Modal realism, counterpart theory, and necessary being

It is standard practice among philosophers to analyse modal claims in terms of possible worlds. For instance, on a possible worlds semantics, the proposition <Humphrey could have won the election> is true if and only if there is a possible world where Humphrey does win the election. For most philosophers, such a framework is relatively innocuous, since possible worlds are merely taken to be abstract entities which represent the various ways things could be. For David Lewis, however, possible worlds are just as real as the universe that you and I live in. On his view, for instance, since unicorns are possible, it follows that there are real, concrete worlds where real, material unicorns exist. This is ‘modal realism’. Modal realism is often rejected simply because it is too strange (this is the ‘incredulous stare’ objection). But, there is a better reason for rejecting it, if one is a theist. For instance, Paul Sheehy (Reference Sheehy2006) has argued that the two views are incompatible. More recently, Ross Cameron (Reference Cameron2009) has argued that Sheehy's criticisms are misguided, and that Lewis's modal realism is well-equipped to deal with them. Here, I will demonstrate that Cameron is mistaken. That is, I will argue that modal realism is incompatible with the classical version of theism, which maintains that there is but one God, where God is understood to be a necessarily existing, omniscient, omnipotent, morally perfect, omnipresent, and simple being (that is, lacking proper parts) responsible for bringing all of creation into existence.Footnote ¹

Now, Sheehy raises three difficulties for any theist looking to adopt modal realism, but here I will address only one of them. First, Sheehy points out that modal realism gives rise to a problem for God's omniscience, since God's knowledge of what is possible is either dependent on the existence of possible worlds (in which case his omniscience seems limited), or it is not (in which case, we cannot analyse propositions in the way that the modal realist does; namely, as sets of worlds). I will not address this problem here.Footnote ² Second, Sheehy notes a problem for God's moral perfection that arises in the event that God creates all of the possible worlds (such that they completely exhaust the logical space).Footnote ³ For, if the amount of evil in this world gives rise to a problem of evil that conflicts with God's moral perfection, we should find it much more troublesome to learn that God has also created worlds where every human being endures nothing but unimaginable pain and suffering, with no chance for redemption. I will not address this problem either.Footnote ⁴

It is Sheehy's third criticism which will be of greatest interest to metaphysicians, and it is also, I think, the most problematic. (Furthermore, it is the only criticism that Cameron attempts to address.) I am referring to the problem of reconciling God's necessary existence with modal realism. On a possible worlds semantics, <Necessarily, God exists> is true if and only if, at every world, God exists. But, for the modal realist, strictly speaking, nothing exists at more than one world. For Lewis, all individuals are ‘world-bound’; that is, ‘there is nothing that inhabits more than one world. . . . Things that do inhabit worlds – people, flames, buildings, puddles, concrete particulars generally – inhabit one world each, no more’ (Lewis (Reference Lewis and Loux1979), 126).

Rather than endorsing ‘trans-world identity’ (the view that some of the individuals in distinct worlds are numerically identical; i.e. literally one and the same thing), modal realists must instead adopt ‘counterpart theory’. For example, though Lewis would agree that <Humphrey could have won the election> is true if and only if there exists some world where Humphrey does win the election, strictly speaking, the victorious Humphrey is only Humphrey's counterpart (or doppelgänger, if you will). On Lewis's view, there is another universe where someone exists who bears a striking resemblance to the Hubert Humphrey of our actual world, and that man became a US president – but that man is not numerically one and the same individual as our Humphrey. He is merely an individual who bears certain relevant relations of similarity to our Humphrey (i.e. he is one of Humphrey's ‘counterparts’). This spells trouble for the claim that God exists in every possible world. For, on counterpart theory, this amounts to nothing more than the claim that the being whom we call ‘God’ exists – strictly speaking – in the actual world only, but is said to exist necessarily in virtue of the fact that he has a God-counterpart in every other world. But, then, there is not really one God, but many – an infinite number of world-bound Gods, in fact – each of them residing in his own world. This picture is at odds with classical theism for two reasons: First, classical theism states that there is but one God, not many. Second, if each god creates nothing outside his own world, then it seems that none of them is responsible for all of creation (i.e. everything that exists; the set of all worlds). Rather, each god is responsible for creating only his little corner of it. On the other hand, if only one of these world-bound gods created absolutely everything, then it turns out that all but one of the ‘gods’ have created nothing at all.Footnote ⁵

Alternatively, the counterpart theorist may claim that God really is just one individual thing, rather than many – namely, the mereological aggregate of all of the gods in each world. However, whereas the former proposal was incompatible with the claims that there is but one God, and he is responsible for all of creation, this latter proposal is incompatible with two others: For, if ‘God’ refers to the mereological aggregate of all of the god-counterparts, then God is not wholly present in the actual world (or any world, for that matter), and, furthermore, God has proper parts. But, God is generally understood to be both mereologically simple and wholly present in all places. Furthermore, it seems that, on this picture, the claim that ‘there is but one God’ is true only in a very unnatural sense. For, on this picture, God is ‘unified’ only in the same sense that my left arm, the Moon, and the Statue of Liberty are all ‘unified’ because they compose a single, scattered object (assuming that they even do so at all). Certainly, God would not be unified in the way that a classical theist would deem important, e.g. by having a unified will, or consciousness.Footnote ⁶ Finally, as Lewis himself admits, ‘such a cross-world sum is not a possible individual. There is no way for the whole of it to be actual. No matter which world is actual, at most a proper part of it actually exists’ (Lewis (Reference Lewis1983), 39–40). As such, God would be, on this latter proposal, strictly speaking, what Lewis calls an ‘impossible individual’. In sum, the conclusion that modal realism is incompatible with classical theism seems at least initially plausible. In the following two sections, I will examine two alternative approaches in which the modal realist may be able to help herself to a special case of trans-world identity (rather than counterpart theory) in order to reconcile the necessary existence of God with modal realism. I will argue that each of these proposals is at least as unsatisfactory as the above.

Modal realism, trans-world identity, and genuine abstract necessary being

The main problem with the portrayal of God as a necessary being just presented is that such a god only seems to be quasi-necessary. That is, God is a ‘necessary’ being only in virtue of the fact that things turned out such that there is a god-counterpart in every world. But, then, the fact that God exists necessarily rather than contingently is nothing more than an enormous cosmic accident. As Michael Jubien puts it, on modal realism, ‘what passes for “necessity” is in effect just a bunch of parallel “contingencies” ’ (Jubien (Reference Jubien2009), 75). Because God just happens to have a counterpart in every world, he achieves the title of ‘necessary being’. But, if just one of those worlds happened to lack a god, then God's existence would instead be contingent. On this picture, God's necessary existence seems rather precarious – the result not of his divine perfection, but of something closer to luck. What is wanted by the theist is the sort of being who is what I will call ‘genuinely necessary’; i.e. necessary in virtue of his existing as numerically one and the same being in (or at) every possible world. In short, what is wanted is necessity as understood by those who endorse trans-world identity rather than counterpart theory.

As it turns out, there is room within modal realism for the existence of things that are genuinely necessary in this way. Indeed, David Lewis explicitly acknowledges the existence of such entities. Before elaborating, it will be helpful to identify the three categories into which Lewis divides all existing things. In his (1983), Lewis says that there exist:

1. (i) Possible individuals: entities that exist wholly within a world; i.e. as a part of that world (e.g. planets, human beings, atoms, etc.).

2. (ii) Impossible (cross-world) individuals: entities that do not exist wholly in any world, but are composed of possible individuals from two or more worlds (e.g. the mereological aggregate of all of the god-counterparts, discussed in the previous section).

3. (iii) Non-individuals (i.e. sets): entities which do not exist in any world, but nevertheless exist ‘from the standpoint of a world’ because they are members of the domain according to which we evaluate the truth values of quantified sentences (Lewis points out that pure sets fall into this category).Footnote ⁷

Immediately following his statement of the three categories just given, Lewis clarifies that the second axiom of modal realism – which he paraphrases as ‘the principle that nothing is in two worlds’ – applies only to those entities in category (i), the possible individuals. In other words, only the type-(i) individuals are world-bound individuals. This leaves entities of types (ii) and (iii), i.e. the so-called ‘impossible individuals’ and the ‘non-individuals’, as viable candidates for what I have called a ‘genuinely necessary being’, i.e. the sort of being that, rather than being bound to one world, literally exists (as numerically one and the same entity) either in or at every world. Now, we have already seen reason for the theist to reject the existence of a type-(ii) God; i.e. a God of the cross-world mereological aggregate variety. I will now turn to the question of whether or not God might be a being of type (iii).

Certainly, Lewis endorses the existence of necessary beings of this third variety; namely, the pure sets belong to this category. He writes: ‘There will be many sets that even exist from the standpoint of all worlds, for instance the numbers’ (Lewis (Reference Lewis1983), 40). One of Ross Cameron's suggestions is that the theist accept the existence of a god of this sort, writing ‘the theist should grant God the same status as the pure sets have’ (Cameron (Reference Cameron2009), 97). Sheehy (Reference Sheehy2009) criticizes this suggestion for being contrary to the goal of parsimony that the modal realist strives for (since it would entail accepting the existence of a new kind of abstract entity into one's ontology), but we can do better than that. For, there are three important differences between God, as he is traditionally understood, and an entity of type-(iii). As it turns out, any entity falling into Lewis's third category of being (a) is one to which the part–whole relation does not apply, (b) does not stand in spatio-temporal relations to other things, and (c) is causally impotent. I maintain that such a being is simply not the sort of thing which could be described as a deity. I will now examine each of these three features (a)–(c) in turn.

(a) God and the part–whole relation. The God of the theists is one to whom the part–whole relation applies. For instance, on classical theism, God is said to be wholly present in the world. David Lewis agrees, clearly stating that he understands deities (if they exist) to be parts of worlds:

For Lewis, the part–whole relation applies to type-(i) beings, or the so-called ‘individuals’. However, it does not apply to type-(iii) beings, or the so-called ‘non-individuals’ (e.g. the pure sets):

(b) God and spatio-temporal relations. The God of the theists stands in spatio-temporal relations to things in the world (e.g. by virtue of being omnipresent, creating things in time and space, etc.). Lewis is again in agreement here. Now, for Lewis ‘a world is a maximal mereological sum of spatiotemporally interrelated things’ (Lewis (Reference Lewis1986), 73). As such, one might suspect that modal realism rules out the possibility of the existence of gods and spirits, since such entities are traditionally thought to exist outside of space and time. But Lewis handles this criticism by pointing out that his worlds are compatible with the existence of non-spatio-temporal entities such as gods and spirits, so long as those entities are related to space and time in the appropriate way:Footnote ⁹

But, as we have already seen, Lewis's type-(iii) beings are ones that exist outside space and time altogether. This is why, for instance, the pure sets are said to exist at worlds, rather than in them.Footnote ¹⁰

(c) God and causal efficacy. The God of the theists is causally potent (or, rather, omni-potent). Lewis attributes causal potency to gods as well. He writes: ‘The worlds are not of our own making. It may happen that one part of a world makes other parts, as we do; and as other-worldly gods and demiurges do on a grander scale’ (ibid., 3). However, abstract objects are traditionally thought to be causally inert. Gideon Rosen writes (Reference Rosen and Zalta2012): ‘Indeed, if any characterization of the abstract deserves to be regarded as the standard one, it is this: An object is abstract if and only if it is non-spatial and causally inefficacious.’ This is controversial, of course, but keep in mind that we are exploring the possibility that God is a genuinely necessary being ontologically on par with a pure set (i.e. a set which does not contain any non-set, or set of non-sets, etc., as a member), and it is far less controversial that this type of (pure) abstract entity is causally inert.

In sum, type-(iii) entities do not make suitable candidates for deities. The God of the theists is simply not an individual that is ontologically on a par with the pure sets (or any other entity which might fall into this category). For, both theists and Lewis agree that God (a) is one to whom the part–whole relation applies, (b) stands in spatio-temporal relations, and (c) is causally potent. Meanwhile, any entity classified by the modal realist as a type-(iii) entity will be one that lacks these features. Following Cameron's suggestion to ‘grant God the same status as the pure sets have’ would therefore deliver an impoverished deity who is neither omnipresent nor a creator.

Modal realism, trans-world identity, and genuine concrete necessary being

We began by establishing that, in order to satisfy the theist, the modal realist must supply a God who, if he exists, is ‘genuinely necessary’, i.e. wholly located in (or at) every possible world as numerically one and the same individual thing. Next, we established that a genuinely necessary being who merely exists ‘at’ every world (or, ‘from the standpoint of all worlds’) will not do. For, such a thing cannot be the omnipresent, causally potent creator that the theist requires. What is wanted, therefore, is a God who (if he exists) is wholly present in every world. In short, God must be a type-(i) being (or what Lewis calls a ‘possible individual’). Let us call such a being ‘concrete’, for lack of a better term. Note that applying this term to God seems to be in keeping with the standard usage of that label. For instance, Alvin Plantinga (Reference Plantinga, Tomberlin and van Inwagen1985, 90) writes: ‘God . . . is the only concrete object that exists in every possible world.’Footnote ¹¹

Now, as we have seen, Lewis states that no entity of this sort enjoys trans-world identity, but rather only ever has counterparts in other worlds (recall that type-(i) entities are the ones to which ‘the principle that nothing is in two worlds’ applies). But perhaps there is room within modal realism to reject his claim. As Cameron points out, the modal realist may help herself to trans-world identity rather than counterpart theory for any individual that lacks accidental intrinsic properties;Footnote ¹² and, ‘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’ (Cameron (Reference Cameron2009), 100, emphasis mine). Here, we appear to have within modal realism a viable path towards a God of the sort that is posited by the classical theist. Namely, if all of God's properties are essential rather than accidental (which seems plausible), then the modal realist could grant that God is a genuinely necessary being – and by this she would not mean that God has counterparts in every world, nor that he is a cross-world aggregate of beings (one in every world), but rather that he literally exists in every world, wholly present as numerically one and the same individual.Footnote ¹³

Unfortunately, this suggestion will not do either, for the following reason: whereas an abstract God ontologically on a par with entities such as pure sets was incompatible with classical theism because he lacked certain crucial traits, a concrete God of the sort just described is incompatible with modal realism because he has them. The modal realist simply cannot endorse the existence of a causally potent God who wholly exists in every possible world, for the simple reason that worlds of the modal realist are, by definition, causally isolated. Of his worlds, Lewis writes,

If every world shares numerically one and the same causally potent part in common – and not just a causally potent one, but an omnipotent one – then it would follow that they are not causally isolated. For, any causally potent being is surely causally related to itself. But, then, on the present proposal it would turn out that, for any two possible worlds, u and v, u has a part (namely, God) that is causally related to a part of v (namely, God). Alternatively, we may illustrate this point in a slightly different way: on the proposal being examined, it would be true that God exists at, say, worlds w₂ and w₃, and is wholly present in both worlds as a part of each. But, then, in that case, it would be true that a part of w₂ (namely, God) caused a part of w₃ to exist (namely, the entire physical universe). So, on the present proposal, there would be causal relations across worlds – yet this is exactly what Lewis denies. To reiterate, for Lewis, ‘the worlds are isolated: there is no causation from one to another’ (Lewis (Reference Lewis1986), 78). Lewis requires this causal (and spatio-temporal) isolation between worlds because it is their principle of individuation. That is, on modal realism, for any two possible worlds, u and v, u is numerically distinct from v if and only if there are no causal or spatio-temporal relations between them. It is worth noting that Stephanie Lewis's interpretation of David Lewis is consistent with the one I have presented here. She writes:

In short, the modal realist cannot help herself to the claim that two worlds share a causally potent concrete particular in common.Footnote ¹⁴ For, as we have just seen, Lewis's worlds are individuated by their spatio-temporal and causal isolation from one another – the result being that, if ‘multiple’ worlds did share a causally potent part in common, they would not be distinct worlds at all. David Lewis writes: ‘Worlds are spatiotemporally and causally isolated from one another; else they would be not whole worlds, but parts of a greater world’ (Lewis (Reference Lewis1986), 84).Footnote ¹⁵ The existence of a genuinely necessary, causally potent God would therefore result in the collapse of the entire multitude of possible worlds (or, the ‘pluriverse’) into one enormous world – in which case there would no longer be any non-actual, possible worlds, but only the actual world (which would just be the pluriverse itself). Such a collapse would completely undermine modal realism, as well as the analysis of modal claims that it offers.Footnote ¹⁶ As Lewis himself admits (ibid., 112), ‘If the other worlds would be just parts of actuality, modal realism is kaput.’ In sum, the proposal of this section (that God is a genuinely necessary, causally potent concrete being) fares no better than the proposal from the previous section (that God is a genuinely necessary, causally inert abstract being).

Finally, I should like to point out one further problem which any modal realist version of theism faces: On modal realism, <God creates w₃> would be necessarily true, since there is no world at which it is false. If God is omnipotent, however, then it should follow that he could have chosen not to create one of these worlds (say, w₃). In other words, on classical theism, the modal proposition <God could have failed to create w₃> should come out true. But, it does not.Footnote ¹⁷ So, the modal realist's God is one who lacks the power to have created a different number of worlds than he did in fact create. Thus, even setting aside the host of issues identified in this article, any theist looking to adopt modal realism will require a revisionary account of what it means to be ‘all-powerful’.Footnote ¹⁸