In a recent article in this journal, Paul Sheehy argues that there is a conflict between David Lewis's modal realism and the tenets of classical theism.Footnote ¹ The most potentially damaging of his claims, to my mind, is that the modal realist cannot satisfactorily allow for the necessity of God's existence. In this short paper, I show that Sheehy has under-appreciated the resources available to the modal realist. A more careful attention to what Lewis actually says shows that the modal realist theist has no problem in accounting for the necessity of God's existence.

Before I begin, let me make clear the terms of the debate. I take modal realismFootnote ² to be a conjunction of three claims: (1) for every complete way the world could be, there is a world that is exactly that way; (2) worlds, both actual and non-actual, are concrete objects: they are maximal mereological sums of spatio-temporally connected individuals; (3) ‘actual’ is an indexical, serving to pick out the world of the utterer: there is nothing special about the actual world other than it is the one we happen to be in.

That acceptance of these three doctrines is necessary and sufficient to make one a modal realist is largely a matter of stipulation. (Sheehy does not himself define the doctrine.) There are, of course, other doctrines concerning the space of possible worlds that Lewis – the paradigm modal realist – accepts, such as that properties are to be identified with sets of possibilia, propositions with sets of worlds, etc., but theses (1)–(3) seem to me to capture what is essential to modal realism. If these three theses can be shown not to be in tension with theism then there is at least a good sense of ‘modal realism’ that is not in tension with theism.

Now to Sheehy's alleged problem for the modal realist theist. It is no accident that God exists; He couldn't have failed to exist. A necessary existent is one that exists at every possible world, so the theist modal realist must hold that God exists at every possible world. Sheehy then raises a dilemma for the theist modal realist. Either God is a spatio-temporal being or He isn't. If He isn't, then He doesn't exist at any possible world, since to exist at a world is to be spatio-temporally related to a part of that world; and if God doesn't exist at any world, a fortiori He doesn't exist at them all (given that we know that there is at least one world – namely, our own); hence God is not a necessary existent. If God is a spatio-temporal being, on the other hand, then there's no problem with saying He exists at a world, but there is now a problem with saying that He exists at more than one. For the modal realist denies trans-world identity.

For the modal realist, objects, strictly and literally speaking, only exist at one world, and claims about how they might have been are to be understood by the method of counterpart theory. The claim that God necessarily exists, then, should be understood by the theist as the claim that, at every possible world, there is a counterpart of the thing that is God in our world. But while that might secure the truth of the sentence ‘God necessarily exists’, Sheehy thinks it falls short of getting the theist what she wants when she proclaims the necessity of God's existence. He says,

I think the main dilemma here is a false one: both horns are blunt. Suppose God is not a spatio-temporal entity. Sheehy says God can't then exist at a world because the modal realist says that to exist at a world is to be spatio-temporally related to a part of that world. But isn't the natural thing to say simply that that's only what it is for a spatio-temporal entity to exist at a world? Isn't it just obvious that the modal realist will need to say something different about entities that simply aren't located in space and time?

It is indeed obvious. And it's also exactly what Lewis himself says. Lewis firmly believed in two types of entity: sets and individuals. (He was agnostic about universals, a type of entity we will come back to below.) Now, perhaps impure sets – sets with non-sets in their transitive closure (x is in the transitive closure of a set S iff x is a member of S, or x is a member of a set S* which is itself a member of S, or x is a member of a set S** which is a member of a set S* which is a member of S, or … etc.) – are located where those non-sets are located; but pure sets (sets with only other sets in their transitive closure) are not located anywhere. Do pure sets not exist at any world then? The question is just ambiguous, says Lewis; he distinguishes between three ways of being ‘in a world’: there is being wholly in a world, being partly in a world, and existing from the standpoint of a world.Footnote ⁴ An entity is wholly in a world iff every part of that entity is spatio-temporally related to a part of that world. An entity is partly in a world iff it has a part that is spatio-temporally related to a part of that world. An entity exists from the standpoint of a world iff it ‘belongs to the least restricted domain that is normally … appropriate in evaluating the truth at that world of quantifications’.Footnote ⁵

Now, pure sets neither wholly nor partly exist at any world. But for each of them, there is a world such that they exist from the standpoint of that world, and there are some of them that exist from the standpoint of every world. Lewis cites the numbers as an example of the latter (he is accepting the usual identification of the numbers with pure sets). Lewis is perfectly happy to say that the numbers are necessary existents, then. The numbers necessarily exist; they exist at every world, meaning (as is appropriate when the entities in question are pure sets) that they exist from the standpoint of every world. Now Lewis was an atheist, but it's natural to suppose that, for the theist, an atemporal non-spatial God should be said to exist from the standpoint of every world. After all, the entities that are said by Lewis to exist from the standpoints of some, but not all, worlds are those abstracta that depend for their existence on some contingently existing concreta: such as, say, a concrete object's singleton. Since no theist thinks of God being thus dependent, the theist should grant God the same status as the pure sets have in this regard. Hence the theist modal realist has no more problem in claiming God to be a necessary existent than Lewis has in claiming the numbers to be necessary existents: which is to say, she has no problem at all.

Sheehy anticipates this line of response. (As you would hope, since it is the response Lewis had already given; Sheehy, however, does not acknowledge that Lewis holds this view.) But he seems to think that this response would undermine (some of) the reasons for being a modal realist in the first place. He says,

Sheehy does not say why he thinks modal realism might ever be thought to provide the resources to do away with abstracta such as numbers. (It's certainly true that Lewis offers as motivation for modal realism an ontological reduction of properties; but he doesn't thereby aim to get rid of commitment to abstracta: as I said above, Lewis aims to identify properties with sets of possibilia.) But in any case, as we saw above, it is certain that Lewis didn't think this, and that this wasn't among his motivations for modal realism. In the absence of an argument to the effect that Lewis was wrong, and that modal realism is only motivated if it can allow for a nominalist reduction of abstracta, then, I see no reason not to simply use the resources Lewis gave us for dealing with the necessary existence of the numbers to also deal with the necessary existence of a non-spatiotemporal God.

The other horn of Sheehy's dilemma also only seems worrying to one who is unaware of what Lewis has already said. I agree that it is indeed unsatisfying to say that God is necessary due to the existence of a vast plurality of Gods, one existing at each world. We face a dilemma. Either each God created the world He exists at, or He didn't. If the former, then there is no sense in which God is responsible for all of creation since, for the modal realist, all of creation is the pluriverse of worlds, not just the actual world. But if there are Gods that didn't create the world they exist at then it's not clear why they deserve to be called ‘God’; being the creator is essential to God if anything is, so a God that didn't create the world He exists at would seem not deserve the title, thus undercutting the claim that He is in fact a counterpart of the actual God, and hence undercutting the claim that God is a necessary existent.

But there is no need for the theist modal realist to go the route of postulating distinct counterparts of our actual God at each non-actual world. The denial of trans-world identity is motivated by analogous considerations that motivate perdurantism: the account of persistence whereby objects are said not to wholly exist at distinct times but rather to have temporal parts that exist wholly and entirely at each instant the object exists. Perdurantism is motivated by the problem of temporary intrinsics. If an object a is F at time t and not-F at time t* then there is an apparent violation of Leibniz's law. The perdurantist solves this by saying that a is F at t in virtue of having a part that exists wholly and entirely at t and is F simpliciter, and that a is not-F at t* in virtue of having a part that exists wholly and entirely at t* and is not-F simpliciter.

Likewise, the denial of trans-world identity is motivated by the problem of accidental intrinsics. If an object a is F at world w and not-F at world w* then there is an apparent violation of Leibniz's law. The counterpart theorist solves this by saying that a is F at w in virtue of existing wholly and entirely at w and being F simpliciter, and that a is not-F at w* in virtue of having a counterpart that exists wholly and entirely at w* and is not-F simpliciter.

Now, the presentist – one who thinks that only the present time exists – has no problem with temporary intrinsics. If a is now intrinsically F but was intrinsically not-F then there's no problem for the presentist: ‘a is F but was not-F’ does not even have the appearance of being in conflict with Leibniz's law. The problem only arises once one allows for the inference from ‘a was F’ to ‘there is a time at which a is F’. The presentist thinks this inference is invalid, because she denies that there are past times. But the eternalist – one who holds that the past and future times are as real as the present time – will accept this inference, and this is what leads to the problem. For now ‘a is F but was not-F’ entails that there is a time at which a is F and that there is a time at which a is not-F. But since F is an intrinsic property it is not the kind of property that is had relative to anything, a fortiori it is not had relative to a time. Hence, if a is F at a time, it would appear to be F simpliciter. But now we seem committed to saying that a is both F and non-F simpliciter, which is a straightforward violation of Leibniz's law. And so the eternalist must appeal to perdurantism and claim that the thing which exists at one time and is F is distinct from the thing which exists at the other time and is not F.

This argument that the eternalist should be a perdurantist can be used, mutatis mutandis, to argue that the modal realist should be a counterpart theorist. The actualist – one who thinks that only the actual world exists – has no problem with accidental intrinsics. If a is actually intrinsically F but could be intrinsically not-F then there's no problem for the actualist: ‘a is F but could be not-F’ does not even have the appearance of being in conflict with Leibniz's law. The problem only arises once one allows for the inference from ‘a could be F’ to ‘there is a world at which a is F’. The actualist thinks this inference is invalid, because she denies that there are non-actual worlds. But the modal realist will accept this inference, and this is what leads to the problem. For now ‘a is actually F but could be not-F’ entails that there is a world at which a is F and that there is a world at which a is not-F. But since F is an intrinsic property it is not the kind of property that is had relative to anything, a fortiori it is not had relative to a world. Hence, if a is F at a world, it would appear to be F simpliciter. But now we seem committed to saying that a is both F and non-F simpliciter, which is a straightforward violation of Leibniz's law. And so the modal realist must appeal to counterpart theory and claim that the thing which exists at one world and is F is distinct from the thing which exists at the other world and is not F.

Now, what is crucial for present purposes is that in both the case of perdurantism and counterpart theory, the doctrines are motivated only for entities that allow for certain flexibility in their intrinsic natures. There is no problem of temporary intrinsics for entities that cannot undergo intrinsic change: if there is an entity x such that ‘x is intrinsically F’ implies ‘x is always intrinsically F’ then there is no problem in holding that x persists by enduring – by being wholly present at every time at which it exists – because there will never arise a potential conflict with Leibniz's law, since there will never be one time at which x is intrinsically F and another at which x is intrinsically not-F. So we only need say that objects which can undergo intrinsic change persist by perduring; other objects can safely be said to endure.

And just as perdurantism is unmotivated for objects that cannot undergo intrinsic change, counterpart theory is unmotivated for objects that have their intrinsic properties essentially. If there is an entity x such that ‘x is intrinsically F’ implies ‘necessarily, x is intrinsically F’ then there is no problem in holding that x strictly and literally exists at more than one world. There will never arise a potential conflict with Leibniz's law, since there will never be one world at which x is intrinsically F and another at which x is intrinsically not-F. So we only need invoke counterpart theory for objects that could have differed in their intrinsic nature; all other objects can safely be said to enjoy trans-world identity.

Since God plausibly has His intrinsic properties essentially, there is thus no barrier to even the modal realist claiming that He literally exists in more than one world – indeed, that He exists in every world. So there is still no problem for the modal realist claiming that God necessarily exists. What I say here about God is exactly what Lewis said about universals: since universals don't have any of their intrinsic properties contingently, Lewis saw no problem in holding that they enjoy (in contrast to individuals) literal trans-world identity. He says,

Likewise, what contingent, non-relational property of God could we put in place of the shape of the coin? If God has His intrinsic nature essentially, as I think is overwhelmingly plausible, then there is none. As before, then, Sheehy appears to be raising problems that Lewis already has the resources to deal with. I conclude that there is no threat to the modal realist claiming that God necessarily exists.