## 1. What is transworld identity?


### 1.1 Why transworld identity?



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



How are we to extend this framework to statements about what is
possible and necessary for *particular* individuals--what
are known as *de re* modal statements ('*de
re*' meaning 'about a thing')--for example,
that Clover, a particular (actually existing) four-legged cow, could
not have been a giraffe, or that she could have had just three legs? A
natural extension of the framework is to treat the first statement as
equivalent to the claim that there is no possible world in which
Clover is a giraffe, and the second as equivalent to the claim that
there is some possible world in which Clover is three-legged. But this
last claim appears to imply that there is some possible world in which
Clover exists and has three legs--from which it seems inescapably
to follow that one and the same individual--Clover--exists
in some merely possible world as well as in the actual world: that
there is an identity between Clover and some individual in another
possible world. Similarly, it appears that the *de re* modal
statements 'George Eliot could have been a scientist rather than
a novelist' and 'Bertrand Russell might have been a
playwright 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 some
possible world in which Bertrand Russell (exists and) is a playwright
and not a philosopher'. Again, each of these appears to involve
a commitment to an identity between an individual who exists in the
actual world (Eliot, Russell) and an individual who exists in a
non-actual possible world.



To recapitulate: the natural extension of the possible-worlds
interpretation to *de re* modal statements involves a
commitment to the view that some individuals exist in more than one
possible world, and thus to what is known as 'identity across
possible worlds', or (for short) 'transworld
identity'. (It is questionable whether the shorthand is really
apt. One would expect a 'transworld' identity to mean an
identity that holds across (and hence within) *one* world, not
an identity that holds between objects in *distinct* worlds.
(As David Lewis (1986) has pointed out, our own Trans World Airlines
is an intercontinental, not an interplanetary, carrier.) Nevertheless,
the term 'transworld identity' is far too well established
for it to be sensible to try to introduce an alternative, although
'interworld identity' or even 'transmodal
identity' would in some ways be more appropriate.) But is this
commitment acceptable?


### 1.2 Transworld identity and conceptions of possible worlds



To say that there is a transworld identity between *A* and
*B* is to say that there is some possible world
*w*1, and some distinct possible world
*w*2, such that *A* exists in
*w*1, and *B* exists in
*w*2, and *A* is identical with *B*.
(Remember that we are treating the actual world as one of the possible
worlds.) In other words, to say that there is a transworld identity is
to say that the *same* object exists in distinct possible
worlds, or (more simply) that some object exists in more than one
possible world.



But what does it mean to say that an individual exists in a merely
possible world? And--even if we accept that paraphrases of modal
statements in terms of possible worlds are in general
acceptable--does it even make *sense* to say that actual
individuals (like you and your neighbour's cat and the Eiffel
Tower) exist in possible worlds other than the actual world? To know
what a claim of transworld identity amounts to, and whether such
claims are acceptable, we need to know what a possible world is, and
what it is for an individual to exist in one.



Among those who take possible worlds seriously (that is, those who
think that there are possible worlds, on some appropriate
interpretation of the notion), there is a variety of conceptions of
their nature. On one account, that of David Lewis, a non-actual
possible world is something like another universe, isolated in space
and time from our own, but containing objects that are just as real as
the entities of our world; including its own real concrete objects
such 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 possible
worlds'. We call our world 'actual' simply because
we are in it; the inhabitants of another world may, with equal right,
call *their* world 'actual'. In other words,
according to Lewis, 'actual' in 'the actual
world' 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 possible
worlds, it looks as if, for Clover to exist in another possible world
as well as the actual world would be for her to be a part of such a
world: Clover would somehow have to exist as a (concrete) part of two
worlds, 'in the same way that a shared hand might be a common
part of two Siamese twins' (Lewis 1986, 198). But this is
problematic. Clover actually has four legs, but could have had three
legs. Should we infer that Clover is a part of some world at which she
has 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 in
our world and three in the alternative world)? Worse still, we appear
to be ascribing contradictory *properties* to Clover: she has
four legs, and yet has no more than three.



Those who believe in the 'extreme realist' notion of
possible worlds may respond by thinking of Clover as having a
four-legged part in our world, and a three-legged part at some other
world. This is Yagisawa's (2010) view (cf. Lewis 1986,
210-220). Yagisawa thinks of concrete entities--everyday
things such as cats, trees and macbooks--as extended across
possible worlds (as well as across times and places), in virtue of
having *stages* (or parts) which exist at those worlds (and
times and places). Ordinary entities thus comprise spatial, temporal
and modal stages, all of which are equally real. Metaphysically, modal
stages (and the worlds at which they exist) are on a par with temporal
and 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 persists
through time by having 'temporal parts' that are located
at different times.) Thus, when we say that Clover has four legs in
our world but only three in some other world, we are saying that she
has 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 comprising
many modal stages--has awfully many legs, even though she
actually has only four.)



Another option for the 'extreme realist' about possible
worlds is to hold that Clover is four-legged relative to our world,
but three-legged relative to some other world. In general, qualities
we would normally think of as monadic properties are in fact relations
to worlds. McDaniel (2004) defends a view along these lines. A
feature of this account is that one and the same entity may exist
according to many worlds, for that entity may bear the
*exists-at* relation to more than one world. Accordingly, the
view is sometimes called *genuine modal realism with overlap*
(McDaniel 2004). This view, transposed to the temporal case, is
precisely what the *endurantist* says: objects do not have
temporal parts; each object is wholly present at each time. (See the
separate entry on Temporal Parts.)



Lewis rejects both of these options. He rejects the overlap view
because of what he calls 'the problem of accidental
intrinsics'. On the overlap view, *having four legs* is a
relation to a world, and hence not one of Clover's intrinsic
properties. In fact, any aspect of a particular that changes across
worlds turns out to be non-intrinsic to that particular. As a
consequence, every particular has all its intrinsic properties
essentially, which Lewis thinks is unacceptable (1986,
199-209).



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



However, Lewis's version of realism is by no means the only
conception of possible worlds. According to an influential set of
rival accounts, possible worlds, although real entities, are not
concrete '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; Stalnaker
1995; also the separate entry on Possible Worlds. A state of affairs
*S* is 'maximal' just in case, for any state of
affairs *S\**, either it is impossible for both *S* and
*S\** to obtain, or it is impossible for *S* to obtain
without *S\**: the point of the restriction to the maximal is
just that a possible world should be a possible state of affairs that
is, in a relevant sense, complete.)



On the face of it, to treat possible worlds as abstract entities may
seem only to make the problem of transworld identity worse. If it is
hard to believe that you (or a table or a cat) could be part of
another Lewisian possible world, it seems yet harder to believe that a
concrete entity like you (or the table or cat) could be part of an
*abstract* entity. However, those who think that possible
worlds are abstract entities typically do not take the existence in a
merely possible world of a concrete actual individual to involve that
entity'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 to
Plantinga's (1973, 1974) version of this account, to say that
George Eliot exists in some possible world in which she is a scientist
is just to say that there is a (maximal) possible state of affairs
such that, had it obtained (i.e., had it been actual), George Eliot
would (still) have existed, but would have been a scientist. On this
(deflationary) account of existence in a possible world, it appears
that the difficulties that accompany the idea that George Eliot leads
a double life as an element of another concrete universe as well as
our own (or the idea that she is partially present in many such
universes) are entirely avoided. On Plantinga's account, to
claim that an actual object exists in another possible world with
somewhat different properties amounts to nothing more risque
than the claim that the object could have had somewhat different
properties: something that few will deny. (Note that according to this
account, if the actual world is to be one of the possible worlds, then
the actual world must be an abstract entity. So, for example, if a
merely possible world is 'a way the world might have
been', the actual world will be 'the way the world
is'; if a merely possible world is a maximal possible state of
affairs that is not instantiated, then the actual world will be a
maximal possible state of affairs that *is* instantiated. It
follows that we must distinguish the actual world *qua*
abstract entity from 'the actual world' in the sense of
the collection of spatiotemporally linked entities including you and
your surroundings that constitutes 'the universe' or
'the cosmos'. The sense in which you exist in this
concrete universe (by being part of it) must be different from the
sense in which you exist in the abstract state of affairs that is in
fact instantiated (cf. Stalnaker 1976; van Inwagen 1985, note 3;
Kripke 1980, 19-20).)



The discussion so far may suggest that whether the notion of
transworld identity (that an object exists in more than one world) is
problematic depends solely on whether one adopts an account of
possible worlds as concrete entities such as Lewis's (in which
case it is) or an account of possible worlds as abstract entities such
as Plantinga's (in which case it is not). However, matters are
not so simple, for a variety of reasons (to be discussed in Sections
3-5 below).


## 2. Transworld identity and Leibniz's Law



There may seem to be an obvious objection to the employment of
transworld identity to interpret or paraphrase statements such as
'Bertrand Russell could have been a playwright' or
'George Eliot might have been a scientist'. A fundamental
principle about (numerical) identity is Leibniz's Law: the
principle that if *A* is identical with *B*, then any
property of *A* is a property of *B*, and vice versa. In
other words, according to Leibniz's Law, identity requires the
sharing of all properties; thus any difference between the properties
of *A* and *B* is sufficient to show that *A* and
*B* are numerically distinct. (The principle here referred to
as 'Leibniz's Law' is also known as the
Indiscernibility of Identicals. It must be distinguished from another
(more controversial) Leibnizian principle, the Identity of
Indiscernibles, which says that if *A* and *B* share all
their properties then *A* is identical with *B*.)
However, the whole point of asserting a transworld identity is to
represent the fact that an individual could have had somewhat
*different* properties from its actual properties. Yet does not
(for example) the claim that a philosopher in the actual world is
identical with a non-philosopher in some other possible world conflict
with Leibniz's Law?



It is generally agreed that this objection can be answered, and the
appearance of conflict with Leibniz's Law eliminated. We can
note that the objection, if sound, would apparently prove too much,
since a parallel objection would imply that there can be no such thing
as genuine (numerical) identity through change of properties over
time. But it is generally accepted that no correct interpretation of
Leibniz's Law should rule this out. For example, Bertrand
Russell was thrice married when he received the Nobel Prize for
Literature; the one-year-old Bertrand Russell was, of course,
unmarried; does Leibniz's Law force us to deny the identity of
the prize-winning adult with the infant, on the grounds that they
differ in their properties? No, for it seems that the appearance of
conflict with Leibniz's Law can be dispelled, most obviously by
saying that the infant and the adult share the properties of *being
married in 1950* and *being unmarried in 1873*, but
alternatively by the proposal that the correct interpretation of
Leibniz's Law is that the identity of *A* and *B*
requires that there be no time such that *A* and *B*
have different properties *at that time* (cf. Loux 1979,
42-43; also Chisholm 1967). However, it seems that exactly
similar moves are available in the modal case to accommodate
'change' of properties across possible worlds. Either we
may claim that the actual Bertrand Russell and the playwright in some
possible world (say, *w*2) are alike in possessing
the properties of *being a philosopher in the actual world* and
*being a non-philosopher in w2*, or we may argue
that Leibniz's Law, properly interpreted, asserts that the
identity of *A* and *B* requires that there be no time,
and no possible world, such that *A* and *B* have
different properties *at that time and world*. The moral
appears to be that transworld identity claims (combined with the view
that some of an individual's properties could have been
different) need no more be threatened by Leibniz's Law than is
the view that there can be identity over time combined with change of
properties (Loux 1979, 42-43).



It should be mentioned, however, that David Lewis has argued that the
reconciliation of identity through change over time with
Leibniz's Law suggested above is oversimplified, and gives rise
to a 'problem of temporary intrinsics' that can be solved
only by treating a persisting thing that changes over time as composed
of temporal parts that do not change their intrinsic properties. (See
Lewis 1986, 202-204, and for discussion and further references,
Hawley 2001; Sider 2001; Lowe 2002; Haslanger 2003.) In addition, it
is partly because Lewis regards the analogous account of transworld
identity in terms of modal parts as an unacceptable solution to an
analogous 'problem of accidental intrinsics' that Lewis
rejects transworld identity in favour of counterpart theory (Lewis
1986, 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 (when
the issue came to prominence as a result of developments in modal
logic), it was debated whether the notion of transworld identity is
genuinely problematic, or whether, on the contrary, the alleged
'problem of transworld identity' is merely a
pseudo-problem. (See Loux 1979, Introduction, Section III; Plantinga
1973 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 be
at the heart of this dispute. In particular, although the main
proponents of the view that the alleged problem is a pseudo-problem
clearly intended to attack (*inter alia*) Lewis's version
of modal realism, they did not attempt to rebut the thesis (discussed
in Section 1.2 above) that *if* one is a Lewisian realist about
possible worlds, then one should find transworld identity problematic.
Matters are complicated by the fact that proponents of the view that
the alleged problem of transworld identity is a pseudo-problem were to
some extent responding to hypothetical arguments, rather than
arguments presented in print by opponents (see Plantinga 1974, 93).
However, one central issue was whether the claim that an individual
exists in more than one possible world (and hence that there are cases
of transworld identity) needs to be backed by the provision of
*criteria of transworld identity*, and, if so, why.



The term 'criterion of identity' is ambiguous. In an
epistemological sense, a criterion of identity is a way of telling
whether an identity statement is true, or a way of recognizing whether
an individual *A* is identical with an individual *B*.
However, the notion of a criterion of identity also has a metaphysical
interpretation, according to which it is a set of (non-trivial)
necessary and sufficient conditions for the truth of an identity
statement. Although a criterion of identity in the second
(metaphysical) sense might supply us with a criterion of identity in
the first (epistemological) sense, it seems that something could be a
criterion of identity in the second sense even if it is unsuited to
play the role of a criterion of identity in the first sense.



The most influential arguments *against* the view that there is
a genuine problem of transworld identity (or 'problem of
transworld identification', to use Kripke's preferred
terminology) are probably those presented by Plantinga (1973, 1974)
and Kripke (1980). Plantinga and Kripke appear to have, as their
target, an alleged problem of transworld identity that rests on one of
three assumptions. The first assumption is that we must possess
criteria of transworld identity in order to ascertain, on the basis of
their properties in other possible worlds, the identities of (perhaps
radically disguised) individuals in those worlds. The second
assumption is that we must possess criteria of transworld identity if
our references to individuals in other possible worlds are not to miss
their mark. The third assumption is that we must possess criteria of
transworld identity in order to understand transworld identity claims.
Anyone who makes one of these assumptions is likely to think that
there is a problem of transworld identity--a problem concerning
our entitlement to make claims that imply that an individual exists in
more than one possible world. For it does not seem that we possess
criteria of transworld identity that could fulfil any of these three
roles. However, Plantinga and Kripke provide reasons for thinking that
none of these three assumptions survives scrutiny. If so, and if these
assumptions exhaust the grounds for supposing that there is a problem
of transworld identity, the alleged problem may be dismissed as a
pseudo-problem.



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



(1)
The 'epistemological' assumption: We must possess a
criterion of transworld identity for George Eliot in order to be able
to tell, on the basis of knowledge of the properties that an
individual has in some other possible world, whether that individual
is identical with Eliot.
(2)
The 'security of reference' assumption: We must
possess a criterion of transworld identity for Bertrand Russell in
order to know that, when we say such things as 'There is a
possible world in which Russell is a playwright', we are talking
about Russell rather than someone else.
(3)
The 'intelligibility' assumption: We must possess a
criterion of transworld identity for George Eliot in order to
understand the claim that there is a possible world in which she is a
scientist.

### 3.1 Against the epistemological assumption



The epistemological assumption appears to imply that the point of our
having a criterion of transworld identity for George Eliot would be
that we could then *employ* the criterion in order to ascertain
which 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 out
or identify her in other possible worlds (Plantinga 1973; 1974, Ch. 6;
Kripke 1980, 42-53; cf. Loux 1979, Introduction; Kaplan
1967/1979). However, this suggestion, as stated, is vulnerable to the
charge that it is the product of confusion. For how *could* we
use a criterion of identity in the way envisaged? We must dismiss as
fanciful the idea that if we had a criterion of transworld identity
for George Eliot, we could use it to tell, *by empirical
inspection* of the properties of individuals in other possible
worlds (perhaps using a powerful telescope (Kripke 1980, 44) or
'Jules Verne-o-scope' (Kaplan 1967/1979, 93; Plantinga
1974, 94)), which, if any, of those individuals is Eliot. For no one
(including an extreme realist like Lewis) thinks that our
epistemological access to other possible worlds is of this kind.
(According to Lewis, other possible worlds are causally isolated from
our own, and hence beyond the reach of our telescopes or any other
perceptual devices.) But once we face up to the fact that a criterion
of transworld identity (if we had one) could have no such empirical
use, the argument based on the epistemological assumption appears to
collapse. It is tempting to suggest that the argument is the product
of the (perhaps surreptitious) influence of a misleading picture of
our 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 it
were like a foreign country. One looks upon it as an observer. Maybe
Nixon has moved to the other country and maybe he hasn't, but
one is given only qualities. One can observe all his qualities, but,
of course, one doesn't observe that someone is Nixon. One
observes that something has red hair (or green or yellow) but not
whether something is Nixon. So we had better have a way of telling in
terms 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 these
other possible worlds, who was Nixon. (1980, 43)



(It is possible, though, that in this passage Kripke's principal
target is not a mistaken conception of our epistemological access to
other possible worlds, but what he takes to be a mistaken
('foreign country') conception of their nature: a
conception that (when divorced from the fanciful epistemology) would
be 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 transworld
identity is that its possession would enable me to tell which
individual I am referring to when I say (for example) 'There is
a possible world in which Russell is a playwright'. Suppose that
I am asked: 'How do you know that the individual you are talking
about--this playwright in another possible world--is
Bertrand Russell rather than, say, G. E. Moore, or Marlene Dietrich,
or perhaps someone who is also a playwright in the actual world, such
as Tennessee Williams or Aphra Behn? Don't you need to be able
to supply a criterion of transworld identity in order to secure your
reference to Russell?' (Cf. Plantinga 1974, 94-97; Kripke
1980, 44-47.) It seems clear that the right answer to this
question is 'no'. As Kripke has insisted, it seems
spurious to suggest that the question how we know which individual we
are referring to when we make such a claim can be answered only by
invoking a criterion of transworld identity. For it seems that we can
simply *stipulate* that the individual in question is Bertrand
Russell (Kripke 1980, 44).



Similarly, perhaps, if I say that there is some past time at which
Angela Merkel is a baby, and am asked 'How do you know that
it's the infant *Angela Merkel* that you are talking
about, rather than some other infant?', an apparently adequate
reply is that I am *stipulating* that the past state of affairs
I am talking about is one that concerns *Merkel* (and not some
other individual). It seems that I can adequately answer the parallel
question in the modal case by saying that I am *stipulating*
that, when I say that there is some possible world in which Russell is
a playwright, the relevant individual in the possible world (if there
is one) is *Russell* (and not some other potential or actual
playwright).


### 3.3 Against the 'intelligibility' assumption



A third job for a criterion of transworld identity might be this: in
order to *understand* the claim that there is some possible
world in which George Eliot is a scientist, perhaps we must be able to
give an informative answer to the question 'What would it take
for a scientist in another possible world to be identical with
Eliot?' Again, however, it can be argued that this demand is
illegitimate, at least if what is demanded is that one be able to
specify a set of properties whose possession, in another possible
world, by an individual in that world, is non-trivially necessary and
sufficient 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, in
order to *understand* the claim that there is some past time at
which Angela Merkel is a baby, we have to be able to answer the
question 'What does it take for an infant at some past time to
be identical with Merkel?' in any informative way. Secondly, it
may be proposed that in order to understand the claim that there is
some possible world in which George Eliot is a scientist, we can rely
on our prior understanding of the claim that she might have been a
scientist (cf. Kripke 1980, 48, note 15; van Inwagen 1985).


### 3.4 Remaining issues



However, even if all three of these assumptions can be dismissed as
bad, or at least inadequate, reasons for supposing that transworld
identity requires criteria of transworld identity (and hence for
supposing that there is a problem of transworld identity), it does not
follow that there are no *good* reasons for this supposition.
In particular, even if the three assumptions are discredited, a fourth
claim may survive:



(4)
There must *be* a criterion of transworld identity for
Russell (in the sense of a set of properties whose possession by an
object in any possible world is non-trivially necessary and sufficient
for being Russell) if the claim that there is a possible world in
which Russell is a playwright is to be true. (Such a set of properties
would be what is called a non-trivial *individual essence* of
Russell, where an individual essence of an individual *A* is a
property, or set of properties, whose possession by an individual in
any possible world is both necessary and sufficient for identity with
*A*.)


That this possibility is left open by the arguments so far considered
is suggested by at least two points. The first concerns the analogy
drawn above between transworld identity and identity through time.
Even if we can understand the claim that there is some past time at
which Angela Merkel is a baby without being able to specify
informative (non-trivial) necessary and sufficient conditions for the
identity of the adult Angela Merkel with some previously existing
infant, it does not follow that there *are* no such necessary
and sufficient conditions. And many philosophers have supposed that
there are such conditions for personal identity over time. Secondly,
the fact that one may be able to ensure, by stipulation, that one is
talking about a possible world in which *Bertrand Russell* (and
not someone else) is a playwright (if there is such a world) does not
imply that, when making this stipulation, one is not
*implicitly* stipulating that this individual satisfies, in
that world, conditions non-trivially necessary and sufficient for
being Russell, even if one is not in a position to say what these
conditions are.



This second point is an extension of the observation that, if (as most
philosophers believe) Bertrand Russell has some essential properties
(properties that he has in all possible worlds in which he exists), to
stipulate that one is talking about a possible world in which Russell
is a playwright is, at least implicitly, to stipulate that the
possible world is one in which someone with Russell's essential
properties is a playwright. For example, according to Kripke's
'necessity of origin' thesis, human beings have their
parents essentially (Kripke 1980). If this is correct, then, when we
say 'There is a possible world in which Russell is a
playwright', it seems that, if our stipulation is to be
coherent, we must be at least implicitly stipulating that the possible
world is one in which *someone with Russell's actual
parents* is a playwright, even if the identity of Russell's
parents is unknown to us, and even though we are (obviously) in no
position to conduct an empirical investigation into the ancestry, in
the possible world, of the individuals who exist there. Thus, it
seems, even if Kripke is right in insisting that we need not be able
to *specify* non-trivial necessary and sufficient conditions
for being Russell in another possible world if we are legitimately to
claim that there are possible worlds in which he is a playwright, it
might nevertheless be the case that there *are* such necessary
and sufficient conditions (cf. Kripke 1980, 46-47 and 18, note
17; Lewis 1986, 222).



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


## 4. Individual essences and bare identities



The principal argument for this view--that transworld identities
require non-trivial individual essences--is that such essences
are needed in order to avoid what have been called 'bare
identities' across possible worlds. And some regard bare
identities as too high a price to pay for the characterization of
*de re* modal statements in terms of transworld identity. If
they are right, and if (as many philosophers believe) there are no
plausible candidates for non-trivial individual essences (at least for
such things as people, cats, trees, and tables) there is, indeed, a
serious problem about transworld identity. (The expression 'bare
identities' is taken from Forbes 1985. The notion, as used here,
is approximately the same as the notion of 'primitive
thisness' employed by Adams (1979), although Adams's
notion is that of an identity that does not supervene on qualitative
facts, rather than an identity that does not supervene on any other
facts at all.)



Suppose that we combine transworld identity with the claim (without
which the introduction of transworld identity seems pointless) that a
transworld identity can hold between *A* in
*w*1 and *B* in *w*2 even
though the properties that *B* has in *w*2
are somewhat different from the properties that *A* has in
*w*1 (or, to put it more simply, suppose that we
combine the claim that there are transworld identities with the claim
that not all of a thing's properties are essential to it). Then,
it can be argued, unless there are non-trivial individual essences, we
are in danger of having to admit the existence of possible worlds that
differ from one another only in the identities of some of the
individuals that they contain.


### 4.1 Chisholm's Paradox and bare identities



One such argument, adapted from Chisholm 1967, goes as follows. Taking
Adam and Noah in the actual world as our examples (and pretending, for
the sake of the example, that the biblical characters are real
people), then, on the plausible assumption that not all of their
properties are essential to them, it seems that there is a possible
world in which Adam is a little more like the actual Noah than he
actually was, and Noah a little more like the actual Adam than he
actually was. But if there is such a world, then it seems that there
should be a further world in which Adam is yet more like the actual
Noah, 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 is
exactly like the actual world, except that Adam and Noah have
'switched roles' (plus any further differences that follow
logically from this, such as the fact that in the
'role-switching' world Eve is the consort of a man who
plays the Adam role, but is in fact Noah). But if this can happen with
Adam and Noah, then it seems that it could happen with any two actual
individuals. For example, it looks as if there will be a possible
world that is a duplicate of the actual world except for the fact that
in this world *you* play the role that Queen Victoria plays in
the actual world, and *she* plays the role that you play in the
actual world (cf. Chisholm 1967, p. 83 in 1979). But this may seem
intolerable. Is it really the case that Queen Victoria could have had
all *your* 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 are
they to be avoided? The obvious answer is that what is needed, in the
Adam-Noah case, is that the roles played by Adam and Noah in the
actual world include some properties that are essential to their
bearers' being Adam and Noah respectively: that Adam and Noah
differ non-trivially in their *essential* properties as well as
in their accidental properties: more precisely, that Adam has some
essential property that Noah essentially lacks, or vice versa. For if
'the Adam role' includes some property that Noah
essentially lacks, then, of course, there is no possible world in
which Noah has that property, in which case the Adam role (in all its
detail) is not a possible role for Noah, and the danger of a
role-switching world such as the one described above is avoided.



The supposition that Adam and Noah differ in their essential
properties in this way, although sufficient to block the generation of
this example of a role-switching world, does not by itself imply that
each of Adam and Noah has an *individual essence:* a set of
essential properties whose possession is (not only necessary but also)
sufficient for being Adam or Noah. Suppose that Adam has, as one of
his essential properties, living in the Garden of Eden, whereas Noah
essentially lacks this property. This will block the possibility of
Noah's playing the Adam role, although it does not, by itself,
imply that *nothing 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-switching
concerning actual individuals, we must suppose that every actual
individual has some essential property (or set of essential
properties) that every other actual individual essentially lacks. For
example, to block all cases of role-switching concerning Adam and
other actual individuals, there must be some component of 'the
Adam role' that is not only essential to being Adam, but also
cannot be played, in any possible world, by any actual individual
other than Adam.



Even if we suppose that all actual individuals are distinguished from
one another by such 'distinctive' essential properties,
this still does not, strictly speaking, imply that they have
individual essences. For example, it does not rule out the existence
of 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 by
some *merely possible* individual (distinct from all actual
individuals). However, if we find intolerable the idea that there are
such possible worlds--worlds that, like the role-switching world,
differ from the actual world only in the identities of some of the
individuals that they contain--then, it seems, we must suppose
that individuals like Adam (and Noah and you) have (non-trivial)
individual essences, where an individual essence of Adam is (by
definition) some property (or set of properties) that is both
essential to being Adam and also such that it is not possessed, in any
possible world, by any individual other than Adam--i.e., an
essential property (or set of properties) that guarantees that its
possessor is Adam and no one else.



Chisholm (1967) arrives at his role-switching world by a series of
steps. Thus his argument appears to rely on the combination of the
transitivity of identity (across possible worlds) with the assumption
that a succession of small changes can add up to a big change. And
'Chisholm's Paradox' (as it is called) is sometimes
regarded as relying crucially on these assumptions, suggesting that it
has the form of a *sorites* paradox (the type of paradox that
generates, from apparently impeccable assumptions, such absurd
conclusions 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 not
rely on the cumulative effect of a series of small changes. Suppose we
assume that Adam and Noah do not differ from one another in their
essential properties; in other words, that all the differences between
them are accidental (i.e., contingent) differences. It seems
immediately to follow that any way that Adam could have been is a way
that Noah could have been, and vice versa. But one way that Adam could
have been is the way Adam actually is, and one way that Noah could
have been is the way Noah actually is. So (if Adam and Noah do not
differ in their essential properties) it seems that there is a
possible world in which Adam plays the Noah role, and a possible world
in which Noah plays the Adam role. But there is no obvious reason why
a world in which Adam plays the Noah role and a world in which Noah
plays the Adam role shouldn't be the very same world. And in
that case there is a possible world in which Adam and Noah have
swapped their roles. This argument for the generation of a
role-switching world does not rely on a series of small changes: all
that it requires is the assumption that there is no essential
difference between Noah and Adam: or, to put it another way, that any
essential property of Noah is also an essential property of Adam, and
vice 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 have
non-trivial individual essences there will be 'bare'
transworld identities: identities that do not supervene on (are not
grounded in) other facts, is presented by Graeme Forbes. (Strictly
speaking, Forbes is concerned to avoid identities that are not
grounded in what he calls 'intrinsic' properties.) A
sketch of a type of argument used by Forbes is this. (What follows is
based on Forbes 1985, Ch. 6; see also Mackie 2006, Ch. 3.) Suppose (as
is surely plausible) that an actually existing oak tree could have
been different in some respects from the way that it is; suppose also
that, even if it has some essential properties (perhaps it is
essentially an oak tree, for example), it has no non-trivial
individual essence consisting in some set of its intrinsic properties.
Then there is the danger that there may be three possible worlds (call
them '*w*2',
'*w*3', and
'*w*4'), where in *w*2
there is an oak tree that is identical with the original tree
(*w*2 representing one way in which the tree could
have been different), and in *w*3 there is an oak
tree that is identical with the original tree (*w*3
representing another way in which the tree could have been different),
and in *w*4 there are *two* oak trees, one of
which is an intrinsic duplicate of the tree as it is in
*w*2, and the other an intrinsic duplicate of the
tree as it is in *w*3. *If* all of
*w*2, *w*3, and
*w*4 are possible, then, given that at least one of
the trees in *w*4 is not identical with the original
tree (since two things cannot be identical with one thing) there are
instances of transworld identity (and transworld distinctness)
concerning a tree in one possible world and a tree in another that are
not grounded in (do not supervene on) the intrinsic features that
those trees possess in those possible worlds. For example, suppose
that, of the two trees in *w*4, the intrinsic
duplicate of the *w*2 tree is *not* identical
with the original tree. Then, obviously, the distinctness
(non-identity) between this *w*4 tree and the tree
in *w*2 is not grounded in the intrinsic features
that the trees have in *w*2 and
*w*4--and nor is the identity between the tree
in *w*2 and the original tree grounded in the
intrinsic features that the tree has in *w*2 and in
the actual world.



Forbes argues that, in order to avoid this (and similar) consequences,
we should suppose that (contrary to the second assumption used in
setting up the 'reduplication argument' sketched above)
the oak tree *does* have a non-trivial individual essence
consisting in some of its intrinsic properties, and his favoured
candidate for its essence is one that includes the tree's coming
from the particular acorn from which it actually originated. If the
tree does have such an 'intrinsic' individual essence,
then, *if* *w*2 and *w*3
are both possible, each of them must contain a tree that has (in that
world) intrinsic properties that are guaranteed to be
*sufficient* for identity with the original tree, in which case
(as a matter of logic) there can be no world such as
*w*4 that contains intrinsic duplicates of both of
them. (See Forbes 1985, Ch. 6, and, for discussion, Mackie 1987;
Mackie 2006; Robertson 1998; Yablo 1988; Chihara 1998; Della Rocca
1996; further discussions by Forbes include his 1986, 1994, and
2002.)



Finally, it is obvious that the structure of Forbes's argument
has nothing to do with the fact that the chosen example is a tree.
Forbes's 'reduplication argument' therefore appears
to pose a general problem for the characterization of *de re*
modal 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 identities
across possible worlds.


### 4.3 Transworld identity and conditions for identity over time



So far it has been assumed that (non-trivial) necessary and sufficient
conditions for transworld identity with a given object would involve
the possession, by that object, of an individual essence: a set of
properties that it carries with it in every possible world in which it
exists. But one might wonder why we should make this assumption. Those
who believe that there are (non-trivial) necessary and sufficient
conditions for identity over time need not, and almost universally do
not, believe that these conditions consist in the possession, by an
object, of some 'omnitemporal core' (to use a phrase
suggested by Harold Noonan) that it has at every time in its
existence. So why should things be different in the modal case?



The obvious answer seems to be this. In the case of identity over
time, we can appeal to relations (other than mere similarity) between
the states of an individual at different times in its existence. For
example, it looks as if we can say that the adult Russell is identical
with the infant Russell in virtue of the existence of certain
spatiotemporal and causal continuities between his infant state in
1873 and his adult state in (say) 1950 that are characteristic of the
continued existence of a human being. But no such relations of
continuity are available to ground identities across possible worlds
(cf. Quine 1976).



However, on reflection, it may seem that this is too swift. If we
suppose that any possible history for Russell is a *possible*
spatiotemporal and causal extension of the state that he was actually
in at some time in his existence, then perhaps we may appeal to the
same continuities that ground his identity over time in the actual
world in order to ground his identity across possible worlds (cf.
Brody 1980, 114-115; 121). For example, perhaps to say that
Russell could have been a playwright is to say that there was some
time in his actual existence at which he could have *become* a
playwright. If so, then perhaps we can hold that for a playwright in a
possible world to be identical with Russell is for that playwright to
have, in that world, a life that is, at some early stage, exactly the
same as Russell's actual life at some early stage, but which
develops from that point, in the spatiotemporally and causally
continuous fashion that is characteristic of the continued existence
of a human being, into the career of a playwright rather than that of
a philosopher. However, although such a conception may seem initially
attractive, it runs into difficulties if it is intended to provide
conditions that are genuinely both necessary and sufficient for the
identity of individuals across possible worlds. These difficulties
include the fact that it seems too much to demand that Russell have
*exactly* the same early history (or origin) as his actual
early history (or origin) in every possible world in which he exists.
Yet if Russell's early history could have been different in
certain respects, we face the question: 'In virtue of what is an
individual in another possible world with a slightly
*different* early history from Russell's actual early
history identical with Russell?'--a question of precisely
the type that the provision of necessary and sufficient conditions for
transworld identity was intended to answer. (For discussion of this
'branching' conception of possibilities, and its
implications for questions of transworld identity and essential
properties, see Brody 1980, Ch. 5; Mackie 1998; Mackie 2006, Chs
6-7; Coburn 1986, Section VI; McGinn 1976; Mackie 1974; Prior
1960.)


### 4.4 Responses to the problems



The fact that, in the absence of non-trivial individual essences, a
transworld identity characterization of *de re* modal
statements appears to generate bare identities (via arguments such as
Chisholm's Paradox or Forbes's reduplication argument) may
produce a variety of reactions.



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



A third reaction is to *accept* bare identities--or, at
least, to accept that individuals (including actual individuals) may
have qualitative duplicates in other possible worlds, and that
transworld 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 entry
on Haecceitism.)



A fourth reaction, that of Forbes, is to propose a mixed solution: he
holds 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 for
others (including most artefacts) it may be that no suitable
candidates are available, in which case counterpart theory should be
adopted 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 transworld
identity for certain individuals including people: one that can be
solved only by attributing to them non-trivial individual essences;
she argues that these consist in their individual forms. Such an
individual form would provide a substantial answer to questions such
as 'what makes an individual Noah in the "role-switching" world rather
than Adam?' Thus, it would appear, the problem of transworld identity
for individuals such as Noah and Adam is replaced by a problem of
transworld identity for their individual forms. But why is this
supposed to represent an improvement? As Fine puts it: 'Why should we
not simply take the crossworld identity of [non-form] entities as
given and not standing in any need of a criterion?' (2020, 430). One
reason (considered by Koslicki) is conceptual. It is thought that we
need to make sense of *de re* modal claims in terms of *de
dicto* modal claims. However, if individual forms are to come to
the rescue, the question arises how the individual forms are to be
distinguished from one another. The problem is acute in cases where
the individuals in question are otherwise indiscernible (Fine 2020,
432). Moreover, it is not clear that Koslicki's invocation of the fact
that individual forms--unlike, say, unanalysable haecceities--have
a 'qualitative' element (2020, Sections 3.3.4-3.5) is supposed to help
with this problem.



It is perhaps significant, though, that no theorist appears to have
argued that a 'non-trivial individual essence' solution
can be applied to *all* the relevant cases. In other words, the
consensus appears to be that the price of interpreting *all*
*de re* modal claims in terms of transworld identity (as
opposed to counterpart theory) is the acceptance of (some) bare
identities across possible worlds.



Salmon (1996) claims 'something like a proof' of this
implication, from transworld identities to bare identities. He argues
for what he calls *Extreme Haecceitism,* the view that
transworld identities cannot be grounded in general facts about the
individuals concerned. The purported proof goes as follows. We
consider *x* in world *w* and *y* in world
*w*2 and suppose, for *reductio*, that *x = y*
and that this fact is reducible to (or grounded in, or entailed by)
general facts about *x* in *w* and *y* in
*w*2. But, says Salmon, the fact that *x = x* is not
reducible (grounded, etc.) in this way, since it is a fact of logic.
So, says Salmon, '*x* differs from *y* in at least
one respect. For *x* lacks *y*'s feature that its
identity with *x* is grounded in general (cross-world) facts
about *x* and it' (1996, 216), and hence (by
Leibniz's Law), *x [?] y*, contrary to assumption. So if
there are any transworld identities, those identities cannot be
grounded in general facts about those individuals. They must be
'bare'.



Salmon's argument is a variant on Evans's (1978) argument
against the possibility of vague objects. It is controversial in
general whether arguments of this form succeed, for applications of
Leibniz's Law in intensional contexts are questionable.
Catterson (2008) argues on independent grounds that Salmon's
argument is not sound. We should also note that, even if the argument
is successful, it does not directly establish Salmon's Extreme
Haecceitism, but only the conditional thesis that *if* there
are any true transworld identity statements *x = y*, then they
are not reducible to general facts about *x* and
*y*.


### 4.5 Leibniz and hyper-essentialism



Finally, it can be noted that the problems concerning transworld
identity discussed here arise only because it is assumed that not all
of an individual's properties are essential to it (and hence
that, if it exists in more than one possible world, it has different
properties in different worlds). If, instead, one were to hold that
*all* of an individual's properties are essential
properties--and hence, for example, that George Eliot could not
have existed with properties in any way different from her actual
ones--then no such problems would arise. Moreover, this
suggestion, implausible though it may be, is of some historical
interest. For, according to a standard interpretation of the views of
Gottfried Leibniz, the philosopher who is the father of theories of
possible worlds, Leibniz's theory of 'complete individual
notions' commits him to the thesis that an individual such as
George Eliot *does* 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 be
committed, any individual, in any possible world, whose properties in
that world differ from the actual properties of George Eliot is not,
strictly speaking, identical with Eliot. However, it also seems clear
that this does not represent a way of saving a transworld identity
interpretation of *de re* modality. On the contrary: if there
is no possible world in which George Eliot exists with properties
different from her actual properties, then it is plausible to conclude
that there is no possible world, other than the actual world, in which
she exists at all. For unless possible worlds can be exact duplicates
(something that Leibniz himself would deny), any merely possible world
must differ from the actual world in some respect. If so, then the
properties of any individual in another possible world must differ in
*some* respect from the actual properties of Eliot (even if the
difference is only a difference in relational properties), in which
case, if all Eliot's properties are essential to her, that
individual is not Eliot. (Leibniz's views may, however, be seen
as a partial anticipation of counterpart theory, which attempts to
save the truth of the claim that George Eliot *could* have been
different in some respects (thus denying
'hyper-essentialism') while preserving the metaphysical
thesis that no individual who is, strictly speaking, identical with
Eliot exists in any other possible world (cf. Kripke 1980, 45, note
13).)


### 4.6 Haecceities and haecceitism



The view that an individual's transworld identity is
'bare' is sometimes described as the view that its
identity consists in its possession of a 'haecceity' or
'thisness': an unanalysable non-qualitative property that
is necessary and sufficient for its being the individual that it is.
(The term 'individual essence' is sometimes used to denote
such a haecceity. It should be noted that according to the terminology
used in this article, although a haecceity would be an individual
essence, it would not be a *non-trivial* individual essence.)
However, it is not obvious that the belief in bare identities requires
the acceptance of haecceities. One can apparently hold that transworld
identities may be 'bare' without holding that they are
constituted by any properties at all, even unanalysable haecceities
(cf. Lewis 1986, 225; Adams 1979, 6-7). Thus we should
distinguish what is standardly known as 'haecceitism'
(roughly, the view that there may be bare identities across possible
worlds in the sense of identities that do not supervene on qualitative
properties) from the belief in haecceities (the belief that
individuals have unanalysable non-qualitative properties that
constitute their being the individuals that they are). (For more on
the use of the term 'haecceitism' see Lewis 1986, Ch. 4,
Section 4; Adams 1979; Kaplan 1975, Section IV; also the separate
entry on Haecceitism. For the history of the term
'haecceity', see the entry on Medieval Theories of
Haecceity.)



In addition, it should be noted that to believe in 'bare'
transworld identities, in the sense under discussion here, is not to
believe in 'bare particulars', if to be a bare particular
is to be an entity devoid of (non-trivial) essential properties. As
the arguments discussed in Sections 4.1-4.2 above demonstrate, a
commitment to a 'bare' (or 'ungrounded')
difference in the identities of two individuals *A* and
*B* in different possible worlds (two human beings, or two
trees, for example) does not imply that those individuals have no
non-trivial essential properties. All it implies is that *A*
and *B* do not *differ* in their non-trivial essential
properties--and hence that, although there may well be
non-trivial necessary conditions for being *A* in any possible
world, and non-trivial necessary conditions for being *B* in
any possible world, there are no non-trivial necessary conditions for
being *A* that are not also necessary conditions for being
*B*, and vice versa. (Cf. Adams's 'Moderate
Haecceitism' (1979, 24-26).)


## 5. Transworld identity and the transitivity of identity



It was argued above that the proponent of transworld identity without
non-trivial individual essences faces the prospect of bare
('ungrounded') identities across possible worlds. One such
argument is Chisholm's Paradox, which relies on the transitivity
of identity to produce the result that a series of small changes in
the properties of Adam and Noah leads to a world in which Adam and
Noah have swapped their roles. However, the transitivity of identity
generates additional problems concerning transworld identity, some of
which have nothing particularly to do with role-switching
possibilities or bare identities.


### 5.1 Chandler's transitivity argument



One such argument is given by Chandler (1976). It can be illustrated
simply as follows (adapting Chandler's own example). Suppose
that 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 two
wheels.) Suppose we think that any bicycle could have been originally
composed of any two thirds of its original parts, with a substitute
third component. We may call this (following Forbes 1985) 'the
tolerance principle'; it is a development of the intuitively
appealing thought that it is too much to demand, of an object such as
a bicycle, that it could not have existed unless *all* of its
original parts had been the same. Suppose, further, that we think that
no bicycle could have been originally composed of just one third of
its original parts, even with substitutes for the other two thirds.
Call this 'the restriction principle'. The combination of
these assumptions appears to generate a difficulty for the paraphrase
of *de re* modal claims about bicycles in terms of transworld
identity. For if there is (as the tolerance principle allows) a
possible world *w*2 in which our bicycle comes into
existence composed of parts A1 + B1 + C2, where C1 [?] C2, then, if
we apply the tolerance principle to *this* bicycle we must say
that *it* could have come into existence (in some further
possible world *w*3) with any two thirds of
*those* parts, with a substitute third component: for example,
that it could have come into existence (in *w*3) composed of A1
+ B2 + C2, where B1 [?] B2 and C1 [?] C2. The bicycle in
*w*3 is, *ex hypothesi*, identical with the
bicycle in *w*2, and the bicycle in
*w*2 is, *ex hypothesi*, identical with the
original bicycle; so, by the transitivity of identity, the bicycle in
*w*3 is identical with the original bicycle. Hence
our assumptions have generated a contradiction. We have a bicycle in
*w*3, originally composed of A1 + B2 + C2, that both
is identical with the original bicycle (by the repeated application of
the tolerance principle, together with the transitivity of identity)
and is not identical with the original bicycle (by the restriction
principle).



One might complain that the version of the tolerance principle cited
above is too lenient. Perhaps it is not true that the bicycle could
have come into existence with just two thirds of its original
components: perhaps a threshold of, say, 90% or more is required.
However, the simple argument given above can be adapted to generate a
contradiction between the restriction principle and any tolerance
principle that permits *some* difference in the bicycle's
original composition, simply by introducing a longer chain of possible
worlds. Thus the transitivity argument appears to force the proponent
of transworld identity to choose between two implausible claims: that
an object such as a bicycle has all of its original parts essentially
(thus denying any version of the tolerance principle) and that an
object such as a bicycle could have come into existence with few (if
any) of its original parts (thus denying any (non-trivial) version of
the restriction principle). Moreover, it is clear that the problem can
be generalized to any object to which versions of the tolerance
principle and the restriction principle concerning its original
material composition have application, which appears to include all
artefacts, if not biological organisms.



It seems legitimate to call this puzzle a 'problem of transworld
identity', for it turns partly on the transitivity of identity,
and can be avoided by interpreting claims about how bicycles could
have been different (*de re* modal claims about bicycles) in
terms of a counterpart relation that is not transitive (Chandler
1976). Thus a counterpart theorist may admit that the bicycle could
have been originally composed of A1 + B1 + C2 rather than A1 + B1 +
C1, on the grounds that (according to the tolerance principle) it has
a counterpart (in *w*2) that is originally so
composed. And the counterpart theorist may admit that a bicycle (such
as the one in *w*2) that is originally composed of
A1 + B1 + C2 could have been originally composed of A1 + B2 + C2,
since (by the tolerance principle) it has a counterpart (in
*w*3) that is originally so composed. However, since
the counterpart relation (unlike identity) is not transitive, the
counterpart theorist need *not* say that the bicycle in
*w*3 that is originally composed of A1 + B2 + C2 is
a counterpart of the bicycle in the actual world
(*w*1) originally composed of A1 + B1 + C1, for its
similarity to the bicycle in *w*1 may be
insufficient to allow it to be that bicycle's counterpart. Thus
the non-transitivity of the counterpart relation (a relation based on
resemblance) appears neatly to allow the counterpart theorist to
respect 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 transworld
identity in favour of counterpart theory. But how--given the
structure of the puzzle--can the theorist who wishes to resist
that move, and retain transworld identity, respond?



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



A second response would be to give up the tolerance principle, and
adopt what Roca-Royes (2016) calls an 'inflexible' version
of the principle that the material origin of an artefact is essential
to it, holding that an artefact such as a bicycle could not have come
into existence with a material composition in any way different from
its actual original composition. Although this view is admittedly
counterintuitive, Roca-Royes argues that it provides the best solution
to the 'Four Worlds Paradox' to be discussed in the next
section.



A third solution to the transitivity problem has been proposed (by
Chandler, followed by Salmon) which apparently allows us to reconcile
all three of the transitivity of identity, the tolerance principle,
and the restriction principle. This is to say that although there
*are* possible worlds (such as *w*3) in which
the bicycle is originally composed of only a small proportion of its
actual original parts, such worlds are not possible relative to (not
'accessible to') the initial world *w*1.
From the standpoint of *w*1, such an original
composition for the bicycle is only possibly possible: something that
would have been possible, had things been different in some possible
way, but is not, as things are, possible (Chandler 1976; Salmon 1979;
Salmon 1982, 238-240). Whether this solution is satisfactory is
disputed. (See, for example, Dorr, Hawthorne, and Yli-Vakkuri 2021,
Chs 7-8.) Admittedly, there are some contexts in which we talk of
possibility in a way that may suggest that the 'accessibility
relation' between possible worlds is non-transitive: that not
everything that would have been possible, had things been different in
some possible way, is possible *simpliciter*. (If Ann had
started writing her paper earlier, it would have been possible for her
to finish it today. And she *could* have started writing her
paper earlier. But, as things are, it is not possible for her to
finish it today.) Nevertheless, the idea that, as regards the type of
metaphysical possibility that is involved in puzzles such as that of
the bicycle, there might be states of affairs that are possibly
possible and yet not possible (and hence that *de re*
metaphysical possibility and necessity do not obey the system of modal
logic known as S4) is regarded with suspicion by many
philosophers.



It should be noted that the 'non-transitivity of
accessibility' response is distinct from an even more radical
response, which rejects the principle of the transitivity of
identity--a principle definitive of the classical notion of
identity. For example, Priest (2010) denies the transitivity of
identity in the context of his dialetheism about truth and a
paraconsistent logic in which the material conditional does not obey
the principle of *modus ponens*. Discussion of this extreme
position is, however, beyond the scope of this article. (On
dialetheism and paraconsistent logic, see the separate entry on
Dialetheism. On the logic of identity, see the entry on Identity.)



Finally, Dorr, Hawthorne, and Yli-Vakkuri 2021 propose that, in some
cases, 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 between
possible worlds. They appeal to two principles: a metaphysical
principle of 'plenitude' and a metasemantic principle of 'semantic
plasticity' (for the relevant terms). This solution is defended by
Dorr *et al* partly by considering difficulties for rival
solutions (including that of Chandler and Salmon). The details are
complex, however: interested readers should consult Dorr *et
al* 2021. As with other proposed solutions to the puzzle, the
principles to which Dorr *et al* appeal (plenitude and semantic
plasticity for the relevant terms) are controversial.



It is fair to say that there is no consensus about how the proponent
of transworld identity should respond to the transitivity problem
posed by Chandler's example.


### 5.3 The 'Four Worlds Paradox'



Chandler's transitivity argument can be adapted to produce a
puzzle that is like those discussed in Sections 4.1-4.2 above in
that it involves the danger of 'bare identities', a puzzle
that Salmon (1982) has called 'The Four Worlds Paradox'.
To illustrate the puzzle: suppose that the actual world
(*w*1) contains a bicycle, *a*, that is
(actually) originally composed of A1 + B1 + C1, and suppose that there
is a possible world, *w*5, containing a bicycle,
*b* (not identical with *a*), that is originally
composed (in *w*5) of A2 + B2 + C1 (where A1 [?] A2
and B1 [?] B2). Then, it seems, the application of the tolerance
principle to each of *a* and *b* may generate two
further possible worlds, in one of which (*w*6)
there is a bicycle with the original composition A1 + B2 + C1 that is
identical with *a*, and in the other of which
(*w*7) there is a bicycle with the original
composition A1 + B2 + C1 that is identical with *b*. Since
there need apparently be no further difference between the intrinsic
features of *w*6 and *w*7 on which
this difference in identities could depend, we appear to have a case
of bare identities. This 'Four Worlds Paradox' is like
Chandler's original transitivity puzzle in that it does not seem
that an appeal to individual essences could solve it without
conflicting with the tolerance principle. If that is so, the proponent
of transworld identity (as opposed to counterpart theory) appears to
be left with two options consistent with the transitivity of identity:
the denial of the tolerance principle, and the acceptance of bare
identities. (But cf. Dorr, Hawthorne, and Yli-Vakkuri 2021.) It may be
argued, however, that the acceptance of bare identities can be made
more palatable in this case by the adoption of a non-transitive
accessibility relation between possible worlds. (See Salmon 1982,
230-252; and, for discussion, Roca-Royes 2016. For a defence of
the employment of counterpart theory to solve the Four Worlds Paradox,
see Forbes 1985, Ch. 7. For discussion of a radical response that
retains the tolerance principle and yet avoids bare identities, but
only at the cost of claiming that two bicycles could completely
coincide in one possible world, simultaneously sharing all their
parts, see Roca-Royes 2016, discussing Williamson 1990. On the
relevance to the Four Worlds Paradox to Kripke's principle of
the necessity (essentiality) of origin for artefacts, see also
Robertson 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 a
commitment to transworld identity--the view that an individual
exists in more than one possible world--is an acceptable
commitment for one who believes in possible worlds. The considerations
of Sections 4-5 above suggest that this commitment does involve
genuine (although perhaps not insuperable) problems, even for one who
rejects David Lewis's extreme realism about the nature of
possible worlds. The problems do not arise *directly* from the
notion of an individual's existing in more than one possible
world with different properties. Rather, they derive principally from
the fact that it is hard to accommodate all that we want to say about
the modal properties of ordinary individuals (including all the things
we want to say about their essential and accidental properties) if
*de re* modal statements about such individuals are
characterized in terms of their existence or non-existence in other
possible worlds.



There is currently no consensus about the appropriate resolution of
these problems. In particular, there is no consensus about whether the
adoption of counterpart theory is superior to the solutions available
to a transworld identity theorist. A full examination of the issue
would require a discussion of the objections that have been raised
against counterpart theory as an interpretation of *de re*
modality. And a detailed discussion of counterpart theory is beyond
the scope of this article. (For David Lewis's presentation of
counterpart theory, the reader might start with Lewis 1973,
39-43, followed by (the more technical) Lewis 1968. Early
criticisms of Lewis's counterpart theory include those in Kripke
1980; Plantinga 1973; and Plantinga 1974, Ch. 6. Lewis develops the
1968 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 of
counterpart theory include Hazen 1979, the relevant sections of Divers
2002, Melia 2003, and the more technical treatment in Forbes 1985.
More recent critiques of the theory (postdating Lewis's 1986
response 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 the
defensive strategies discussed in Sections 4 and 5 above) is what we
might call 'the argument from logical simplicity' (Linsky
and Zalta 1994, 1996; Williamson 1998, 2000). The argument begins by
noting that Quantified Modal Logic--which combines individual
quantifiers and modal operators--is greatly simplified when one
accepts the validity of the Barcan scheme,
[?]*x*#*A* -
#[?]*x**A* (Marcus 1946). The resulting logic
is sound and complete with respect to *constant domain
semantics*, in which each possible world has precisely the same
set of individuals in its domain. The simplest philosophical
interpretation of this semantics is that one and the same individual
exists at every possible world.



Several remarks on this argument are in order. First, its conclusion
is very strong: it says that any entity that in fact exists or that
could have existed exists *necessarily*. There is no contingent
existence. This goes far beyond the claim that there are genuine
identities across worlds. (Williamson (2002) defends this conclusion
on independent grounds.) Second, the argument does not offer an
explanation of how transworld identities are possible; it insists only
that there are genuine transworld identities. (Nevertheless, the
metaphysical picture that can most naturally be 'read off'
the constant-domain semantics treats properties-at-a-world as
relations between particulars and worlds, as on McDaniel's
*modal realism with overlap* (McDaniel 2004), discussed in
Section 1.2 above.)



Third, the argument is not best understood as the claim that, if one
does not accept transworld identities, then one is *forced*
into denying the Barcan scheme (and hence forced into uncomfortable
logical territory). That claim would be true only if the Barcan scheme
were validated *only* by constant-domain semantics, which is
not the case. Counterpart-theoretic semantics can be restricted so as
to validate the Barcan scheme, by insisting that the counterpart
relation is an equivalence relation which, for each particular
*x* and world *w*, relates *x* to a unique
particular in *w*. (One could not then interpret the
counterpart relation in terms of similarity, as Lewis does.) Rather,
the argument should be understood as the claim that the best way to
gain the advantages of a logic containing the Barcan scheme is by
adopting constant-domain semantics (and genuine transworld identities
along 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 the
one hand, but also arguments of the kind raised by Lewis against modal
realism 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 to
the self-styled champions of 'transworld identity' to
explain *why* the view that they insist on deserves to be
called a commitment to transworld identity at all.



Throughout this article, it has been assumed that a commitment to
transworld identity may be differentiated from a commitment to
counterpart theory on the grounds that the transworld identity
theorist accepts, while the counterpart theorist denies, that an
object *exists in* more than one possible world (cf. Section
1.2 above). However, as Lewis points out, there is a notion of
'existence *according to* a (possible) world' that
is completely neutral as between a counterpart-theoretic and a
'transworld identity' interpretation. In terms of this
neutral conception, as long as the counterpart theorist and transworld
identity theorist agree that Bertrand Russell could have been a
playwright instead of a philosopher, they must agree that Russell
exists *according to* more than one world. In particular, they
must agree that, *according to our world*, he exists and is a
philosopher, and *according to some other worlds*, he exists
and is a non-philosopher playwright (cf. Lewis 1986, 194). The
difference between the theorists, then, allegedly consists in their
different interpretations of what it is for Russell to exist
'according to' a world. In the view of the counterpart
theorist, for Russell to exist according to a possible world in which
he is a playwright is for him to have a *counterpart* in that
world who is (in that world) a playwright. According to the transworld
identity theorist, it is supposed to be for Russell (himself) to
*exist in* that world as a playwright.



If the transworld identity theorist were a Lewisian realist about
possible worlds, this notion of existence *in* a world could be
clearly distinguished from the neutral notion of existence
*according to* a world, on the grounds that the existence of
Russell in a world would require his complete or partial presence as a
part of such a world (cf. Section 1.2 above). But, as Lewis notes, the
self-styled champions of 'transworld identity' who oppose
his counterpart theory are philosophers who repudiate a Lewisian
realist conception of what it takes for Russell to exist in more than
one possible world. Hence, he argues, there is a question about their
entitlement to claim that, according to their theory, Russell exists
*in* other possible worlds in any sense that goes beyond the
neutral thesis (compatible with counterpart theory) that Russell
exists *according to* other worlds. Thus Lewis writes (using
the 1968 US presidential candidate Hubert Humphrey as his
example):



The philosophers' chorus on behalf of 'trans-world
identity' is merely insisting that, for instance, it is Humphrey
himself who might have existed under other conditions, ... who
might have won the presidency, who exists according to many worlds and
wins according to some of them. All that is uncontroversial. The
controversial question is *how* he manages to have these modal
properties. (1986, 198)



A natural reaction to Lewis's challenge is to point out that a
proponent of transworld identity who is not a Lewisian realist will
typically reject Lewis's counterpart theory on the grounds that
his counterpart relation does not have the logic of identity. If so,
then (*pace* Lewis) it is not the case, strictly speaking, that
the 'philosophers' chorus on behalf of "trans-world
identity"' is merely insisting on the neutral claim that
objects exist according to more than one world. However, even if this
is 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 between
worlds'. What would distinguish, *in the case of a theorist
who is not a Lewisian realist about possible worlds*, between, on
the one hand, a commitment to the interpretation of *de re*
modal statements in terms of such an 'identity-resembling'
counterpart relation, and, on the other hand, a commitment to genuine
transworld identity (and hence to the view that an individual
genuinely *exists in* a number of distinct possible worlds)?
The aficionado of transworld identity owes Lewis a reply to this
challenge.