God’s place in the world

Lewisian theism is the view that both traditional theism and Lewis’s modal realism are true. On Lewisian theism, God must exist in worlds in one of the following ways: (1) God can be said to have a counterpart in each world; (2) God can be said to exist in each world in the way that a universal can be said to exist in worlds (if universals exist), i.e. through transworld identity; (3) God can be said to be a scattered individual, with a part of God existing in each world; and, (4) God can be said to exist in each world, through His existing from the standpoint of each world. In the literature, (1)–(4) have been rejected as viable options. I grant that (1) and (3) are not viable. However, I believe that (2) and (4) have been too hastily rejected. Herein, I develop ways to respond to objections to (2) and (4), and conclude that (4) is a viable option for Lewisian theists.


Introduction
According to traditional theism, God exists necessarily. According to the biconditional for necessity, to exist necessarily is to exist in all possible worlds. According to Lewis's (1986) modal realism, worlds are maximal mereological sums of spatiotemporally connected individuals. If we assume the truth of both modal realism and traditional theism, a view I call Lewisian theism, then to say that God exists necessarily is to say that God exists in every modal realist world. 1

Lewisian theism and the chief objection thereto
Before I provide a defence of the consistency of Lewisian theism, I shall briefly elucidate the theory.
Lewisian theism is the conjunction of traditional theism and Lewis's (1986) modal realism. Modal realism's chief ontological postulates are rehearsed by Collier (2019a: 332-333): theory entails polytheism. That is, Cameron argues that God's existence can be rendered necessary by employing the machinery of transworld identity, which, roughly articulated, claims that to say of two individuals, x and y, that they are transworld identical is to say that there exist at least two numerically distinct worlds, w and u, such that in w, x wholly exists, and in u, y wholly exists, and x and y are identical; i.e., a numerically identical individual exists in numerically distinct worlds. Now, the reason why Cameron believes that Lewisian theists can opt for transworld identity to analyse God's necessity is that modal realism provides the theoretical resources for the existence of transworld individuals. Individuals can be considered transworld individuals only if they fail to instantiate accidental intrinsic properties, where an accidental intrinsic property of an individual x is one that is intrinsic, but contingent, to x. Plausibly, God is an accidental intrinsic property-lacking individual, and thus could be said to wholly exist in more than one world. Indeed, transworld identity is invoked by modal realists to represent de re the modal properties of individuals which lack accidental intrinsic properties; God can be said to lack such properties, and so transworld identity can be invoked to represent de re God's necessary existence: one and the same God, therefore, can be said to wholly exist in all worlds. 4 Three counters to Cameron's objection to Sheehy and Davis exist in the literature. The first, raised by Sheehy (2009: 103-4), argues that Cameron's proposal commits Lewisian theists to a revisionary account of the indexical term 'actual'; the second, levied by Collier (2019a: 341), concerns the transitivity of worldmateship; and the third, propounded by Vance (2016: 567-8), and outlined above, argues that God's being a transworld individual entails modal collapse. Now, the two former counters I believe are the most easily dealt with-the third is significantly more challenging to Lewisian theists (indeed, this type of objection, as noted above, is the 'chief' objection to (2) and (4)). Nevertheless, I repudiate all three. Sheehy's (2009: 103-4) counter relies upon the principle that if two individuals, x and y, are part of the same world, then x and y are worldmates. This, Sheehy believes, gives rise to a problem over the indexical term 'actual'. When the term 'actual' is used in a certain world, w, by a certain (non-transworld) individual therein, only w (or w's parts) is (or are) quantified over by that individual-only w (and its parts) is (or are) actual to that individual. However, since God exists in all worlds, when He uses the term 'actual', all worlds are quantified over-all worlds, to God, are actual. However, this is supposedly at odds with modal realism's interpretation of 'actual'; the same quantificational scope should hold for any two worldmates' usage of the term 'actual'. Collier (2019a: 341) assents here and distils the problem: …if God and I agree on a single usage of 'actual', the appropriate quantificational restrictions are forsworn; if I follow God's usage of 'actual', I quantify over too much, and if He follows my usage, He quantifies over too little. Now, apart from merely claiming, as Lewis (1986: 95) and others have (such as Collier (2019a: 341)), that the question of what is actual is not the grandest of questions, Sheehy's counter can be repudiated.
I think Sheehy confuses a distinction: to be actual versus to be partly actual. Here is Lewis (1986: 96, fn61) on the distinction: In Philosophical Papers, volume I, pages 39-40, I distinguished three ways of 'being in a world': (1) being wholly in it, that is, being part of it; (2) being partly in it, that is, having a part that is wholly in it; and (3) existing from the standpoint of it, that is, `belonging to the least restricted domain that is normally -modal metaphysics being deemed abnormal -appropriate in evaluating the truth at that world of quantifications'. If the world in question is actual, that is almost my present distinction between being actual, being partly actual, and being actual by courtesy; the only difference in the terminologies being that I would not now throw all sets into the lower grade.
Given the above, it is not necessarily the case that the quantificational scope of the term 'actual' should be the same for any two worldmates: if we take two worldmates, x and y, where x is wholly in world w and y is partly in w, then what is actual for x and y will differ, since x will be an actual individual and y will be a partly actual individual. The Lewisian theist could say that transworld individuals which wholly exist in worlds they are part of fall into the second category of actuality: they are partly actual, where 'partly' does not entail metaphysical complexity-or, if one objected here, perhaps on terminological-confusion grounds, one could say that transworld individuals of this sort are multiply actual. (If modal realists can allow entities which exist in many worlds through having parts that wholly exist in each world they are part of to be partly actual, then there seems to be good reason to say that modal realism can allow entities which wholly exist in every world they are part of to be wholly actual in each world they are a part of; that is, multiply actual. If the level of actuality generally tracks the level of being in a world, then if an individual is wholly in multiple worlds, we might expect that that individual is wholly actual in multiple worlds-hence my term 'multiply actual'). Moreover, to not afford this type of actuality to the transworld God, who wholly exists in each world He is part of, would mean that we would deny this type of actuality to universals-but surely one would want to say that universals are actual in worlds they are part of.
So, all of this is to say: Firstly, if Sheehy's actuality concern is a problem for the transworld God, then it should be a problem for any transworld individual; and, moreover, one cannot avoid this by declaring that no transworld individual exists (which includes universals), since it should also be a problem for pure sets which are actual by courtesy, and so 'actual', in some sense (perhaps the least restricted sense), in many worlds. But secondly, the problem seems parasitic upon issues over what exists at a world and whether things can exist in multiple worlds; once the ontological questions are dealt with, the indexical questions seem to admit of answers as well: if I am wholly in this world and not transworld existent and so is, say, my brother, then we are both actual in the fullest sense-however, in our world, God is partly-or perhaps wholly, but multiply-actual. And, what is more, given that what exists at a world is not an inflexible matter, since that 1 3 matter depends upon contextual factors' determining of quantificational scope, it seems reasonable to say, as Lewis (1986: 95) does, that "[t]here is no need to decide, once and for all and inflexibly, what is to be called actual"; if there are different ways for different things to be actual-wholly, partly, multiply, or by courtesy-it seems reasonable to say that context determines the quantificational scope of 'actual': sometimes only wholly actual things will be quantified over, sometimes all things said to be actual in some way or another will be quantified over. So, Sheehy's counter either simply serves to highlight a potential problem faced by modal realists more generally or it can be repudiated by noting the different levels of actuality available to members of different ontological categories. Now onto Collier's counter: the problem of worldmateship. Lewis (1986: 71) claims that: "things are worldmates iff they are spatiotemporally related". Collier (2019a: 341) notes that: "world-mateship is transitive: if x is a world-mate of y, and y is a world-mate of z, then x is a world-mate of z-this is because worldmateship is grounded in the spatiotemporal relation, which is, itself, transitive". So, Collier (2019a: 341) argues: God, by existing in all worlds, is my @-world-mate, but is also otherworldly-Bill's w-world-mate. Now, if I am God's world-mate, and God is Bill's world-mate, then, by transitivity of world-mateship, I am also Bill's world-mate, despite my being wholly in @ and his being wholly in w. The problem is thus: since world-mateship is grounded in the spatiotemporal relation, and since I am, through God's existing in both @ and w, Bill's world-mate, I am spatiotemporally related to otherworldly-Bill. But, since worlds are spatiotemporally isolated individuals, and since Bill's w and my @ are, by God's existing in both, spatiotemporally connected, w and @ are one and the same world. …total modal collapse ensues.
Collier's objection can be distilled in the following way: Because Collier and Bill are worldmates through having a worldmate in common, i.e. God, (since if two things have a worldmate in common, they are worldmates, given the transitivity of worldmateship), Collier and Bill are spatiotemporally connected (given Lewis's biconditional, "things are worldmates iff they are spatiotemporally related"). But, Lewisian theists can reject Collier's objection by denying Lewis's biconditional. There is non-ad hoc reason to do this: Lewisian theists must drop the necessity of the spatiotemporal relation for worldmateship if they are to say that individuals which exist from the standpoint of worlds and individuals, like universals (if they exist), which wholly exist in multiple worlds, can qualify for worldmateship-i.e. if Lewisian theists wish to say that I am a worldmate of a pure set, or a worldmate of a certain universal, they will need to reject the biconditional. Plausibly, if a universal exists in my world, then I am a worldmate of that universal-plausibly, the same is true of pure sets. This gives Lewisian theists reason to reject the biconditional, at least in its general form. But, since the transitivity of worldmateship is grounded in the transitivity of the spatiotemporal relation, once the biconditional is rejected, the transitivity of worldmateship will not necessarily be grounded in the spatiotemporal relation. Perhaps the transitivity of worldmateship will only hold for individuals who exist in a world either as International Journal for Philosophy of Religion (2021) 89:43-65 a part or from its standpoint. Here we can distinguish between different types of worldmateship.
Accordingly, if grades of actuality can be established, I see no reason why worldmateship should not similarly admit of grades. Specifically, Lewisian theists can distinguish between something's being wholly, partly, multiply, or by courtesy a worldmate of something else. Here are the grades' respective biconditionals. Individuals x and y are wholly/wholly worldmates at world w iff the whole of x and the whole of y are spatiotemporally related at w, and neither x nor y exist in worlds other than w in any way (i.e. through being partly or wholly existent in other worlds or existent from the standpoint of other worlds). x and y are part/part worldmates at w iff a part of x (wholly existent at w) and a part of y (wholly existent at w) are spatiotemporally related at w, and both x and y partly exist in worlds other than w. x and y are multiply/ multiply worldmates at w iff the whole of x and the whole of y are spatiotemporally related at w, and both x and y wholly exist in worlds other than w. x and y are courtesy/courtesy worldmates at w iff both x and y exist from the standpoint of w. Lewisian theists can also accept the following heterogeneous worldmate relations. x and y are wholly/partly worldmates at w iff the whole of x and part of y (wholly existent at w) are spatiotemporally related at w, where x does not exist in worlds other than w in any way but y partly exists in other worlds. x and y are wholly/multiply worldmates at w iff the whole of x and the whole of y are spatiotemporally related at w and x does not exist in any world other than w but y wholly exists in other worlds. x and y are wholly/courtesy worldmates at w iff the whole of x is spatiotemporally related to w and y exists from w's standpoint. The reader can now probably see how the other heterogeneous relations will work (e.g. multiply/courtesy, multiply/partly, etc.).
With these grades established, Lewisian theists can highlight that the Bill/God worldmateship and the Collier/God worldmateship are both instances of the wholly/ multiply worldmate relation. So, whilst Bill and God are wholly/multiply worldmates in @ and Collier and God are wholly/multiply worldmates in w, Collier and Bill will not be wholly/multiple worldmates. Thus, the wholly/multiple worldmate relation will not be applicable to Bill and Collier.
So, how can Collier and Bill be worldmates? They must be wholly/wholly worldmates, which means the whole of both Collier and Bill must be spatiotemporally connected to the same world; but how could this be? Perhaps, because God is spatiotemporally connected to all worlds, through His being causally connected to all worlds, which are spacetimes, and since the spatiotemporal relation is transitive, God's being spatiotemporally connected to Collier's world and spatiotemporally connected to Bill's world renders Bill's and Collier's worlds the same world, and thus Bill and Collier are spatiotemporally connected to each other? If this is so, we get to Vance's objection-not Collier's. If Lewisian theists can argue that God's being spatiotemporally connected to all worlds, through His being causally connected to worlds where worlds are isolated spacetimes, does not entail modal collapse, then they can deny that Bill and Collier are wholly/wholly worldmates. What this response to Collier demonstrates is that Bill's having a certain worldmate relation to God and Collier's having a certain worldmate relation to God does not entail that Bill and Collier have that same or indeed have any worldmate relation to each other.
So, now onto Vance's counter. As mentioned above, Vance (2016: 567-568) raises the following argument: If God wholly exists in worlds w and u, and created and sustains w and u, and creating and sustaining are causal relations, then w and u are causally connected, and thereby w and u are numerically one and the same world. Thus, Lewisian theists are committed to modal collapse, and thus inconsistency, if they maintain that God is causally active in all worlds, and one and the same God wholly exists in all worlds through His being a transworld individual.
This objection is rather formidable. However, I believe that Lewisian theists possess the resources to provide a response. Let us, then, explore the ways to defuse the objection.
The first attempt at a repudiation of the objection runs as follows. The phrase 'w and u are causally connected' seems ambiguous. Having a grasp of its different interpretations might provide a roadmap of the various responses (un-)available to Lewisian theists. If, for instance, 'w and u are causally connected' means that w and u are causally connected by virtue of their respective existences' being owed to the causal activity of one and same individual, then it will be true that w and u are causally connected, since both worlds will have been created by God. If, however, 'w and u are causally connected' means that w and u are members of one and the same chain of causes, then it need not be the case that w and u are causally connected in any way other than by both being created by one and the same individual, since w's and u's respective causal histories will originate in separate causal acts of God. Thus, the options are: (a) what causally connects w and u is God Himself, and (b) what causally connects w and u is God's act of creation. (a) is necessarily true, since on Lewisian theism, God is the creator and sustainer of all existence, which includes all worlds. 5 (b), however, is not necessarily true, since God's creation of each world will correspond to a distinct causal act. 6 Lewisian theists, then, can insist that what matters for modal collapse-inducing causal connectedness of worlds is that at least two worlds belong to an identical causal chain-they can insist upon (b). Now, whilst it is true that Lewisian theists are committed to (a)'s being necessarily true, this itself does not commit Lewisian theists to adopting (b) as the correct interpretation of 'w and u are causally connected'. Certainly, (b) is imbued with some ambiguity; for instance, it might be said that (b1) what 'w and u are causally connected' means is that they belong to the same causal chain, even though they may belong to separate branches of that causal chain; or, it might be said that (b2) what 'w and u are causally connected' means is that they belong to the same branch of a causal chain. Perhaps what matters for causal connectedness is that w and u belong to the same branch of a causal chain; perhaps what matters for causal connectedness is that w and u belong to the same causal chain, even though they may belong to separate branches thereof. Assuredly, there is theistic reason for distinguishing between (b1) and (b2): if divine simplicity commits theists to saying that God's creating and sustaining of numerically distinct worlds is one act, then it will not be possible that there be a separate causal act for each created world-if that is true, then each world will belong to the same causal chain, and so according to (b1), all worlds will be causally connected. So, (b2) might be insisted upon by Lewisian theists, if (b) is to be insisted upon at all. However, it is clear that Lewis (1986: 206-209) rules out the possibility of branch worlds. Thus, if branch worlds are not admitted into Lewisian theism, and Lewisian theism requires that there be branching, since divine simplicity requires Lewisian theists to say that it is not possible for God to have separate causal acts and so worlds causally branch off from God's original causal act, then Lewisian theism will be inconsistent. So, by insisting upon (b2) and being committed to divine simplicity's entailment of God's having one causal act, branch worlds are admitted into Lewisian theism; but this is something that is theoretically prohibited. Now, providing a comprehensive appraisal of divine simplicity-despite being helpful for Lewisian theists-will demonstrably lead this paper off-piste. Let us thence assume either that the doctrine of divine simplicity does not commit theists to saying that it is not possible for God to have more than one causal act, or that God's one causal act does not commit Lewisian theists to branch worlds, since perhaps one act might not entail that only one causal chain is possible. 7 Even with this assumption, Lewisian theists still incur a problem, however. Under (b1), it seems that w and u will be connected for the following reason. God in w sustains w (and the sustaining relation is a causal relation). God in u sustains u. But, if God is wholly in both w and u, then there will be a part of w sustaining u (and a part of u sustaining w), and sustaining is causal-so, there will be a part of w causing something in u (and a part of u causing something in w). Thus, w and u will be numerically identical. And so, it will not be possible that two worlds belong to separate branches of the same causal chain; it could not be the case that one world is not sustained by God (for any part of its existence), and so all worlds will belong to the same causal branch. This, then, would also entail that w and u are causally connected under (b2). Thus, this attempt at a repudiation of the objection fails.
The second way to defuse the objection is to give up on the causal isolation of worlds, thus modifying their individuation conditions. Perhaps worlds need only be spatiotemporally isolated but not causally. There is independent motivation for this response: Lewis's preferred account of causation will not work for Lewisian theism as a truly general account of causation; indeed, Lewis (1986: 3) contends that "nothing outside a world ever makes a world". To see why, here is Lewis (1986: 78): When we have causation within a world, what happens is roughly as follows. … We have a world W where event C causes event E. Both these events occur at W, and they are distinct events, and it is the case at W that if C had not occurred, E would not have occurred either. The counterfactual means that at the closest worlds to W at which C does not occur, E does not occur either.
Let us now apply this account to God's creation of the actual world: A divine creation event Ec occurs, where Ec is the creating of the actual world, and where Ec causes Ew to occur, where Ew is my writing of this sentence. Thus, we have the counterfactual: were Ec not to occur, Ew would not occur. However, there is a problem here. Events are identified with sets of spacetime regions; so, if there are no spacetime regions, there are no events. But, if there are no events, then there are no causal events. But, if there are no causal events, then there is no divine act of world creation. So, by hypothetical syllogism, if there are no spacetime regions, then there is no divine act of world creation. Thus, since Ec is not a set of spacetime regions (since there exist no actual spacetime regions 'at the point of' the actual world's creation), Ec is not an event, and since causal acts are identified with events, there is no divine act of world creation. 8 Moreover, the account cannot merely be adapted such that it only applies to possible causation-God's creating of the world, and the pluriverse, being deemed, perhaps, amodal. Here is why. Lewis (1986: 78) applies his account to transworld causation: Try to adapt this to a case of trans-world causation, in which the events of one world supposedly influence those of another. Event C occurs at world Wc , event E occurs at world EE, they are distinct events, and if C had not occurred, E would not have occurred either. This counterfactual is supposed to holdwhere? It means that at the closest worlds to -where? -at which C does not occur, E does not occur -where? -either.
So, the causal isolation of worlds, and their lack of divine creation, falls out of Lewis's account of causation. Given this, Lewisian theists may contend that since God created worlds, and is causally active in all worlds as a transworld individual, they are committed to rejecting the counterfactual account of causation. The counterfactual account of causation is a reason why Lewis includes causal isolation as an individuation condition for worlds. So, once the counterfactual account of causation is rejected, Lewisian theists may contend that causal isolation is not an individuation condition for worlds.
This response, however, will not do. Yes, Lewis's counterfactual account of causation will have to be rejected by Lewisian theists, and certainly Lewis's account of events makes God's creation of the pluriverse a non-event (which, we may think, does not track felicitous usage of the term), 9 but it is clear in Lewis (1986) that the causal isolation of worlds is something Lewis would insist upon even in the absence of his counterfactual account of causation. Here is Lewis (1986: 78): If need be, I would put this causal isolation alongside spatiotemporal isolation as a principle of demarcation for worlds.
So, even if there is some independent motivation to reject the causal isolation of worlds (e.g. that the counterfactual account of causation must be rejected, and that account entails the causal isolations of worlds), Lewis clearly sees that causal isolation is necessary for world-hood.
However, a response is forthcoming: Lewisian theists may contend that divine causation, that involves creating and sustaining worlds, is different in kind to nondivine causation, so there is no non-divine, standard, causal connectedness between worlds, and perhaps that is what matters for causal isolation. It is important to note that this response is not merely the claim that God be afforded a derogation from the principle of causal isolation (since that would seem ad hoc), but, rather, that God's causal activity is different in kind from standard causal activity. This 'standard' causation is, Lewisian theists might argue, what matters for worlds' being causally isolated. Now, there are two problems here, both of which, I believe, can be avoided. The first is Christological and the second is Lewisian. Concerning the former, one might highlight that Christ was on Earth, and upon Earth did some causal stuff. 10 Some of this causal stuff would have involved, say, His doing some carpentry, or His scratching His head. This causal stuff seems to be standard causal stuff, even if performed by Christ.
A response here might be: just because these acts appear standard causal acts, since, for instance, they seem everyday acts, does not entail that they are standard causal acts. Moreover, if different kinds of causal act are to be countenanced, then it is plausible that the kind of causal act that an individual can engage in is determined by the nature of that individual: here Christ is God, and so Lewisian theists may claim that the only kind of causal act that Christ can engage in is divine, and divine acts, it is contended, are different in kind to non-divine acts. 11 And, to claim that all Christ's causal acts were different in kind to standard causal acts, even though for the most part they appeared the same, provides a neater causal story than suggesting that, whilst perhaps His miracles were one kind of causal act, His, say, knocking up 10 Now, of course, it is possible that some Lewisian theists are not (non-Unitarian) Christians. 11 It might also be argued that the modal properties of Christ Incarnate should receive a counterpart theoretic analysis, but the modal properties of Christ, qua His divine nature, should receive a transworld identity analysis. If that is so, then it is possible that Christ Incarnate engages in standard causal acts without there being causal connectedness of worlds, since the actual world Christ Incarnate and His otherworldly Incarnate counterparts will be world-bound (where those counterparts are identical to Christ qua His divinity, but different but sufficiently similar to Christ Incarnate). Christ qua His divinity will be transworld causal, since the causal activity He engages in is divine in kind; and, Christ Incarnate's standard causal acts will be world-bound. So, even if Christ Incarnate engages exclusively in standard causal acts, there will not be a causal connectedness of worlds. Of course, such a proposal will touch upon questions concerning Christ's hypostatic union-i.e. His dual nature; His being both fully God and fully Man. Collier (2019b) and Paul (2019) mention this suggestion. of some wooden structure was a different kind of causal act; only one kind of causal act was performed by Christ. 12 Now, before I examine why we might think that God's creating and sustaining of worlds is different in kind from standard causal acts, here is the Lewisian problem. Lewis (1986: 75) claims the following: …each world is interrelated (and is maximal with respect to such interrelation) by a system of relations which, if they are not the spatiotemporal relations rightly so called, are at any rate analogous to them.
It then seems reasonable that the following can be said concerning causation: each world is interrelated by a system of relations which, if they are not causal relations rightly so called, are at any rate analogous to them. If divine causation is analogous to non-divine causation, then it would cohere with Lewis to claim that the exact type of causation at play does not matter for the causal isolation of worlds.
Saying something here about why God's causal acts of creating and sustaining worlds seem different in kind from standard causal acts will, I think, help us see why divine causation might not be analogous to standard causation. Certainly, bringing concreta into existence ex nihilo and sustaining those concreta in existence seem very different acts from standard creating and sustaining acts. Yes, we can think of 'bringing something into existence' by combining certain things that already existbut that is not creation ex nihilo. Likewise, with sustaining: we can think of holding a breakable vase in the air, and so our causal activity holds that vase in existence in some sense. But this is very different to God's holding all existence, each and every subatomic particle, in existence; if God stops sustaining a world, all of it will cease to exist in an unmediated fashion-if I drop a vase, however, all of its fundamental constituents will continue to exist.
So, it seems plausible to say that the creation of worlds ex nihilo and the sustaining thereof is something disanalogous to our simply patching together component parts to create objects and our sustaining of certain things, where those actions are mediated and dependent upon, for instance, the laws of nature-God's creation of worlds is ex nihilo and His sustaining of existence does not depend upon anything outside Himself and is unmediated.
Certainly, it is plausible that one may object here, and reject the claim of there being a disanalogy between divine and non-divine, standard causation. In this case, we fortunately have another way to respond to Vance's objection.
Almeida (2017a: 11, fn.31)) maintains the following: …it should be noted that Lewis allows that some objects exist in more than one world and have causal effects in more than one world. …Lots of things are in more than one world, and many of those things enter into causal rela- tions. Universals can enter into causal relations, since something's being red or yellow, for instance, can cause someone to notice it. But that same universal enters into causal relations in many possible worlds.
And so, Almeida notes, the principle of the causal isolation of worlds does not entail that no individual can causally relate to numerically distinct worlds. If transworld causation is permitted for members of a sub-category of transworld individual, i.e. universals (assuming they exist), then it might be said to be true of a member of a different subcategory of transworld individual, i.e. God. However, there is a good reason why God cannot be taken to be like a universal inasmuch as He is wholly a part of every world and causal therein. The reason is that by maintaining the above, Lewisian theists commit themselves either to denuding God of His particularity or to an ad hoc prevention of other accidental intrinsic property-lacking particulars from being transworld causally active individuals.
Here is my argument. God is a simple particular. Concerning His simplicity: He is not composed of proper parts; He does not instantiate an array of properties (or universals, if such things there be); He does not admit of metaphysical distinctions. On His particularity: He is not and cannot be instantiated by particulars; there is no particular which instantiates God-He is not a universal or a property. The distinction between particulars and universals is often given by way of supplying paradigmatic qualitative differences. Universals are said to be possibly wholly multiplylocated, but particulars are not. But, maintaining that such a distinction is not merely paradigmatic but fundamental would either beg the question against God's existing in multiple worlds or would render God a universal. Moreover, some philosophers hold that some non-divine particulars are multiply-located-indeed, for those who believe in the possibility of time travel, some particulars will be multiply-located, and some predicate multiple-location of sub-atomic particles. Not even the observation that particulars instantiate properties and bear relations to other individuals is sufficient for the distinction, since this may violate divine simplicity, requiring that there be a distinction between God and His attributes, but also since universals themselves instantiate properties and relations. 13 Instead, what distinguishes particulars from universals is the attribution of non-instantiability to the former; particulars cannot be instantiated. 14 So, God is a particular. 15 If God is a particular and is theoretically permitted by Lewisian theism to wholly exist in all worlds through transworld identity by His not having accidental intrinsic properties, then we should think that this should hold for non-divine accidental 13 Here I distinguish between 'particular' and 'individual'-I take 'individual' to include sets, universals (if they exist) and particulars. 14 Sometimes particulars are said to exist by or in themselves. I find this confusing. If this means that their existence is not dependent upon anything else, that will not do-for one thing, on traditional theism, all is dependent upon God. If this is cast in contradistinction to universals' existing within things, then again this will not clearly do-for one thing, worlds are said to exist within logical space, and for another, composite particulars have distinct particulars existing within them. I will thereby try to steer clear of such Delphic phrases. 15 For an introduction to particulars, see Bigelow (1998)-indeed, a lot of the themes in this paragraph are found in his work.

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intrinsic property-lacking particulars as well. Now, take sub-atomic particles: plausibly, they are particulars which lack accidental intrinsic properties. If we allow that such particulars wholly exist in a transworld-fashion, then we arrive at, what Lewis (1986: 205-6, fn6) denominates, the problem of accidental external relations-a parallel problem to the problem of accidental intrinsics, which affects transworld individuals that instantiate accidental intrinsic properties. Here is Lewis (1986: 205-6, fn6): Suppose we have a pair of two of these simple particulars A and B, both of which are common parts of various worlds. A and B are a certain distance apart. Their distance, it seems, is a relation of A and B and nothing else -it is not really a three-place relation of A, B, and this or that world. That means that A and B are precisely the same distance apart in all the worlds they are both part of. That means (assuming that we explain representation de re in terms of trans-world identity when we can) that it is impossible that A and B should both have existed and been a different distance apart. That seems wrong: it is hard to suppose that the distance is essential to the pair, equally hard to suppose that distance is not the plain two-place relation that it seems to be. So trans-world identity, even for simple particulars without accidental intrinsic properties, is prima facie trouble. An advocate of it will have some explaining to do, both as to how he gets around the problem of accidental external relations, and also as to what motivates it when it cannot provide a fully general account of representation de re. Now, Lewisian theists can motivate the claim that at least some simple particulars are transworld individuals, since God is a simple particular and all His intrinsic properties are essential. However, they are still left with the problem of accidental external relations. Moreover, on the option of saying that divine causation is disanalogous to standard causation, the above problem will also arise: if God is an accidental intrinsic property-lacking particular and is causally efficacious in multiple worlds, then the same problem rears its head. Thus, Lewisian theists sympathetic to this option will not only face problems concerning the persuasiveness of the disanology between divine and non-divine creation, but will also face the problem of accidental external relations.
Certainly, one way to circumvent the problem is to claim that God is sui generis insofar as only He is a transworld simple particular. Moreover, a defence is forthcoming against the following inevitable response: 'but the other simple particulars also lack accidental intrinsic properties, so why ought they not be transworld individuals as well, other than simply for ad hoc reasons?' It is clear that simply because an individual-particular or universal or set-does not have accidental intrinsic properties does not mean that that individual is a transworld individual, since if that were the case, pure sets would be transworld individuals-but they are not; Lewis (1986: 96, fn61;1983, 39-40) maintains that they exist from the standpoint of worlds. So, clearly, this condition is not sufficient for transworldhood. Lewisian theists cannot insist that sufficiency would be achieved by an individual existing wholly in the world (and satisfying the first condition), since sub-atomic particles do as well-it may be necessary, but, in addition to the first condition, not sufficient.
International Journal for Philosophy of Religion (2021) 89:43-65 Perhaps, in addition to the first condition (and perhaps the second), sufficiency would be achieved by an individual's being outside, but related to, spacetime, in the way that God is outside but related to spacetime? But why ought the satisfaction of this condition (along with the first and perhaps the second) mean that an individual is transworld existent? I do not see why-and at any rate, I suspect that including this condition would be ad hoc. And, what is more, Lewisian theists will have a hard time explaining why sub-atomic particles can be multiply-located in the actual world (if they believe they can be), but are not transworld located. 16 Another response is to insist that only God lacks accidental intrinsic properties. This, I do not think, will get very far: indeed, as Lewis (1986: 205, fn6) Horgan andPotrč (2012, Horgan andPotrč 2008) variety, is to be attributed to God-perhaps attributed to God is priority monism, of perhaps Schaffer's (2010) variety. 18 The exact type of substance theory on offer I do not think matters here: what matters here is whether substances can be instantiated-if they cannot be, which seems true, then, analytically, they turn out to be particulars. 19 So, the most plausible ways for Lewisian theists to circumvent Lewis's problem fail. Luckily, for Lewisian theists, there is another option: endorse (4) instead.

Arguments contra (4), and my responses thereto
Let us now examine (4): God can be said to exist in each world, through His existing from the standpoint of each world. But, what does it mean to exist from the standpoint of a world? Lewis (1983: 39-40) explains: by virtue of being included as members of the least restricted domain that is generally regarded as being suitable for evaluating truth values of quantifications at worlds, things exist from the standpoint of worlds. The chief example of such beings is abstract pure sets. Although not 'in the world' in the same way that, say, puddles wholly exist in the world, or in the way that, say, some cross-world individual might partly exist in one world and partly exist in another, where the whole of the being is comprised of all its parts, where those parts wholly exist in their respective worlds (if such a being exists in Lewisian theism), a pure set exists 'in the world' through existing from its standpoint. 20 Now, Almeida (2017a: 6-7; 2017b: 4) and Cameron (2009: 97) suggest that God can be said to exist in worlds in the way that pure sets exist in worlds: i.e. from their standpoints. Almeida (2017b: 4) notes that pure sets, with which numbers are identified, are not spatiotemporal entities and exist from the standpoint of worlds; thus, " [t]here is no reason why other beings that are not spatiotemporally located might also exist from the standpoint of all possible worlds". God is one such being, and so it seems reasonable to contend that God exists from the standpoint of worlds.
Here, Sheehy (2009), Collier (2019a and Vance (2016) object. Vance's (2016: 565) objection that this mechanism of accounting for God's necessity in Lewisian theism entails that God's omnipresence is forsworn is countered by Collier (2019a: 343). Collier (2019a: 343-344) also counters one aspect of Sheehy's (2009: 103) objection: such a mechanism renders God abstract and so Lewisian theism is committed to violating its ontological parsimony, which is generated by its only containing sets and concreta-now Lewisian theism is committed to positing within its ontological inventory of primitives one additional entity type, an abstract God, and given theists' antecedent commitment thereto, the motivation for its being posited seems ad hoc when compared with the motivation for positing sets and concreta. Collier argues that such motivation is not ad hoc. And, moreover, Collier (2019a: 346) counters Vance's (2016: 565-566) objection that God's being abstract precludes Him from being causal. However, where all the above detractors agree is that such a mechanism entails God's abstractness. Indeed, Sheehy (2009: 103), Vance (2016: 565-6) and Collier (2019a: 345-346), all clearly think that God is rendered abstract.
International Journal for Philosophy of Religion (2021) 89:43-65 Abstractness, I believe, need not be predicated of God under (4). That is, I agree with Almeida's (2017a: 6) view that, under this mechanism, "God is no doubt a concrete individual-unlike properties and propositions, which are reducible to sets". 21 However, since Almeida does not give much of an argument for this view, here is one. Now, it is true that on modal realism, all that exists from the standpoint of worlds is pure sets. However, existing from the standpoint of worlds is neither necessary nor sufficient for something's being abstract. On the necessity claim, Lewisian theists can point to Lewis (1986: 83) who contends that impure sets exist where their concrete members exist-i.e. (generally) wholly within worlds, and so within spacetime-but are still paradigmatic abstract entities. So, existing 'outside' worlds does not seem to be a necessary condition for something's being abstract. 22 On the sufficiency claim, traditional theists of any modal theoretic persuasion will reject the contention that something's existing 'outside' spacetime entails that that something is abstract. Since, on traditional theism, God is taken as being concrete and the creator of spacetime, to hold the contention that something's existing 'outside' spacetime entails that that something is abstract is to hold that traditional theism is inconsistent from the get go. However, I take it that the current proposal's detractors do not wish to claim that traditional theism is inconsistent in this way-if it were, they would have a knock-down objection to Lewisian theism, whatever the mechanism to render God necessary therein. Thus, we can circumvent objections concerning God's being rendered abstract under the proposal; existing 'outside' worlds is neither necessary nor sufficient for something to be abstract.
Let us now examine a more serious objection to the proposal: the modal collapse objection. Collier (2019a: 346), adopting Vance's (2016: 567-8) objection against God as a transworld individual, contends that the present proposal entails modal collapse: If God exists in worlds w and u, through existing from their standpoints, and created and sustains w and u, and creating and sustaining are causal relations, then w and u are causally connected, and thereby w and u are numerically one and the same world. Thus, Lewisian theists are committed to modal collapse, and thus inconsistency, if they maintain that God is causally active in all worlds, and one and the same God wholly exists in all worlds through His existing from their standpoints. Now, the first way around this objection is to argue, like in the above section on (2), that divine causation is disanalogous to non-divine causation, and the latter is what counts for causal connectedness. However, even though I believe this view to be somewhat promising, I shall eschew spelling it out again. If an argument against the claim of disanalogy is in the offing for (2), it should be applicable to (4) as well.
The second way focuses on the notion of causal isolation. Lewis (1986) contends that something in one world cannot cause something in another. However, it is not entirely clear that Lewisian theists are committed to the view that beings that exist from the standpoint of worlds cannot be causally active in other worlds. Indeed, if we take something in a world to mean a world-part particular, then Lewisian theists sympathetic to the standpoint view can avoid the modal collapse objection. On this way, Lewisian theists can contend that all that matters for causal isolation in modal realism is causal isolation amongst world-part particulars. What is proscribed on modal realism, Lewisian theists may argue, is that some world-part particular causes something to happen to an other-worldly world-part particular. Since God exists from the standpoint of worlds, this will not be the case for God. Now there are two things to be said in support of this response. The first concerns ambiguity from Lewis. It is unclear from Lewis (1986) what he thinks about the causal isolation of worlds concerning beings which exist from the standpoint of worlds. Certainly, Lewis leaves open the option of positing transworld causal universals-thus, it does not seem unreasonable to think that beings which exist from the standpoint of worlds may also enter into causal relationships across worlds, if positing such beings is independently motivated. What is clear from Lewis (1986) is that particulars which wholly or partly exist in worlds cannot be transworld causal (since, if they were, then: if they had accidental intrinsic properties, then they would be world-bound, and if they only had essential intrinsic properties, then they would face the problem of accidental external relations). But, God's existence in worlds, under (4), is not of either of those two kinds, and His existence is also independently motivated. And secondly, it is not clear that Lewisian theists are committed to saying that God is even transworld causal under (4). Here is Almeida (2017a: 11, fn31), for example: I take the restriction [causal isolation] to state that there is no inter-world causation. No events in world w have causal effects in world w'. If so, then God's causal action in w does not violate the restriction. It has no effects in w'.
Although Almeida does not provide a defence of the above, I believe one is forthcoming. For Lewis, events are sets of spacetime regions. Since God is not a part of any spacetime region, His causal activity in one spacetime region will not affect a region of spacetime in another world. Now, like I mentioned earlier, Lewisian theists must reject Lewis's event theory, but what the above might demonstrate is that Lewis conceived of causal connectedness of worlds as arising from regions of spacetime affecting other-worldly regions of spacetime-under (4), that will not happen. 23 There is a worry for the above. We have simply assumed that God is causally efficacious from the standpoint of worlds. However, here is a question from Almeida (2017a: 11, fn31): "[d]oes causal isolation entail that nothing that is not in a world can be causally efficacious?". Within Almeida (2017a: 11, fn31), there is a hint at an answer: Paradigmatic among those things that exist from the standpoint of worlds are sets. But it is possible that sets enter into causal relations. For Lewis, events are sets, and certainly, events enter into causal relations. This, response, however, is not a good one. On Lewisian theism, impure sets exist in worlds, and not from their standpoints: indeed, "a set of located things does seem to have a location, though perhaps a divided location: it is where its members are" (Lewis 1986: 83). However, the seeds of a better response are suggested in Almeida's (2017a: 11, fn31) quoting of Lewis: Lewis (1986: 83) asks "[i]s it true that sets or universals cannot enter into causal interaction?", and then proceeds to suggest that impure sets enter into causal interaction-we are also aware that universals are causally efficacious. Thus, worldly particulars, impure sets and universals can all enter into causal relations. I therefore see no reason why at least some beings which exist from the standpoint of worlds cannot; it seems plausible to think that Lewis does not speak of such an option simply because pure sets are the only beings which exist from the standpoint of worlds within his modal realist framework-once God, a particular, rubs shoulders with pure sets (in the respect that He exists from the standpoint of worlds), I see no reason why Lewisians would deny the ability to engage in causal interaction to God simply because God exists from the standpoint of worlds.
This, however, leads to a further challenge for the proposal: viz., how can something be causally connected to a world and exist only from its standpoint? If something's being causally connected to worlds entails that that thing is a world-part, then my response above fails: nothing can be causal and exist from the standpoint of worlds, since something's being causal renders that something a world-part. 24 We can also present the problem differently: God will be causally connected to spacetime, and will be related thereto by virtue of His being causally related thereto. And, plausibly, beings that are related to spacetime are such that they exist 'in' worlds, in the sense of being partly or wholly 'in' worlds. 25 Now, a response here, I believe, is forthcoming, and goes as follows. Perhaps what matters is that to exist 'in' worlds (i.e. to wholly or partly exist therein), something must be spatiotemporally located therein. Indeed, plausibly, what makes Lewis think that universals and impure sets are 'in' worlds is that they are located where their concrete members are located. It thence seems reasonable to think that if something is not located within spacetime, it is not 'in' a world-even if it is related thereto. Universals, world-bound particulars and impure sets all have spatiotemporal location, and thus seem to be 'in' worlds; if something does not have spatiotemporal 24 It (epistemically) could be the case, however, that something is causal and exists from the standpoint of worlds: we could imagine that God caused the pure sets to exist, but not worlds. In this case, God would not be causally connected to worlds, and so God would not be a world-part (if something's being causally connected to worlds entails that that something is a world-part), but He would be causally efficacious. 25 I use inverted commas for 'in' here to indicate that beings which exist in worlds do so by being wholly or partly a part of worlds-beings which exist in worlds (without an italicised 'in') do so by being wholly or partly a part of worlds or by existing from their standpoints. See footnote 20 above. 1 3 location, then it seems plausible to say that it is not 'in' a world. But how can something be merely related to spacetime but not located therein, and so not 'in' a world?
Firstly, within the discourse on God's omnipresence, there is a lively debate between those who think that God is fundamentally-omnipresent in the world in the sense that my laptop is fundamentally-present upon my desk and those who think that God is derivatively-omnipresent in the world in the sense that He bears, say, causal and epistemic relations thereto. On fundamental-omnipresence, it seems plausible to ascribe a location to God (i.e. a fundamental-location); on derivativeomnipresence, it does not-or at least if one were to ascribe a location to God, it would only be an ascription of a derivative-location-but it still seems reasonable to ascribe God spatiotemporal relatedness. 26 It seems that Lewisian theists, sympathetic to (4), can opt for the derivative-omnipresence model. Perhaps, in fact, what distinguishes (2) from (4) is the notion of fundamental-locatedness: since God's essential intrinsic properties do not change from world to world, whether we conceive of God according to (2) or (4), we need an additional feature to distinguish (2) from (4); plausibly, this feature is spatiotemporal locatedness. If this feature is spatiotemporal locatedness, then this feature will be crucial in deciding, in some cases, whether something exists in worlds through existing from the standpoint of worlds or exists in worlds through transworld identity. 27 If fundamental-locatedness is necessarily predicated of God within the transworld model, then Lewisian theists will have to either provide a story of how an atemporal God can be fundamentallylocated in the world or rule out the transworld model altogether. Lewisian theists may, then, have further reason to avoid the transworld model: providing an account of God's fundamental-locatedness, but denying Him temporality (or the related notion of mutability) will be a tall order: if that were to fail, then Lewisian theists would have to reject the transworld model. They would have to reject it, moreover, even if divine causation is disanalogous to standard causation.
But, the supporter of (2) may claim that he need not necessarily predicate fundamental-omnipresence of God. Lewis (1986: 83) speaks of impure sets and universals' being located in a "special way"-indeed, universals are "wholly present" where their particulars (in a non-special way) are located. Accordingly, there seems nothing in here to rule out the notion that the transworld God is located likewise in a "special way", but His way concerns derivative-location; He is wholly present in spacetime, but still only derivatively-located. Perhaps universals are only derivatively-located as well.
The problem here is that the supporter of (2) will still owe the supporter of (4) a reason why the transworld model should be used for God and not the standpoint of worlds model. Since God's essential intrinsic properties should not change whether we employ (2) or (4), we will need an extra condition to distinguish between the two models. The supporter of (4) can provide such a condition: what distinguishes (2) from (4) is the notion of fundamental-locatedness. I cannot think of a more plausible condition than this one. And so, in the absence of a theistically unproblematic replacement for the fundamental-locatedness-condition to distinguish between (2) and (4), I think Lewisian theists continue to face the above problem: if fundamental-locatedness is necessarily predicated of God under the transworld model, then Lewisian theists will have to either provide a story of how an atemporal God can be fundamentally-located in the world or rule out the transworld model altogether.
Here, then, is the second reason why something can be spatiotemporally related to worlds but not thereby 'in' worlds. We can imagine that impure sets do not exist 'in' worlds, by not being located where their members are located, but are still spatiotemporally related to worlds, through their depending upon their spatiotemporally located, worldly members. If this is plausible (and indeed it seems like, firstly, a viable option, and, secondly, a common pre-theoretical understanding of 'where' impure sets exist), then it seems plausible that God can fail to be 'in' worlds, but can be spatiotemporally related thereto through His being their creator and sustainer.
Thus, given the two points above, if location is what matters for something's being 'in' a world, as seems to be the case, then a causal God can still exist from the standpoint of worlds. Derivative-omnipresence, whilst it rules out fundamental-location, does not rule out God's being spatiotemporally and causally related to worlds; and, impure sets, if they lack fundamental-locatedness and so exist from the standpoint of worlds, can still be said to be spatiotemporally related to worlds by virtue of their depending upon their spatiotemporally located, worldly members.
And so, Lewisian theists can argue that God is causal and exists from the standpoint of worlds, and there is no problematic causal connectedness of worlds, and so there is no modal collapse. God's not being spatiotemporally located allows Lewisian theists to maintain that He exists from the standpoint of worlds, and that causal connectedness of worlds only concerns world-bound, world-part-particulars. 28

Conclusion
Herein I have demonstrated that many of the arguments in the literature against (2) and (4) do not work. However, I have provided two novel objections to (2): firstly, I have levied Lewis's accidental external relations objection to the proposal, and secondly, I have argued that fundamental-location is a plausible condition that distinguishes (2) from (4), to the effect that the supporter of (2) will have to provide a story of how an atemporal God can be fundamentally-located in the world. I think that the first objection may be averted; I think that the second objection may admit of a response. However, the most straightforward way to render God necessary in Lewisian theism is to adopt (4): under (4), God can be concrete, spatiotemporally and causally related to worlds, exist from the standpoint of worlds, and worlds can remain causally isolated, and so modal collapse is avoided. Lewisian theists must argue, then, that God has no place 'in' the world-He exists 'outside' it.