prove that reality is finite. Simply that it contains everything that exists, but this is just the definition of reality.
    – Speakpigeon
    Oct 4, 2020 at 8:34

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