Counterparts

Counterparts

Richard Woodward*Universitat de Barcelona

Abstract

Possible worlds represent you as being certain ways, as having a different lives, different hopes,and different friends. A foundational question in the philosophy of modality thus emerges: in vir-tue of what does a world represent you in these ways? In this paper, we focus on David Lewis’sanswer to this metarepresentational question: Counterpart Theory.

Philosophers find it congenial to talk about modal space, the space of possibilities, in twovery different ways. On the one hand, we talk about modal space by means of talkingabout possible things and how they are. And we talk not only about possible worlds andwhat goes on at them, but also about the inhabitants of those worlds, the possibilia. Onthe other hand, we talk about modal space in a more familiar way, by talking about howthings might have been, couldn’t have failed to be, by talking about what is possible andwhat is not.

It is useful to think of these two ways of talking about modal space as correspondingto two different languages: the possibilist language of worlds and their parts, and the modallanguage of mights and might nots. Thus when it comes to expressing the possibility thattalking donkey exist, we have many options. Speaking the possibilist language, we mightsay: ‘there is world at which donkeys talk’ or ‘some possible donkeys are talkative’.Speaking the modal language, we might say: ‘donkeys might have talked’ or ‘possibly,there are donkeys that talk’. These sentences share a subject matter, in the sense that theyare all about the same thing: modal space, and how it is.

Since they share their subject matter, it’s not too surprising to learn that sentences ofthe one language can be paired up with sentences of the other. This pairing is encapsu-lated, in part, by two famous biconditionals:

Possibly p iff there is a possible world at which pNecessarily p iff there is no possible world at which not-p

Phrased in our terms, what these biconditionals are getting at is the idea that wheneverthere is some claim about modal space that we can express using modal sentences of theform ‘possibly p’ or ‘necessarily p’, then there is some way of expressing that same claimby talking about possible worlds and what goes on at them, i.e., some sentence of thepossibilist language which expresses the relevant claim about modal space.

Some comments. Firstly, though I might have given the impression that the sentencesfrom the one language can always be paired with the sentences of the other, that’s toostrong. What’s true is that the sentences of the two languages can be paired off in a hostof cases. Whether they can be paired off in all cases will depend on whether the modallanguage and the possibilist language have the same expressive power, i.e., on whether ornot everything you can say about modal space in the one you can say in the other. Anda standard worry is that there are things you can say in the possibilist language which

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resist expression in the modal language. And if that’s right, there will be some sentenceof the possibilist language which has no partner in the modal language. For more discus-sion of these issues, see Hazen (1979), Melia (1992), and Nolan (2002).

Secondly, though many philosophers have thought that talking about possible worlds isexplanatory of modality (see, e.g., Stalnaker 1976; Lewis 1986; and many others), such aclaim isn’t mandatory. Indeed, talking in terms of possible worlds might be useful even ifthe direction of explanation goes the other way round so that there being a possibleworld at which p is explained in terms of its being possible that p (see, e.g., Forbes1985). That’s not to say to say that such an approach is attractive, just that it’s one thingto hold that modal sentences and possibilist sentences can be paired off with each other,and quite another to hold that one of these languages is more explanatorily fundamentalthan the other.

Finally, though the possibilist language talks about possible worlds and their inhabitants,we’ve not said anything yet about how the sentences of that language should be inter-preted. Some (most famously, David Lewis 1973, 1986) think that we should take thepossibilist language at face-value and embrace an ontology of merely possible things, talk-ing donkeys and the rest. Others (Stalnaker 1976 and Plantinga 1974 being cases in point)think we should take the possibilist language to be about abstract representations of Lewi-sian worlds and individuals, rather than the real thing. And others still (e.g., Rosen 1990;Yablo 1996) think that we shouldn’t take the possibilist language to be about worlds andindividuals at all, whether or not they are conceived of as being the real thing or ersatzsurrogates. And it’s worth noting that the previous two points, regarding the expressivepower of our two languages and explanatory relations they bear to one another, are notindependent of this third, interpretative question. That is, whether or not the possibilistlanguage is more explanatory of modal space than the modal language, and how expres-sively powerful it is, will in part turn on how it is interpreted.1

For the most part, and with these qualifications in mind, I’ll assume that the possibilistlanguage is to be interpreted as really involving quantification over possible worlds. Andwhatever you think about them – i.e., whether you’re a fan of Lewis’s account or someabstract alternative – a central question concerns how a possible world represents that such-and-such is the case. For notice that our Leibnizian biconditionals talk about what is trueat a possible world, and the relevant notion here is representational: to say that p is true‘at’ a world w is to say that w represents p as being the case. But it’s one thing to hold thatthere are possible worlds that represent the existence of talkative donkeys, quite another totell a story about how this happens. And one’s answer to this metarepresentational questionwill vary depending upon one’s view about the nature of possible worlds. Counterpart The-ory, though it has subsequently been adopted by those who reject his modal metaphysics(Heller 1998; Sider unpublished manuscript; Stalnaker 1986; Woodward unpublishedmanuscript), is Lewis’s own answer to the metarepresentational question.2

1. Lewis on Representation

Lewis’s theory of possible worlds is often lazily contrasted with so-called ‘representational’alternatives. This is understandable. For where Lewis’s possible objects (be they worlds orinhabitants of worlds) are the real thing, concrete objects much like you and I, his oppo-nents have things (sets of sentences, or what have you) which act as surrogates for Lewis’spossible objects, things which represent Lewis objects without being the real thing. Butwhat’s misleading about the contrast is that Lewis himself relies heavily on the notion ofwhat a possible world represents as being the case: his worlds represent things as being

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one way rather than another, and Lewis is happy to say it’s true ‘at’ one of his worldsthat there are talking donkeys and that it’s true ‘at’ one of his worlds that you are a foot-baller rather than a philosopher.

When it comes to purely general facts like that there are dinosaurs and that everything isred, Lewis holds that what a world represents is fixed solely by what that world contains.Thus a world represents the existence of dinosaurs by having dinosaurs as parts, and if allof a world’s parts are red, then that world represents that everything is red. And so whensay things like ‘it’s possible for there to be talking donkeys’, Lewis’s account has it thatsuch a claim is true iff there is possible world which contains talking donkeys.

This account of representation is incomplete because though it tells us (e.g.) how pos-sible worlds represent the existence of humans in general, it doesn’t tells us how a worldrepresents the existence of specific humans in particular. Saying that world representshumans by containing human parts isn’t to say that a world represents Billy by containingBilly as a part. Perhaps, however, we can just extend the story to cover these cases too,and say that a world represents Billy as existing by containing him as a part and that aworld represents Alice as being happy by containing a happy part that is identical toAlice.

Lewis finds this move suspicious. For since different worlds represent Billy and Alicedifferently – in w Alice is happy, in v she is sad – we’re going to be end up saying thatBilly and Alice are literally part of more than one world. Thus worlds can ‘overlap’ inthe sense that one and the same object can be part of more than one world. But considermy foot. I’m lucky enough to be normal and have exactly five toes, but I might havehad an extra one. But that means that whereas the actual world represents me as havingexactly five toes, another world represents me as having six. So within the present setting,it looks like we’ll have to say that one and the same thing, my foot, has exactly five toesand exactly six toes. And that sounds like a contradiction: if x has exactly five toes, xcan’t also have exactly six toes.

Perhaps there are things we can say here. Perhaps when we say that my foot has exactlyfive toes and exactly six toes what we mean is that my foot has exactly five toes in thisworld and exactly six toes in some other world. On this picture, there isn’t really any prop-erty of having five toes simpliciter: there is just the property of having five toes relative to apossible world. (See McDaniel 2003 for discussion of this approach.) But Lewis rejectsthis picture, and holds that properties like that of having exactly five toes are monadicrather than relational. He therefore rejects the idea that one and the same object can bein more than one world, telling us that his possible individuals are ‘worldbound’ in thesense that they are part of just one world. When it comes to explaining how a world rep-resents Billy, we’re thus back to the drawing board.

Even though objects like you and I are part of exactly one world, that’s not to say thatother worlds don’t represent us as existing ‘at’ them. So on the picture to be developed,it will be true to say that I exist at more than one world, even though it will be false tosay that I am part of one than one world. The question is: if worlds don’t represent meby containing me, how are their representational properties fixed?

Even though other worlds don’t contain me, they do contain things to which I amvery similar. Thus some world w might contain an object that is male philosopher, whohas brown hair and blue eyes, is writing a paper on counterpart theory, and so on. Thisobject, though not really me, resembles me in various ways. It is, Lewis (1968) says, isone of my counterparts. And the core idea of counterpart theory is that worlds representme as existing in virtue of containing one of my counterparts. Or to phrase that differ-ently: other worlds represent me by containing one of my representatives, and something

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counts as one of my representatives if I bear the counterpart relation to it. So when wesay that w represents me as being happy, Lewis’s theory has it that this is true iff w con-tains a counterpart of me who is happy. In turn, whether or not it is possible for me tobe happy depends, for the counterpart theory, on whether or not I have a counterpartwho is happy.

Counterpart theory thus incorporates two ideas. First, that my existence ‘at’ otherworlds is ensured by those worlds having elements that are distinct from me: my counter-parts. Call this the distinctness thesis. Second, that whether something is one of my coun-terparts depends on whether or not that object is similar to me in certain ways. Call thisthe similarity thesis. It’s important to see that these two theses are independent, and thatthe second is the really distinctive thing about counterpart theory.

To see this, note that some philosophers (e.g., Plantinga 1987) can be read as holdingthat whether or not I exist at another world turns on whether or not my essence, theproperty of being Richard, is an element of that world.3 But my essence is not really me: Iam not, I hope, a property. So in that sense, the mere fact that my existence at otherworlds is ensured by that world containing an element that is distinct from me, i.e., thedistinctness thesis, is not distinctive of or unique to counterpart theory. And to see why,just note that Plantinga, unlike Lewis, believes in the thesis of transworld identity, whichcan here be understood as the claim that the thing which represents me at one world isliterally identical to the thing that represents me at any other world. That is, my existence‘at’ any world w is always traceable to the fact that my essence is an element of w.

Perhaps, then, the distinctive aspect of counterpart theory is the coupling of the dis-tinctness thesis with the idea that what represents me ‘at’ one world is never the samething as what represents me ‘at’ another world. Call this the variation thesis. But even thisisn’t quite right. For it’s relatively easy to tweak the Plantingan view to ensure that boththe distinctness and variation theses are upheld. For instance, the Plantingan might holdthat whether or not I exist at a world w turns upon whether or not w has the orderedpair <being Richard, w> as an element. But that means that each world will use a differentobject to represent me: w will use <being Richard, w>, v will use <being Richard, v>, andso on. None of these objects is really me, and so distinctness thesis is respected. But eachworld uses a different object to represent me, and so the variation thesis is respected too.We might even call these different objects my ‘counterparts’, if only to highlight the sim-ilarity between this view and Lewis’s own.

We can now see why the similarity thesis is the crucial one. For suppose we ask whyit is, on the neo-Plantingan view we’re considered, that <being Richard, w> and <beingRichard, v> represent the same thing. That is: if these two things are counterparts, in vir-tue of what is this true? Then the answer will be: because their initial element is thesame. (More generally: the theory says that <l, w> represents the same thing as <q, v>iff l ¼ q.) So in this way, even though the theory upholds both the distinctness thesisand the variation thesis, it fails to quality as a version of counterpart theory because itrelies, at a crucial point, upon the notion of identity. That is, when it comes to explain-ing why two things are counterparts, the theory’s answer is couched in terms of numeri-cal identity. The contrast with Lewis couldn’t be clearer. When Lewis is faced with thequestion of why two things are counterparts, his answer is not couched in terms of iden-tity, but in terms of similarity: one of his representatives is a counterpart of another justin case the former is similar to the latter is some important way. As we’ll see in the nextsection, it’s precisely this aspect of Lewis’s counterpart theory, i.e., the similarity-basedaccount of the counterpart relation, that gives rise to the benefits that many have associ-ated with Lewis’s account of representation.

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To take stock, counterpart theory is Lewis’s answer to the question of how the repre-sentational features of possible worlds are fixed. The theory says that a world representsthe existence of blue swans just in case it contains blue swans as parts. So when wemodalize about blue swans and say things like ‘there could have been blue swans’ – a caseof what philosophers call de dicto modalizing – Lewis tells us that this de dicto modal claimis true iff there is a world that contains blue swans. More importantly, the theory also saysthat a world represents Billy as being happy by containing an object which is both happyand one of Billy’s counterparts. So when we modalize about Billy and say things like‘Billy could have been happy’ – a case of what philosophers call de re modalizing – Lewistells us that this de re modal claim is true iff there is a world that contains a counterpartof Billy who is happy. Much of this is acceptable to the non-Lewisian. But where coun-terpart theory gets its bite, i.e., what makes it a distinctive and interesting view of de rerepresentation, is the claim that whether one thing is a counterpart of another turns noton facts about numerical identity but instead turns on facts about similarity.

2. The Benefits of Counterparts

Counterpart theory, as we have seen, makes the notion of similarity centrally importantwhen answering the question of when one thing is a counterpart of another. And as Iintimated a moment ago, this feature has a number of consequences that many havethought to be beneficial. Space constraints forbid a thoroughly comprehensive survey,however, and we shall focus on two related benefits that many associate with counterparttheory.4

2.1. INCONSTANCY

Our modal judgements are highly inconstant. Thus in one moment, we might feel happyto judge that something could have travelled faster than the speed of light – after all, noth-ing in the laws of logic rule it out. But in the next moment, we might feel happy to judgethat nothing could have travelled faster than the speed of light – even though logic doesn’trule it out, physics surely does. The standard move at this point is to explain this incon-stancy by holding that there are different notions of possibility – or, as it is sometimes put,different modalities – and that our two apparently inconsistent judgements can happilyco-exist because the notion of possibility that is relevant in the one case is distinct from thenotion of possibility that is relevant in the other. Our first judgement is correct because itis logically possible for something to travel faster than the speed of light; our second judge-ment is correct because it is physically impossible for anything to travel that quickly.

Lewis thinks our modal judgements are inconstant in another way:

I think there is a grant range of cases in which there is no determinate right answer to questionsabout representation de re, and there no right answer about modality de re. Could Hubert Hum-phrey have been an angel? A human born to different parents? A human born to different partsin ancient Egypt? A robot? A clever donkey that talks? An ordinary donkey? A poached egg?Given some contextual guidance, these questions should have sensible answers. There are waysof representing whereby some worlds represent him as an angel, there are ways of representingwhereby none do. Your problem is that the right way is determined, or perhaps underdeter-mined, by context – and I supplied no context. (1986: 251)

There are two ideas that need to pulled apart here. The first is that our de re modal judg-ements are inconstant in the sense that we oscillate between judging it to be true that

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Billy could have been a robot/angel/donkey/poached egg and judging those de re modalclaims to be false. The second is that the truth-values of de re modal claims are deter-mined in part by features of the context in which those claims are uttered, so that thereis no acontextual answer to the question of whether Billy could have been a robot/angel/donkey/poached egg. These ideas are obviously connected: inconstancy in ourde re modal judgements would provide some evidence in favor of contextualism. But thetwo ideas are nonetheless independent. Even if we grant that there is no acontextualanswer to the question of whether there is a world at which Billy is a poached egg, andthereby no acontextual answer to the question of whether Billy could have been a poa-ched egg, it doesn’t follow that our judgements will be inconstant – to get that conclu-sion, we’d need to allow that there are different contexts which deliver different verdicts.For all that’s been said so far, however, we might always be in a context which deter-mines that there is no world at which Billy is a poached egg and that would mean thatit would always be appropriate to say that Billy couldn’t have been a poached egg. Soit’s worth noting that even if one grants Lewis’s claim that questions of de re modality arecontext-sensitive, inconstancy doesn’t follow automatically.5

Nevertheless, it is not difficult to see how the inconstancy which Lewis finds in our dere modal judgements would be explicable given counterpart theory. For counterpart rela-tions are relations of comparative similarity: whether one thing is a counterpart of Billydepends on whether it is similar to Billy in some appropriate way. But we have manyand varied relations of comparative similarity and some relations differ from others byweighting different respects of similarity. I might, e.g., be similar to you in respect of haircolor and nationality, but different from you in respect of gender and sexual orientation.So whether you should be classified as being similar to me depends, largely, on which ofthese features we care about. And given that counterpart relations are relations of qualita-tive similarity, the upshot is that whether (e.g.) I have a counterpart who is happy willdepend on which counterpart relation – which notion of similarity – we have in mind.Relative to one notion of similarity, it might be true that two things are counterparts,even though relative to other notions of similarity, it might not. Given that there are nocontext-independent answers to questions of comparative similarity, there will, givencounterpart theory, be no context-independent answers de re modal questions either.

Again, however, what counterpart theory naturally suggests is just the truth-values ofde re modal claims are determined in part by facts about which counterpart relation is rel-evant in a given context.6 And that doesn’t automatically predict that our judgementsabout de re modal claims will be inconstant. To get that conclusion one would also needto accept that, as a matter of fact, different counterpart relations are relevant in differentcontexts. But for all that’s been said so far, it might be a interesting fact about humanpsychology that, for creatures like us, certain notions of similarity are just far more inter-esting than others and that some notions of similarity are totally uninteresting.7 So coun-terpart relations based on the uninteresting notions will never be relevant and we willnever find ourselves in a context where the truth of a de re modal claim is determined bysuch a counterpart relation. The upshot is that counterpart theory is itself neutral on thequestion of whether or not our de re modal judgements are inconstant, but well posi-tioned from an explanatory point of view in either scenario.8

2.2. RESOLUTION OF MODAL PARADOXES

Granting that our de re modal judgements are inconstant, we’ve seen that counterpart the-ory is able to allow that we can, in one moment, truly claim that Billy could have been a

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contender while, in the next, truly claim that Billy couldn’t have been a contender. Solong as context shifts between our two token utterances, so long as the counterpart rela-tion that’s relevant in the former case is different to the one that’s relevant in the latter,the counterpart theorist can happily regard our inconstant judgements as expressing, intheir respective contexts, true claims. But Lewis also thinks that we can find opposingde re modal judgements even within a single context.

Consider, for instance, a statue and the lump of clay out of which it is made. Howmany things do we have here? As Lewis points out, it ‘reeks of double counting’ to saythat we have a statue and also a statue-shaped bit of clay that is just where the statue isand weighs just as much. What we want to say, Lewis thinks, is that the statue is thelump. But now reflect on the fact that our judgements about the de re modal propertiesof the statue and the lump are different. The statue, for example, couldn’t survive beingsquashed, but the lump of clay surely could. How, then, can the statue be identical tothe lump given that they have different properties? Didn’t Leibniz teach us that identicalobjects share all their properties?

On the face of things, then, we have a paradox. The following three claims all seemtrue, but it also seems that they cannot all be true together:

1. The state ¼ the lump.2. The lump could survive squashing.3. The statue couldn’t survive squashing.

Counterpart theory helps us to see how this paradox can be resolved. The first point isthat even though the statue is the lump, counterpart theory allows that the lump and thestatue can be distinguished. For what we have is one thing – call it Frank – that can bepresented in two ways: as a statue and as a lump. And the counterpart theorist thinks thatwhether Frank satisfies a given de re modal predicate will depend, in part, on whetherFrank is presented as a lump or as a statue. Presenting as a lump of clay, Frank can sur-vive squashing because when Frank is so presented, a counterpart relation is evokedwhich underwrites the truth of (2). But when presented as a statue, Frank cannot survivesquashing because when Frank is so presented, a different counterpart relation is evoked,a relation which underwrites the truth of (3). But both ways of presenting Frank are waysof presenting the same thing, meaning that the thing you present when you presentFrank as a statue is identical to the thing you present when you present Frank as a lump,thus underwriting the truth of (1).

As Lewis notes, though his resolution of our paradox doesn’t involve the doublecounting of objects, it might be thought that it involves double thinking since we haveto concede the identity of the statue and the lump and then distinguish them when itsuits us. Lewis replies:

I only distinguish what everyone must distinguish: two different references, in different words,to one thing. And I say that these different references tend to evoke different ways of represent-ing.... You can double up ways of representing... or else you can double up entities... I submitthat the first doubling is more credible than the second. (1986: 253)

Notice that Lewis doesn’t claim that the counterpart-theoretic resolution of the paradoxis the only solution – for a defence of double counting, see Fine (2003); for an overviewof the debate, see Paul (2010) – just that the resolution it offers is more credible (lesscostly, simpler, more elegant) than its rivals. And it’s also clear that the counterpart-theoretic resolution applies in other cases too: thus Lewis (1971) applies it in defence of

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the claim that you are identical to your body, even though you might have existed with-out your body. In any case, just as counterpart theory was well-positioned to explain theinconstancy that Lewis detected in our de re modal judgements, it is also well-positionedto resolve the paradoxes that are based upon such inconstancy.

3. Essentialism

It is natural to hold that some of your properties are essential; the rest are accidental. Andso a natural question is: what picture of essential properties does counterpart theoryunderwrite?

None. Counterpart theory, in the first instance, is a theory of de re representation and,in the second, a theory of de re modality. It gives an account of that in virtue of which apossible world represents de re possibilities, an account which naturally underwrites a cer-tain picture of the truth-conditions of de re modal claims. Whether or not objects haveessential properties, and in virtue of what they do so, are further, independent questions.

The literature often gives a different impression. Lewis himself tells us that counterparttheory supports a soft and sensible version of essentialism, a version which even the anti-essentialist can be happy with. But in making this claim, Lewis was presupposing a certainconception of the connection between essence and modality, namely, that an object’sessential properties are those properties that it has necessarily. In this setting, it’s clear thatthe counterpart theorist will say exactly the same things about essentialist claims that shesays about de re modal claims: there are no context-insensitive facts about which proper-ties an object has essentially, that whether an object has a property essentially will dependin part on how that object is presented to us in language, and so on. Thus understood,counterpart theory gives us a version of essentialism, but one that is freed from any prim-itive or language-independent notion of essence. Essence, in Lewis’s view, is reduced tode re modality, which is in turn reduced to facts about counterparts. If the connectionbetween essence and modality were severed, the first step in this analytic chain would bebroken.

Hyper-essentialists hold that all of an object’s properties are essential to it. JonathanSchaffer (2010) has recently claimed that counterpart theory is a form of hyper-essential-ism:

The hyper-essentialist looks over her worlds and... sees no individual at more than one world.For if she sees some individual x at a world w, then she will see x as essentially having the prop-erty of being in a world with the distinctive features of w. In this respect the counterpart theo-rist has exactly the same picture of the worlds as the hyper-essentialist. The counterpart theoristsand the hyper-essentialist merely have a semantic dispute, as to how to interpret claims in themodal language against their shared metaphysical picture.

But this mischaracterizes counterpart theory, given the reduction of essence to modality.The hyper-essentialist holds that objects have real and genuine essences that are fixedindependently of how we refer to those objects, and we have seen that the counterparttheorist thinks otherwise. So when the counterpart theorist sees an object x in a world wshe will emphatically not see x as essentially having the property of being in a world withthe distinctive features of w. And that is just to say that the only notion of essence thatLewis allows is one specified in terms of what’s true of all of x’s counterparts, i.e., onethat reduces to modality. So the dispute isn’t merely semantic: it’s metaphysical too.

Moreover, Lewis does not first admit the same notion of essence that the hyper-essen-tialist offers, and then goes on to find a clever way to interpret de re modal claims

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‘to make the metaphysical picture more palatable’, as Schaffer (2010: 28) suggests. Forcounterpart theorists simply reject the notion of essence that is integral to hyper-essential-ism and replaces it with one specified in terms of counterparts. At best, a hyper-essential-ist picture of essence could be coupled with a counterpart-theoretic account of de remodality. But then we would have to allow that while Billy (e.g.) is essentially human,he is not necessarily human. Feel free to make sense of that if you want. Just don’t thinkthat such a bizarre view follows from counterpart theory, or is even a natural option forthe counterpart theorist to take.

4. Kripke’s Concerns

In one of Naming and Necessity’s more famous footnotes, Saul Kripke (1972) pours scornon Lewis’s counterpart theory:

The counterpart of something in another possible world is never identical with the thing itself.Thus, if we say ‘Humphrey might have won the election...’ we are not talking about somethingthat might have happened to Humphrey but to someone else, a ‘counterpart’. Probably, how-ever, Humphrey does not care whether someone else, no matter how much resembling him,would have been victorious in another possible world. Thus, Lewis’s view seems to me evenmore bizarre than the usual notions of transworld identity it replaces.

Kripke here makes two different complaints. The first is that the counterpart theoristidentifies the subject matter of claims like ‘Humphrey might have won’ as concerning thede re properties of Humphrey’s counterparts rather than Humphrey himself. The secondis that the counterpart theorist makes a mockery of de se modal psychology – de re modal-ity where the relevant re is oneself – since Humphrey cares about whether he could havewon and doesn’t care at all about whether his counterparts could have won.

The first complaint is easily dealt with. Counterpart theory simply doesn’t say thatwhen we claim that Humphrey might have won we are talking about what might havehappened to Humphrey’s counterparts. At best, it says that whether we speak truly whenwe say that Humphrey might have won depends on facts about the (non-modal) proper-ties of Humphrey’s counterparts. But the theory also says that the question of whetherHumphrey, the man himself, satisfies the relevant de re modal predicate (e.g., ‘could havewon’) just is the question of whether Humphrey has a counterpart who satisfies the corre-sponding non-modal predicate (e.g., ‘wins’). But that is not to identify the question ofwhether Humphrey could have won with the question of whether one of his counter-parts could have won.

Perhaps the complaint is that counterpart theory marginalizes Humphrey. But thismisses the fact that the theory says that whether Humphrey might have won depends onwhether a certain relational fact involving Humphrey obtains. Humphrey is still verymuch ‘in the picture’ since which de re modal properties he has depends on what hiscounterparts are like. Of course it would be silly to say that which de re modal propertiesHumphrey has depends on what someone else’s counterparts are like. But that, whateverKripke says, is not what the counterpart theorist thinks. Nor does counterpart theorydivorce Humphrey’s de re modal profile from facts about what Humphrey is like. Foreven if it’s true that which de re modal properties Humphrey has depends on what hiscounterparts are like, whether Humphrey has such a counterpart depends very much onwhat Humphrey himself is like.

What of the other objection, that counterpart theory fails to capture our de se modalconcerns? There are a number of points available to the friend of counterpart theory.

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Firstly, there is the tu quoque response of Lewis (1986: 196). The thought here is thateveryone, be they counterpart theorists or not, is going to face a version of the complaintwhich Kripke lodges against Lewis. For what should be uncontroversial that is Humphreycares very much about whether or not he could have won. But now suppose we’re try-ing to say something substantial about which facts settle whether or not Humphrey couldhave won. Then in doing so, we’re going to end up saying something non-obvious,whether the particular thing we say is about Humphrey’s counterparts, or about hisessence, or about something else. So when push comes to shove, we’re going to end upidentifying (e.g.) the fact that Humphrey might have won with some other fact, X, andwe’re going to concede that our identification is non-obvious. The objection only hasany chance of working if we can find an X such that Humphrey cares not only aboutwhether he might have won but about X too. The challenge Kripke faces is to find suchan X. And as Lewis points out, those who, like Kripke, believe in abstract representationsof Lewis’s possibilia and genuine transworld identity don’t also believe that Humphreyhimself is part of those abstract representations. Something other than Humphrey, his rep-resentative, whether it is one of his counterparts or some abstract what-not, is going to getin on the act. And it’s difficult to see why Humphrey would care about what theseabstract what-nots represent him as being, and thereby difficult to see why Kripke’s com-plaint reveals anything uniquely problematic about counterpart theory.

Secondly, even putting the previous point to one, it’s a familiar point that an agentcan care about one thing without caring about another, even though the former is neces-sarily equivalent to the latter.9 Consider Alice. Being very thirsty, Alice cares very muchwhether there is any water nearby. But being ignorant of chemistry, she doesn’t care atall whether there is any H2O around. And all that despite the fact that water is necessarilyH2O! In general then, there is no mystery about how a rational agent could care aboutone thing Y about some other thing Z, even when Y is necessarily Z, so long as theagent is ignorant of the connection between Y and Z. Of course, upon coming to learnof the connection between Y and Z, a rational agent should care about one whenever hecares about the other. But applied to the present case, that’s just to say that if one learnedthat counterpart theory was the right theory of de re modality, then one should eitherbeing to care about what happens to one’s counterparts or stop caring about one’s de remodal properties. Perhaps there is a worry lurking around here – one wants to ask: ifLewis is right that de re modality consists in that then why on earth did we care about dere modality in the first place? (cf. Divers 2007) – but again, the question is whether thereis any substantial analysis of de re modality that avoids this worry.

Finally, there is, as Richard Miller (1992) points out, a serious question about whethercounterpart theory really does make a mockery of our de se modal concerns. Supposeyou have recently gone for a job interview. Sadly, you didn’t get the job: the swinesappointed Charles instead. Reflecting on your misfortune, the following thoughts runthrough your mind:

I could have got that job. After all, Charles got it, and he’s no better than me. I’m just as goodas he is – I have comparable qualifications, equally good references. Okay, his people skillsmight be a bit better, but such factors are irrelevant in this case since the work would havebeen mainly solitary. Yeah, I could have got the job. And I’d have been much happier if I had.

Such reasoning is familiar. But what’s going on here is that much as you care very muchabout whether you could have got the job, you also care very about whether or not thereis someone else, someone who is similar to you in the right ways, who did get the job.Indeed, notice that you are also weighing different respects of similarity against one

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another, and dismissing others as being irrelevant in context. For all intents and purposes,you’re judging whether or not you could have won by assessing whether or not youhave a counterpart who does win.

It’s unclear whether this consideration is decisive, however. For even if we grant thatyou do care about whether you have a counterpart who got the job, it’s equally impor-tant to you that your counterpart is an actual person who got the job at this world.10

If you learned that there was no actual person to whom you were relevantly similar whojob, you may well be forgiven for revising your de re modal beliefs and concluding thatyou couldn’t have got the job. But though the move isn’t decisive, it doesn’t providesome reason for thinking that the issues are far subtler than Kripke lets on. In a host ofcases, our de re modal judgements are formed with issues to do with how similar we areto other people very much in view.

In sum, there are at least three reasons why Kripke’s complaint against counterpart the-ory is shaky. Firstly, there is a question about whether his complaint reveals anythinguniquely problematic about counterpart theory. Second, there is a question aboutwhether the phenomenon that underlies his objection is really that surprising. Finally,there is a question about whether he is right that counterpart-theoretic facts are alwaysirrelevant to our de re modal concerns. At the very least, these considerations suggest thatKripke’s objection is far from convincing.

5. Further Issues

The account of representation that Lewis offered us, couched in terms of counterparts,remains an attractive and powerful theory which is able to explain many facets of ourde re modal judgements. No survey article of this nature could aim to be complete, andI shall close by pointing to two further issues that the interested reader may want tofollow up.

Firstly, counterpart theory as we’ve developed it is a theory which has a key placewithin Lewis’s own modal metaphysic, a metaphysic which contains a staggering amountof things, from talking donkeys to blue swans and beyond. Whatever its benefits andattractions, then, it would be a mark against counterpart theory if it were only availableto those who shared Lewis’s metaphysical outlook. A central question facing the counter-part theorist, then, is that of whether its account of representation can be made workablewithin the context of the kind of approach to possible objects we associated with Stalna-ker and Plantinga, where possible worlds and the rest are reduced to things which repre-sent Lewis’s objects without being the real thing. There are two central questions facingsomeone who wanted to conjoin such a view with a counterpart-theoretic account ofrepresentation. The first is that of what counterparts are, if not the flesh and blood thingswhich Lewis took them to be. This is a question about the relata of the counterpart rela-tion. The second is that of in virtue of what two things count as counterparts. This is aquestion about the grounds of the counterpart relation itself. Lewis, as we know, thoughtthat whether two things were counterparts turned on whether they were similar in theright kinds of ways. And it is precisely this similarity-based approach which generated thegood-making features of counterpart theory that we examined in Section 2. Whatremains to be seen is whether such a story can be developed within the context of a con-ception of counterparts on which counterparts represent Lewis objects without being thereal thing. For relevant discussion, you should consult Heller (1998), Merricks (2003),Sider (2002), Stalnaker (1986), and Woodward (unpublished manuscript).

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Secondly, counterpart theory has here been understood as a giving us an account ofhow possible worlds represent de re possibilities. But there are well-known analogiesbetween worlds and time, and it is an interesting question whether a temporal version ofcounterpart theory can be made viable. In analogy with its modal cousin, temporal coun-terpart theory analyzes tensed predications in terms of temporal counterparts. So, e.g., thetheory says that a object will be F just in case that object has a temporal counterpart atsome future time such that that temporal counterpart is (tenselessly) F. For defences anddiscussions of temporal counterpart theory, see Sider (2001), Hawley (2001), and Haslan-ger (2003).

Acknowledgement

With thanks to Ross Cameron, John Divers, Tatjana von Solodkoff, and an audience atthe University of Barcelona. My research on this paper was partially supported by myinvolvement in the Nature of Assertion: Consequences for Relativism and Fictionalism project(FFI2010-169049), the Vagueness and Physics, Metaphysics, and MetaMetaphysics project(FFI2008-06153), and the PERSP-Philosophy of Perspectival Thoughts and Facts project(CSD2009-00056). Many thanks to the DGI, MICINN, and the Spanish Governmentfor supporting these projects.

Short Biography

Richard Woodward wrote his doctoral thesis on fictionalist accounts of merely possibleentities at the University of Sheffield. He went on to hold two postdoctoral positions atthe University of Leeds, funded respectively by the Analysis Trust and the Centre forMetaphysics and Mind. He then spent a year at the University of Cambridge, before tak-ing up a Juan de la Cierva fellowship at the University of Barcelona. Richard’s researchinterests are located in metaphysics (esp. modality; fictionalisms; indeterminacy; metaon-tology), the philosophy of language (esp. vagueness; conditionals; metasemantics), the phi-losophy of logic (logical consequence; the semantic paradoxes), and aesthetics (metaphor;fiction; the imagination). His research has been published in journals including Nous,Analysis, Philosophical Studies, and Oxford Studies in Metaphysics. For more informa-tion, please visit his website: http://carvingnature.wordpress.com/.

Notes

* Correspondence: LOGOS, Facultat de Filosofia, Universitat de Barcelona, c/ Montalegre 6, Barcelona 08001,Spain. Email: [email protected].

1 For overview of the debate, see deRosset (2009a,b) and Divers (2002).2 Counterpart theory is normally traced to Lewis (1968), though I’ll take the ‘official’ version of the view to bethat of Lewis (1986, Ch.4) since it is here where the metarepresentational role of counterparts emerges most clearly.See also Lewis (1971, 1976). Another very useful resource is the relevant chapter of Divers (2002).3 This isn’t how Plantinga should be read – whatever role essences play within Plantinga’s theory, they are not‘parts’ of possible worlds in the sense that Lewis’s counterparts are parts of possible worlds – but the view is illustra-tive nonetheless.4 In particular, I won’t have space to discuss the logical flexibility that counterpart theory offers. The basic point isthat (in general) counterpart relations are not equivalence relations since they are not guaranteed to be symmetricor transitive. So, e.g., the counterpart theorist can resist the inference from ‘it is possible that Billy could have beenhappy’ to ‘Billy could’ve been happy’ because though Billy’s counterpart might have a counterpart who is happy,we cannot conclude that Billy himself has a counterpart who is happy (due to the failure of transitivity). For discus-sion of the logical picture supported by counterpart theory, see Lewis (1968) and Divers (2002).

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5 For more discussion of this, see Divers (2007).6 Just to be clear: the point is that considerations of context and relevance contribute to determining the truth-con-ditions of claims like ‘Billy could have been happy’. But once the truth-condition (in a context) is determined, thequestion of whether that truth-condition obtains is context insensitive. To put that otherwise: context plays a rolein determining what is said by an utterance of de re modal claim, but it plays no role in determining whether whatis in fact said by an utterance of a de re modal claims is true or false.7 To be clear, I do not mean to suggest that this is what the counterpart theorist should say or that it’s what Lewiswould say. The point is just that counterpart theory doesn’t predict inconstancy by itself.8 cf. Divers (2002: 147–8).9 For discussion of this point in the context of counterpart theory, see Divers (2002).10 Compare Divers (2002).

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189–231.Rosen, Gideon. ‘Modal Fictionalism.’ Mind 99 (1990) 327–54.Schaffer, Jonathan. ‘The Internal Relatedness of All Things.’ Mind 119 (2010) 341–76.Sider, Theodore. ‘Beyond the Humphrey Objection.’ Unpublished manuscript.——. ‘The Ersatz Pluriverse.’ Journal of Philosophy 99 (2002): 279–315.——. Four-Dimensionalism. Oxford: Clarendon, 2001.Stalnaker, Robert. ‘Counterparts and Identity.’ Midwest Studies in Philosophy XI: Studies in Essentialism. Ed. Peter

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——. ‘Possible Worlds.’ Nous 10 (1976): 65–75.Woodward, Richard. ‘Counterparts for Actualists.’ unpublished manuscript.Yablo, Stephen. ‘How in the World?’ Philosophical Topics 24 (1996): 255–86.

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