A common premise found in most modern ontological arguments is “◊□G”. This of course, according to the S5 axiom of modal logic, implies “□G”. Here I argue that if one does not assume a realist interpretation of modality, then this implies that ontological arguments which use this premise are question-begging. I further argue that a theist is not justified in holding to a realist interpretation of modality, and thus (most) modern ontological arguments are in fact question-begging.
Modality, Worlds, and Propositions
What does it mean to say, “◊□G”? The modal operators can be defined in terms of each other, such that ◊x = ~□~x, and □x = ~◊~x. Furthermore, the S5 axiom tells us that essentially only the last modal operator matters, such that □□◊□◊□◊□x = □x. If you accept ◊□G as true, you’re implicitly also accepting □G as true, due to the logical equivalence. But anyway, let’s look at how modal propositions work according to both realism and fictionalism. On realism, possible worlds are no different than our own, and beings which exist in them can look around their world and rightly claim that that is the actual world. On fictionalism, these possible worlds are merely sets of propositions, and these sets exist in the actual world (since the actual world is the only possible world that exists, everything that exists must exist in the actual world). Essentially, modal claims are nothing more than counterfactuals.
In addition to worlds being merely sets of propositions, worlds are merely sets of propositions on fictionalism. There are no beings, no objects, no anything contained within them. On realism, however, there are in fact beings, objects, and things contained within worlds. So, to make the claim “◊□G” something more than merely a counterfactual claim, modal realism needs to be true – for it makes no sense for any object to exist within a proposition. But if it did, then the ontological argument runs into a bigger problem; as this would imply that the object we call “G” (God) exists in the actual world, within a set of propositions.
Far Beyond The Stars
Is modal realism true? Possibly (bazinga). But I don’t think we’re justified in believing it. There are several arguments for this, but I’ll focus on one that is specific to theism. There seems to be a conflict between God’s omnipotence and the very idea of a realist interpretation of possible worlds. Erik Wielenberg gives a charitable definition of omnipotence which I will use here:
x is omnipotent if and only if it is not the case that there is some state of affairs, p, such that x is unable to bring about p at least partially because of a lack of power in x.
Possible worlds are causally and temporally isolated from each other (if they were not, they would be one world). God does of course, as a necessary being, exist in every possible world. But one must wonder whether God can will cross-world acts. For instance, could God will a rock to move from w1 to w2? Or for an atom from w1 to collide with an atom from w2? If he can, then the plethora of causally isolated worlds would seem to collapse into one world, leaving us with fictionalism. If he cannot, the only explanation that seems reasonable would be a lack of power. Modern philosophy of religion tells us that God has all kinds of causal power foreign to us (such as creating the universe ex nihilo). Why then would he not be able to cause things across worlds? There seems to be no contradiction in doing so, and no limit imposed by any of his other attributes.
It may be claimed that modal realism has support via Ockham’s razor; because while the realist is only positing additional worlds of the same kind as our own, the fictionalist is positing additional worlds of a different kind than our own – thus the fictionalists’ ontology is inflated, while the realists’ is not. But this seems backwards. The fictionalist is not positing additional worlds at all, but merely sets of propositions. Whatever the fictionalist takes propositions (and sets) to be, no additional kinds of entities are being posited when she talks about possible worlds.
The realist, on the other hand, is positing an additional kind of entity. The realist claims that worlds are indexical, such that a being in any possible world can rightly claim that that world is the actual world. But it is reasonable to say this about the actual world (regardless of whether one is a realist or a fictionalist): The actual world is a world in which we have at least some causal power. But the realist wants to say that there is another kind of world – a world to which we are causally isolated, in which we have no causal power. This alone is not enough to defeat realism, but it is enough to lower our confidence in it.
Are all propositions necessarily true? Are contradictions true?
A critique of fictionalism by a realist may look something like this: “If I say, ‘P is true at w1, and ~P is true at w2′, then fictionalism implies that a contradiction is true, since w1 and w2 exist in the actual world”. But this is a misunderstanding of fictionalism. The correct interpretation of the apparent contradiction is merely a framing of modality in terms of counterfactuals: “P would have been true if w1 were the actual world, and ~P would have been true if w2 were the actual world”.
Another criticism might be offered: “since there are no other real possible worlds, then P -> □P. Thus all true statements are necessarily true”. But this is again solved by talking about modality in terms of counterfactuals: □P just means, “~P would have been true if w2 were the case” is false. In the case of propositions for which this second-order proposition is true, ~( P -> □P) is also true.
So, I think that we are more justified in believing fictionalism over realism, based on the fact that criticisms of fictionalism do not work, and because realisms’ ontology is inflated compared to fictionalism. I further think that the theist is especially committed to fictionalism over realism. Given this, and that ontological arguments which use ◊□G as a premise require realism in order to not be question-begging, I think that such arguments are most likely question-begging.
As always, I welcome questions, comments, and criticisms.
 Wielenberg, Erik (2000). Omnipotence Again. Faith and Philosophy