Ersatz Counterparts†

R W‡

Forthcoming in Oxford Studies in Metaphysics, vol..

: Counterpart theory has many benefits, but few are happy to acceptthe metaphysical setting in which this account of de remodality was developedby its architect, David Lewis. I argue here that counterpart theory can be madeacceptable by the lights of those who repudiate the existence of merely possibleobjects. To the ‘ersatz’ counterpart theorist I offer two stories: one about therelata of the counterpart relation and one about the relation itself. With thesein place, I then defend ersatz counterpart theory from a number of objectionsthat can be found in the literature.

: Modality; Counterparts; Possibilia; Actualism.

: ,.

†Thanks to Elizabeth Barnes, Ross Cameron, Shamik Dasgupta, John Divers, ThomasKrödel, Ted Sider, Tatjana von Solodkoff, Jason Turner, Isabel van der Linde, Barbara Vet-ter, Jennifer Wang, and Robbie Williams. Earlier versions of this paper were presentedat the Universities of Barcelona, Leeds, and Hamburg, and at Humboldt-Universität zuBerlin — many thanks to my audiences on those occasions for discussion. My research onthis paper was conducted within the context of the DFG Emmy Noether Research GroupOntology After Quine and was supported by my involvement in the Nature of Assertion:Consequences for Relativism and Fictionalism project (FFI-), the Vaguenessand Physics, Metaphysics, and MetaMetaphysics project (FFI-), and the P-Philosophy of Perspectival Thoughts and Facts project (CSD-). Many thanks tothe DFG, the DGI, MICINN, and the Spanish Government for supporting these projects.

‡Emmy Noether Research Group Ontologie nach Quine, Philosophisches Seminar derUniversität Hamburg, Hamburg , Germany. Email: richard.woodward@uni-hamburg.de

W congenial to talk not only of what goes on at possible worlds,but also of their inhabitants, the possibilia. Thus we talk not only of

worlds where donkeys talk but also of talkative possible donkeys. And whenwe talk this way, we can think of ourselves as speaking a certain language:the possibilist language.

We speak the possibilist language to talk about possibilities, by means oftalking about possible things. But we also talk about possibilities in a morefamiliar way, by talking about what might have been and what might not, bytalking about what is contingent and what is necessary. Here, we can thinkof ourselves as speaking a different language, one that is readily amenableto regimentation using boxes and diamonds: the modalist language.

These languages share a subject matter, modal space, and the sentencesof each express claims about this subject matter. It’s not so surprising, then,that we can pair sentences of the one language with sentences of the other.The modalist sentence ‘there might have been talking donkeys’ can, e.g., bepaired with the possibilist sentence ‘there is a world where donkeys talk’ andthe modalist sentence ‘round squares are impossible’ can be paired with thepossibilist sentence ‘there is no world where squares are round.’ Of course,there are questions about whether everything you can say in the one languageyou can say in the other, and there are questions about whether one of theselanguages is more fundamental than the other. But set these issues aside.

Our focus is on some delicate issues relating to de re possibilities. Whenwe try to pair a modal claim like ‘Messi might have won’ with some sentenceof the possibilist language, it’s natural to appeal to worlds whereMessi wins:worlds which represent Leo Messi as winning. But how does a world repre-sent Messi as winning? You might think it does so by containing that man.But nearly everyone thinks that this is false. Even Alvin Plantinga (),a card carrying believer in transworld identity, thinks that talk of possibiliaisn’t to be understood in terms of flesh and blood individuals like you andme, but in terms of special abstract objects: individual essences. Whateverare the constituents of other worlds, it seems, Messi is not one of them.1

And David Lewis, who does think that talk of possibilia should be under-stood in terms of objects like you and me, explicitly tells us that “nothing isin more than one world” (, p.). So how is de re representation to

1 Phrasing the point in terms of ‘constituents’ is perhaps misleading. It’s not clear thatPlantinga believes that possible worlds have constituents in any sense. What’s really at stakehere is the semantic point that in a standard Kripke semantics each world is associated with adomain of possible individuals. And on Plantinga’s view, these domains are sets of essences.

be understood?A natural answer to this question begins by appealing to representatives

of Messi: objects that, though numerically distinct from Messi, stand in animportant relation to the man himself. The thought is then that Messi’srepresentative, Messi*, can go where he cannot. To see how this helps, con-sider how things play out for Plantinga. Plantinga has an easy time identify-ing Messi’s representative: it’s his individual essence, the property of beingMessi. This property is distinct from Messi and stands in an important re-lation to the man himself. Plantinga cannot hold that Messi’s essence winsat any world: essences don’t do that kind of thing. But that just meansthat he needs to be creative when interpreting sentences like ‘Messi* wins’.Plantinga’s preferred option is to take ‘wins’ to express the property of beingco-instantiated with the property of being a winner. In this way, Plantingacan tell a story about how it can be true at a world that Messi wins.

Lewis appeals to representatives too. But his representatives are the realthing: flesh and blood concrete objects just likeMessi. Andwhereas Plantingaonly has only one representative, Lewis has many. So whereas Plantinga canhold that Messi’s actual representative is identical to his representatives else-where — it’s always Messi’s essence — Lewis needs a different story.

Lewis’s story is familiar. Messi’s representatives are his counterparts:possible objects that are similar to him in some contextually salient way.Speaking loosely, we might say that Messi’s counterparts in other worlds arehim in those worlds, but Lewis (, p.) insists that this is not identityin any literal sense, and that it would be better to say that Messi’s counter-parts are the men he would have been, had things been different. But thoughMessi’s counterparts in other worlds are not really him, the distinctness ofMessi and his representatives is not a unique feature of counterpart theory.Even someone who believes in transworld identity can accept that Messi’srepresentatives are not really him. Plantinga is a case in point.2

What is distinctively counterpart-theoretic, and what transworld identitytheorists cannot accept, is Lewis’s account of when something counts as arepresentative of Messi. For one thing, whether one object is a counterpartof another is a context-sensitive matter: what counts as a counterpart in onecontext need not count as a counterpart in another. For another thing, thecounterpart relation is not an equivalence relation: though reflexive, it isneither symmetric nor transitive. And as is well-known, these two features

2 For more on this point, see Woodward ().

are beneficial, allowing us to account for the inconstancy of our de re modaljudgements, solve puzzles generated by the conflicting modal properties ofstatues and lumps of clay, and avoid commitment to the idea that the logicof de re modality is S5 (see, e.g., Lewis (, , )).3

Is this beneficial package Lewis’s and Lewis’s alone? Could you jettisonLewis’s robustly realist interpretation of the possibilist language and still be acounterpart theorist? Those attracted to an ‘ersatz’ counterpart theory mustanswer two questions. They must tell us what counterparts are, if not theflesh and blood things that Lewis takes them to be. And once they have toldus that, they must tell us in virtue of what these things are counterparts ofeach other. That is, they must tell us two stories: one about the relata of thecounterpart relation and one about the relation itself.4

1 Ersatz counterparts

The benefits that I just associated with counterpart theory were semantical,conceptual, and logical in character. The theory gives us a neat semantictreatment of de re modal predications, it ‘fits’ our de re modal concepts andgives us a nice logic. A further benefit is more metaphysical in character:counterpart theory allows Lewis to reduce de re representation to de dictorepresentation. This point is often lost, partially because there is a tendencyin the literature to contrast Lewis’s theory with ‘representational’ theorieslike Plantinga’s. But don’t be misled: Lewis needs a story about representa-tion just as much as anyone else. And he gives us two, one for the de dictocase and one for the de re.

3 There are two ways of doing counterpart-theoretic accountancy, and I have just playedfast and loose and with the distinction. Going one way, we might count many relations ascounterpart relations and then think is that (ideally) one of these is selected in a context,with the other counterpart relations being ignored or excluded. Going this way, what weshould say is that counterpart relations in general are not equivalence relations. Goingthe other way, we might count (in a context) a single relation as the counterpart relation,and then think that which relation counts as the counterpart relation shifts around fromcontext to context. Going this way, what we should say is there is no semantic guaranteethat the counterpart relation is an equivalence relation, even though (in some contexts) thecounterpart relation will be an equivalence relation. Thanks to John Divers for discussion.

4 Question: Can’t the actualist refuse to tell a story about the counterpart relation, andtake it as a primitive? Answer: The story needn’t be an analysis. Lewis never gives us aformal definition of the counterpart relation, but he does his best to explain the notion.

What a Lewis world represents de dicto — which purely qualitative factsit represents as holding, which purely general propositions it represents asbeing true — is analyzed in mereological terms. So, e.g., a Lewis worldrepresents the existence of talking donkeys just in case it contains talkingdonkeys and has talking donkey as parts. And once we’ve settled what eachLewis world de dicto represents, we can introduce de re representation byappealing to the qualitative features of the possibilia that populate Lewis’sworlds and the similarity relations that they bear to each other.

Some dislike this way of setting things up. Representation, I’m often told,is a notion that only has real application in connection with ersatz views ofworlds and doesn’t do much work for someone like Lewis. He has his worldsand that is enough to get his analysis up and running. Well, what’s true isthat representation isn’t part of the fundamental ideology of Lewis’s view:it’s reduced to a combination of mereology and similarity. I find it difficultto see how this reduction means that representation doesn’t do any work forLewis, but in any case, Lewis (a, ) is clear that a possibility is notalways a possible world: individuals represent possibilities too. And it bearsemphasis that which possibility an individual represents depends on whichcounterpart relation we have in mind. Thought of as one of my counterparts,a given object may represent a possibility for me; thought of as one of yours,the very same thing may represent a possibility for you. Moral: forgo wordslike ‘representation’ if you want, but don’t pretend that Lewis himself didn’tmakemore than enough room for them, and don’t pretend that Lewis doesn’tappeal to the notion of representation to do important work.

Ersatz counterpart theorists hope to reduce de re representation to its dedicto cousin too. The first thing to remember is that when the ersatzer speaksof the actual possible world, she is not speaking about concrete reality but aspecial abstract world: the one that is actualized. And concrete reality is thething that does the actualizing, not the thing that is actualized.5 A similarpoint appeals to possible individuals. When the ersatzer speaks of actualpossible individuals, she is not speaking about concrete things like you andme, but about their abstract representatives at the actual world. Real thingslike you and me are the things which are represented, not the things whichdo the representing. We are not medium but message.

5 See Divers (, pp.-) for more on this distinction.

At this point, the challenge to specify the relata of the ersatz counterpartrelation becomes pressing. How should it be met? Well, think of all thepurely qualitative predicates that Lionel Messi satisfies.6 Then think of hisrepresentative at the actual world, Messi*, as the set of those predicates:

• Messi* = {x is male, x is a footballer, x is Argentinian . . . }

This generalizes to give us representatives for each actual individual. We canintroduce representatives for the merely possible individuals by rememberingthat my ersatzer aims to reduce de re representation to de dicto representa-tion. Think of what a world represents de dicto as the purely qualitativesentences that it makes true. Each of the objects that exist at w can then beassociated with the set of qualitative predicates that w says they satisfy. So ifw says that there is a talking donkey called ‘Robin’, then our representativewill be the set of qualitative predicates that Robin satisfies at w:

• Robin* = {x is a donkey, x talks, x has a tail, . . . }

In this way, our erstazer is able to construct representatives for not onlyactual individuals, but merely possible ones too.7

When I asked you to think of all of the qualitative predicates that Messisatisfies, I really did mean all of them. So our set-theoretic representationdoesn’t only include predicates like ‘x is male’ but also ones like ‘x is part ofworld containing a no talking donkeys’ and ‘x is such that there are exactlyn stars’. As Lewis puts it:

The ersatz individual is by no means a purely intrinsic descrip-tion; the description is extrinsic in a big way. By the time we aredone describing an individual completely, we have en passant de-scribed the world wherein it is situated. (, p.)

Our setting thus has an important consequence: it entails that Messi* andRobin* are worldbound. This isn’t obvious, since we’ve identified them withsets of open sentences and one might think that such things exist at everyworld. What’s going on?

6 See Lewis (, pp.-).7 There are famously a number of issues regarding the descriptive adequacy of this kind

of ersatz setting, but I think it’s become clear that they can be addressed: see, e.g., Melia() and Sider ().

Notice that to each ersatz individual there corresponds a very complexqualitative property. Let’s say that something plays the Robin-role just incase it satisfies each of the predicates in Robin*, that is, iff it is a donkey,who talks, and has a tail, and so on. Our LeoMessi, then, has the qualitativeproperty of being such that there is no player of the Robin-role. Indeed, foreach role associated with eachmerely possible object, Messi has the propertyof being such that there is no player of that role. Moreover, for each roleassociated with each actually existing object, Messi has the property of beingsuch that there is a player of that role.

The point is that Messi* is bound to the actual world in the sense thatonly the actual world represents the existence of a player of the Messi-role.8

If a world w represents the existence of a player of the Messi-role, then wrepresents that existence of a player of each qualitative role associated witheach actual individual. And this is because part of what’s involved in playingthe Messi-role is being worldmates with a player of the me-role, a player ofthe you-role, and so on. So if w contains Messi* and thereby represents theexistence of a player of the Messi-role, wmust also represent the existence ofa player of the you-role and so must contain you*. Moreover, ifw representsthe existence of a player of the Messi-role, then w must also represent thenon-existence of a player of each qualitative role associated with each non-actual individual. And this is because part of what’s involved in playing theMessi-role is being worldmates with no player of the Robin-role, no playerof the Alice-role, and so on. So if w contains Messi* and thereby representsthe existence of a player of the Messi-role, w cannot also represent that thereis a player of the Robin-role and so cannot contain Robin*.

To be clear: this is not to say that only the actual world represents Messi,nor that there is a bizarre necessary connection between Messi and me, northat there is a bizarre necessary disconnection between Messi and Robin.The point is rather that ersatz worlds don’t represent the existence of Messiby representing the existence of a player of the Messi-role. Questions of dere representation — and in turn questions of de re modality itself — are an-swered by looking to the facts about counterparts, just as on Lewis’s account.In essence, all we have is an ersatz surrogate for Lewis’s original demand thatnothing is in more than one world.

8 Setting aside worries about whether there could be distinct worlds that were nonethelessindiscernible in terms of what they de re represent. Compare Lewis (, p.) and seeDivers () for discussion. A few seasons back, theMessi-role might be called False Nine.

So much for specifying the relata of the ersatz counterpart relation. Whatcan the ersatzer say about the relation itself?

2 Ersatz counterpart relations

Remember that Lewis explains his counterpart relation in terms of similarity:whether two things are counterparts depends on whether they are similar toeach other in some contextually important way. When asked to explain hercounterpart relation, can’t the ersatzer just say the same thing?

No. Lewis’s explanation has it that two individuals are counterparts iffthose very things are similar in some contextually salient way. If the ersatzerparroted this, she’d end up saying that Messi* and Robin* are counterpartsiff those very things are relevantly similar. And this seems to me to get thingsback to front: whether Messi* and Robin* count as counterparts shouldn’t,I think, turn on whether or those two sets — for that’s what they are — aresimilar. Rather, whether these representations are counterparts should turnon whether the things they represent are similar.9

The trouble is that the ersatzer can’t accept this. For Robin* representsa player of the Robin-role, and the ersatzer doesn’t believe that there is anysuch thing. The present proposal works when two actual individuals arecounterparts: the ersatzer can hold that whether Messi* is a counterpart ofme* depends on whether he is similar to me in some contextually relevantway. But the proposal simply breaks down when one of the relata representsa merely possible individual.

When it comes to explaining the counterpart relation, the ersatzer facestroubles that Lewis does not. But though she has fewer ontological resourcesthan Lewis, the ersatzer has extra ideology: primitive modality. Her worldsare maximally consistent sets of sentences or maximally possible states ofaffairs (or whatever), where consistency and possibility are either taken asprimitive or defined in primitively modal terms. So whereas Lewis uses hisplentiful ontology to explain the counterpart relation, couldn’t the ersatzerdeploy her extra ideological resources to do the same thing?

9 Sider (, p.) agrees. The point can bemade a little more vivid by remembering thatwe could have associated each qualitative predicate with a unique number, and then takenMessi* and Robin* to be sets of numbers. But whetherMessi* and Robin* are counterpartsshouldn’t turn on whether {, , . . .} is similar to {, , , . . .}. It should turn on whetherthe things that these sets represent are similar to each other.

This strategy runs into trouble too. Suppose that the ersatzer tried toexplain her ersatz counterpart relation as follows:

• Messi* is a counterpart of Robin* iff Necessarily, for any two thingsx and y, if x plays the Messi-role and y plays the Robin-role then x isrelevantly similar to y

The problem, as Lewis notes, is that the right-hand side of this biconditionalis trivial.10 There is no possible world containing both a player of the Messi-role and a player of the Robin-role. For remember that it’s built into theMessi-role that anything that plays the role is such that there is no player ofthe Robin-role, due to the fact that the ersatz descriptions are ‘extrinsic in abig way’. Our modal explanation of the counterpart relation is a failure andthe ersatzer seems to be running out of options pretty quickly.

(The problem with the modal analysis considered above arises because itrequires an intra-world similarity relation between a player of the Messi-roleand a player of the Robin-role. And so one might naturally think that thecounterpart theorist should require an inter-world similarity relation instead.That is, one might think that the counterpart theorist should endorse thefollowing modal analysis of the counterpart relation:

• Messi* is a counterpart of Robin* iff Necessarily, for any thing x, ifx plays the Messi-role then, necessarily, for any thing y, if y plays theRobin-role then x is relevantly similar to y

Certainly this analysis fares better that its predecessor since its adequacy doesnot require the existence of a single world containing players of both roles.But the result comes at a price: it commits the ersatz counterpart theorist toprimitive modality that is de re in character. And remember that the coun-terpart theorist’s project, as it is being conceived here, is similar to Lewis’s:she aims to reduce representation de re to representation de dicto. In thissetting, the appeal to primitive de re modality is off-limits. To put that pointotherwise, the counterpart theorist aims to reduce the de re modal facts tofacts about ersatz counterparts and and our present question is whether theselatter facts can themselves be further reduced. Within this context, it is clearthat the ersatz counterpart theorist cannot explicate the ersatz counterpartrelation in the manner suggested.)

10 Lewis (, p.). Compare Sider (, p.).

At this stage, it’s worth repeating a point that I made earlier. Even if wegrant that no world contains both a player of the Messi-role and a playerof the Robin-role, we are not thereby forced to deny the Humean thoughtthat anything can co-exist with or without anything else. For one thing, theersatz counterpart theorist, like Lewis, thinks that the question of whether acould exist without b turns on whether or not there is a world containing acounterpart of a but not b. For another thing, and as Philip Bricker ()stresses, the Humean denial of necessary connections is best articulated interms of duplication: there are no necessary connections between distinctthings iff for any two distinct things, it it possible for a duplicate of the oneto exist without a duplicate of the other. Crucially, however, duplicationis cashed out in terms of intrinsic properties: x is a duplicate of y iff x andy have the same intrinsic properties. Even if the extrinsic information con-tained within the Messi-role and the Robin-role means that there is no worldcontaining both a player of the Messi-role and a player of the Robin-role,the Humean picture is in place as there are world containing duplicates ofMessi and Robin: things which satisfy the intrinsic information containedwithin the Messi-role and the Robin-role.

Next, consider the following explanation of the counterpart relation:

• Messi* is a counterpart of Robin* iff Necessarily, for any two thingsx and y, if x is a Messi-duplicate and y is a Robin-duplicate then x isrelevantly similar to y

This explanation is better than the original modal analysis insofar as someworlds contain both Messi-duplicates and Robin-duplicates. The problem isthat it is crucial to counterpart theorists that things can count as counterpartsbecause they are similar in highly extrinsic respects: you may count as acounterpart of mine by being twelve feet from a cat, for instance. Be thatas it may, the explanation nonetheless hints at how the counterpart theoristcan explain her relation. For what we have in effect done is restricted theMessi-role and the Robin-role so as to ensure that there is a world containingplayers of both roles. This idea was a good one, but by focusing solely onthe intrinsic information contained within the roles, we went too far. Whatwe are after, then, is a way of constructing worlds that contain copies ofMessi and Robin, and we know that ‘copying’ needs to be handled carefully.If we are too liberal, our resultant explanation of the counterpart relationwill go trivial, but if we are too conservative, our explanation will be overlyrestrictive.

At this point, we need to make an assumption about the extent of modalspace, and grant that disjoint spacetimes are possible so that some worldsrepresent the existence of a plurality of disjoint ‘island’ universes. I takeit that this assumption is legitimate in context: even Lewis accepts that itis a cost of his account that it cannot allow for the possibility of disjointspacetimes. Lewis of course thinks the cost is negotiable and outweighed byother lovely features of his view but, be that as it may, the point is just thatit is generally accepted that it is a benefit of ersatz proposals that they canallow for the possibility of disjoint spacetimes. Moreover, suppose that w1

and w2 represent the existence of a single universe. Then I assume that thereis a third world w3 that represents the existence of two disjoint spacetimesv1 and v such that v1 is a duplicate of w1 and v2 is a duplicate of w2.11 Wehave:

Now, ifw1 contains a player of theMessi-role andw2 contains a player of theRobin-role, then w3 will contain duplicates of each. The trick is now to un-derstand the arrows in such a way as to ensure that the extrinsic informationabout Messi and Robin carries over into w3 too.

Theodore Sider (MS.) suggests a neat way to pull off this trick. Earlier wesaw that an object o plays the Messi-role only if o satisfies the open sentence‘x is such that there are no talking donkeys’ and that an object o* playsthe Robin-role only if o* satisfies the open sentence ‘x is such that there aretalking donkeys’. Suppose, however, that we restrict the quantifiers of theseopen sentences by different predicates. In our toy example, say that an objectis on the right iff it is spatio-temporally connected to a talking donkey andthat an object is on the left iff it is not on the right. Then even though it is

11 This is the ‘hefty metaphysical assumption’ mentioned in Sider (MS.). I’ll mount a defenceof the assumption in due course.

impossible for there to be two objects o and o* that satisfy the predicates ‘xis such that there are no talking donkeys’ and ‘x is such that there are talkingdonkeys’ respectively, it is possible for there to be two objects that satisfy thepredicates ‘x is such that there are (on the left) no talking donkeys’ and ‘x issuch that there are (on the right) talking donkeys’ respectively.

Moreover, suppose that we restrict all of the quantifiers of all of the opensentences that are members of Messi* by the predicate ‘is on the left’ andall of the quantifiers of all of the sentences that are members of Robin*by the predicate ‘is on the right’. This allows us to delineate two complexqualitative roles: the Messi-copy role and the Robin-copy role. We can thenexplain the ersatz counterpart relation as follows:

• Messi* is a counterpart of Robin* iff Necessarily, for any two thingsx and y, if x is a Messi-copy and y is a Robin-copy then x is relevantlysimilar to y

Given the assumption about the possibility of disjoint spacetimes, i.e. giventhat for any twoworldsw1 andw2 there is a third worldw3 containing copiesof w1 and w2, it turns out that the right-hand side is non-trivial. But thecopying exports into w3 not only the intrinsic information contained withinMessi* and Robin* but the extrinsic information too: if w1 represents theplayer of the Messi-role as being twelve feet from a cat and w2 representsthe player of the Robin-role as being twelve feet from a cat, then w3 willrepresent both the Messi-copy and the Robin-copy as being twelve feet froma cat. In these ways, our explanation of the counterpart relation avoids theproblems that afflicted its predecessors.

Before we move on, I want to forestall a possible misunderstanding aboutthe role that disjoint spacetimes play within the proposed account. Theworry can be illustrated if we suppose that Messi could have been lonelyand thereby could have existed in isolation from any distinct thing. Onthe present account, representing this possibility requires that Messi* has alonely counterpart — call this counterpart Loner*. And Messi* and Loner*being counterparts requires (in part) that there is a world w which repre-sents the existence of a player of the Messi-copy role and a player of theLoner-copy role. One might now worry that this means that we have in factnot represented the possibility of Messi being lonely; what we have insteadrepresented is the possibility of Messi and Loner co-existing.

Now, what is true on the present proposal is that Messi* and Loner* be-ing counterparts requires (in part) that there is a world w which represents

the co-existence of players of the Messi-copy role and the Loner-copy role.But even though the theory says that whether Messi* and Loner* are coun-terparts depends on what goes on in worlds containing copies of both, repre-senting the possibility of Messi being lonely does not require that any playerof the Loner-copy role is lonely. What is instead required is that Messi* hasa counterpart who is lonely*. And given a) that Loner* and Mesi* are coun-terparts and b) that Loner* is lonely* insofar as any player of the Loner-roleis lonely, we thereby represent the possibility of Messi being lonely. So notethat even though the theory appeals at a crucial stage to the existence of aworld w that represents the de dicto possibility of the copies co-existing, wdoes not itself represent the de re possibility of Messi being lonely. Giventhat Messi* and Loner* are counterparts, the worlds which represent thatpossibility are instead those which contain a player of the Loner-role.

Now, as Sider (MS.) points out, the explication of the ersatz counterpartrelation that we are considering requires a rather hefty assumption aboutwhat possibilities there are. But as hefty as it is, the assumption seems wellmotivated given a Humean picture according to which there are no necessaryconnections between distinct things.

3 The Principle of Solitude

Intuitively, there are necessary connections between distinct things just incase there is an x such that, necessarily, x coexists with some y that is distinctfrom x. But as Bricker (, p.) points out, this claim is ambiguous. Ifwe treat ‘some y’ as having wide-scope, we get one anti-Humean principle:

∃x∃y(x is distinct from y ∧ □(x exists ⊃ y exists))

But if ‘some y’ has narrow-scope, we get another anti-Humean principle:

∃x□(x exists ⊃ ∃y(x is distinct from y)

(These principles are somewhat sloppy: remember that what’s really at stakeis not the necessity of x coexisting with y but the necessity of a duplicate ofx coexisting with a duplicate of y. I’ll take this qualification as read.)

Now, when Lewis (, p.), as a good Humean, says that anythingcan fail to coexist with anything else, he is denying the first principle above.Take any two distinct things, and it is possible for (a duplicate of) the one

to exist in isolation from (a duplicate of) the other. But that does not entailthat, for any x, it it is possible for (a duplicate of) x to exist all by itself. Soone could deny the first anti-Humean principle whilst accepting the second.

With Bricker, I think that rejecting only the first anti-Humean principle isunattractive: its denial is too weak to capture the full range of possibilities.Consider a red ball and a blue candle. Given that we are rejecting the firstanti-Humean principle, we know that it is possible for the red ball to existwithout the blue candle. Maybe the blue candle is replaced by a blue pencil?But, intuitively, it is also possible for the red ball to exist without anythingblue existing. Maybe the blue pencil is replaced by a green one? But surelyit is also possible for the red ball to exist without any other coloured thingexisting, and also possible for the red ball to exist without any other extendedthing existing, and also possible for the red ball to exist without... We aresliding down a slippery slope, and the denial of the second anti-Humeanprinciple lies at the end of our journey.

To deny the second of the anti-Humean principles outlined above is toendorse the Principle of Solitude:

∀x^(x exists ∧ ¬∃y(y is distinct from x))

Properly understanding this principle requires us to be quite specific aboutthe range of the quantifiers. After all, we do not want it to turn out that thePrinciple of Solitude rules out the necessary existence of things like numbersand sets, and to avoid this result it’s crucial that the quantifiers are takento range only over objects that are located in space and time. Moreover,existing in insolation is not quite the same as being surrounded by emptyspacetime. In the world where Messi exists all by himself, spacetime haswhatever shape Messi has.

Even within a Lewisian setting, endorsing the Principle of Solitude doesnot by itself deliver the possibility of disjoint spacetimes. For even thoughthe quantifiers range only over objects that are located in spacetime, it is stillnatural to think that the quantifiers range over what John Divers () callsordinary individuals: individuals that are wholly located in a single world.But suppose that we understood the quantifiers in the Principle of Solitudeas ranging over not only ordinary individuals but also over extraordinary ortransworld individuals that are partially located in different worlds. Call thisthe Generalized Principle of Solitude, or GPS for short. Then the possibilityof disjoint spacetimes follows immediately by by instantiating the quantifierto any transworld individual.

Now, Bricker’s defence of GPS is based on the thought that there shouldbe no restriction on what can be actualized. He invites us to look at thingsfrom God’s perspective. To insist that only single worlds can be actualized“would be to put a limitation on God’s power to choose, one not groundedin any logical necessity” (, p.). He continues:

Suppose that, in surveying the worlds prior to actualization, Godfound that two or more worlds were tied for best. Why mustGod choose between actualizing one world, or the other? He’sall-powerful! He can simply say: “Actualize those!”

It’s important to see that Bricker isn’t proposing to redefine the Lewisianconcept of a world so that there are worlds which contain spatiotemporallydisconnected parts. Rather, what he is in effect proposing is that there isanother sense in which Lewis was right to say that a possibility is not alwaysa possible world: a possibility is sometimes some possible worlds, where‘some’ is plural. Two worlds taken together can represent the possibility ofdisjoint spacetimes even if no world taken in isolation can do the same thing.So whilst embracing Bricker’s picture might force the Lewisian to tweak heranalysis of modality, the Lewisian concept of a world can remain fixed.

Though Bricker mounts his defence of GPS in a Lewisian setting, his pointcan be developed in an ersatz setting too. But we need to tread carefully. Tobegin, note that there is a certain sense in which it doesn’t matter, from(Bricker’s) Lewisian perspective, which worlds are actualized. Consider twoscenarios. In the first, God actualizes a single world containing talking don-keys; in the second, He actualizes a single world containing no talking don-keys. Either way, it is still true that there are, quantifiers wide open, talkingdonkeys: the scenarios only generate different answers to the question ofwhether talking donkeys are actualized. That is just to say that when weassume a possibilist metaphysic, the class of things which exist simpliciterincludes but is not exhausted by the class of things which are actual sim-pliciter. Actualization will therefore make a metaphysical difference, not anontological one.

When we assume an actualist metaphysic, however, the class of existingthings just is the class of actual things. So it makes an ontological differencewhether God actualizes a world where donkeys talk as opposed to a worldlacking talking donkeys. In the former scenario, God makes it the case thatthere are, quantifiers wide open, talking donkeys; in the second, He makesit the case that there are, quantifiers wide open, no talking donkeys.

Next, consider a third scenario in which God actualizes two worlds, onewhich contains talking donkeys and one which doesn’t. This scenario istroubling for the actualist in a way that it is not troubling for the possibilist.For in actualizing a world where donkeys talk, God seems to make it the casethat there are, quantifiers wide open, talking donkeys. But in actualizing aworld containing no talking donkeys, God seems to make it the case thatthere are, quantifiers wide open, no talking donkeys. But God can’t make itthe case that there are and are not talking donkeys.

A second difference between the Lewisian setting and the ersatz settingis that Lewisian worlds are concrete objects whereas ersatz worlds are atbest abstract representations of concrete objects. Suppose that God looksdown on the worlds (be they concrete or abstract) and finds that two ofthem, w1 and w2, are equally good candidates to be actualized. If the worldsGod looks down upon are Lewisian, He cannot try to solve His problem bycreating a third world containing copies of w1 and w2. Lewisian worlds arespatiotemporally unified by definition, after all. Moreover, He doesn’t needto do this: He can just take w1 and w2 together and actualize both. But if theworlds He looks down on are abstract representations of worlds, God can tryto solve His problem by creating a third world that represents the existence oftwo disjoint spacetimes. Nothing in the definition of abstract worlds requiresthat they represent spatiotemporally unified wholes. Moreover, there is atleast a prima facie case for thinking that God has to solve His problem inthis way: for, as we saw, if God were to actualize both w1 and w2, there isa worry that He would make a contradiction the case, by making it the caseboth that talking donkeys exist and that talking donkeys don’t exist.

Time to take stock. We have seen that there are good reasons to thinkthat Humeans should accept the Generalized Principle of Solitude. And wehave also seen that GPS suggests that it is possible for more than one Lewisworld to be actualized simpliciter. Exactly how to transpose GPS into anersatz setting is a delicate issue, however. Suppose that w1 and w2 are ersatzworlds that represent the existence of single unified spacetimes v1 and v2.Then GPS does not require that it be possible for both w1 and w2 to beactualized: GPS will be upheld if it is possible for both v1 and v2 to coexistin isolation from each other. This would be underwritten if the ersatzer wereto accept that it is possible for more than one ersatz world to be actualized.But there is a clear logical problem with this idea, and the ersatzer doesn’tneed to pursue this strategy in any case. She can instead hold that GPS issatisfied because there is a third world, w3 that contains copies of v1 and v2.

Insofar as the ersatz counterpart theorist is a Humean, then, I submit thatGPS is both well motivated and supports the hefty metaphysical assumptionrequired to underpin our explanation of the ersatz counterpart relation.

(Question: What if the logical problems can be solved? Won’t it thenturn out that GPS is underwritten not by the hefty metaphysical assumptionrequired for the explanation of the counterpart relation but by the possibilityof more than one ersatz world being actualized?

Answer: Suppose that w1 represents the existence of a player of theMessi-role and w2 represents the existence of a player of the Robin-role.Even if the logical problems can be solved, so that w1 and w2 can be jointlyactualized, it does not follow that it is possible for a player of the Messi-roleto coexist with a player of the Robin-role. Indeed, the set of sentences thatwould have been true had w1 and w2 been jointly actualized is seeminglyidentical to the set of sentences that would have been true had w3 been actu-alized, where w3 is the world constructed by the copying process describedearlier. In this sense, the possibilities generated via multiple actualizationjust are the possibilities generated by the copying process. Put otherwise,there is no difference, within an actualist metaphysic, between actualizingw3 and jointly actualizing w1 and w2. Either way, we get the same range ofpossibilities required to underpin our explanation of the ersatz counterpartrelation.)

4 Semantics versus metaphysics

Ersatz counterpart theorists hope to enjoy the benefits of counterpart theorywithout footing the ontological bill. But TrentonMerricks () has arguedthat ersatz counterpart theories simply don’t work. He is owed an answer,and I shall give mine.12

Merrick’s criticisms, surprisingly, focus not on the ersatzer’s story aboutthe counterpart relation itself, but on her story about its relata. He objectsthat the method by which we constructed ersatz individuals is just one ofmany. Instead of taking possibilia to be sets of open sentences, we couldequally well have associated each sentence with a number and taken ersatzindividuals to be sets of numbers. Or we could have used different sentences,

12 Merricks’ main target is the ersatz counterpart theory developed by Heller (), andsome of his criticisms focus upon quite specific details of Heller’s proposal. But others aremore general, and can be levelled against any ersatz counterpart theory.

written in a different language. But remember that the theory reduces the factthat Messi is possibly F to facts about Messi* and his counterparts. ThatMessi is possibly F might, e.g., be reduced to something like:

• There is some set of open sentences x such that x is a counterpart ofMessi* and x is F*

(Where x is F* iff it has ‘x is F’ as a member.) But why, Merricks wonders, isthis any better than reducing the target modal fact to facts about some otherset-theoretic candidate? The multitude of candidates is thus problematic asit “absurdly implies that no single analysis of a modal property is better thansome incompatible analyses” (, p.).13

Notice that Merricks thinks of the counterpart theorist as offering us ananalysis of modal properties like being possibly F. But even if we grant this,it’s far from clear exactly what kind of analytic project she’s engaged in. Andto see that, just observe that philosophers use possible worlds and individualsfor a variety of different purposes.14

Most obviously, some philosophers cast possible worlds and individualsin a foundational role, and this is precisely the key role that counterparts playin their original Lewisian setting: on Lewis’s view, to be possibly F just is tohave a counterpart who is F. Perhaps the ersatz counterpart theorist agrees.If so, let’s say that she is deploying counterpart theory to give a metaphysicalanalysis of de re modality.

Possible worlds and individuals aren’t only used to ground modal truths:they’re also used as semantical tools. Thus possible worlds can be used tospecify the semantic values of modal operators, functions from worlds tosets of objects can be used to specify the intensions of predicates, and sets ofworlds can be used to specify the conditions under which a sentence is true.When we give a semantical theory of a language which incorporates claims

13 Worse still, there is a qualitative problem: ersatz counterparts are not cut out to representthe possibilities that they are designed to represent. For they fail to represent intrinsicallysince, being sets, they “just sit there” (p.). Good candidates, Merricks thinks, must havetheir representational properties ‘in and of themselves.’ I won’t say much about this worryhere, since I think that it’s been adequately dealt with by Sider (MS.). The basic point is thatwhat matters is that Messi* represents Messi relative to the structure in terms of which thecounterpart theorist’s semantic theory is given. And this relative notion of representation isperfectly objective, even if there is no ‘intrinsic’ sense in which Messi* represents Messi.14 Here I agree with Agustín Rayo (), from whom the terminology introduced belowis borrowed.

such as these, we need entities for our (metalinguistic) quantifiers to rangeover, and possible worlds, individuals, and other things constructed out ofthem can serve as those entities. Perhaps the ersatz counterpart theorist seesher counterparts as playing this role. If so, let’s say that she is deployingcounterpart theory to give a semantical analysis of de re modality.

It’s important to realize that it is one thing to hold that ersatz counterpartsplay a foundational role and quite another to hold that they play a semanticalrole. This point isn’t new: Allen Hazen (, p.) made it over thirtyyears ago, telling us that the question of what grounds de re modal truthsis “irrelevant” to the assessment of counterpart theory qua semantic theory.There has been a tendency to overlook this, however, a tendency traceableto the fact that counterparts play both roles within the context of Lewis’smodal philosophy. But the two roles should be sharply distinguished, andjust as one might use possible worlds in one’s semantics without thinkingthat what it is for ϕ to be possible is for ϕ to be true at some possible world,one might use counterparts in one’s semantics without thinking that de remodality can be metaphysically analyzed in counterpart-theoretic terms.

Once foundational issues are divorced from semantical ones, Merricks’complaint can be understood in two ways: either as a complaint about theadequacy of ersatz counterpart theory qua semantical analysis or as a com-plaint about its adequacy qua metaphysical analysis.

The latter complaint can be answered quickly. For whether or not someersatz counterpart theorists are aiming to provide a foundation from whichde re modality can be constructed, that’s certainly not the role which ersatzcounterparts play within the theory developed earlier. I distinguish betweenthe counterpart* relation, which holds between ersatz individuals, and thecounterpart relation, which holds between the things represented by ersatzindividuals. What’s true is that the theory tells us that ‘Messi is possibly F’is true iff Messi* has a counterpart* who is F*. But that’s not the end of thestory: whether this truth condition obtains depends on whether certain dedicto modal facts obtain. And so what’s ultimately going on, foundationallyspeaking, is that we have a de dicto reduction of de re modality. Facts con-cerning Messi* and his counterparts* are, in this setting, not being appealedto in order to provide a foundation to which de re modality can be reduced.The foundational version of Merricks’ objection simply doesn’t arise.15

15 As Jason Turner pointed out to me, there is a further aspect to this issue. When we accepta certain metaphysical analysis, there might be different routes to the analysis. Ultimately,

What if Merricks is objecting to the deployment of ersatz counterparts ina semantical analysis of de re modality? Here, it’s worth remembering thatthe distinction between foundational and semantical projects wasn’t lost onLewis. He tells us early on in Plurality that when we are doing semantics:

. . .we need no possible worlds. We need sets of entities which,for heuristic guidance, ‘may be regarded as’ possible worlds, butwhich in truth may be anything you please. We are doing math-ematics, not metaphysics. (p.)

So even Lewis — arch enemy of all things ersatz — is careful not to complainthat sets of sentences (or other abstract whatnots) are incapable of servingas adequate semantic values within an intensional semantics. His complaintis rather that ersatz constructions are inadequate tools when our project ismetaphysical in character, and the anti-ersatzer diatribe in Plurality is meantto convince us only that ersatz constructions are not up to the foundationaltask. Their semantic adequacy is granted from the beginning, and Lewis(, p.-) is careful to point out that their foundational inadequaciesneed not render ersatz possibilia inadequate semantical tools.16

But hang on, how can the fact that there are different ways to constructersatz possibilia not have a negative effect on the semantic project? Won’twe end accepting that no single semantical analysis of a language is betterthan some incompatible analysis based on some other way of constructingersatz possibilia? Isn’t that what the semantical version of Merricks’ worryamounts to?

How we answer these questions will depend on how we conceive of theexplanatory ambitions of semantic theorizing.17 On what we can think ofas the ‘folklore’ conception of (model-theoretic) semantics, the model theory

my counterpart theorist offers a de dicto analysis of de re modality. But the route to theanalysis is indirect: we first analyze de re modality in terms of counterpart* relations andthen offer a de dicto analysis of counterpart* relations. That’s not the only route: I couldhave instead analyzed de re modality in terms of counterpart** relations and then offeredan analysis of those. But the end result is the same either way, and the fact that there aredifferent routes to the ultimate analysis isn’t important.16 A similar point is made in a different context by Sider (, §), who points out that thefact that ordered pairs can be constructed in different ways isn’t a problem unless the con-structions are being used to give a metaphysical analysis of relations. But that doesn’t meanthat other uses of pairs are illegitimate because on those uses no metaphysical significanceis claimed: the pairs are only used to get a job done.17 This way of putting the point is perhaps a little tendentious. Rather than think that

ranges over a class of interpretations of a language, amongst which we hopeto find the ‘intended’ one: the one that ‘gets the interpretation right’. The roleof a semantic theory emerges as that of providing a constitutive account ofboth logical consequence (truth-preservation under every interpretation) andtruth simpliciter (true on the intended interpretation). But this conception ofthe explanatory ambitions of a semantic theory is not mandatory. On whatwe can think of as the ‘instrumentalist’ conception of semantics — a viewrecently defended by Hartry Field () — the goal of a semantic theory isnot that of providing constitutive accounts of truth or consequence but ratherthat of providing an extensionally correct account of logical consequence.What we want to know is what follows from what? and, for the Fieldianinstrumentalist, any value that we might associate with a semantic theory liesin its provision of extensionally correct answers to this question. (Which is arelief, given that Field’s take on logical consequence is that it is best viewed asa primitive notion, meaning that semanticists trying to provide a constitutiveaccount of it are barking up the wrong tree.)

If the explanatory ambitions of semantic theorizing are understood alonginstrumentalist lines, the existence of many equally good semantic theoriesis harmless. For the goodness of a semantical analysis (of a language ℓ)depends, from the instrumentalist’s point of view, on how well that analysistracks the extension of the consequence relation (of ℓ). And so the existenceof more than one equally good semantic theory would only show that wehave more than one way to provide an extensionally accurate specificationof logical consequence. And the mere fact the entities these semantic theoriesquantify over are not intrinsically suited to represent possibilities does notprevent them from serving this instrumental end. We are, after all, doingmathematics, not metaphysics.

If we conceive of semantic theorizing as being more ambitious — if weaccept something like the folklore conception — then the instrumentalist’sreply to Merricks is unavailable: now the goodness of a semantic theoryamounts to more than its mere ability to offer correct answers to questions ofconsequence. But saying that isn’t saying very much: there is still a questionof what the ambitions of semantics are. Lewis’s (, pp.-) discussionof the role of possible worlds and individuals in the analysis of language is

there is this single project, semantics, and a debate about its explanatory ambitions, onemight instead think that there are a bunch of different projects, each of which might becalled ‘semantics’ and each of which has different explanatory ambitions. Compare thediscussion of the role Plantinga’s semantics serves in Woodward ().

particularly revealing in this regard.18

Lewis’s starting point is that language is used to convey information: youknow something; you want me to know it too; I take you to my source ofknowledge and to speak truthfully; via this mechanism I come to possess thepiece of information you wanted me to possess. But though I rely on you tospeak truly, the words you use will be true on some interpretations and falseon others. The right interpretation is the one that specifies those conditionsunder which you are indeed truthful and my trust is well-placed. So a se-mantics must associate each sentence of a language with a truth condition,conceived of as a set of worlds. And the assignment must be systematic, andtell us “which speakers at which times at which worlds are in a position toutter which sentences truly” (p.).

This means that we must assign, by finite means, truth conditions to aninfinite number of sentences, and Lewis’s story about how this can be doneis familiar: we list the vocabulary of the language, assign to each expres-sion a syntactic category and a semantic value, list the rules for buildingnew expressions from old ones in such a way as to ensure that the semanticvalue of the new is a function of the semantic values of the old, and specifytruth conditions for sentences as a function of the semantic values of theirsubsentential constituents.

Lewis then gives us a job description for semantic values, and it’s at thispoint where things get interesting. Semantic values are there to do two thingsand two things only: to generate other semantic values and to generate truthconditions for sentences. The object, Lewis (p.) insists, is not that weshould find entities capable of deserving names “from the established jargonof semantics”, but just that we find entities capable of doing these two things.It’s for this reason that Lewis uses the colourless term semantic value ratherthan a more established piece of jargon like referent. After all, the thoughtthat my name refers to me rather than to a set of open sentences is aMooreanfact. But “there is no reason not to say both that my name has me as itsreferent and also that it has a certain [set] as its semantic value” (p.). Solong as a set of open sentences carries enough information to generate othersemantic values, it will be deserving of the name.

Notice, then, that the mere observation that semantic values come cheap

18 Even before we get into the details, we can see that there are crucial differences betweenthe Fieldian picture and the Lewisian one. For whereas Field thinks that semantic theoriesserve an instrumental role in the analysis of logical consequence, Lewis thinks that theyserve a genuinely explanatory role in the analysis of linguistic communication.

wouldn’t have bothered Lewis a great deal. For semantic theories are judgedto the extent that they associate sentences with the right truth conditions andso long as the truth conditions are generated systematically, which entitiesare used as semantic values is unimportant. In a sense, subsentential mattersare irrelevant if sentential questions are answered systematically. As Lewisput it much earlier: “Semantic values may be anything, so long as their jobgets done” (, p.). And again, their only job is to generate semanticvalues and truth conditions.19

This isn’t instrumentalism. As far as the Fieldian instrumentalist is con-cerned, a semantic theory can assign to sentences whatever truth conditionsit likes so long as it answers questions of consequence correctly. And to seethat, note that the notion of a ‘intended’ interpretation doesn’t play any rolefor the instrumentalist. On the Lewisian picture, by contrast, semantics doesaim to specify the conditions in which speakers are in a position to utter asentence truly and a semantic theory which assigned silly truth conditionswould be a silly theory even if it delivered extensionally correct answers toquestions of consequence.

What is true, admittedly, is that the Lewisian picture involves an instru-mentalism of sorts about semantic values: semantic theories which assignsilly semantic values might sill assign the right truth conditions after all.True enough, we might have pause for thought were we to think that thesemantic project was to specify something like ‘what we were referring toall along.’ But it’s hard to see what the problem is once the notion of a se-mantic value is divorced from more everyday semantic jargon. Moreover,even if we are happy with something like the picture Lewis sketches, it’s stillan open question exactly how instrumental our account of semantic valuesneeds to be. For instance, even if we are careful to distinguish the referentof a term from its semantic value, it doesn’t automatically follow that thereis no connection between the two. Consider, e.g., the values assigned to or-

19 Doesn’t naturalness constrain subsentential interpretation too? Well, Lewis () doesaccept naturalness as a constraint on interpretation, but he prefaces that entire discussion byconceding to Putnam that semantics takes ordinary things like you and me to be semanticvalues. If the relevant pages of Plurality (pp.-) are anything to go by, Lewis doesn’tbelieve this for a second. And though Lewis does mention naturalness in relation to hispreferred convention-based approach to language — see, e.g., Lewis () — it’s far fromclear that he endorses anything like the magnetic conception of subsentential reference thathe’s often associated with (cf. Schwarz ()) and Weatherson ()). Thanks to RobbieWilliams for discussion of these issues.

dinary names in a Montagovian setting: sets of properties. Though thesesets clearly aren’t what ordinary uses of proper names refer to, they can beused to specify ordinary referents: thus whereas the semantic value of ‘LeoMessi’ is a set of properties, that name refers to the object that instantiatesthose properties. And this point has an analogue in the context of Merricks’complaint against ersatz counterpart theory. For though the present pictureinvolves the thought that ‘Leo Messi’ has a set of open sentences as its se-mantic value, we can at least define up an intuitive referent in terms of it:the name refers in the ordinary sense to that object which in fact satisfies allof those open sentences.

These issues are rich and deserving of more attention. But I hope thatthey can be set aside in the present context. For remember that Merricksobjected to ersatz counterpart theories on the grounds that there is no goodreason why ersatz individuals should be identified with sets of open sentencesrather than something else. But whether the fact that ersatz individuals canbe constructed in many ways is problematic depends on which roles they areplaying within our account of de remodality. Perhaps the problemsMerrickssees are genuine if the ersatzer were trying to deploy ersatz counterparts toprovide a metaphysical reduction of de re modality. But on the version ofthe view I’ve defended, ersatz counterparts are not playing a foundationalrole. Rather, ersatz counterparts are semantical tools, to be used as semanticvalues. And the semantic adequacy of ersatz counterparts is neither vitiatedby the fact that they can be constructed in many ways nor by the fact thatthey fail to be intrinsically representational. What matters is just that theyget the job done.

Conclusion

Lewis (, p.) calls his realist account of modal space “a paradise forphilosophers” and challenges his opponents to deliver the theoretical benefitsthat realism offers more cheaply. Whether she can enjoy all of the benefits ofLewisian realism is doubtful, but I contend that the ersatzer can enjoy thoseassociated with of his treatment of de re modality. For the counterpart-theoretic analysis of de re modality Lewis offers can be made acceptable bythe lights of those of who reject Lewis’s ontology. To those of us who findcounterpart theory attractive, this should come as something of a relief.

References

Bricker, Phillip. . “Island Universes and the Analysis of Modality.” InGerhard Preyer and Frank Siebelt (eds.), Reality and Humean Superve-nience: Essays on the Philosophy of David Lewis, –. Lanham, MD:Rowman & Littlefield.

Divers, John. . “On the Prohibitive Cost of Indiscernible Concrete Pos-sible Worlds” Australasian Journal of Philosophy :–

— . “A Genuine Realist Theory of Advanced Modalizing.” Mind:–.

— . Possible Worlds. London: Routledge.

Field, Hartry. . Saving Truth from Paradox. Oxford: Oxford UniversityPress.

Hazen, Allen. . “Counterpart-Theoretic Semantics for Modal Logic.”Journal of Philosophy :–.

Heller, Mark. . “Property Counterparts in Ersatz Worlds.” Journal ofPhilosophy :–.

Lewis, David. . “Counterpart Theory and Quantified Modal Logic.”Journal of Philosophy :–.

— “Counterparts of Persons and their Bodies.” Journal of Philosophy:-

— . “Index, Context, and Content.” In Stig Kanger and Sven Ohman(eds.), Philosophy and Grammar, –. Dordrecht: D. Reidel.

— a. “Individuation by Acquaintance and by Stipulation.” The Philo-sophical Review :–.

— b. “Postscript to “Counterpart Theory and Quantified ModalLogic”.” In Philosophical Papers, Volume , –. Oxford: Oxford Uni-versity Press.

— . “Putnam’s Paradox.” Australasian Journal of Philosophy :–.

— . On the Plurality of Worlds. Oxford: Basil Blackwell.

— . “Meaning Without Use: Reply to Hawthorne.” Australasian Jour-nal of Philosophy :–.

Melia, Joseph. . “Reducing Possibilities to Language.” Analysis :–.

Merricks, Trenton. . “The End of Counterpart Theory.” Journal ofPhilosophy :–.

Plantinga, Alvin. . TheNature of Necessity. Oxford: Oxford UniversityPress.

Rayo, Agustín. . “An Actualist’s Guide to Quantifying-In.” Crítica:–.

Schwarz, Wolfgang. . “Against Magnetism.” Australasian Journal ofPhilosophy :–.

Sider, Theodore. . “Naturalness and Arbitrariness.” Philosophical Stud-ies :–.

— . “The Ersatz Pluriverse.” Journal of Philosophy :–.

— MS. “Beyond the Humphrey Objection.” Unpublished.

Weatherson, Brian. . “The Role of Naturalness in Lewis’s Theory ofMeaning” Journal for the History of Analytical Philosophy :–.

Woodward, Richard. . “The Things That Aren’t Actually There.” Philo-sophical Studies :–.

— . “Counterparts.” Philosophy Compass :–.