## 1. Introduction



As a number of philosophers have remarked, one of the many puzzles
about identity, given its apparent simplicity, is why it proves so
puzzling. Indeed, one pervasive sentiment is that identity cannot pose
any philosophical problems. Anything that looks like a problem about
identity must really be a problem about something else. David Lewis
gives striking expression to this sentiment when he says:



> 
> More important, we should not suppose that we have here any problem
> about *identity*. We never have. Identity is utterly simple and
> unproblematic. Everything is identical to itself; nothing is ever
> identical to anything except itself. There is never any problem about
> what makes something identical to itself; nothing can ever fail to be.
> (Lewis 1986, 192-193)
> 



Despite that, problems about identity appear to play a central role in
a large number of philosophical issues whose discussion dates back to
the ancient world. One of the most venerable concerns identity and
change. Things change, but remain the same. The same poker is at one
time hot, another time cold. How can something be both identical and
different from one time to another? At first sight this problem
evaporates once we draw the time honored distinction between numerical
and qualitative identity. To say that *a* and *b* are
qualitatively identical is to say that *a* exactly resembles
*b*. To say that *a* and *b* are numerically
identical is, at least, to say *a* and *b* are one thing
and not two. Whether *a* and *b* can have *all*
their qualities in common without being numerically identical is
controversial. Nevertheless, it seems that *a* and *b*
can be numerically identical without being qualitatively identical by
having different qualities at different times.



Some find problematic the very same thing having different properties
at different times (see the problem of temporary intrinsics discussed
below). Setting that general problem aside, there are special cases of
it that generate some of the most intractable issues about identity.
One results from persisting things putatively having different parts
at different times. Consider an object capable of changing its parts,
such as a cup at a time when its handle is still attached. At that
time the cup appears to consist of the following two parts: a smaller
one, its handle, together with a larger one consisting of the rest of
the cup. Call the larger of these parts the truncated cup. The cup,
otherwise unscathed, proceeds to lose its handle. At the earlier time,
with its handle still intact, the cup is surely distinct from the
truncated cup. Later, after the removal of the cup's handle, the cup
spatially coincides with the truncated cup. Each object is, at the
later time, composed from exactly the same atoms. As one philosopher
has put it about a different example, at the later time the cup and
the truncated cup are as alike as one pea in a pod (Denis Robinson, in
conversation). Should we say that the cup and truncated cup are
earlier distinct, but later identical? The problem is that saying so
arguably conflicts with a fundamental principle governing identity
called Leibniz's Law.



Identity looms large in Leibniz's philosophy. He is responsible for
articulating two principles that, he claims, are constitutive of
identity. The first, more controversial, of these, called the identity
of indiscernibles, says that qualitative indiscernibility implies
identity. The second, often referred to as Leibniz's Law or the
Indiscernibility of Identicals, says that identity implies qualitative
indiscernibility. According to Leibniz's Law, if *a* is
identical with *b*, every quality of *a* will be a
quality of *b*. (See the entry on
 identity of indiscernibles.)



Here are two ways in which, it seems, saying that the cup is earlier
distinct from, but later identical with, the truncated cup conflicts
with Leibniz's Law. Ostensibly one of the cup's later properties is
having earlier had a handle. That is the property the truncated cup
never has. So, identifying the later cup and truncated cup appears to
violate Leibniz's Law. There is, at least, one property, having
formerly had a handle, that the cup and truncated cup never have in
common.



Here is a second way in which the claim that the cup and truncated cup
are sometimes, but not always, identical appears to violate Leibniz's
Law. Let us bestow a name on the cup. Call it 'Cup'. Let
us also call the truncated cup 'Tcup'. We are envisaging
that Cup is sometimes, but not always, identical with Tcup. Leibniz's
Law tells us that Cup and Tcup share all their properties at any time
they are identical. Some properties are commonly referred to as modal
properties. A modal property is the property of possibly or
necessarily having some further property. Modal properties include
such properties as being possibly red, necessarily extended, possibly
taller than a giraffe, or necessarily cup shaped. Arguably one of
Cup's modal properties is the property of being necessarily identical
with Cup. Suppose Cup and Tcup are at some time identical. In that
case, by Leibniz's Law, Tcup will, at some time, share with Cup the
modal property of being necessarily identical with Cup. So, if Cup is
ever identical with Tcup, then Tcup has the modal property of being
necessarily identical with Cup. But if Tcup is necessarily identical
with Cup, there can be no time when Tcup is distinct from Cup.



Let us say that the identity of *a* with *b* is
temporary if *a* is sometimes, but not always, identical with
*b*. Later we shall look at other types of puzzle cases that
provide some motivation for countenancing temporary identity. Despite
the existence of such cases the majority of philosophers are
reluctant, principally because of the putative conflict with Leibniz's
Law, to allow temporary identity. Instead, to deal with puzzles about
identity through time a wide range of alternatives have been proposed.
These include: maintaining that Cup is later constituted by Tcup
(where constitution does not imply identity); denying that Tcup is
earlier a proper part of Cup; maintaining that Cup and Tcup are never
identical, but only share a later temporal part in common; holding
that the identity between the earlier Tcup and later Cup is not
literal, but only loose and popular.



By synchronic identity we mean an identity holding at a single time.
By diachronic identity we mean an identity holding between something
existing at one time and something existing at another. One question
is whether synchronic and diachronic identity are different kinds of
identity. Some philosophers are willing to countenance different kinds
of identity. Others are reluctant to do so. One philosopher who is
willing to postulate a multiplicity of different kinds of identity is
Peter Geach. Geach, among others, has addressed puzzles about both
synchronic and diachronic identity by denying that there is a single
absolute relation of identity rather than a host of relative identity
relations. On this view we cannot simply say that *a* is
identical with *b*. Instead there must be a concept of a kind
of thing, a so called sortal concept, that serves to answer the
question: *a* is the same *what* as *b*? This is
so, according to the champions of relative identity, because the
following can happen: *a* and *b* both fall under the
sortal concepts *F* and *G*, *a* is the same
*F* as *b*, but *a* is not the same *G* as
*b* (Geach 1967, and see the entry on
 relative identity).



Consider the case of Cup and Tcup. Is Cup at the later time
*t*' identical with Tcup? Is Tcup at *t*'
identical with Tcup at *t*? A relative identity theorist would
deny that these questions have answers. For such a theorist to have an
answerable question we would need to replace, for example, the first
with: At *t*' is Cup the same *cup as* Tcup?



How could insisting on the relativity of the answer to an identity
question to a kind help with the diachronic identity puzzle posed by
Cup and Tcup? Here is one way that it could. Suppose that nothing is a
cup when it is a proper part of a cup. Then Tcup fails to qualify as a
cup at t when it is a proper part of Cup. In that case a relative
identity theorist can say the following. At the later time
*t*' Cup is the same cup as Tcup. Since Tcup is not a cup
at the earlier time *t*, neither Cup not Tcup at
*t*' is the same cup as Tcup at *t*. Moreover, for
any kind *K*, Cup is not the same *K* as Tcup at
*t*. Identifying Cup with Tcup as the same cup at
*t*' places us under no constraint to identify Cup with
one of its proper parts, Tcup, at *t*.



Some of those who reject relative identity nevertheless accept that
*a* cannot be identical with *b*, unless there is a more
specific answer to the question whether *a* is the same
*thing* as *b*. Many philosophers distinguish between
two kinds of concepts which are applicable to whatever can persist
through time. One kind is illustrated by the concepts of gold (as
opposed to a quantity or piece of gold), snow, or rain. In the case of
any such concept *F*, there is no answer to the question: how
many *F*s are there? In contrast, in the case of other concepts
such as the concept of a horse, a tall person, an artwork, or a statue
there is an answer to the question: how many *F*s are there?
For example, though we may not know it, there is an answer to the
question: how many statues are there? Concepts of this last kind are
often referred to as sortal concepts. Those who take the view that the
question whether *a* is the same as *b* is illegitimate,
unless it is construed as elliptical for the question whether
*a* is the same thing of such and such a kind as *b*
typically also hold the following views. We should distinguish between
two types of sortal concepts: phase and substance sortals. A phase
sortal such as child, utensil or prize is a concept that something can
cease to fall under without ceasing to exist. If, in contrast,
something falls under a substance sortal, it must always do so. If
*a* at some time *t* is the same as *b* at the
same, or a different time *t*', it must, say advocates of
the view in question, be that, for some sortal *S*, *a*
at *t* is the same *S* as *b* at
*t*'. For example, if John's favorite artwork at
*t* is identical with Sally's most valuable possession at
*t*', there must be a substance sortal, the concept of a
statue as it may be, under which John's favorite artwork at
*t*, and Sally's most valuable possession at *t*'
both fall. Moreover, a substance sortal is said to go together with a
criterion of identity where a criterion of identity associated with
substance sortal *S* is, inter alia, a criterion for some
earlier *S* being the same *S* as some later
*S*.



Finally, there are a group of issues that fall under the heading of
the dispensability of identity. According to one tradition that goes
back, at least, to Wittgenstein's *Tractatus*, we can
theoretically dispense with identity talk without loss of information.
Some, but by no means all, who take this view, do so because they hold
that the predicate 'is identical with' corresponds to no
genuine property. Issues about the dispensability of identity engage
with issues about identity across time in the following way. This
section opened with a quote from David Lewis claiming that there is
never any philosophical problem about identity. The case of Cup and
Tcup raises what is ostensibly a problem about identity across time.
That problem only arises, it seems, because the later Cup is
putatively identical with the earlier Tcup. If the problem is not, in
part, about that putative identity holding, what is it about?



According to a four dimensionalist like David Lewis a table is
extended through the time of its life, and constituted from temporal
parts which are themselves short lived tables. As such a four
dimensionalist like Lewis would not hesitate to give the following
answer to the above question. The problem is, in part, a problem about
whether a cup-like object that exists only at *t*' is
suitably related to a cup-like object, itself a proper part of a
larger cup-like object, that exists only at *t* so that both
cup-like objects are temporal stages or parts of a four-dimensionally
extended cup.



If we are not prepared to endorse four dimensionalism, it remains to
be seen how the putative problem about Cup and Tcup's identity through
time can be reformulated so that it is no longer a problem about
identity through time.


## 2. Identity and Change


### 2.1 Diachronic and Synchronic Identity



It is customary to distinguish identity at a time from identity across
time. An example of an identity holding at a single time is: the table
in the next room is (now) identical with my favorite table. An example
of an identity holding across different times is: The table in the
next room is identical with the one you purchased last year.
Diachronic identities pose some of the most intractable problems about
identity. Before looking at those problems, and some of the most
frequently proposed solutions to them, let us ask whether there is
anything that distinguishes identity from other relations.



The most commonly agreed on distinguishing feature of identity is that
it conforms to the Indiscernibility of Identicals, what was earlier
called Leibniz's Law. Taking '[?]*F*' to be a
quantifier ranging over properties, here is one way to formulate
Leibniz's Law:



> 
> LL: [?]*x*[?]*y*[*x*=*y* -
> [?]*F*(*F**x* - *F**y*)]
> 



LL, understood to range over identity properties, if any, such as
being identical with a, says that if *x* is identical with
*y*, then any property of *x* is a property of
*y*. 


### 2.2 Identity as an Equivalence Relation



A relation *R* is reflexive if each thing stands in *R*
to itself. It is symmetrical if *a*'s standing in *R* to
*b* implies that *b* stands in *R* to *a*.
It is transitive if *a*'s standing in *R* to *b*
and *b*'s likewise standing in *R* to *c*
together imply that *a* stands in *R* to *c*.
Identity is trivially reflexive. Each thing trivially stands in the
relation of identity to itself. That identity is also symmetrical and
transitive follows from Leibniz's Law. Suppose identity fails to be
symmetrical, and for some *a* and *b*, *a* is
identical with *b*, but *b* is not identical with
*a*. In that case, *a* has a property, being identical
with *b*, which *b* fails to have. Suppose identity is
not transitive, and, for some *a*, *b* and *c*,
*a* is identical with *b* and *b* is identical
with *c*, but *a* is not identical with *c*. In
that case *b* has a property, being identical with *c*,
that *a* lacks.


### 2.3 Leibniz's Law and the Possibility of Change: The Problem of Temporary Intrinsics



Identity through time generates a number of problems posed by puzzle
cases such as the case of Cup and Tcup. Later we will review a number
of solutions to those problems offered in the literature. One problem
about identity through time is not raised by consideration of puzzle
cases. It arises simply because persisting things can change their
intrinsic properties. For that reason it has been labeled by David
Lewis the problem of temporary intrinsics (Lewis 1986,
202-205).



A decent test for distinguishing between extrinsic and intrinsic
properties is this. A property *F* is an extrinsic property of
an object *o* if *o* having *F* implies that
something distinct from, and not a proper part of, *o* exists.
For example, being married to Sally is an extrinsic property of John's
since John can only have that property if something, Sally, distinct
from, and not a proper part, of him exists. A property *F* is
an intrinsic property of *o* if and only if *o* having
*F* is compatible with nothing apart from *o* and its
proper parts existing, and also compatible with something apart from
*o* existing. For example, the property of being round is an
intrinsic property because a surface *S* having that property
is compatible with nothing other than *S* and its proper parts
existing. Here is one reason why this is only a rough way of drawing
the distinction between intrinsic and extrinsic properties. It looks
as though the property of existing in complete isolation, which Lewis
calls loneliness, is extrinsic. Nevertheless being, in this sense,
lonely is not only compatible with, but requires that nothing else
exists. (For more discussion, see the entry on
 intrinsic vs. extrinsic properties.)
 



Suppose some object, a metal plate we will call Plate, changes from
being round at *t*1 to being square at
*t*2. How can that be? After all, though something
can have a round part and a square part, nothing can be round and
square. No problem, you might say. Nothing can be round and square at
a single time, place and world. But something can be round at one time
and square at another.



According to Lewis the original problem of temporary intrinsics
remains, unless we can show how something can have incompatible
properties at different times. To show how that can be so we need to
give at least a partial answer to the following question. What is it
for something to have a property at a time?


### 2.4 Candidate Solutions



Lewis considers three answers to this question. According to the first
for some object *O* to be *F* at *t* is for the
relation of being *F* to tenselessly, or timelessly, hold
between *O* and time *t*. For example, for Plate to be
round at *t*1 is for the two-place relation of being
round at to hold between Plate and *t*1. Something
can stand in the relation of being round at to the earlier time
*t*1 without standing in that relation to the later
time *t*2. So there is no reason to think that
standing in the relation of being round at to *t*1
is incompatible with standing in the relation of being square at to
*t*2. By transmuting the ostensibly one place
relational properties of being round and being square into the two
place relational properties of being round at and being square at we
can show how something can be round at one time and square at
another.



Lewis' principle objection to this first solution is that it
transforms intrinsic into extrinsic properties. He takes it as evident
that properties such as being round and being red are intrinsic. Why
so? Call the view that putatively one place intrinsic properties are
two place relational properties the relational view. Why does Lewis so
adamantly reject that view? One difficulty with answering this
question is a difficulty about locating the source of Lewis' disquiet
with the relational view.



Is it that Lewis rejects the relational view because it treats
putatively intrinsic properties as extrinsic, or because it discerns
an extra place in a putatively monadic property? That it is the latter
is suggested by the following. The problem of temporary intrinsics
appears to arise because nothing can have the intrinsic properties of
being round and being square, unless it has those properties at
different times. The same goes for pairs of extrinsic properties. The
property of being the same height as the Eiffel Tower is extrinsic as
is the property of being different in height from the Eiffel Tower.
Something can change from being the same height as the Eiffel Tower to
being different in height from that structure even though nothing can
simultaneously have the properties of being the same height as, and
being different in height from, the Eiffel Tower. Suppose we say that
something can be the same height as the Eiffel Tower at some time
*t*1 without being the same height as the Eiffel
tower at some distinct time *t*2. In that case we
appear to be confronted with the same problem as the one that
originally raised the problem of temporary intrinsics. We are
confronted with the task of explaining what it is for something to
have, in this case, the property of being the same height as the
Eiffel Tower at time *t*1. If we respond, it is for
the three place relation of being the same height as at to hold
between some object, the Eiffel Tower, and time *t*1
we are, treating an ostensibly two place relation as a three place one
even though we are not treating an intrinsic property as
extrinsic.



Lewis considers an alternative explanation of what it is for an object
to have a property at a time. What might be called the
'according to' explanation. We are used to something
having a property according to one story, but failing to have that
property according to another. If we think of a time as a set of
propositions describing what holds at that time, we can say that
according to one such set plate is round, but according to another it
is square.



Lewis gives the according to explanation short shrift. We may think it
cannot be so readily dismissed if it is combined with a view about
existence and time that has received considerable discussion in recent
years. The view is called Presentism. On the Presentist view the only
things that exist without qualification are things that presently
exist. Suppose *t*1, a time when Plate is round, is
the present. In that case if Plate is ever square it will be, or was
square. What is it for Plate to be round? Given that plate is
presently round what makes it the case that Plate is round is not just
that Plate is round according to some set of propositions about the
present. Instead what makes it the case that Plate is presently round
is that plate exists and is round. So, what makes it the case that
Plate, say, will be square? Not, the Presentist will say, this: Plate
tenselessly or timelessly exists, and will be square. So what makes it
the case that Plate will be square? Perhaps this. What makes it true
that Plate will be square is that Plate is square according to some
relevant future tensed presently existing propositions.



Here is one reason why we might think that Presentism does not, in the
end, help with the problem of temporary intrinsics. Suppose that, at
*t*1, we send a circular object forward in time to
*t*2. At *t*2 the shape of the
circular object changes so that it becomes elliptical. Retaining its
elliptical shape the object is sent back to *t*1. Even
if Presentism is true at *t*1 we have an object with
incompatible intrinsic properties.



Of course, to embrace this combination of an according to explanation
with Presentism is to embrace just one of a number of options
available to the Presentist for giving the truthmakers of future and
past tense propositions.



Whether or not a Presentist wishes to take over in this way the
'according to' explanation, Presentism provides a solution
to the problem of temporary intrinsics. Presentists can deny that it
follows from something at one time being round that will at another
time be square that there exists something both round and square.


2.5 Alternative Solutions


Lewis, we saw, denies that a sentence such as 'Plate is square
at *t*1' states something true just in case
Plate stands in the square at relation to *t*1. In
his original exposition of the problem of temporary intrinsics, Lewis
does not consider a variety of other ways of understanding sentences
attributing ostensibly intrinsic properties to objects at times. Here
is one. Many take it that a relation of instantiation holds between a
property and its instances. Suppose instantiation is not a two place,
but, at least, a three place relation holding between an object,
property and time. If so, Plate is round at *t*1 if
and only if Plate stands in the instantiation relation to the
(non-relational) property of roundness and *t*1.
Moreover Plate standing in the instantiation relation to roundness and
*t*1 is clearly consistent with Plate failing to
stand in the instantiation relation to roundness and the different
time *t*2.

 The key difference between this view
and the relational view that Lewis considers is the following. On the
relational view we take an ostensibly non-relational property such as
being circular to be relational and extrinsic [extrinsic because
having it requires an object to stand in a relation to a time]. On the
instantiation view we are taking something, the instantiation
relation, that is already an extrinsic relation to have an extra
place. So, our intuitions about what counts as an intrinsic
non-relational property are not violated.


Alternative ways of taking '*a* is red at
*t*' include treating 'at *t*' as an
adverbial modifier, or as a sentential operator. According to the
first 'at *t*', better written as 'at
*t*-ly', is an adverbial modifier specifying the way in
which something has a property. So 'Plate is round at
*t*1' is true just in case Plate has roundness
at-*t*1-ly. Plate, on this view, can be round at
*t*1, but square at *t*2 because
Plate can have roundness at *t*1-ly without having
roundness at-*t*2-ly (See Johnston 1987, Haslanger
1989).



According to the temporal operator view 'at
*t*1' and 'at
*t*2' should be understood as the temporal
operators: 'at *t*1 it is true that
...' and 'at *t*2 it is true that
...'. Just as 'it is possible that Plate is
round' is consistent with 'it is possible that Plate is
square' so 'at *t*1 it is true that
Plate is round' is consistent with 'at
*t*2 it is true that Plate is square'.



Solutions to the problem of temporary intrinsics abound. Here is
another that treats being true and being false as three place
relations between propositions, facts and times. Consider the
propositions:



> 
> (i) Plate is round,
> 



And:



> 
> (ii) Plate is square.
> 



We should distinguish between a property of a proposition, and a
property that is a constituent of a proposition. Being a proposition
is a property of (i), but is not a constituent of (i). In contrast,
being round is a constituent of (i), but is not a property of (i).
Propositions have no shape. Can we hold that (i) and (ii) are both
true compatibly with taking roundness and squareness to be intrinsic
properties?



It is plausible to suppose that that the truth value of a proposition
such as (i) or (ii) depends on the existence of something distinct
from that proposition. Since that is so, let us, as some adherents of
a correspondence theory of truth would do, allow that if (i), say, is
true, it has a relational property of being true. For example being
true may be a relation that holds between (i) and the fact that Plate
is round.



How many places are there in what we may call the truth relation? It
is often though to be a two place relation. Suppose that is wrong, and
truth is a three place relation holding between a proposition, fact
and time. In that case, the three place relation of truth can hold
between (i), the fact that Plate is round, and *t*1,
without holding between (i), the same fact and
*t*2.



Of course whether this is a solution to the problem of temporary
intrinsics depends on what that problem is. It is a solution if the
problem is to explain time indexing without turning intrinsic into
extrinsic properties. After all, no correspondance theorist would
allow truth is an intrinsic property. It is not a solution if the
problem is to explain time indexing without adding extra places to, it
may be, relational properties.



Alternatively, we can follow Haslanger in Haslanger 1989 and Lowe in
Lowe 1987 and treat the relevant propositions as tensed. A change in
an intrinsic property corresponds, on this view, to a change in the
tense of a proposition atrributing that property.



Lewis (2002) objects to this last solution on the grounds that a
tensed proposition should itself be identified with a relational
property. But, such identification leaves it unexplained how something
can change its non-relational intrinsic properties. Ben Caplan in
Caplan 2005 has replied to Lewis that Lewis's objection depends on a
view about propositions that is not compulsory.



Lewis favors a different solution to the problem of temporary
intrinsics (Lewis 1986). Whether or not there is a problem with the
same object being round and square, there is no problem with the same
object having a round part and a square part. To solve the problem of
temporary intrinsics, Lewis invokes the view that, in addition to
their spatial parts, objects have temporal parts or stages. This
allows him to hold that Plate is round at *t*1 and
square at *t*2 because Plate has a round part at
*t*1 and a square part at *t*2.
Plate's round *t*1 part exists only at
*t*1, and Plate's square *t*2 part
exists only at *t*2. Hence there is no problem posed
by either temporal part changing its shape. Plate itself is an object
consisting of a suitably interrelated sequence of such temporal parts.
For the *t*1 temporal part of Plate to be round is
just for it to be round. For the longer lived Plate to be round at
*t*1 is for Plate to be appropriately related to a
round temporal part at *t*1.



As we have seen in invoking temporal parts or stages Lewis endorses
one species of what has come to be called Four Dimensionalism. The
expression 'Four Dimensionalism' has been applied to a
number of different positions that it is well to distinguish here
since not all of them are relevant to identity across time.
'Four Dimensionalism' has sometimes been used for the
thesis, particularly associated with Relativity Theory, that time is
space like. On another use of 'Four Dimensionalism' a
persisting thing is identical with its history. On this view an object
is a sequence of events. Sometimes 'Four Dimensionalism'
is used to label the view that, contra Presentism, things past present
and future are equally real.



Lewis' version of Four Dimensionalism should be distinguished from all
of the above. It is the view that, just as an object such as Plate is
extended in space with spatial parts, so it is extended in time with
temporal parts.



The problem of temporary intrinsics focuses on the possibility of
persisting things changing their properties, or, at least, changing
their intrinsic properties. Many of the problems about identity
through time are posed by puzzle cases that involve change of parts.
Four dimensionalism is one, widely accepted, solution to those
puzzles. It is not overstretching it to suggest that each of the
puzzle cases we will shortly consider appears to be a case of
temporary identity. That is, each one appears to be a case of the
following. For some *x* and *y*, at some time *t*
*x* is identical with *y*, and at some time
*t*' *x* is distinct from *y*.



In the first section we briefly looked at one argument, the so-called
modal argument for the necessity of identities, for denying that there
could be temporary identities. Some philosophers have responded to
some of the diachronic identity puzzles by maintaining that there
could be indeterminate identities. An argument with a similar
structure to the modal argument has been deployed to rule out
indeterminate identities. Give their implications for identity across
time the modal argument and the argument against indeterminate
identities are set out in more detail in the next section.


## 3. Necessary and Determinate Identities



Here are two examples of identity statements:



> 
> (i) The table in the next room is (now) identical with my favorite
> table.
> 
> 
> (ii) The table in the next room is identical with the one you
> purchased last year.
> 
> 
> 



(i) and (ii) are contingent. Even if the table in the next room is my
favorite table, it might not have been. Even if the table in the next
room is the one you purchased last year, it might not have been. One
of the most important discussions of identity is to be found in Saul
Kripke's paper 'Identity and Necessity' and his book
*Naming and Necessity* (in Munitz 1971, Kripke 1980). One
lesson to be learned from Kripke's discussion is that it is
illegitimate to infer from identity statements such as (i) and (ii)
having their truth value contingently that the relation of identity
can hold contingently.



Why is this inference illegitimate? Compare (i) with:



> 
> (iii) The table in the next room is the same size as my favorite
> table.
> 



Being the same size as is an equivalence relation that holds
contingently. What does it take for that relation to hold contingently
between the table in the next room and my favorite table? Thinking in
terms of possible worlds the table in the next room is contingently
the same size as my favorite table just in case the following is so.
The table in the next room is the same size as my favorite table, but,
in some possible world *W*, something identical to (or a
counterpart of) the actual table in the next room is not the same size
as what is actually my favorite table.



Without having recourse to possible worlds, what this comes to is that
the table in the next room is contingently the same size as my
favorite table only if, in addition to (iii), the following is
true:



> 
> (iv) ([?]x)([?]y)[(*x* = the table in the next room)
> & (*y* = my favorite table) & (possibly, *x* is
> not the same size as *y*)].
> 



Likewise the table in the next room is contingently identical with my
favorite table only if, in some world *W*, what is actually my
favorite table is not identical with what is actually the table in the
next room. That condition need not be satisfied for (i) to be
contingently true. All it takes for (i) to be contingently true is
that, for example, (i) is true, but in some world *W* something
qualifies as my favorite table without also qualifying as the table in
the next room. For that to be so nothing need be identical, or
counterpart related, across worlds.



Kripke and Ruth Barcan Marcus offer an argument to show that there are
no contingent identities. Here is one version of that argument often
referred to as the Modal Argument for the Necessity of Identities:



Suppose:



> 
> (1) *a*=*b*.
> 



But each thing is necessarily identical with itself. Hence;



> 
> (2) # (*a*=*a*)
> 



Taking '[l*x* Ph]' to mean: being an
*x* such that Ph (where Ph is some logical formula in
which '*x*' is a free variable), we supposedly
have:



> 
> (3) [l*x* #(*x*=*a*)]*a*
> 



Since, by Leibniz's Law, if (1) then *a* and *b* share
all properties in common. Hence (1) and (3) yield:



> 
> (4) [l*x* #(*x*=*a*)]*b*
> 



which in turn yields:



> 
> (5) #(*a*=*b*).
> 



Though widely accepted this type of argument can be contested.
Leibniz's Law, again understood as ranging over identity properties,
is used to derive step (4)--*b* has the property of being
necessarily identical with *a*--from step (3), *a*
has the property of being necessarily identical with *a*. We
might deny that there are any such modal properties. Doing so blocks
the argument if the application of LL is restricted to properties.
Alternatively we might allow that there are such properties as being
necessarily identical with *a*, but deny that (3) follows from
(2). On one view all that follows from (2) is that *a* has the
property of being necessarily identical with itself expressed by the
predicate
'[l*x* *x*=*x*]'. We need
to distinguish the property of being necessarily identical with
itself, which every existent has, from the property of being
necessarily identical with *a*--which only *a* has
(Lowe 1982). Finally, we might reject (2) on the following grounds.
There is a well entrenched convention that repeated tokens of the same
type of name, constant or variable are assigned the same value. From
the existence of this convention it follows that '*a* =
*a*' expresses a truth. It does not follow that
'*a* = *a*' expresses something necessarily
true.



Here is one way of making clear why it does not follow. According to
what we may call the identity convention two tokens of the same name
standardly refer to the same thing. So in, for example, the sentence
'Napoleon admires Napoleon' we are, unless otherwise
indicated, to take the second occurrence of 'Napoleon' to
have a referent identical with the referent of the first. In the case
of 'Napoleon admires Napoleon' the relation Napoleon is
said to stand in to himself is different from the relation governing
the repeated use of a proper name. In the one case it is the relation
of admiration. In the other it is identity. But, suppose they were the
same relation. Suppose, the repeated use of a proper name were
governed, not by the identity convention, but by what we may call the
admiration convention. According to the admiration convention a
subsequent occurrence of a proper name in a sentence should be taken
to refer to something only if it is admired by the referent of the
first occurrence. In the light of this, admittedly bizarre, convention
what should we say about the truth value of 'Napoleon admires
Napoleon'. Well if the second occurrence of
'Napoleon' refers, it will refer to someone admired by the
referent of the first occurrence. So, if the admiration convention is
adhered to, 'Napoleon admires Napoleon' will, if it
expresses any proposition, will express a true one. Despite that,
'Napoleon admires Napoleon' expresses a contingent truth.
Likewise, '*a*=*a*' expresses a true proposition
if it expresses any proposition at all, since the relation governing
the repeated use of '*a*' is the same as the one that
a is said to stand in to a. But, as with 'Napoleon admires
Napoleon' given the admiration convention, there is no reason to
suppose that the truth expressed by '*a*=*a*' is
a necessary one. A like observation applies to '*a* is
identical with itself'.



Philosophers have appealed to contingent identities to solve identity
puzzles. They have also appealed to vague or indeterminate identities
to solve such puzzles. Consider a club that over an extended time
changes its rules, membership and location. Is the original club
identical with the club having a new location, rules and membership?
Call the original club the Identity Club, and the club with new rules,
membership and location the Constitution Club. Is the following
true?:



> 
> C: The Identity Club = The Constitution Club.
> 



Some would say that that the identity stated by C is vague or
indeterminate. What does it mean to say that an identity is vague or
indeterminate? At least this. C is not determinately true, or
determinately false. If C does lack a determinate truth value, is that
enough to ensure that the identity of the clubs referred to by C is
indeterminate?



In the case of the identity sentence:



> 
> (i) The table in the next room is (now) identical with my favorite
> table.
> 



we saw the need to distinguish between (i) having its truth value
contingently, and (i) stating an identity that holds only
contingently. We likewise need to distinguish C having an
indeterminate truth value from C stating an identity that holds only
indeterminately. C may lack a determinate truth value because one, or
both, of the referring expressions 'The Identity Club' and
'The Constitution Club' lacks a determinate referent.
Nevertheless for any determinate choice of referents for those
expressions C has a determinate truth value.



Can it happen that the referring expressions '*a*'
and '*b*' refer precisely in the identity sentence
'*a*=*b*' without that sentence being
determinately true or false? Here is one version of an argument, due
to Gareth Evans and Nathan Salmon, that is supposed to show that it
cannot (Evans 1978, Salmon 1981). Let '*Ip*' mean:
it is indeterminate whether *p*, that is *p* is neither
determinately true nor determinately false, and let
'*Dp*' mean: it is determinate that *p*. We
have:



> 
> (1') *I*(*a*=*b*).
> 



But:



> 
> (2') *D* (*a*=*a*).
> 



(2') yields:



> 
> (3')
> [l*x* *D*(*x*=*a*)]*a*
> 



Suppose:



> 
> (4') *a*=*b*
> 



Applying Leibniz's Law to (3') and (4') gives:



> 
> (5')
> [l*x* *D*(*a*=*x*)]*b*
> 



from which it follows that:



> 
> (6') *D*(*a*=*b*),
> 



which contradicts (1'). Hence (1') implies:



> 
> (7') !(*a*=*b*)
> 



If (7') is true then it is not true that *a* is identical
with *b*. So if (7') is true, *a* is determinately
distinct from *b*. (1') cannot be true.



Of course, defenders of indeterminate identity do not let this pass
unquestioned. One assumption of the argument is that (7')
implies that *a* is determinately distinct from *b*
rather than just that *a* is not determinately identical with
*b*.



Arguments against contingent and indeterminate identities appeal to
Leibniz's Law. Seen as a principle about the transmission of
properties across identity Leibniz's Law has rarely been challenged.
Still, it has been challenged. One interesting challenge is brought by
Benjamin Schnieder in Schnieder 2006. Similarly, Evans' argument has
been challenged from a number of directions. A recent challenger is
Elizabeth Barnes who in Barnes 2009 invokes counterpart theory to
defuse it.


## 4. Diachronic Identity Puzzles



In the introduction we encountered one type of puzzle about identity
across time: the case of Cup and Tcup. The puzzle arose because we
envisaged Cup losing one of its parts, and coming to have the same
material constitution (being, for example, composed of exactly the
same atoms as), and spatial boundaries as Tcup. Call this the cup
case. Let us say that *a* and *b* are coincident at a
time *t* just in case the following holds. Something is a
proper part of *a* at *t* if and only if it is a proper
part of *b* at that same time. Cup and Tcup are coincident at
the later time since something at that later time is, for example, and
atomic part of *a* if and only if it is an atomic part of
*b*.



There are cases that pose similar diachronic identity puzzles that do
not involve change of parts. One of the best known involves a lump of
clay which, at an earlier time, is coincident with a statue, but, at a
later, say as a result of deformation, is just a shapeless lump of
clay. Other much discussed cases of putatively distinct things at one
time being coincident at another involve fission or fusion. One of the
most famous examples of a fission case is provided by the ship of
Theseus. Over a long period all of the planks composing a certain ship
are replaced one by one. Eventually a ship indiscernible from the
original, but composed of entirely different planks, results. Call
that later ship Replacement. As each plank is removed from the
original ship it is used to construct a ship that is constituted from
all and only the planks belonging to the original ship. Call the ship
composed of the same planks as the ones initially composing the
original ship Reassembly.



Identity is, very plausibly, an equivalence relation (see
 Section 2.2).
 One consequence of it being an equivalence relation is that it is
subject to transitivity: the principle that if *aRb* and
*bRc*, then *aRc*. Saying that, in the case of Theseus'
ship, Replacement and Reassembly are both identical with the original
ship putatively conflicts with the transitivity of identity since
Replacement seems to be later clearly distinct from Reassembly.



What is the best account of these cases? Here are some of the major
ones on offer:


### 4.1 Constitution



Constitution accounts pivot on the distinction between constitution
and identity. Defenders of such accounts hold that constitution,
unlike identity, is not an equivalence relation (Baker 2002).
Constitution is said to be, at least, non-symmetrical. According to a
constitution account, we say the following about the three types of
puzzle cases described above. Cup is never identical with Tcup. Later
Cup is constituted by Tcup [alternatively: Cup and Tcup never
constitute each other, but later are constituted from the very same
atoms]. Likewise the lump of clay is never identical with the statue,
but earlier only constitutes the statue. Finally, the reassembly ship
is never identical, but only constituted from exactly the same planks
as, the original.



Kit Fine has deployed a number of novel Leibniz's Law arguments in
favour of a constitution accounts. Such arguments are replied to by
Brian Frances in Frances 2006.



The constitution view has come in for its share of criticisms. Some
think it engages in metaphysical multiple vision, seeing a
multiplicity of things at a given place and time where there is
plausibly only one. Others argue that constitution *is*
identity (see Noonan 1993).



A number of objections have been raised against constitution views.
One is an objection from causal overdetermination. Another is an
objection from grounding. Consider a statue allegedly constituted from
a statue shaped piece of clay. Someone throws the statue against a
pane of glass, which breaks. What caused the glass to break? Surely,
the statue impacting it. But the glass was also impacted by the statue
shaped piece of clay with sufficient force to break it. So, if
constitution is not identity, the glass breaking has two causes. Some
would say that is one cause too many.



The objection from grounding is not so much an objection to the
constitution view, but an objection designed to undermine a principle
reason for adopting it. A principle reason for adopting the
constitution view is that it seems to allow, for example, the statue
and the piece of clay to have different properties. In particular, it
seems to allow them to have different modal properties such as being
squashable. Since constitution, unlike identity, does not conform to
the indiscernibility of identicals, the clay can be squashable even if
the statue is not.



The problem is that the clay and the statue are made up of exactly the
same atoms organized in the same way. Since that is so it is hard to
see how the clay can be squashable without the statue being so as
well.



A further problem for constitution views is the so called too many
minds objection (see Olsen 1997 and Shoemaker 1999). Advocates of
constitutionalism typically hold that a person is constituted by a
living organism. If so, the person and the living organism
constituting that person share the same thoughts. Whenever you
encounter a person you encounter a distinct living organism having
occupying the same region and having the same thoughts. Not a good
result.


### 4.2 Relative Identity



Advocates of relative identity deny that there is a single identity
relation (see Geach 1967, Griffin 1977). On their view it is improper
to ask whether, say, the statue is the same thing as the later lump of
clay. Instead we should ask whether it is the same statue, or the same
lump of clay. For an advocate of relative identity denying that the
earlier statue is the same statue as the later lump of clay is
consistent with allowing that the earlier statue is the same lump of
clay as the later lump of clay. It is natural for the relative
identity theorist to insist on relativising the transitivity of
identity to the same sortal concept in the following way. What the
relativised transitivity principle says is that: *a* is the
same *F* as *b*, and *b* is the same *F*
as *c* implies only that *a* is the same *F* as
*c* (see Griffin 1977).



One objection to relative identity is that it conflicts with Leibniz's
Law. Here is one way in which such conflict may be thought to arise.
Consider the property version of Leibniz's Law:



> 
> LL: [?]*x*[?]*y*[*x*=*y* -
> [?]*F*(*F**x* - *F**y*)]
> 



The relation of identity mentioned in the antecedent of LL is
unrelativised to a sortal. To make it acceptable to the relative
identity theorist, let us amend LL to:



> 
> LLR:
> [?]*x*[?]*y*[[?]*F*(*x* is
> the same *F* as *y*) -
> [?]*G*(*G**x* - *G**y*)]
> 



Suppose we replace 'is the same *F* as *y*'
in LLR with 'is the same lump of clay',
'*x*' with 'the earlier statue',
'*y*' with 'the later clay lump', and
instantiate the quantifier [?]*G* with 'is the same
statue as the earlier statue'. We then obtain:



> 
> R: the earlier statue is the same lump of clay as the later clay lump
> - (the earlier statue is the same statue as the earlier statue
> - the earlier statue is the same statue as the later clay lump ).
> 



The trouble is that R is false. The earlier statue is the same lump of
clay as the clay lump, and the earlier statue is the same statue is
the same statue as the earlier statue, but the earlier statue is not,
contrary to LLR, the same statue as the later clay lump.


### 4.3 Identity: 'Strict' and 'Loose'



Following Bishop Butler [see
 Section 5],
 Roderick Chisholm distinguishes between a strict and a loose sense of
identity (see Chisholm 1969a). To see what this distinction comes to,
and how it might help with the puzzle cases, consider the case of Cup
and Tcup. For Chisholm things have their parts essentially in the
following sense. It is impossible for *a* to be identical with
*b* in the strict and philosophical sense, unless *a*
and *b* have all their parts in common. Earlier Cup has a part,
a handle, that later Cup, not to say earlier and later Tcup, lacks.
Hence, on Chisholm's view, earlier Cup is not strictly identical with
later Cup.



Earlier Cup is nontheless identical with later Cup in a loose and
popular sense. What then, according to Chisholm, is it for earlier Cup
and later Cup to be identical in a loose and popular sense? To
simplify let us suppose, unrealistically, that the only change of
parts that Cup in, Chisholm would say, a loose and popular sense
undergoes is loss of a handle. Call Hcup the object that consists of
Cup's handle together with Tcup. Chisholm would say this. Cup is
earlier wholly constituted by Hcup, that is Tcup plus handle, and
later wholly constituted by Tcup alone. Moreover Tcup is related to
Hcup in such a way that, as Chisholm puts it, Tcup at
*t*2 is the *ens successivum* of Hcup at an
earlier time *t*1*.* For Chisholm what makes
Tcup at *t*2 an *ens successivum* of Hcup at
*t*1 seems to be this. Tcup is a proper part of Hcup
at *t*1. There is a sequence *S* of cups such
that each member of *S* that is not identical with Hcup is, at
some time, a proper part of some member of *S*. For each time
between and including *t*1 and
*t*2 Cup is wholly constituted by some member of
*S*.



Cup is wholly constituted by Tcup at *t*2. Since the
later Cup is wholly constituted by something, Tcup, that is an *ens
successivum* of something, Hcup, that wholly constitutes Cup we
may say that earlier cup is loosely identical with later Cup.


### 4.4 Arbitrary Undetached Parts



One solution to the problem posed by the cup case is to reject what
Peter van Inwagen calls the Doctrine of Arbitrary Undetached Parts
(see van Inwagen 1981). In setting the problem up we assumed that
earlier Cup consists of the following parts: a handle together with
Tcup. That assumption is justified if the following is. Tcup existed
as a part of Cup when Cup still had its handle. Van Inwagen would
reject that assumption. According to him it is illegitimate to assume
that any old way of notionally dividing up an object yields an
existing undetached part.



Instead of denying that Tcup exists at *t*1 when it
is ostensibly a proper part of Cup, we might instead deny that Tcup at
*t*1 is identical with what looks very much like
Tcup at *t*2. In this way we can preserve
transitivity without having to identify the earlier cup with one of
its proper parts.



One way to allow that Tcup earlier exists without conceding its later
identity with Cup is, following Michael Burke, to maintain that Tcup
goes out of existence when Cup loses its handle (see Burke 1994).


### 4.5 Four Dimensionalism



Here is what a classical four dimensionalist would say about the case
of the cup. Suppose the interval from *t*1 to
*t*2 is the time during which Cup has a handle
attached to it, and *t*2 to *t*3
the interval during which Cup is without a handle, and, so, putatively
identical with Tcup. As before Hcup is the fusion of Tcup and Cup's
handle. According to the four dimensionalist, Cup, Tcup and Hcup are
all extended in time as well as space. Tcup has a temporal part that
extends from *t*1 to *t*2 together
with a temporal part that extends from *t*2 to
*t*3. Tcup's *t*1 to
*t*2 and *t*2 to
*t*3 temporal parts are distinct from each other as
well as being distinct from the temporally longer Tcup. Hcup, that is
Tcup plus handle, is a four dimensional object that extends from
*t*1 to *t*2. Cup itself consists
of the following two, among indefinitely many other, temporal parts:
Hcup and the *t*2 to *t*3 part of
Tcup.



What we should say according to the classical four dimensionalist is
this. The *t*1 to *t*2 temporal
part of Tcup is a proper temporal and spatial part of Hcup. Hcup and
the *t*2 to *t*3 temporal parts of
Tcup are proper temporal parts of Cup. Cup is not identical with any
of Hcup, Tcup from *t*1 to *t*2,
Tcup from *t*2 to *t*3, or Tcup
from *t*1 to *t*3. In particular
there is no question of Cup being literally identical with Tcup from
*t*2 to *t*3, when they are
indiscernible, though, following David Lewis, we may say that Cup and
Tcup are identical at any time between *t*2 and
*t*3 in the sense that they share temporal parts
during those times (see Lewis 1986).



Many four-dimensionalists subscribe to a principle that a number of
writers call unrestricted mereological composition. According to that
principle any set of, in this case four-dimensional, objects
constitute a further four dimensional object. Armed with the
unrestricted mereological composition principle a four-dimensionalist
can say that what there is, in the case of Theseus' ship, is a Y
branching object dividable in an indefinite number of ways into four
dimensional proper parts an indefinite number of which are ships. For
example the ship consisting of the stem together with the replacement
branch has as two of its proper parts a ship consisting of just the
stem, and one consisting of just the replacement branch.



Apart from the argument that it provides the best solution to
diachronic identity puzzles four dimensionalism has been defended on a
number of other grounds. One we have reviewed already; the argument
that four dimensionalism gives the best solution to the problem of
temporary intrinsics. Another, also offered by David Lewis, invokes
the principle that facts in general supervene on facts about the
instantiations of intrinsic properties and external relations. Call
facts about the instantiation of intrinsic properties and external
relations basic facts, and let *R* be the spatio-temporal
region occupied by Plate throughout its career. According to Lewis
there is a world *W* in which a sequence of shorter Plate-like
objects occupy *R*, and all of the basic facts that obtain in
our world obtain in *W*. Lewis' supervenience principle tells
us that all facts supervene on basic facts. The same basic facts
obtain in both our world and *W*. So whatever is true of the
occupant of *R* in *W* is true of the occupant of
*R* in our world. The occupant of *R* in *W* is a
sequence of, appropriately interrelated Plate-like objects. Hence the
occupant of *R* in our world, that is Plate, is likewise a
sequence of interrelated Plate-like objects.



Recently Sider (2002) developed an argument for Four Dimensionalism
from considerations about vagueness. He argues that Four
Dimensionalism is true if it cannot be vague how many things there
are, and also that it cannot be vague how many things there are.



It should be noted that Sider and Katherine Hawley defend an
alternative version of Four Dimensionalism which identifies objects
with what, on the first version, would qualify as their stages (Hawley
2001, Sider 2002). In order to make this identification Sider invokes
something close to Lewis' counterpart relation. Will the table I am
currently looking at persist through the next ten minutes? According
to the classical four-dimensionalist, otherwise known as the
perdurantist, the table will persist through that period provided it
has a present and a ten minutes from now table stage that are both
stages of the table without either one being identical with the table.
In contrast the stage theorist identifies the table with the present
stage of the table. How can that be since the present table stage only
exists now, and the table is supposed to be around ten minutes from
now? It can be, says the stage theorist, because, though the ten
minute from now table stage is not now identical with the table, it
will be identical with the table. Moreover it will be identical with
the table since it stands in the appropriate counterpart relation to
the present table stage.



Stage theory enjoys the following advantage over classical
four-dimensionalism. Consider the case of a person fissioning into two
later people. A classical four-dimensionalist like Lewis will say that
before the fission there are two separate people that cannot be told
apart. The stage theorist has no need to say that. Instead the stage
theorist can say there is a single present person who will be
identical with each of a pair of later individuals in virtue of
standing in the relevant counterpart relations to each one.



It should also be noted that four dimensionalism differs from
Chisholm's invocation of loose and popular identity in, at least, the
following way. The persistence of an object for any length of time
will, on a four dimensionalist view, require the existence of shorter
lived objects setting aside the possibility of extended simples. The
persistence for any length of time, on Chisholm's view, of a three
dimensional object does not require the existence of shorter lived
three dimensional objects. It does not do so because the object
persisting for a lengthy period may undergo no change of parts.


### 4.6 Temporary Identity



In the case of, for example, the truncated cup we saw that one option
is to claim that Cup is earlier distinct from Tcup [cup minus its
handle], but later identical with Tcup. According to this option the
identity of Cup with Tcup is only temporary. We also saw that many
refuse to countenance temporary identity because it allegedly
conflicts with Leibniz's Law [LL]. After all, later Cup, but not Tcup,
apparently later has the property of having had a handle.



Despite this putative conflict with LL, some philosophers are prepared
to defend temporary identity as the best solution to the puzzles about
diachronic identity. George Myro does so by restricting the scope of
LL to exclude such properties as having had a handle (Myro 1985).
Gallois (1998) does so by arguing that if the identity of Cup and Tcup
is temporary, we cannot infer from Tcup having had a handle earlier
that earlier Tcup has a handle.


### 4.7 Further Puzzle Cases



We have focused attention on one type of case that raises a puzzle
about diachronic identity. Such a case involves something ostensibly
becoming, or ceasing to be identical with something that is ostensibly
one of its earlier or later proper parts. It would be wrong to give
the impression that such a "Deon-Theon" case named after
the individuals involved in the example is the only, or even main,
type of case posing a problem about diachronic identity. In addition
there are what are often referred to as fission and fusion cases. A
fission case has the following features. We have putatively distinct
things *b* and *c* existing at some later time
*t*2. Each of *b* and *c* is related
to *a*, which exists at an earlier time *t*1,
in such a way that each one is ostensibly identical with
*a*.



Fission cases come in two varieties: symmetrical and asymmetrical.
Examples of symmetrical fission cases include amoebic and hemispheric
division [for the latter see Personal Identity below]. In a
symmetrical case there is some relation that each of *b* and
*c* stand in to *a*, where standing in that relation is
what makes each one putatively identical with *a*. In an
asymmetric case, *b* is putatively identical with a because it
stands in a certain relation to *a*, but *c* is
putatively identical with *a* because it stands in a different
relation to *a*. The best known example of a symmetrical
fission case is the Ship of Theseus described at the beginning of this
section.



Let us see how the proposals for dealing with the cup case apply to
fission cases. Constitution only delivers a candidate solution in a
symmetric fission case. As we noted above, a constitution theorist can
say the following about Theseus' Ship. The ship resulting from the
replacement of the original planks is identical with, but not
constituted from the original planks. The ship reconstituted from the
original planks is not identical with the one originally constituted
from those planks.



Some relative identity theorists have this to say about Theseus' Ship.
In that case conflict with the transitivity of identity is avoided by
maintaining the following. The replacement ship is the same ship as
the original, and the original is the same collection of planks as the
reassembly ship. Conflict with transitivity is avoided because we need
not allow that the reassembly ship is the same ship as the
original.



Distinguishing between a strict and loose sense of
'identical' yields the following solution in the case of
Theseus' Ship. Let Original be the original ship, Replacement be the
ship that results from replacing Original's original planks, and
Reassembly the one that results from their reassembly. In that case,
deploying the distinction between a strict and loose sense of
identity, we can say this. Reassembly is strictly identical with
Original, but Replacement is only loosely identical with Original. A
conflict with transitivity of identity is avoided for the following
reason. It follows by transitivity from Replacement being identical
with Original, and Original being identical with Reassembly, that
Replacement is identical with Reassembly only if a single relation of
identity is involved.



Here is what a four dimensionalist such as Lewis will say about
Theseus' ship. In that case there are two initially indiscernible
ships. The first is a four dimensionally extended ship located where
the original ship is initially located that ends up coinciding only
with the reassembly ship. The second, also initially located where the
original ship is initially ends up coinciding with the replacement
ship. We thus have a Y-branching four dimensionally extended object
with one ship constituted by the stem together with one branch, and
the other constituted by the stem together with the remaining
branch.



Four Dimensionalism, like the thesis that identities can be temporary,
applies to both symmetric and asymmetric cases of fission.



A temporary identity theorist will hold that Replacement and
Reassembly are identical at *t*1, but distinct ships
at *t*2.



In the previous section we reviewed an argument designed to rule out
indeterminate identities. If that argument can be met, it is open to
us to say the following about Theseus' Ship. Each of Replacement and
Reassembly is indeterminately identical with Original.



The puzzle cases are puzzle cases because they bring into putative
conflict intuitions all of which we want to subscribe to. Consider a
statue and the collection of atoms that constitute it. We wish to say
that the statue is identical with the collection of atoms. We also
wish to say that the statue, but not the collection, can survive the
loss of one atom belonging to that collection. Leibniz's Law appears
to force us to renounce one of these intuitions. Thomas Sattig argues
for a compatibilist view according to which we can hold on to both
intuitions without giving up, or modifying, Leibniz's Law. We can do
so by relativising identities to different perspectives. From the
ordinary object perspective the statue is distinct from the atoms that
constitute it. From the material object perspective the statue is
identical with the atoms that constitute it.


## 5. Personal Identity



Personal identity is perhaps the most extensively discussed special
case of identity. What is it for a person existing at one time to be
identical to a person existing at another? This question was first
clearly posed by John Locke in his celebrated discussion of personal
identity in the *Essay* (Locke 1975). Locke distinguishes
between being the same man and being the same person. To be the same
man is to be the same member of the species human being. For Locke
what is crucial is that having the same consciousness is not
sufficient for being the same man, but is sufficient for being the
same person.



Famously Locke calls the concept of a person a forensic concept. For
Locke much of the importance attaching to being the same person is
that moral responsibility for past deeds goes with being the same
person, rather than being the same man or even the same immaterial
substance, as a past person. In his view it is enough to be morally
responsible for some deed that one is the same person as its
performer. It is not required that one be the same man or the same
immaterial substance as the one who performed the act in question.



What then, according to Locke, is it to have the same consciousness as
some past person? He is customarily interpreted as holding that person
*A* is the same person as earlier person *B* just in
case *A* is able to remember enough of what happened to
*B*. This is sometimes referred to as the memory criterion of
personal identity. The memory criterion was criticized by Butler and
Reid principally because it was said to be circular, and, as a
criterion of personal identity, incompatible with the transitivity of
identity. (See Section 2.2, and Joseph Butler 'Of Personal
Identity' and Thomas Reid 'Of Mr. Locke's Account of Our
Personal Identity' in Perry 1975.)



The argument for the circularity of the memory criterion went like
this. Suppose we think of the memory criterion as giving what would be
later called an analysis of *A* being the same person as
*B*. If so, we are invited to analyze *A* being the same
person as *b* in terms of *A* remembering enough of what
happened to *B*. But any plausible analysis of *A*
remembering what happened to *B* will mention, in the
analysans, *A* being the same person as *B*.



Sydney Shoemaker has responded to the circularity charge by
distinguishing remembering from what he calls Q-remembering (Shoemaker
1975). *A* Q-remembers something that happened to *b*
just in case there is an appropriate causal link between the event
Q-remembered and *A*'s memory impression of that event. Unlike
remembering, Q-remembering a past experience does not imply the
identity of the one having the Q-memory with the one who had the
experience. We can avoid the charge of circularity by restating the
memory criterion in the following way. *A* is the same person
as some earlier individual *B* if and only if *A*
Q-remembers enough of what happened to *B*.



The charge that the memory criterion conflicts with the transitivity
of identity was illustrated by the famous case of the schoolboy, the
young lieutenant and the elderly general (Reid 1975). The elderly
general can Q-remember enough of what happened to the young lieutenant
to qualify, by the memory criterion, as being the same person as the
young lieutenant. The young lieutenant in turn Q-remembers enough of
what happened to the young schoolboy. But the elderly general can
remember almost nothing of what happened to the young schoolboy. Since
the memory criterion has it that *A* Q-remembering enough of
what happened to *B* is a necessary condition for *A*
being the same person as an earlier person *B*, it follows
that, according to the memory criterion, the elderly general is not
the same person as the young schoolboy. Hence, the memory criterion
implies, contrary to the transitivity of identity, that, although the
elderly general is the same person as the young lieutenant, and the
young lieutenant is the same person as the schoolboy, the elderly
general is not the same person as the young schoolboy.



The memory criterion came to be modified in two further ways. The
first modification provides a way of reconciling the memory criterion
with the transitivity of identity in the light of cases such as the
elderly general. Instead of saying that *A* is the same person
as some earlier *B* if and only if *A* can Q-remember
enough of what happened to *B*, we say the following.
*A* is the same person as *B* if and only if there is a
Q-memory chain linking *A* with *B*. For there to be a
Q-memory link between *A* and *B*, either *A*
remembers enough of what happened to *B*, or *A*
remembers enough of what happened to someone who remembers enough of
what happened to *B*, or *A* remembers enough of what
happened to someone who remembers enough of what happened to someone
who remembers enough of what happened to *B*, and so on. In the
case of the elderly general, the elderly general does remember enough
of what happened to, someone, the young lieutenant, who remembers
enough of what happened to the young schoolboy to count, by the
modified criterion, as the same person as the young schoolboy.



The second modification extends the memory criterion to include
forward looking psychological connections, such as that between
present intention and future action, as determinants of personal
identity.



With these modifications incorporated the memory criterion has come to
be known as the psychological continuity criterion of personal
identity. The psychological continuity criterion is an improvement on
the original memory criterion. Nevertheless one of the problems
confronting the original memory criterion, its putative conflict with
the transitivity of identity, can be brought against its successor in
a different form. We saw that making certain identifications in a
fission case such as the ship of Theseus [see Section 4: Diachronic
Identity Puzzles] threatens the transitivity of identity. One much
discussed type of fission case, hemispheric division, is taken by many
to show that the psychological continuity criterion is, after all,
incompatible with the transitivity of identity (Nagel 1975).



Suppose, as may one day be medically feasible, an individual
*A*'s still functioning upper brain is transplanted from
*A*'s body to the debrained, but living, body formerly
belonging to *B*. Upon being transplanted A's upper brain is
connected to what remains of *B*'s central nervous system so
that a person, call her *A*-*B*, results.
*A*-*B* believes herself to be *A*, can
Q-remember what happened to *A*, has *A*'s psychological
dispositions, and so on. Should we say that *A*-*B* is
the same person as *A*, the same person as *B*, or an
altogether new person? Psychological continuity theorists will have
little hesitation in answering that *A*-*B* is the same
person as *A*.



A person can function fairly normally with much of their brain
destroyed. Suppose *A* loses an entire brain hemisphere. Given
the plasticity of the brain, and aided by our hypothetical future
medical technology, it may be that *A* could survive such a
loss. If so, it would be unreasonable to deny that *A* could
survive the transplantation of only one brain hemisphere given that
she could survive the transplantation of he entire intact upper
brain.



The putative conflict with transitivity arises when we consider a case
in which both of the separated hemispheres of *A*'s original
brain are transplanted to separate bodies resulting in what certainly
look to be distinct individuals. Suppose, one of *A*'s brain
hemispheres is transferred to *B*'s body, resulting in a person
*PB*, and the other to C's body resulting in a person
*PC*. It flouts transitivity to say that *PC* is
identical with *A*, and that *A* is identical with
*PB*, but deny, at it seems we should, that *PC* is
identical with *PB*.



There are a number of ways that defenders of a psychological
continuity criterion have attempted to evade this result. One, adopted
by David Lewis, goes like this (Lewis 1976). We say that earlier, when
*A* is around with an intact brain, there are two indiscernible
individuals, *PB* and *PC*, sharing a single body.
Another, advocated by Robert Nozick, concedes that if both hemispheres
are successfully transplanted, neither of the later individuals with
just one brain hemisphere is identical with the earlier one with an
intact brain, but insist that if only one hemisphere is transplanted,
the resulting individual is identical with the former possessor of two
hemispheres. On this view whether, for example, *PB* is
identical with the earlier person with *A*'s body depends on
whether there is an equally good later candidate, such as *PC*,
for being the earlier *A*-body person (Nozick 1981).



In one of the most influential discussions of personal identity Derek
Parfit defends a view close to Nozick's by distinguishing between
survival and identity (in Perry 1975). In Nozick's view what
psychological continuity guarantees is not identity, but survival. In
the case where both of *A*'s hemispheres are transplanted to
yield *PB* and *PC*, *A* survives as *PB*,
and survives as *PC*, though she is identical with neither
*PB* nor *PC*.



Parfit, Nozick and Lewis all take psychological continuity to be
integral to personal identity in the following sense. In cases where
there is no branching psychological continuity is sufficient to ensure
the identity of a later with an earlier person. A number of
philosophers would reject this claim insisting that bodily persistence
is required for personal identity. Some, for example Eric Olson, would
argue that psychological continuity is irrelevant to the identity of
those things, human beings, who are the only things we know to be
persons. Instead, on this view, what is crucial to personal identity
for humans is continuing to be the same animal (Olson 1997).