The notion of transworld identity—‘identity acrosspossible worlds’—is the notion that the same object existsin more than one possible world (with the actual world treated as oneof the possible worlds). It therefore has its home in a‘possible-worlds’ framework for analysing, or at leastparaphrasing, statements about what is possible or necessary.

The subject of transworld identity has been highly contentious, evenamong philosophers who accept the legitimacy of talk of possibleworlds. Opinions range from the view that the notion of an identitythat holds between objects in distinct possible worlds is soproblematic as to be unacceptable, to the view that the notion isutterly innocuous, and no more problematic than the uncontroversialclaim that individuals could have existed with somewhat differentproperties. Matters are complicated by the fact that an importantrival to ‘transworld identity’ has been proposed: DavidLewis’s counterpart theory, which replaces the claim that anindividual exists in more than one possible world with the claim thatalthough each individual exists in one world only, it has counterpartsin other worlds, where the counterpart relation (based on similarity)does not have the logic of identity. Thus much discussion in this areahas concerned the comparative merits of the transworld identity andcounterpart-theoretic accounts as interpretations, within apossible-worlds framework, of statements of what is possible andnecessary for particular individuals. (Similar issues arise concerningthetransworld identity of properties.)

• 1. What is transworld identity?
  • 1.1 Why transworld identity?
  • 1.2 Transworld identity and conceptions of possible worlds
• 2. Transworld identity and Leibniz’s Law
• 3. Is ‘the problem of transworld identity’ a pseudo-problem?
  • 3.1 Against the epistemological assumption
  • 3.2 Against the ‘security of reference’ assumption
  • 3.3 Against the ‘intelligibility’ assumption
  • 3.4 Remaining issues
• 4. Individual essences and bare identities
  • 4.1 Chisholm’s Paradox and bare identities
  • 4.2 Forbes on individual essences and bare identities
  • 4.3 Transworld identity and conditions for identity over time
  • 4.4 Responses to the problems
  • 4.5 Leibniz and hyper-essentialism
  • 4.6 Haecceities and haecceitism
• 5. Transworld identity and the transitivity of identity
  • 5.1 Chandler’s transitivity argument
  • 5.2 Responses to the transitivity problem
  • 5.3 The ‘Four Worlds Paradox’
• 6. Concluding remarks
  • 6.1 Transworld identity and counterpart theory
  • 6.2 Lewis on transworld identity and ‘existence according to a world’
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. What is transworld identity?

1.1 Why transworld identity?

Suppose that, in accordance with the possible-worlds framework forcharacterizing modal statements (statements about what is possible ornecessary, about what might or could have been the case, what couldnot have been otherwise, and so on), we treat the general statementthat there might have been purple cows as equivalent to the statementthat there is some possible world in which there are purple cows, andthe general statement that there could not have been round squares(i.e., that it is necessary that there are none) as equivalent to thestatement that there is no possible world in which there are roundsquares.

How are we to extend this framework to statements about what ispossible and necessary forparticular individuals—whatare known asde re modal statements (‘dere’ meaning ‘about a thing’)—for example,that Clover, a particular (actually existing) four-legged cow, couldnot have been a giraffe, or that she could have had just three legs? Anatural extension of the framework is to treat the first statement asequivalent to the claim that there is no possible world in whichClover is a giraffe, and the second as equivalent to the claim thatthere is some possible world in which Clover is three-legged. But thislast claim appears to imply that there is some possible world in whichClover exists and has three legs—from which it seems inescapablyto follow that one and the same individual—Clover—existsin some merely possible world as well as in the actual world: thatthere is an identity between Clover and some individual in anotherpossible world. Similarly, it appears that thede re modalstatements ‘George Eliot could have been a scientist rather thana novelist’ and ‘Bertrand Russell might have been aplaywright instead of a philosopher’ will come out as‘There is some possible world in which George Eliot (exists and)is a scientist rather than a novelist’ and ‘There is somepossible world in which Bertrand Russell (exists and) is a playwrightand not a philosopher’. Again, each of these appears to involvea commitment to an identity between an individual who exists in theactual world (Eliot, Russell) and an individual who exists in anon-actual possible world.

To recapitulate: the natural extension of the possible-worldsinterpretation tode re modal statements involves acommitment to the view that some individuals exist in more than onepossible world, and thus to what is known as ‘identity acrosspossible worlds’, or (for short) ‘transworldidentity’. (It is questionable whether the shorthand is reallyapt. One would expect a ‘transworld’ identity to mean anidentity that holds across (and hence within)one world, notan identity that holds between objects indistinct worlds.(As David Lewis (1986) has pointed out, our own Trans World Airlinesis an intercontinental, not an interplanetary, carrier.) Nevertheless,the term ‘transworld identity’ is far too well establishedfor it to be sensible to try to introduce an alternative, although‘interworld identity’ or even ‘transmodalidentity’ would in some ways be more appropriate.) But is thiscommitment acceptable?

1.2 Transworld identity and conceptions of possible worlds

To say that there is a transworld identity betweenA andB is to say that there is some possible worldw₁, and some distinct possible worldw₂, such thatA exists inw₁, andB exists inw₂, andA is identical withB.(Remember that we are treating the actual world as one of the possibleworlds.) In other words, to say that there is a transworld identity isto say that thesame object exists in distinct possibleworlds, or (more simply) that some object exists in more than onepossible world.

But what does it mean to say that an individual exists in a merelypossible world? And—even if we accept that paraphrases of modalstatements in terms of possible worlds are in generalacceptable—does it even makesense to say that actualindividuals (like you and your neighbour’s cat and the EiffelTower) exist in possible worlds other than the actual world? To knowwhat a claim of transworld identity amounts to, and whether suchclaims are acceptable, we need to know what a possible world is, andwhat it is for an individual to exist in one.

Among those who take possible worlds seriously (that is, those whothink that there are possible worlds, on some appropriateinterpretation of the notion), there is a variety of conceptions oftheir nature. On one account, that of David Lewis, a non-actualpossible world is something like another universe, isolated in spaceand time from our own, but containing objects that are just as real asthe entities of our world; including its own real concrete objectssuch as people, tables, cows, trees, and rivers (but also, perhaps,real concrete unicorns, hobbits, and centaurs). According to Lewis,there is no objective difference in status between what we call‘the actual world’ and what we call ‘merely possibleworlds’. We call our world ‘actual’ simply becausewe are in it; the inhabitants of another world may, with equal right,calltheir world ‘actual’. In other words,according to Lewis, ‘actual’ in ‘the actualworld’ is an indexical term (like ‘here’ or‘now’), not an indicator of a special ontological status(Lewis 1973, 84–91; Lewis 1986, Ch. 1).

On Lewis’s ‘extreme realist’ account of possibleworlds, it looks as if, for Clover to exist in another possible worldas well as the actual world would be for her to be a part of such aworld: Clover would somehow have to exist as a (concrete) part of twoworlds, ‘in the same way that a shared hand might be a commonpart of two Siamese twins’ (Lewis 1986, 198). But this isproblematic. Clover actually has four legs, but could have had threelegs. Should we infer that Clover is a part of some world at which shehas only three legs? If so, then how many legs does Clover have: four(since she actually has four legs), or seven (since she has four inour world and three in the alternative world)? Worse still, we appearto be ascribing contradictoryproperties to Clover: she hasfour legs, and yet has no more than three.

Those who believe in the ‘extreme realist’ notion ofpossible worlds may respond by thinking of Clover as having afour-legged part in our world, and a three-legged part at some otherworld. This is Yagisawa’s (2010) view (cf. Lewis 1986,210–220). Yagisawa thinks of concrete entities—everydaythings such as cats, trees and macbooks—as extended acrosspossible worlds (as well as across times and places), in virtue ofhavingstages (or parts) which exist at those worlds (andtimes and places). Ordinary entities thus comprise spatial, temporaland modal stages, all of which are equally real. Metaphysically, modalstages (and the worlds at which they exist) are on a par with temporaland spatial stages (and the times and places at which they exist).(This view is the modal analogue of the ‘perdurance’account of identity over time, according to which an object persiststhrough time by having ‘temporal parts’ that are locatedat different times.) Thus, when we say that Clover has four legs inour world but only three in some other world, we are saying that shehas a four-legged modal stage and a distinct three-legged modal stage.Clover herself is neither four-legged nor three-legged. (However,there is a sense in which Clover herself—the entity comprisingmany modal stages—has awfully many legs, even though sheactually has only four.)

Another option for the ‘extreme realist’ about possibleworlds is to hold that Clover is four-legged relative to our world,but three-legged relative to some other world. In general, qualitieswe would normally think of as monadic properties are in fact relationsto worlds. McDaniel (2004) defends a view along these lines. Afeature of this account is that one and the same entity may existaccording to many worlds, for that entity may bear theexists-at relation to more than one world. Accordingly, theview is sometimes calledgenuine modal realism with overlap(McDaniel 2004). This view, transposed to the temporal case, isprecisely what theendurantist says: objects do not havetemporal parts; each object is wholly present at each time. (See theseparate entry on Temporal Parts.)

Lewis rejects both of these options. He rejects the overlap viewbecause of what he calls ‘the problem of accidentalintrinsics’. On the overlap view,having four legs is arelation to a world, and hence not one of Clover’s intrinsicproperties. In fact, any aspect of a particular that changes acrossworlds turns out to be non-intrinsic to that particular. As aconsequence, every particular has all its intrinsic propertiesessentially, which Lewis thinks is unacceptable (1986,199–209).

Lewis himself combines his brand of realism about possible worlds witha denial of transworld identities. According to Lewis, instead ofsaying that George Eliot (in whole or in part) inhabits more than oneworld, we should say that she inhabits one world only (ours), but hascounterparts in other worlds. And it is the existence of counterpartsof George Eliot who go in for a career in science rather than novelwriting that makes it true that she could have been a scientist ratherthan a novelist (Lewis 1973, 39–43; 1968; 1986, Ch. 4).

However, Lewis’s version of realism is by no means the onlyconception of possible worlds. According to an influential set ofrival accounts, possible worlds, although real entities, are notconcrete ‘other universes’, as in Lewis’s theory,but abstract objects such as (maximal) possible states of affairs or‘ways the world might have been’. (See Plantinga 1974;Stalnaker 1976; van Inwagen 1985; Divers 2002; Melia 2003; Stalnaker1995; also the separate entry on Possible Worlds. A state of affairsS is ‘maximal’ just in case, for any state ofaffairsS*, either it is impossible for bothS andS* to obtain, or it is impossible forS to obtainwithoutS*: the point of the restriction to the maximal isjust that a possible world should be a possible state of affairs thatis, in a relevant sense, complete.)

On the face of it, to treat possible worlds as abstract entities mayseem only to make the problem of transworld identity worse. If it ishard to believe that you (or a table or a cat) could be part ofanother Lewisian possible world, it seems yet harder to believe that aconcrete entity like you (or the table or cat) could be part of anabstract entity. However, those who think that possibleworlds are abstract entities typically do not take the existence in amerely possible world of a concrete actual individual to involve thatentity’s being literally a part of such an abstract thing.Rather, such a theorist will propose a different interpretation of‘existence in’ such a world. For example, according toPlantinga’s (1973, 1974) version of this account, to say thatGeorge Eliot exists in some possible world in which she is a scientistis just to say that there is a (maximal) possible state of affairssuch that, had it obtained (i.e., had it been actual), George Eliotwould (still) have existed, but would have been a scientist. On this(deflationary) account of existence in a possible world, it appearsthat the difficulties that accompany the idea that George Eliot leadsa double life as an element of another concrete universe as well asour own (or the idea that she is partially present in many suchuniverses) are entirely avoided. On Plantinga’s account, toclaim that an actual object exists in another possible world withsomewhat different properties amounts to nothing more risquéthan the claim that the object could have had somewhat differentproperties: something that few will deny. (Note that according to thisaccount, if the actual world is to be one of the possible worlds, thenthe actual world must be an abstract entity. So, for example, if amerely possible world is ‘a way the world might havebeen’, the actual world will be ‘the way the worldis’; if a merely possible world is a maximal possible state ofaffairs that is not instantiated, then the actual world will be amaximal possible state of affairs thatis instantiated. Itfollows that we must distinguish the actual worldquaabstract entity from ‘the actual world’ in the sense ofthe collection of spatiotemporally linked entities including you andyour surroundings that constitutes ‘the universe’ or‘the cosmos’. The sense in which you exist in thisconcrete universe (by being part of it) must be different from thesense in which you exist in the abstract state of affairs that is infact instantiated (cf. Stalnaker 1976; van Inwagen 1985, note 3;Kripke 1980, 19–20).)

The discussion so far may suggest that whether the notion oftransworld identity (that an object exists in more than one world) isproblematic depends solely on whether one adopts an account ofpossible worlds as concrete entities such as Lewis’s (in whichcase it is) or an account of possible worlds as abstract entities suchas Plantinga’s (in which case it is not). However, matters arenot so simple, for a variety of reasons (to be discussed in Sections3–5 below).

2. Transworld identity and Leibniz’s Law

There may seem to be an obvious objection to the employment oftransworld identity to interpret or paraphrase statements such as‘Bertrand Russell could have been a playwright’ or‘George Eliot might have been a scientist’. A fundamentalprinciple about (numerical) identity is Leibniz’s Law: theprinciple that ifA is identical withB, then anyproperty ofA is a property ofB, and vice versa. Inother words, according to Leibniz’s Law, identity requires thesharing of all properties; thus any difference between the propertiesofA andB is sufficient to show thatA andB are numerically distinct. (The principle here referred toas ‘Leibniz’s Law’ is also known as theIndiscernibility of Identicals. It must be distinguished from another(more controversial) Leibnizian principle, the Identity ofIndiscernibles, which says that ifA andB share alltheir properties thenA is identical withB.)However, the whole point of asserting a transworld identity is torepresent the fact that an individual could have had somewhatdifferent properties from its actual properties. Yet does not(for example) the claim that a philosopher in the actual world isidentical with a non-philosopher in some other possible world conflictwith Leibniz’s Law?

It is generally agreed that this objection can be answered, and theappearance of conflict with Leibniz’s Law eliminated. We cannote that the objection, if sound, would apparently prove too much,since a parallel objection would imply that there can be no such thingas genuine (numerical) identity through change of properties overtime. But it is generally accepted that no correct interpretation ofLeibniz’s Law should rule this out. For example, BertrandRussell was thrice married when he received the Nobel Prize forLiterature; the one-year-old Bertrand Russell was, of course,unmarried; does Leibniz’s Law force us to deny the identity ofthe prize-winning adult with the infant, on the grounds that theydiffer in their properties? No, for it seems that the appearance ofconflict with Leibniz’s Law can be dispelled, most obviously bysaying that the infant and the adult share the properties ofbeingmarried in 1950 andbeing unmarried in 1873, butalternatively by the proposal that the correct interpretation ofLeibniz’s Law is that the identity ofA andBrequires that there be no time such thatA andBhave different propertiesat that time (cf. Loux 1979,42–43; also Chisholm 1967). However, it seems that exactlysimilar moves are available in the modal case to accommodate‘change’ of properties across possible worlds. Either wemay claim that the actual Bertrand Russell and the playwright in somepossible world (say,w₂) are alike in possessingthe properties ofbeing a philosopher in the actual world andbeing a non-philosopher in w₂, or we may arguethat Leibniz’s Law, properly interpreted, asserts that theidentity ofA andB requires that there be no time,and no possible world, such thatA andB havedifferent propertiesat that time and world. The moralappears to be that transworld identity claims (combined with the viewthat some of an individual’s properties could have beendifferent) need no more be threatened by Leibniz’s Law than isthe view that there can be identity over time combined with change ofproperties (Loux 1979, 42–43).

It should be mentioned, however, that David Lewis has argued that thereconciliation of identity through change over time withLeibniz’s Law suggested above is oversimplified, and gives riseto a ‘problem of temporary intrinsics’ that can be solvedonly by treating a persisting thing that changes over time as composedof temporal parts that do not change their intrinsic properties. (SeeLewis 1986, 202–204, and for discussion and further references,Hawley 2001; Sider 2001; Lowe 2002; Haslanger 2003.) In addition, itis partly because Lewis regards the analogous account of transworldidentity in terms of modal parts as an unacceptable solution to ananalogous ‘problem of accidental intrinsics’ that Lewisrejects transworld identity in favour of counterpart theory (Lewis1986, 199–220; cf. Section 1.2 above).

3. Is ‘the problem of transworld identity’ a pseudo-problem?

In the discussion of transworld identity in the 1960s and 1970s (whenthe issue came to prominence as a result of developments in modallogic), it was debated whether the notion of transworld identity isgenuinely problematic, or whether, on the contrary, the alleged‘problem of transworld identity’ is merely apseudo-problem. (See Loux 1979, Introduction, Section III; Plantinga1973 and 1974, Ch. 6; Kripke 1980 (cf. Kripke 1972); Kaplan 1967/1979;Kaplan 1975; Chisholm 1967; for further discussion see, for example,Divers 2002, Ch. 16; Hughes 2004, Ch. 3; van Inwagen 1985; Lewis 1986,Ch. 4.)

It is difficult to pin down the alleged problem that is supposed to beat the heart of this dispute. In particular, although the mainproponents of the view that the alleged problem is a pseudo-problemclearly intended to attack (inter alia) Lewis’s versionof modal realism, they did not attempt to rebut the thesis (discussedin Section 1.2 above) thatif one is a Lewisian realist aboutpossible worlds, then one should find transworld identity problematic.Matters are complicated by the fact that proponents of the view thatthe alleged problem of transworld identity is a pseudo-problem were tosome extent responding to hypothetical arguments, rather thanarguments presented in print by opponents (see Plantinga 1974, 93).However, one central issue was whether the claim that an individualexists in more than one possible world (and hence that there are casesof transworld identity) needs to be backed by the provision ofcriteria of transworld identity, and, if so, why.

The term ‘criterion of identity’ is ambiguous. In anepistemological sense, a criterion of identity is a way of tellingwhether an identity statement is true, or a way of recognizing whetheran individualA is identical with an individualB.However, the notion of a criterion of identity also has a metaphysicalinterpretation, according to which it is a set of (non-trivial)necessary and sufficient conditions for the truth of an identitystatement. Although a criterion of identity in the second(metaphysical) sense might supply us with a criterion of identity inthe first (epistemological) sense, it seems that something could be acriterion of identity in the second sense even if it is unsuited toplay the role of a criterion of identity in the first sense.

The most influential argumentsagainst the view that there isa genuine problem of transworld identity (or ‘problem oftransworld identification’, to use Kripke’s preferredterminology) are probably those presented by Plantinga (1973, 1974)and Kripke (1980). Plantinga and Kripke appear to have, as theirtarget, an alleged problem of transworld identity that rests on one ofthree assumptions. The first assumption is that we must possesscriteria of transworld identity in order to ascertain, on the basis oftheir properties in other possible worlds, the identities of (perhapsradically disguised) individuals in those worlds. The secondassumption is that we must possess criteria of transworld identity ifour references to individuals in other possible worlds are not to misstheir mark. The third assumption is that we must possess criteria oftransworld identity in order to understand transworld identity claims.Anyone who makes one of these assumptions is likely to think thatthere is a problem of transworld identity—a problem concerningour entitlement to make claims that imply that an individual exists inmore than one possible world. For it does not seem that we possesscriteria of transworld identity that could fulfil any of these threeroles. However, Plantinga and Kripke provide reasons for thinking thatnone of these three assumptions survives scrutiny. If so, and if theseassumptions exhaust the grounds for supposing that there is a problemof transworld identity, the alleged problem may be dismissed as apseudo-problem.

The three assumptions may be illustrated, using our examples of GeorgeEliot and Bertrand Russell, as follows. (The examples are alternatedsimply for the sake of a little variety.)

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The ‘epistemological’ assumption: We must possess acriterion of transworld identity for George Eliot in order to be ableto tell, on the basis of knowledge of the properties that anindividual has in some other possible world, whether that individualis identical with Eliot.

(2)

The ‘security of reference’ assumption: We mustpossess a criterion of transworld identity for Bertrand Russell inorder to know that, when we say such things as ‘There is apossible world in which Russell is a playwright’, we are talkingabout Russell rather than someone else.

(3)

The ‘intelligibility’ assumption: We must possess acriterion of transworld identity for George Eliot in order tounderstand the claim that there is a possible world in which she is ascientist.

3.1 Against the epistemological assumption

The epistemological assumption appears to imply that the point of ourhaving a criterion of transworld identity for George Eliot would bethat we could thenemploy the criterion in order to ascertainwhich individual in a possible world is Eliot; if, on the other hand,we do not possess such a criterion, we shall be unable to pick her outor identify her in other possible worlds (Plantinga 1973; 1974, Ch. 6;Kripke 1980, 42–53; cf. Loux 1979, Introduction; Kaplan1967/1979). However, this suggestion, as stated, is vulnerable to thecharge that it is the product of confusion. For howcould weuse a criterion of identity in the way envisaged? We must dismiss asfanciful the idea that if we had a criterion of transworld identityfor George Eliot, we could use it to tell,by empiricalinspection of the properties of individuals in other possibleworlds (perhaps using a powerful telescope (Kripke 1980, 44) or‘Jules Verne-o-scope’ (Kaplan 1967/1979, 93; Plantinga1974, 94)), which, if any, of those individuals is Eliot. For no one(including an extreme realist like Lewis) thinks that ourepistemological access to other possible worlds is of this kind.(According to Lewis, other possible worlds are causally isolated fromour own, and hence beyond the reach of our telescopes or any otherperceptual devices.) But once we face up to the fact that a criterionof transworld identity (if we had one) could have no such empiricaluse, the argument based on the epistemological assumption appears tocollapse. It is tempting to suggest that the argument is the productof the (perhaps surreptitious) influence of a misleading picture ofour epistemological access to other possible worlds. As Kripke writes(using President Nixon as his example):

One thinks, in this [mistaken] picture, of a possible world as if itwere like a foreign country. One looks upon it as an observer. MaybeNixon has moved to the other country and maybe he hasn’t, butone is given only qualities. One can observe all his qualities, but,of course, one doesn’t observe that someone is Nixon. Oneobserves that something has red hair (or green or yellow) but notwhether something is Nixon. So we had better have a way of telling interms of properties when we run into the same thing as we saw before;we had better have a way of telling, when we come across one of theseother possible worlds, who was Nixon. (1980, 43)

(It is possible, though, that in this passage Kripke’s principaltarget is not a mistaken conception of our epistemological access toother possible worlds, but what he takes to be a mistaken(‘foreign country’) conception of their nature: aconception that (when divorced from the fanciful epistemology) wouldbe entirely appropriate for a Lewisian realist about worlds.)

3.2 Against the ‘security of reference’ assumption

It might be suggested that the point of a criterion of transworldidentity is that its possession would enable me to tell whichindividual I am referring to when I say (for example) ‘There isa possible world in which Russell is a playwright’. Suppose thatI am asked: ‘How do you know that the individual you are talkingabout—this playwright in another possible world—isBertrand Russell rather than, say, G. E. Moore, or Marlene Dietrich,or perhaps someone who is also a playwright in the actual world, suchas Tennessee Williams or Aphra Behn? Don’t you need to be ableto supply a criterion of transworld identity in order to secure yourreference to Russell?’ (Cf. Plantinga 1974, 94–97; Kripke1980, 44–47.) It seems clear that the right answer to thisquestion is ‘no’. As Kripke has insisted, it seemsspurious to suggest that the question how we know which individual weare referring to when we make such a claim can be answered only byinvoking a criterion of transworld identity. For it seems that we cansimplystipulate that the individual in question is BertrandRussell (Kripke 1980, 44).

Similarly, perhaps, if I say that there is some past time at whichAngela Merkel is a baby, and am asked ‘How do you know thatit’s the infantAngela Merkel that you are talkingabout, rather than some other infant?’, an apparently adequatereply is that I amstipulating that the past state of affairsI am talking about is one that concernsMerkel (and not someother individual). It seems that I can adequately answer the parallelquestion in the modal case by saying that I amstipulatingthat, when I say that there is some possible world in which Russell isa playwright, the relevant individual in the possible world (if thereis one) isRussell (and not some other potential or actualplaywright).

3.3 Against the ‘intelligibility’ assumption

A third job for a criterion of transworld identity might be this: inorder tounderstand the claim that there is some possibleworld in which George Eliot is a scientist, perhaps we must be able togive an informative answer to the question ‘What would it takefor a scientist in another possible world to be identical withEliot?’ Again, however, it can be argued that this demand isillegitimate, at least if what is demanded is that one be able tospecify a set of properties whose possession, in another possibleworld, by an individual in that world, is non-trivially necessary andsufficient for being George Eliot (cf. Plantinga 1973; Plantinga 1974,94–97; van Inwagen 1985).

For one thing, we may point to the fact that it is doubtful that, inorder tounderstand the claim that there is some past time atwhich Angela Merkel is a baby, we have to be able to answer thequestion ‘What does it take for an infant at some past time tobe identical with Merkel?’ in any informative way. Secondly, itmay be proposed that in order to understand the claim that there issome possible world in which George Eliot is a scientist, we can relyon our prior understanding of the claim that she might have been ascientist (cf. Kripke 1980, 48, note 15; van Inwagen 1985).

3.4 Remaining issues

However, even if all three of these assumptions can be dismissed asbad, or at least inadequate, reasons for supposing that transworldidentity requires criteria of transworld identity (and hence forsupposing that there is a problem of transworld identity), it does notfollow that there are nogood reasons for this supposition.In particular, even if the three assumptions are discredited, a fourthclaim may survive:

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There mustbe a criterion of transworld identity forRussell (in the sense of a set of properties whose possession by anobject in any possible world is non-trivially necessary and sufficientfor being Russell) if the claim that there is a possible world inwhich Russell is a playwright is to be true. (Such a set of propertieswould be what is called a non-trivialindividual essence ofRussell, where an individual essence of an individualA is aproperty, or set of properties, whose possession by an individual inany possible world is both necessary and sufficient for identity withA.)

That this possibility is left open by the arguments so far consideredis suggested by at least two points. The first concerns the analogydrawn above between transworld identity and identity through time.Even if we can understand the claim that there is some past time atwhich Angela Merkel is a baby without being able to specifyinformative (non-trivial) necessary and sufficient conditions for theidentity of the adult Angela Merkel with some previously existinginfant, it does not follow that thereare no such necessaryand sufficient conditions. And many philosophers have supposed thatthere are such conditions for personal identity over time. Secondly,the fact that one may be able to ensure, by stipulation, that one istalking about a possible world in whichBertrand Russell (andnot someone else) is a playwright (if there is such a world) does notimply that, when making this stipulation, one is notimplicitly stipulating that this individual satisfies, inthat world, conditions non-trivially necessary and sufficient forbeing Russell, even if one is not in a position to say what theseconditions are.

This second point is an extension of the observation that, if (as mostphilosophers believe) Bertrand Russell has some essential properties(properties that he has in all possible worlds in which he exists), tostipulate that one is talking about a possible world in which Russellis a playwright is, at least implicitly, to stipulate that thepossible world is one in which someone with Russell’s essentialproperties is a playwright. For example, according to Kripke’s‘necessity of origin’ thesis, human beings have theirparents essentially (Kripke 1980). If this is correct, then, when wesay ‘There is a possible world in which Russell is aplaywright’, it seems that, if our stipulation is to becoherent, we must be at least implicitly stipulating that the possibleworld is one in whichsomeone with Russell’s actualparents is a playwright, even if the identity of Russell’sparents is unknown to us, and even though we are (obviously) in noposition to conduct an empirical investigation into the ancestry, inthe possible world, of the individuals who exist there. Thus, itseems, even if Kripke is right in insisting that we need not be abletospecify non-trivial necessary and sufficient conditionsfor being Russell in another possible world if we are legitimately toclaim that there are possible worlds in which he is a playwright, itmight nevertheless be the case that thereare such necessaryand sufficient conditions (cf. Kripke 1980, 46–47 and 18, note17; Lewis 1986, 222).

But what positive reasons are there for holding that transworldidentities require non-trivial necessary and sufficient conditions(non-trivial individual essences), if arguments that are based on theepistemological, security of reference, and intelligibilityassumptions are abandoned? (Similar issues arise for the transworldidentities of properties, discussed in the supplement ontransworld identity of properties.)

4. Individual essences and bare identities

The principal argument for this view—that transworld identitiesrequire non-trivial individual essences—is that such essencesare needed in order to avoid what have been called ‘bareidentities’ across possible worlds. And some regard bareidentities as too high a price to pay for the characterization ofde re modal statements in terms of transworld identity. Ifthey are right, and if (as many philosophers believe) there are noplausible candidates for non-trivial individual essences (at least forsuch things as people, cats, trees, and tables) there is, indeed, aserious problem about transworld identity. (The expression ‘bareidentities’ is taken from Forbes 1985. The notion, as used here,is approximately the same as the notion of ‘primitivethisness’ employed by Adams (1979), although Adams’snotion is that of an identity that does not supervene on qualitativefacts, rather than an identity that does not supervene on any otherfacts at all.)

Suppose that we combine transworld identity with the claim (withoutwhich the introduction of transworld identity seems pointless) that atransworld identity can hold betweenA inw₁ andB inw₂ eventhough the properties thatB has inw₂are somewhat different from the properties thatA has inw₁ (or, to put it more simply, suppose that wecombine the claim that there are transworld identities with the claimthat not all of a thing’s properties are essential to it). Then,it can be argued, unless there are non-trivial individual essences, weare in danger of having to admit the existence of possible worlds thatdiffer from one another only in the identities of some of theindividuals that they contain.

4.1 Chisholm’s Paradox and bare identities

One such argument, adapted from Chisholm 1967, goes as follows. TakingAdam and Noah in the actual world as our examples (and pretending, forthe sake of the example, that the biblical characters are realpeople), then, on the plausible assumption that not all of theirproperties are essential to them, it seems that there is a possibleworld in which Adam is a little more like the actual Noah than heactually was, and Noah a little more like the actual Adam than heactually was. But if there is such a world, then it seems that thereshould be a further world in which Adam is yet more like the actualNoah, and Noah yet more like the actual Adam. Proceeding in this way,it looks as if we may arrive ultimately at a possible world that isexactly like the actual world, except that Adam and Noah have‘switched roles’ (plus any further differences that followlogically from this, such as the fact that in the‘role-switching’ world Eve is the consort of a man whoplays the Adam role, but is in fact Noah). But if this can happen withAdam and Noah, then it seems that it could happen with any two actualindividuals. For example, it looks as if there will be a possibleworld that is a duplicate of the actual world except for the fact thatin this worldyou play the role that Queen Victoria plays inthe actual world, andshe plays the role that you play in theactual world (cf. Chisholm 1967, p. 83 in 1979). But this may seemintolerable. Is it really the case that Queen Victoria could have hadallyour actual properties (except for identity with you)while you had all of hers (except for identity with her)?

However, if one thinks that such conclusions are intolerable, how arethey to be avoided? The obvious answer is that what is needed, in theAdam-Noah case, is that the roles played by Adam and Noah in theactual world include some properties that are essential to theirbearers’ being Adam and Noah respectively: that Adam and Noahdiffer non-trivially in theiressential properties as well asin their accidental properties: more precisely, that Adam has someessential property that Noah essentially lacks, or vice versa. For if‘the Adam role’ includes some property that Noahessentially lacks, then, of course, there is no possible world inwhich Noah has that property, in which case the Adam role (in all itsdetail) is not a possible role for Noah, and the danger of arole-switching world such as the one described above is avoided.

The supposition that Adam and Noah differ in their essentialproperties in this way, although sufficient to block the generation ofthis example of a role-switching world, does not by itself imply thateach of Adam and Noah has anindividual essence: a set ofessential properties whose possession is (not only necessary but also)sufficient for being Adam or Noah. Suppose that Adam has, as one ofhis essential properties, living in the Garden of Eden, whereas Noahessentially lacks this property. This will block the possibility ofNoah’s playing the Adam role, although it does not, by itself,imply thatnothing other than Adam could play that role.However, when we reflect on the potential generality of the argument,it appears that, if we are to block all cases of role-switchingconcerning actual individuals, we must suppose that every actualindividual has some essential property (or set of essentialproperties) that every other actual individual essentially lacks. Forexample, to block all cases of role-switching concerning Adam andother actual individuals, there must be some component of ‘theAdam role’ that is not only essential to being Adam, but alsocannot be played, in any possible world, by any actual individualother than Adam.

Even if we suppose that all actual individuals are distinguished fromone another by such ‘distinctive’ essential properties,this still does not, strictly speaking, imply that they haveindividual essences. For example, it does not rule out the existenceof a possible world that is exactly like the actual world except that,in this possible world, the Adam role is played, not by Adam, but bysomemerely possible individual (distinct from all actualindividuals). However, if we find intolerable the idea that there aresuch possible worlds—worlds that, like the role-switching world,differ from the actual world only in the identities of some of theindividuals that they contain—then, it seems, we must supposethat individuals like Adam (and Noah and you) have (non-trivial)individual essences, where an individual essence of Adam is (bydefinition) some property (or set of properties) that is bothessential to being Adam and also such that it is not possessed, in anypossible world, by any individual other than Adam—i.e., anessential property (or set of properties) that guarantees that itspossessor is Adam and no one else.

Chisholm (1967) arrives at his role-switching world by a series ofsteps. Thus his argument appears to rely on the combination of thetransitivity of identity (across possible worlds) with the assumptionthat a succession of small changes can add up to a big change. And‘Chisholm’s Paradox’ (as it is called) is sometimesregarded as relying crucially on these assumptions, suggesting that ithas the form of asorites paradox (the type of paradox thatgenerates, from apparently impeccable assumptions, such absurdconclusions as that a man with a million hairs on his head is bald).(See, for example, Forbes 1985, Ch. 7.)

However, there are versions of the role-switching argument that do notrely on the cumulative effect of a series of small changes. Suppose weassume that Adam and Noah do not differ from one another in theiressential properties; in other words, that all the differences betweenthem are accidental (i.e., contingent) differences. It seemsimmediately to follow that any way that Adam could have been is a waythat Noah could have been, and vice versa. But one way that Adam couldhave been is the way Adam actually is, and one way that Noah couldhave been is the way Noah actually is. So (if Adam and Noah do notdiffer in their essential properties) it seems that there is apossible world in which Adam plays the Noah role, and a possible worldin which Noah plays the Adam role. But there is no obvious reason whya world in which Adam plays the Noah role and a world in which Noahplays the Adam role shouldn’t be the very same world. And inthat case there is a possible world in which Adam and Noah haveswapped their roles. This argument for the generation of arole-switching world does not rely on a series of small changes: allthat it requires is the assumption that there is no essentialdifference between Noah and Adam: or, to put it another way, that anyessential property of Noah is also an essential property of Adam, andvice versa. (See Mackie 2006, Ch. 2; also Adams 1979; cf. Dorr,Hawthorne, and Yli-Vakkuri 2021.)

4.2 Forbes on individual essences and bare identities

Another type of argument for the conclusion that unless things havenon-trivial individual essences there will be ‘bare’transworld identities: identities that do not supervene on (are notgrounded in) other facts, is presented by Graeme Forbes. (Strictlyspeaking, Forbes is concerned to avoid identities that are notgrounded in what he calls ‘intrinsic’ properties.) Asketch of a type of argument used by Forbes is this. (What follows isbased on Forbes 1985, Ch. 6; see also Mackie 2006, Ch. 3.) Suppose (asis surely plausible) that an actually existing oak tree could havebeen different in some respects from the way that it is; suppose alsothat, even if it has some essential properties (perhaps it isessentially an oak tree, for example), it has no non-trivialindividual essence consisting in some set of its intrinsic properties.Then there is the danger that there may be three possible worlds (callthem ‘w₂’,‘w₃’, and‘w₄’), where inw₂there is an oak tree that is identical with the original tree(w₂ representing one way in which the tree couldhave been different), and inw₃ there is an oaktree that is identical with the original tree (w₃representing another way in which the tree could have been different),and inw₄ there aretwo oak trees, one ofwhich is an intrinsic duplicate of the tree as it is inw₂, and the other an intrinsic duplicate of thetree as it is inw₃.If all ofw₂,w₃, andw₄ are possible, then, given that at least one ofthe trees inw₄ is not identical with the originaltree (since two things cannot be identical with one thing) there areinstances of transworld identity (and transworld distinctness)concerning a tree in one possible world and a tree in another that arenot grounded in (do not supervene on) the intrinsic features thatthose trees possess in those possible worlds. For example, supposethat, of the two trees inw₄, the intrinsicduplicate of thew₂ tree isnot identicalwith the original tree. Then, obviously, the distinctness(non-identity) between thisw₄ tree and the treeinw₂ is not grounded in the intrinsic featuresthat the trees have inw₂ andw₄—and nor is the identity between the treeinw₂ and the original tree grounded in theintrinsic features that the tree has inw₂ and inthe actual world.

Forbes argues that, in order to avoid this (and similar) consequences,we should suppose that (contrary to the second assumption used insetting up the ‘reduplication argument’ sketched above)the oak treedoes have a non-trivial individual essenceconsisting in some of its intrinsic properties, and his favouredcandidate for its essence is one that includes the tree’s comingfrom the particular acorn from which it actually originated. If thetree does have such an ‘intrinsic’ individual essence,then,ifw₂ andw₃are both possible, each of them must contain a tree that has (in thatworld) intrinsic properties that are guaranteed to besufficient for identity with the original tree, in which case(as a matter of logic) there can be no world such asw₄ that contains intrinsic duplicates of both ofthem. (See Forbes 1985, Ch. 6, and, for discussion, Mackie 1987;Mackie 2006; Robertson 1998; Yablo 1988; Chihara 1998; Della Rocca1996; further discussions by Forbes include his 1986, 1994, and2002.)

Finally, it is obvious that the structure of Forbes’s argumenthas nothing to do with the fact that the chosen example is a tree.Forbes’s ‘reduplication argument’ therefore appearsto pose a general problem for the characterization ofde remodal statements about individuals in terms of transworld identity:either we must admit that their transworld identities can be‘bare’, or we must find non-trivial individual essences,based on their intrinsic properties, that can ground their identitiesacross possible worlds.

4.3 Transworld identity and conditions for identity over time

So far it has been assumed that (non-trivial) necessary and sufficientconditions for transworld identity with a given object would involvethe possession, by that object, of an individual essence: a set ofproperties that it carries with it in every possible world in which itexists. But one might wonder why we should make this assumption. Thosewho believe that there are (non-trivial) necessary and sufficientconditions for identity over time need not, and almost universally donot, believe that these conditions consist in the possession, by anobject, of some ‘omnitemporal core’ (to use a phrasesuggested by Harold Noonan) that it has at every time in itsexistence. So why should things be different in the modal case?

The obvious answer seems to be this. In the case of identity overtime, we can appeal to relations (other than mere similarity) betweenthe states of an individual at different times in its existence. Forexample, it looks as if we can say that the adult Russell is identicalwith the infant Russell in virtue of the existence of certainspatiotemporal and causal continuities between his infant state in1873 and his adult state in (say) 1950 that are characteristic of thecontinued existence of a human being. But no such relations ofcontinuity are available to ground identities across possible worlds(cf. Quine 1976).

However, on reflection, it may seem that this is too swift. If wesuppose that any possible history for Russell is apossiblespatiotemporal and causal extension of the state that he was actuallyin at some time in his existence, then perhaps we may appeal to thesame continuities that ground his identity over time in the actualworld in order to ground his identity across possible worlds (cf.Brody 1980, 114–115; 121). For example, perhaps to say thatRussell could have been a playwright is to say that there was sometime in his actual existence at which he could havebecome aplaywright. If so, then perhaps we can hold that for a playwright in apossible world to be identical with Russell is for that playwright tohave, in that world, a life that is, at some early stage, exactly thesame as Russell’s actual life at some early stage, but whichdevelops from that point, in the spatiotemporally and causallycontinuous fashion that is characteristic of the continued existenceof a human being, into the career of a playwright rather than that ofa philosopher. However, although such a conception may seem initiallyattractive, it runs into difficulties if it is intended to provideconditions that are genuinely both necessary and sufficient for theidentity of individuals across possible worlds. These difficultiesinclude the fact that it seems too much to demand that Russell haveexactly the same early history (or origin) as his actualearly history (or origin) in every possible world in which he exists.Yet if Russell’s early history could have been different incertain respects, we face the question: ‘In virtue of what is anindividual in another possible world with a slightlydifferent early history from Russell’s actual earlyhistory identical with Russell?’—a question of preciselythe type that the provision of necessary and sufficient conditions fortransworld identity was intended to answer. (For discussion of this‘branching’ conception of possibilities, and itsimplications for questions of transworld identity and essentialproperties, see Brody 1980, Ch. 5; Mackie 1998; Mackie 2006, Chs6–7; Coburn 1986, Section VI; McGinn 1976; Mackie 1974; Prior1960.)

4.4 Responses to the problems

The fact that, in the absence of non-trivial individual essences, atransworld identity characterization ofde re modalstatements appears to generate bare identities (via arguments such asChisholm’s Paradox or Forbes’s reduplication argument) mayproduce a variety of reactions.

The moral that Chisholm (1967) drew from his argument was scepticismabout transworld identity, based partly on scepticism about whetherthe non-trivial individual essences that would block the generation ofrole-switching worlds are available. Others would go further, andconclude that such puzzles provide not only a reason for rejectingtransworld identity, but also a reason for adopting counterparttheory. (Note, though, that Lewis’s reasons for adoptingcounterpart theory appear to be largely independent of such puzzles(cf. Lewis 1986, Ch. 4).)

A third reaction is toaccept bare identities—or, atleast, to accept that individuals (including actual individuals) mayhave qualitative duplicates in other possible worlds, and thattransworld identities may involve what have been called‘haecceitistic’ differences. (See Adams 1979; Mackie 2006,Chs 2–3; Lewis 1986, Ch. 4, Section 4; also the separate entryon Haecceitism.)

A fourth reaction, that of Forbes, is to propose a mixed solution: heholds that for some individuals (including human beings and trees)suitable candidates for non-trivial individual essences can be found(by appeal to distinctive features of their origins), although forothers (including most artefacts) it may be that no suitablecandidates are available, in which case counterpart theory should beadopted for these cases (see Forbes 1985, Chs 6–7).

Koslicki (2020) provides another mixed solution. She accepts(primarily for Quinean reasons) that there is a problem of transworldidentity for certain individuals including people: one that can besolved only by attributing to them non-trivial individual essences;she argues that these consist in their individual forms. Such anindividual form would provide a substantial answer to questions suchas ‘what makes an individual Noah in the “role-switching” world ratherthan Adam?’ Thus, it would appear, the problem of transworld identityfor individuals such as Noah and Adam is replaced by a problem oftransworld identity for their individual forms. But why is thissupposed to represent an improvement? As Fine puts it: ‘Why should wenot simply take the crossworld identity of [non-form] entities asgiven and not standing in any need of a criterion?’ (2020, 430). Onereason (considered by Koslicki) is conceptual. It is thought that weneed to make sense ofde re modal claims in terms ofdedicto modal claims. However, if individual forms are to come tothe rescue, the question arises how the individual forms are to bedistinguished from one another. The problem is acute in cases wherethe individuals in question are otherwise indiscernible (Fine 2020,432). Moreover, it is not clear that Koslicki’s invocation of the factthat individual forms—unlike, say, unanalysable haecceities—havea ‘qualitative’ element (2020, Sections 3.3.4–3.5) is supposed to helpwith this problem.

It is perhaps significant, though, that no theorist appears to haveargued that a ‘non-trivial individual essence’ solutioncan be applied toall the relevant cases. In other words, theconsensus appears to be that the price of interpretingallde re modal claims in terms of transworld identity (asopposed to counterpart theory) is the acceptance of (some) bareidentities across possible worlds.

Salmon (1996) claims ‘something like a proof’ of thisimplication, from transworld identities to bare identities. He arguesfor what he callsExtreme Haecceitism, the view thattransworld identities cannot be grounded in general facts about theindividuals concerned. The purported proof goes as follows. Weconsiderx in worldw andy in worldw2 and suppose, forreductio, thatx = yand that this fact is reducible to (or grounded in, or entailed by)general facts aboutx inw andy inw2. But, says Salmon, the fact thatx = x is notreducible (grounded, etc.) in this way, since it is a fact of logic.So, says Salmon, ‘x differs fromy in at leastone respect. Forx lacksy’s feature that itsidentity withx is grounded in general (cross-world) factsaboutx and it’ (1996, 216), and hence (byLeibniz’s Law),x ≠ y, contrary to assumption. So ifthere are any transworld identities, those identities cannot begrounded in general facts about those individuals. They must be‘bare’.

Salmon’s argument is a variant on Evans’s (1978) argumentagainst the possibility of vague objects. It is controversial ingeneral whether arguments of this form succeed, for applications ofLeibniz’s Law in intensional contexts are questionable.Catterson (2008) argues on independent grounds that Salmon’sargument is not sound. We should also note that, even if the argumentis successful, it does not directly establish Salmon’s ExtremeHaecceitism, but only the conditional thesis thatif thereare any true transworld identity statementsx = y, then theyare not reducible to general facts aboutx andy.

4.5 Leibniz and hyper-essentialism

Finally, it can be noted that the problems concerning transworldidentity discussed here arise only because it is assumed that not allof an individual’s properties are essential to it (and hencethat, if it exists in more than one possible world, it has differentproperties in different worlds). If, instead, one were to hold thatall of an individual’s properties are essentialproperties—and hence, for example, that George Eliot could nothave existed with properties in any way different from her actualones—then no such problems would arise. Moreover, thissuggestion, implausible though it may be, is of some historicalinterest. For, according to a standard interpretation of the views ofGottfried Leibniz, the philosopher who is the father of theories ofpossible worlds, Leibniz’s theory of ‘complete individualnotions’ commits him to the thesis that an individual such asGeorge Eliotdoes have all her properties essentially (cf.Leibniz,Discourse on Metaphysics (1687), Sections 8 and 13;printed in Leibniz 1973 and elsewhere). According to the‘hyper-essentialist’ view to which Leibniz appears to becommitted, any individual, in any possible world, whose properties inthat world differ from the actual properties of George Eliot is not,strictly speaking, identical with Eliot. However, it also seems clearthat this does not represent a way of saving a transworld identityinterpretation ofde re modality. On the contrary: if thereis no possible world in which George Eliot exists with propertiesdifferent from her actual properties, then it is plausible to concludethat there is no possible world, other than the actual world, in whichshe exists at all. For unless possible worlds can be exact duplicates(something that Leibniz himself would deny), any merely possible worldmust differ from the actual world in some respect. If so, then theproperties of any individual in another possible world must differ insome respect from the actual properties of Eliot (even if thedifference is only a difference in relational properties), in whichcase, if all Eliot’s properties are essential to her, thatindividual is not Eliot. (Leibniz’s views may, however, be seenas a partial anticipation of counterpart theory, which attempts tosave the truth of the claim that George Eliotcould have beendifferent in some respects (thus denying‘hyper-essentialism’) while preserving the metaphysicalthesis that no individual who is, strictly speaking, identical withEliot exists in any other possible world (cf. Kripke 1980, 45, note13).)

4.6 Haecceities and haecceitism

The view that an individual’s transworld identity is‘bare’ is sometimes described as the view that itsidentity consists in its possession of a ‘haecceity’ or‘thisness’: an unanalysable non-qualitative property thatis necessary and sufficient for its being the individual that it is.(The term ‘individual essence’ is sometimes used to denotesuch a haecceity. It should be noted that according to the terminologyused in this article, although a haecceity would be an individualessence, it would not be anon-trivial individual essence.)However, it is not obvious that the belief in bare identities requiresthe acceptance of haecceities. One can apparently hold that transworldidentities may be ‘bare’ without holding that they areconstituted by any properties at all, even unanalysable haecceities(cf. Lewis 1986, 225; Adams 1979, 6–7). Thus we shoulddistinguish what is standardly known as ‘haecceitism’(roughly, the view that there may be bare identities across possibleworlds in the sense of identities that do not supervene on qualitativeproperties) from the belief in haecceities (the belief thatindividuals have unanalysable non-qualitative properties thatconstitute their being the individuals that they are). (For more onthe use of the term ‘haecceitism’ see Lewis 1986, Ch. 4,Section 4; Adams 1979; Kaplan 1975, Section IV; also the separateentry on Haecceitism. For the history of the term‘haecceity’, see the entry on Medieval Theories ofHaecceity.)

In addition, it should be noted that to believe in ‘bare’transworld identities, in the sense under discussion here, is not tobelieve in ‘bare particulars’, if to be a bare particularis to be an entity devoid of (non-trivial) essential properties. Asthe arguments discussed in Sections 4.1–4.2 above demonstrate, acommitment to a ‘bare’ (or ‘ungrounded’)difference in the identities of two individualsA andB in different possible worlds (two human beings, or twotrees, for example) does not imply that those individuals have nonon-trivial essential properties. All it implies is thatAandB do notdiffer in their non-trivial essentialproperties—and hence that, although there may well benon-trivial necessary conditions for beingA in any possibleworld, and non-trivial necessary conditions for beingB inany possible world, there are no non-trivial necessary conditions forbeingA that are not also necessary conditions for beingB, and vice versa. (Cf. Adams’s ‘ModerateHaecceitism’ (1979, 24–26).)

5. Transworld identity and the transitivity of identity

It was argued above that the proponent of transworld identity withoutnon-trivial individual essences faces the prospect of bare(‘ungrounded’) identities across possible worlds. One suchargument is Chisholm’s Paradox, which relies on the transitivityof identity to produce the result that a series of small changes inthe properties of Adam and Noah leads to a world in which Adam andNoah have swapped their roles. However, the transitivity of identitygenerates additional problems concerning transworld identity, some ofwhich have nothing particularly to do with role-switchingpossibilities or bare identities.

5.1 Chandler’s transitivity argument

One such argument is given by Chandler (1976). It can be illustratedsimply as follows (adapting Chandler’s own example). Supposethat there is a bicycle originally composed of three parts: A1, B1,and C1. (We might suppose that A1 is the frame, and B1 and C1 the twowheels.) Suppose we think that any bicycle could have been originallycomposed of any two thirds of its original parts, with a substitutethird component. We may call this (following Forbes 1985) ‘thetolerance principle’; it is a development of the intuitivelyappealing thought that it is too much to demand, of an object such asa bicycle, that it could not have existed unlessall of itsoriginal parts had been the same. Suppose, further, that we think thatno bicycle could have been originally composed of just one third ofits original parts, even with substitutes for the other two thirds.Call this ‘the restriction principle’. The combination ofthese assumptions appears to generate a difficulty for the paraphraseofde re modal claims about bicycles in terms of transworldidentity. For if there is (as the tolerance principle allows) apossible worldw₂ in which our bicycle comes intoexistence composed of parts A1 + B1 + C2, where C1 ≠ C2, then, ifwe apply the tolerance principle tothis bicycle we must saythatit could have come into existence (in some furtherpossible worldw₃) with any two thirds ofthose parts, with a substitute third component: for example,that it could have come into existence (inw3) composed of A1+ B2 + C2, where B1 ≠ B2 and C1 ≠ C2. The bicycle inw₃ is,ex hypothesi, identical with thebicycle inw₂, and the bicycle inw₂ is,ex hypothesi, identical with theoriginal bicycle; so, by the transitivity of identity, the bicycle inw₃ is identical with the original bicycle. Henceour assumptions have generated a contradiction. We have a bicycle inw₃, originally composed of A1 + B2 + C2, that bothis identical with the original bicycle (by the repeated application ofthe tolerance principle, together with the transitivity of identity)and is not identical with the original bicycle (by the restrictionprinciple).

One might complain that the version of the tolerance principle citedabove is too lenient. Perhaps it is not true that the bicycle couldhave come into existence with just two thirds of its originalcomponents: perhaps a threshold of, say, 90% or more is required.However, the simple argument given above can be adapted to generate acontradiction between the restriction principle and any toleranceprinciple that permitssome difference in the bicycle’soriginal composition, simply by introducing a longer chain of possibleworlds. Thus the transitivity argument appears to force the proponentof transworld identity to choose between two implausible claims: thatan object such as a bicycle has all of its original parts essentially(thus denying any version of the tolerance principle) and that anobject such as a bicycle could have come into existence with few (ifany) of its original parts (thus denying any (non-trivial) version ofthe restriction principle). Moreover, it is clear that the problem canbe generalized to any object to which versions of the toleranceprinciple and the restriction principle concerning its originalmaterial composition have application, which appears to include allartefacts, if not biological organisms.

It seems legitimate to call this puzzle a ‘problem of transworldidentity’, for it turns partly on the transitivity of identity,and can be avoided by interpreting claims about how bicycles couldhave been different (de re modal claims about bicycles) interms of a counterpart relation that is not transitive (Chandler1976). Thus a counterpart theorist may admit that the bicycle couldhave been originally composed of A1 + B1 + C2 rather than A1 + B1 +C1, on the grounds that (according to the tolerance principle) it hasa counterpart (inw₂) that is originally socomposed. And the counterpart theorist may admit that a bicycle (suchas the one inw₂) that is originally composed ofA1 + B1 + C2 could have been originally composed of A1 + B2 + C2,since (by the tolerance principle) it has a counterpart (inw₃) that is originally so composed. However, sincethe counterpart relation (unlike identity) is not transitive, thecounterpart theorist neednot say that the bicycle inw₃ that is originally composed of A1 + B2 + C2 isa counterpart of the bicycle in the actual world(w₁) originally composed of A1 + B1 + C1, for itssimilarity to the bicycle inw₁ may beinsufficient to allow it to be that bicycle’s counterpart. Thusthe non-transitivity of the counterpart relation (a relation based onresemblance) appears neatly to allow the counterpart theorist torespect both the tolerance principle and the restriction principle,without falling into contradiction.

5.2 Responses to the transitivity problem

One reaction to the transitivity puzzle is to abandon transworldidentity in favour of counterpart theory. But how—given thestructure of the puzzle—can the theorist who wishes to resistthat move, and retain transworld identity, respond?

One response would be to give up any non-trivial version of therestriction principle, and hold that an artefact such as a bicyclecould have come into existence with an entirely different materialcomposition from its actual original composition. Although thiscounterintuitive view has been defended (for example, Mackie (2006)argues for it on grounds independent of the transitivity problem), ithas few adherents.

A second response would be to give up the tolerance principle, andadopt what Roca-Royes (2016) calls an ‘inflexible’ versionof the principle that the material origin of an artefact is essentialto it, holding that an artefact such as a bicycle could not have comeinto existence with a material composition in any way different fromits actual original composition. Although this view is admittedlycounterintuitive, Roca-Royes argues that it provides the best solutionto the ‘Four Worlds Paradox’ to be discussed in the nextsection.

A third solution to the transitivity problem has been proposed (byChandler, followed by Salmon) which apparently allows us to reconcileall three of the transitivity of identity, the tolerance principle,and the restriction principle. This is to say that although thereare possible worlds (such asw₃) in whichthe bicycle is originally composed of only a small proportion of itsactual original parts, such worlds are not possible relative to (not‘accessible to’) the initial worldw₁.From the standpoint ofw₁, such an originalcomposition for the bicycle is only possibly possible: something thatwould have been possible, had things been different in some possibleway, but is not, as things are, possible (Chandler 1976; Salmon 1979;Salmon 1982, 238–240). Whether this solution is satisfactory isdisputed. (See, for example, Dorr, Hawthorne, and Yli-Vakkuri 2021,Chs 7–8.) Admittedly, there are some contexts in which we talk ofpossibility in a way that may suggest that the ‘accessibilityrelation’ between possible worlds is non-transitive: that noteverything that would have been possible, had things been different insome possible way, is possiblesimpliciter. (If Ann hadstarted writing her paper earlier, it would have been possible for herto finish it today. And shecould have started writing herpaper earlier. But, as things are, it is not possible for her tofinish it today.) Nevertheless, the idea that, as regards the type ofmetaphysical possibility that is involved in puzzles such as that ofthe bicycle, there might be states of affairs that are possiblypossible and yet not possible (and hence thatde remetaphysical possibility and necessity do not obey the system of modallogic known as S4) is regarded with suspicion by manyphilosophers.

It should be noted that the ‘non-transitivity ofaccessibility’ response is distinct from an even more radicalresponse, which rejects the principle of the transitivity ofidentity—a principle definitive of the classical notion ofidentity. For example, Priest (2010) denies the transitivity ofidentity in the context of his dialetheism about truth and aparaconsistent logic in which the material conditional does not obeythe principle ofmodus ponens. Discussion of this extremeposition is, however, beyond the scope of this article. (Ondialetheism and paraconsistent logic, see the separate entry onDialetheism. On the logic of identity, see the entry on Identity.)

Finally, Dorr, Hawthorne, and Yli-Vakkuri 2021 propose that, in somecases, the combination of (classical) transworld identity, tolerance,and the restriction principle can all be retained, yet without denying(as do Chandler and Salmon) the transitivity of accessibility betweenpossible worlds. They appeal to two principles: a metaphysicalprinciple of ‘plenitude’ and a metasemantic principle of ‘semanticplasticity’ (for the relevant terms). This solution is defended byDorret al partly by considering difficulties for rivalsolutions (including that of Chandler and Salmon). The details arecomplex, however: interested readers should consult Dorretal 2021. As with other proposed solutions to the puzzle, theprinciples to which Dorret al appeal (plenitude and semanticplasticity for the relevant terms) are controversial.

It is fair to say that there is no consensus about how the proponentof transworld identity should respond to the transitivity problemposed by Chandler’s example.

5.3 The ‘Four Worlds Paradox’

Chandler’s transitivity argument can be adapted to produce apuzzle that is like those discussed in Sections 4.1–4.2 above inthat it involves the danger of ‘bare identities’, a puzzlethat Salmon (1982) has called ‘The Four Worlds Paradox’.To illustrate the puzzle: suppose that the actual world(w₁) contains a bicycle,a, that is(actually) originally composed of A1 + B1 + C1, and suppose that thereis a possible world,w₅, containing a bicycle,b (not identical witha), that is originallycomposed (inw₅) of A2 + B2 + C1 (where A1 ≠ A2and B1 ≠ B2). Then, it seems, the application of the toleranceprinciple to each ofa andb may generate twofurther possible worlds, in one of which (w₆)there is a bicycle with the original composition A1 + B2 + C1 that isidentical witha, and in the other of which(w₇) there is a bicycle with the originalcomposition A1 + B2 + C1 that is identical withb. Sincethere need apparently be no further difference between the intrinsicfeatures ofw₆ andw₇ on whichthis difference in identities could depend, we appear to have a caseof bare identities. This ‘Four Worlds Paradox’ is likeChandler’s original transitivity puzzle in that it does not seemthat an appeal to individual essences could solve it withoutconflicting with the tolerance principle. If that is so, the proponentof transworld identity (as opposed to counterpart theory) appears tobe left with two options consistent with the transitivity of identity:the denial of the tolerance principle, and the acceptance of bareidentities. (But cf. Dorr, Hawthorne, and Yli-Vakkuri 2021.) It may beargued, however, that the acceptance of bare identities can be mademore palatable in this case by the adoption of a non-transitiveaccessibility relation between possible worlds. (See Salmon 1982,230–252; and, for discussion, Roca-Royes 2016. For a defence ofthe employment of counterpart theory to solve the Four Worlds Paradox,see Forbes 1985, Ch. 7. For discussion of a radical response thatretains the tolerance principle and yet avoids bare identities, butonly at the cost of claiming that two bicycles could completelycoincide in one possible world, simultaneously sharing all theirparts, see Roca-Royes 2016, discussing Williamson 1990. On therelevance to the Four Worlds Paradox to Kripke’s principle ofthe necessity (essentiality) of origin for artefacts, see alsoRobertson 1998 and Hawthorne and Gendler 2000.)

6. Concluding remarks

6.1 Transworld identity and counterpart theory

One of our initial questions (Section 1 above) was whether acommitment to transworld identity—the view that an individualexists in more than one possible world—is an acceptablecommitment for one who believes in possible worlds. The considerationsof Sections 4–5 above suggest that this commitment does involvegenuine (although perhaps not insuperable) problems, even for one whorejects David Lewis’s extreme realism about the nature ofpossible worlds. The problems do not arisedirectly from thenotion of an individual’s existing in more than one possibleworld with different properties. Rather, they derive principally fromthe fact that it is hard to accommodate all that we want to say aboutthe modal properties of ordinary individuals (including all the thingswe want to say about their essential and accidental properties) ifde re modal statements about such individuals arecharacterized in terms of their existence or non-existence in otherpossible worlds.

There is currently no consensus about the appropriate resolution ofthese problems. In particular, there is no consensus about whether theadoption of counterpart theory is superior to the solutions availableto a transworld identity theorist. A full examination of the issuewould require a discussion of the objections that have been raisedagainst counterpart theory as an interpretation ofde remodality. And a detailed discussion of counterpart theory is beyondthe scope of this article. (For David Lewis’s presentation ofcounterpart theory, the reader might start with Lewis 1973,39–43, followed by (the more technical) Lewis 1968. Earlycriticisms of Lewis’s counterpart theory include those in Kripke1980; Plantinga 1973; and Plantinga 1974, Ch. 6. Lewis develops the1968 version of his counterpart theory in Lewis 1971 and 1986, Ch. 4;he responds to criticisms in his “Postscripts to‘Counterpart Theory and Quantified Modal Logic’”(1983, 39–46) and in Lewis 1986, Ch. 4. Other discussions ofcounterpart theory include Hazen 1979, the relevant sections of Divers2002, Melia 2003, and the more technical treatment in Forbes 1985.More recent critiques of the theory (postdating Lewis’s 1986response to his critics) include Fara and Williamson 2005, Fara 2009,and Dorr, Hawthorne, and Yli-Vakkuri 2021, Ch. 10.)

One way to argue in favour of transworld identity (distinct from thedefensive strategies discussed in Sections 4 and 5 above) is what wemight call ‘the argument from logical simplicity’ (Linskyand Zalta 1994, 1996; Williamson 1998, 2000). The argument begins bynoting that Quantified Modal Logic—which combines individualquantifiers and modal operators—is greatly simplified when oneaccepts the validity of the Barcan scheme,∀x□A →□∀xA (Marcus 1946). The resulting logicis sound and complete with respect toconstant domainsemantics, in which each possible world has precisely the sameset of individuals in its domain. The simplest philosophicalinterpretation of this semantics is that one and the same individualexists at every possible world.

Several remarks on this argument are in order. First, its conclusionis very strong: it says that any entity that in fact exists or thatcould have existed existsnecessarily. There is no contingentexistence. This goes far beyond the claim that there are genuineidentities across worlds. (Williamson (2002) defends this conclusionon independent grounds.) Second, the argument does not offer anexplanation of how transworld identities are possible; it insists onlythat there are genuine transworld identities. (Nevertheless, themetaphysical picture that can most naturally be ‘read off’the constant-domain semantics treats properties-at-a-world asrelations between particulars and worlds, as on McDaniel’smodal realism with overlap (McDaniel 2004), discussed inSection 1.2 above.)

Third, the argument is not best understood as the claim that, if onedoes not accept transworld identities, then one isforcedinto denying the Barcan scheme (and hence forced into uncomfortablelogical territory). That claim would be true only if the Barcan schemewere validatedonly by constant-domain semantics, which isnot the case. Counterpart-theoretic semantics can be restricted so asto validate the Barcan scheme, by insisting that the counterpartrelation is an equivalence relation which, for each particularx and worldw, relatesx to a uniqueparticular inw. (One could not then interpret thecounterpart relation in terms of similarity, as Lewis does.) Rather,the argument should be understood as the claim that the best way togain the advantages of a logic containing the Barcan scheme is byadopting constant-domain semantics (and genuine transworld identitiesalong with it). But just which metaphysical view counts as‘best’ here will involve a trade-off between many factors.These include the simplicity of the constant-domain semantics, on theone hand, but also arguments of the kind raised by Lewis against modalrealism with overlap, on the other.

6.2 Lewis on transworld identity and ‘existence according to a world’

Finally, we can note that Lewis (1986) has presented a challenge tothe self-styled champions of ‘transworld identity’ toexplainwhy the view that they insist on deserves to becalled a commitment to transworld identity at all.

Throughout this article, it has been assumed that a commitment totransworld identity may be differentiated from a commitment tocounterpart theory on the grounds that the transworld identitytheorist accepts, while the counterpart theorist denies, that anobjectexists in more than one possible world (cf. Section1.2 above). However, as Lewis points out, there is a notion of‘existenceaccording to a (possible) world’ thatis completely neutral as between a counterpart-theoretic and a‘transworld identity’ interpretation. In terms of thisneutral conception, as long as the counterpart theorist and transworldidentity theorist agree that Bertrand Russell could have been aplaywright instead of a philosopher, they must agree that Russellexistsaccording to more than one world. In particular, theymust agree that,according to our world, he exists and is aphilosopher, andaccording to some other worlds, he existsand is a non-philosopher playwright (cf. Lewis 1986, 194). Thedifference between the theorists, then, allegedly consists in theirdifferent interpretations of what it is for Russell to exist‘according to’ a world. In the view of the counterparttheorist, for Russell to exist according to a possible world in whichhe is a playwright is for him to have acounterpart in thatworld who is (in that world) a playwright. According to the transworldidentity theorist, it is supposed to be for Russell (himself) toexist in that world as a playwright.

If the transworld identity theorist were a Lewisian realist aboutpossible worlds, this notion of existencein a world could beclearly distinguished from the neutral notion of existenceaccording to a world, on the grounds that the existence ofRussell in a world would require his complete or partial presence as apart of such a world (cf. Section 1.2 above). But, as Lewis notes, theself-styled champions of ‘transworld identity’ who opposehis counterpart theory are philosophers who repudiate a Lewisianrealist conception of what it takes for Russell to exist in more thanone possible world. Hence, he argues, there is a question about theirentitlement to claim that, according to their theory, Russell existsin other possible worlds in any sense that goes beyond theneutral thesis (compatible with counterpart theory) that Russellexistsaccording to other worlds. Thus Lewis writes (usingthe 1968 US presidential candidate Hubert Humphrey as hisexample):

The philosophers’ chorus on behalf of ‘trans-worldidentity’ is merely insisting that, for instance, it is Humphreyhimself who might have existed under other conditions, … whomight have won the presidency, who exists according to many worlds andwins according to some of them. All that is uncontroversial. Thecontroversial question ishow he manages to have these modalproperties. (1986, 198)

A natural reaction to Lewis’s challenge is to point out that aproponent of transworld identity who is not a Lewisian realist willtypically reject Lewis’s counterpart theory on the grounds thathis counterpart relation does not have the logic of identity. If so,then (pace Lewis) it is not the case, strictly speaking, thatthe ‘philosophers’ chorus on behalf of “trans-worldidentity”’ is merely insisting on the neutral claim thatobjects exist according to more than one world. However, even if thisis correct, it does not answer a further potential challenge. Suppose,as seems plausible, that there could be a counterpart relation that(unlike the one proposed by Lewis himself) is an equivalence relation(transitive, symmetric, and reflexive), and ‘one-one betweenworlds’. What would distinguish,in the case of a theoristwho is not a Lewisian realist about possible worlds, between, onthe one hand, a commitment to the interpretation ofde remodal statements in terms of such an ‘identity-resembling’counterpart relation, and, on the other hand, a commitment to genuinetransworld identity (and hence to the view that an individualgenuinelyexists in a number of distinct possible worlds)?The aficionado of transworld identity owes Lewis a reply to thischallenge.

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