## 1. Introduction



You're performing an amazing trick right now: you're in
two places at once. How do you manage to be down there, near the
floor, and yet also be a metre or two up in the air? Well, it's
not so very amazing: your feet are down there on the floor, and your
head is up in the air. Having spatial parts enables you to be in
several different places, and to have different properties in
different places: you're cold down there on the tiled floor, and
also warm up there by the heater, because your feet are cold and your
head is warm. Moreover, having parts could let you be in the same
place as someone else: if you shared a hand with a conjoined
('Siamese') twin, then you could both wear the same glove
without jostling for space.



None of this is special to people: inanimate objects also extend
through space by having spatial parts. They have different properties
in different places, and sometimes they overlap by sharing their
parts. These simple facts about spatial parts explain basic features
about the way things and people occupy space.



Things and people take up time as well as taking up space: you existed
yesterday, and, unless reading this article is a real strain, you will
exist tomorrow too. Just as you can have different properties at
different places (hot up here, cold down there), you can have
different properties at different times (yesterday you hadn't
heard of temporal parts, by tomorrow you'll know plenty about
them). 



Some philosophers believe that you take up time by having different
temporal parts at different times. Your spatial parts are things like
your head, your feet and your nose; your temporal parts are things
like you-yesterday, you-today and you-tomorrow. If you have different
temporal parts, this would explain how you can exist at different
times, and it would also explain how you can have different properties
at different times (you-yesterday hasn't heard of temporal
parts, you-tomorrow is an expert). According to these philosophers,
then, persisting through time is pretty much like extending through
space: it's all a matter of parts.



Other philosophers reject this picture. They argue that you persist
through time as a whole: it's not just a part of you sitting in
front of the computer right now, it's you, the whole you! It was
the very same whole person yesterday who knew nothing about temporal
parts, and, by tomorrow, the very same whole person will be an expert.
'You-yesterday' isn't a name for some mysterious
part of you which only existed for a day; instead, it's a
stilted way of talking about you, and what you were like
yesterday.



Discussions of time, space, identity and change have been part of
philosophy since its earliest days, and not every question about
persistence obviously concerns temporal parts. For example, can we
give criteria of identity through time for artefacts, animals or
people? What happens to a ship if you replace all of its planks one by
one? What if you keep the old planks, then build a new ship out of
them? In addressing these questions during recent decades, however, it
has proven useful to discuss whether objects have temporal parts,
because the answers that philosophers give to these questions can
often depend upon whether they believe in temporal parts.



This article is divided into a number of sections. Section 2 looks
more closely at what exactly temporal parts are supposed to be, and at
what sorts of things are supposed to have them. Sections
 3,
 4 and
 5
 look at a range of arguments in favour of believing in temporal
parts, and at the responses of those who reject temporal parts.
 Section 6
 discusses connections between debate about temporal parts, and debate
about the nature of time more generally.
 Section 7
 considers whether physics can teach us anything about temporal parts.
 Section 8
 discusses a question internal to temporal-parts theories: what
relationship is there between the different temporal parts of a single
object?  Finally,
 section 9
 touches on special concerns about the persistence of people through
time.


## 2. What are temporal parts, and which things are supposed to have them?



The two most popular accounts of persistence are perdurance theory
(perdurantism) and endurance theory (endurantism). Perdurantists
believe that ordinary things like animals, boats and planets have
temporal parts (things persist by 'perduring').
Endurantists believe that ordinary things do not have temporal parts;
instead, things are wholly present whenever they exist (things persist
by 'enduring'). This looks like a straightforward
ontological disagreement, a dispute about what exists. Perdurantists
think that objects have both spatial and temporal parts, while
endurantists think that they only have spatial parts.



From an endurantist point of view, however, it is difficult even to
say what temporal parts are supposed to be. Your temporal parts are
parts of you which lie in the past or in the future. But endurantists
agree that you have different spatial parts at different times: you
exchange molecules with the environment, you grow new hairs or lose a
tooth to decay. So, yes, some of your (former) parts lie in the past,
and some of your (future) parts lie in the future, but that
doesn't mean that you're somehow less than a whole person,
right here and now. Why do perdurantists make such a big deal of the
obvious fact that you have different parts at different times?



Endurantists think about what parts you have at different times, past,
present or future. But perdurantists prefer to think atemporally about
what parts you have, full stop (what parts you have, period). And they
claim that you have you-yesterday, you-today and you-tomorrow amongst
your parts. Endurantists don't accept this atemporal way of
talking about parthood, and so they find it difficult even to say what
they don't like about temporal parts.



What moral should we draw from this communication breakdown? Some
perdurantists think 'so much the worse for endurantists: they
can't even say what they're against'. Some
endurantists think 'so much the worse for perdurantists: their
theory doesn't even make sense'. And some philosophers on
both sides look for a neutral way to spell out the notion of a
temporal part (for more detail on this, see the reading suggestions at
the end of this section). For now, let's take it that the basic
idea of a temporal part is well-enough understood, perhaps via the
analogy with spatial parts; later sections will show how the idea is
put to work.



So the two standard views of persistence are endurance and perdurance
theories. But there are also non-standard views.  According to
mixed views, some persisting objects have temporal parts, and others
do not. For example, perhaps changing objects have temporal parts,
whilst objects with unchanging intrinsic natures do not. Or perhaps
ontologically self-sufficient things like organisms don't have
temporal parts, but ontologically dependent things like ocean waves,
smiles or universities do. (Most endurantists, perdurantists and
others agree that processes or events have temporal parts: whether or
not I have earlier and later parts, my birthday party certainly
does.)



Other non-standard views take the basic perdurantist idea that
persistence is much like spatial extension, then they develop the idea
in different ways. For example, perhaps persisting things stretch out
four-dimensionally through time, but without being subdivided into
temporal parts. Or perhaps, as stage theorists claim, the world is
full of four-dimensional objects with temporal parts, but when we talk
about ordinary objects like boats and people, we talk about brief
temporal parts or 'stages' of four-dimensional
objects.



How is this supposed to work? Imagine that someone refers to you by
name. According to perdurantists, the name refers to a
ninety-year-long (let's hope) four-dimensional object. According
to stage theorists, the name refers to a brief part of that
ninety-year-long object, a different one at different times. This
sounds peculiar: after all, your name refers to you and you have a
future (and quite a past), while stages exist only momentarily. Stage
theorists say that when we speculate about what you're going to
do next week, our speculations are made true or false by the behaviour
of your counterparts next week. These future counterparts of yours are
the very objects which, according to perdurantists, are your future
temporal parts.



Just how brief are temporal parts or stages? Typically, objects which
have any temporal parts are thought to have instantaneous temporal
parts ('time-slices'), which do not themselves persist
through time. (Most perdurantists think that things have
non-instantaneous temporal parts too, like you-during-1999.) But an
alternative is to claim that an object has only as many temporal parts
as it has genuinely differentiated periods in its existence; this is a
mixed view, because changing objects will have temporal parts, while
unchanging objects and temporal parts will persist without having
temporal parts of their own.



Some philosophers and some non-philosophers suspect that debate about
whether things have temporal parts is empty, that there is no genuine
issue at stake here. One idea is that we can't know for sure
whether things have temporal parts: all the theories on offer have
good and bad aspects and we'll never find an undisputed
champion. If this is true, it doesn't undermine the debate
unless consensus and certainty are our only goals. A second idea is
that metaphysical enquiry is pointless, since irrelevant to daily
life. This claim needs support from accounts of relevance, and of the
connection between irrelevance and pointlessness. A third idea is that
metaphysical enquiry is doomed to fail because there are no absolute
metaphysical truths. This claim needs support from accounts of truth,
language and reality. All of these topics are too grand for this
article. A fourth idea is the much more focused claim that, while
certain metaphysical disputes are legitimate, the debate about
temporal parts is empty: this doubt may be reinforced by the
difficulty of giving a neutral account of what temporal parts are
supposed to be, or by scepticism about the so-called 'problem of
change', as discussed in the next section.



As noted above, the debate between endurantists and perdurantists is
an ontological dispute: do temporal parts of ordinary material objects
exist, or not? Moreover the endurantist notion of 'being wholly
present' was understood in terms of parts and wholes. In the
past few years, however, some have suggested that debates about
persistence are better understood as debates about location -
how are material objects located in (or extended through) time, and
how does this compare with the way(s) in which material objects are
located in (or extended through) space? Temporal parts were introduced
at the beginning of this entry via an analogy with spatial parts, but
this recent work challenges even the assumption that
spatially-extended objects inevitably have spatial parts. The present
article focuses, appropriately enough, on persistence questions
understood via the notion of temporal parthood, but you can read about
alternative approaches in the separate entry on
 Location and Mereology,
 especially section 6.3.2.



Before we plunge into arguments about whether temporal parts exist,
it's worth clarifying some terminology. First: perdurance theory
is sometimes called 'worm theory', especially when it is
contrasted with stage theory. This is because perduring objects
stretch out through time just as (we all agree) earthworms stretch out
through space. Worm theory has nothing to do with wormholes, and,
sadly, people don't usually describe themselves as 'worm
theorists'. Second: 'four-dimensionalism' is
sometimes used as an umbrella term for perdurance theory and stage
theory, and 'three-dimensionalism' as a name for endurance
theory. This is because perduring objects (and sums of stages) are
four-dimensional, whereas enduring objects are three-dimensional,
wholly present at each moment. But some non-standard views of
persistence, including 'mixed' views, do not fall neatly
into either category. And beware: other authors use
'four-dimensionalism' and
'three-dimensionalism' as names for different theories of
time, rather than different theories of things in time. Third:
'continuant' is sometimes used as a neutral term for any
ordinary persisting thing. In this sense, we can ask whether
continuants endure or perdure. But the label 'continuant'
is more commonly reserved for enduring, three-dimensional objects.
This marks a contrast with processes or events, and carries the
implication that perdurantists foolishly identify material objects
with events. So it tends only to be endurantists who use the term
'continuant'.



**Suggested Reading**: good introductions to the debate
about temporal parts include Loux (1998, chapter 6), Haslanger (2003),
McGrath (2007), Sider (2008), Effingham (2009), Balashov (2011),
Effingham (2012), Goswick (2013), and Curtis and Robson (2016: chapter
7). Amongst the more recent contributions, Effingham (2009), Goswick,
and Curtis and Robson are good on the basics; Effingham (2012) is more
detailed and comprehensive; Balashov (2011) is more advanced, guided
by relativistic physics. Lewis (1986a, p. 202) introduces the terms
'endurance' and 'perdurance', attributing them
to Johnston. Sider (1997; 2001, section 3.3) discusses the difficulty
of defining 'temporal part'; see also Merricks (1999a),
Hawley (2001, section 1.6) and McKinnon (2002). Wasserman (2016)
argues that we often conflate the ontological question whether things
have temporal parts with the explanatory question whether things
persist in virtue of having those parts. Donnelly (2016) is a very
helpful exploration of different attempts to define endurance -
in terms of parthood, or location, or grounding. Lewis (1976,
postscript B) tries to make the notion of a temporal part acceptable
to endurantists; van Inwagen (2000) and Noonan (2003a) object, whilst
Braddon-Mitchell and Miller (2004) respond. Perdurantists include
Quine (1950; 1960), Taylor (1955), Lewis (1971; 1976; 1986a),
Armstrong (1980), Noonan (1980), Robinson (1982), Heller (1984; 1990),
Le Poidevin (1991), Jubien (1993), and Hudson (2001). Endurantists
include Thomson (1965; 1983), Geach (1966; 1967), Chisholm (1976),
Mellor (1980; 1981; 1998), Lowe (1983; 1998b), Simons (1987), Forbes
(1987), Haslanger (1989a), van Inwagen (1990a; 1990b), Oderberg
(1993), Merricks (1994), Fine (2008/2006), and Shoemaker (2015);
Simons (2008) responds to Fine. Miller (2005b) defines
'endurance', see also Keinanen and Hakkarainen (2010),
while Janzen (2011) defends endurantism. Melia (2000) eliminates
processes in favour of enduring things. Johnston (1987) explores a
mixed view, and so, differently, do Hofweber and Velleman (2011),
Grygianiec (2016), and Brzozowski (2017, 2019). Parsons (2000)
develops four-dimensionalism without temporal parts, and Miller (2009)
develops this further. See also Daniels (2019). Other non-standard
accounts of persistence include Giordani and Costa (2013), Miller
(2013), Costa (2017), and Giberman (2019b). For stage theory see Sider
(1996; 2001) and Hawley (2001); Varzi (2003) is a sympathetic
discussion, whilst Balashov (2007) attempts a precise definition of
'exdurance' aka stage theory. Moyer (2008), Moss (2012)
and Viebahn (2013) compare stage theory with perdurantism. More on
stage theory: Stuchlik (2003), Hansson Wahlberg (2008), Wright (2010),
Rychter (2012), McKeever (2017) and Giberman (2019a). Questions about
how fine-grained temporal parts or stages must be are discussed by Le
Poidevin (2000), Stuchlik (2003), Traynor (2013), Effingham (2013),
Mazzola (2015), Kleinschmidt (2017), and Giberman (2019a); Leonard
(2018) explores endurantism without temporal instants. Cahen (2017)
discusses individuation for temporal parts.



For arguments that there is no real dispute here, see McCall and Lowe
(2003), Lowe and McCall (2004), and Miller (2005); Reydon (2008)
responds by drawing analogies with debate about biological species.
Hirsch (2008) shows how more general scepticism about metaphysical
disputes might play out here; McGrath (2007) draws out a number of
connections with the burgeoning literature on metaontology; see also
Benovsky (2011), Hansson Wahlberg (2014b), and Giberman (2018). The
role of intuitions and 'folk theory' in debate about
persistence is discussed by Rose (2015), Benovsky (2016), and Rose et
al (2018); the role of experience as evidence is discussed by Prosser
(2012), Traynor (2014), Prosser (2015) and Young (2018). Scholl (2007)
connects the philosophy and psychology of object persistence.
Hawthorne (2006, 2008) explores the distinction between three- and
four-dimensionalism (the second of these articles is the more
accessible). For discussion of how to define 'wholly
present', see Wasserman (2004a), Crisp and Smith (2005), Olson
(2006), and Donnelly (2016). Cotnoir's (2015) review of
Kleinschmidt (2014) highlights issues about persistence and location;
Kleinschmidt's introduction is very useful,and provides further
references; see also Eagle (2016a). Donnelly (2011) advocates the
location approach, articulated in Parsons (2007); for further
references see the separate entry on
 Location and Mereology,
 especially section 6.3.2. Steward (2015) discusses continuants. The
present encyclopedia article focuses on contemporary debate in analytic
philosophy; work which makes connections to other times and other
traditions includes Hirsch (1999a), Helm (2009), Gorham (2010), Fan
(2018), McKeever (2018), Costa (2020) and Hayashi (2019).


## 3. Change and Temporal Parts



Enough about what temporal parts are supposed to be. Why believe in
them at all? It's not clear whether ordinary thinking involves
any commitment for or against temporal parts: some believe that it is
neutral, while others believe that the default assumption is that
things don't have temporal parts. Regardless of what ordinary
thinking tells us, advocates of temporal parts argue that their view
offers the best solutions to a number of metaphysical problems.
Endurance theorists respond by offering solutions of their own,
criticising the temporal-parts solutions, or both.



One metaphysical problem concerns how change is possible (this has
become known as the 'problem of temporary intrinsics' or
sometimes the 'problem of change'). The banana in the
fruitbowl was unripe a few days ago, and today it is overripe. Surely
nothing can be both unripe and overripe?  Of course, it's
the fact that the banana is unripe and overripe at different times
which saves it from metaphysical peril: we all know that. But it would
be nice to understand why this fact is crucial: what is it about the
passage of time which makes it possible for one and the same object to
have apparently incompatible properties?



If the banana has temporal parts, this explains how it can change: an
earlier temporal part of the banana is unripe, while a later temporal
part of the banana is overripe. More grandly: an earlier temporal part
has the property *being-unripe*, while a later temporal part
has the property *being-ripe*. There's no mystery here,
any more than there is mystery in your being both hot and cold by
having a hot head and cold feet: we're all familiar with the
fact that different parts of the same object can have different
properties.



Is this a good explanation of change? One objection is that
perdurance-style temporal variation is not really change at all: 
the whole four-dimensional banana is neither unripe nor overripe, so
can't change between these states, and the temporal parts are
either permanently unripe or permanently overripe, so they don't
change either. In response, perdurantists distinguish two ways of
talking about persisting things - an atemporal way, which takes
in all times at once, and a temporal way of talking, relative to
various times. On the atemporal way of talking, the whole
four-dimensional banana is neither unripe nor overripe; nevertheless,
it's true to say in temporal terms that the whole banana is
unripe on Monday, and the whole banana is overripe on Friday, because
of the properties of the relevant temporal parts. Endurantists who
claim that temporal variation is not genuine change must challenge
this combination of temporal and atemporal talk.



Stage theorists give the same basic account of change as perdurantists
do, but they have a slightly different response to the no-change
objection. According to perdurantists, talk about the same banana at
different times is straightforwardly made true by one and the same
four-dimensional object existing at different times. But some fancy
footwork is needed to explain what it is for that object to be
overripe right now: it's for it to have an overripe temporal
part right now. In contrast, according to stage theorists, talk about
the banana being overripe right now is straightforwardly made true by
the banana being overripe, since the banana just is a momentary stage
which exists right now. But some fancy footwork is needed to explain
what it is for the same banana to exist at different times: it is for
the current momentary banana to stand in certain intimate causal
relations to momentary bananas in the past and the future.



Temporal-parts accounts of change seem OK, but can endurantists come
up with anything equally good or better? How can one and the same
thing have different properties at different times? One radical answer
is presentism, the view that only present objects, events and states
exist: past and future do not exist. Presentism seems to dissolve the
problem of change: since only the overripe banana is present, its
unripe state does not exist, so there's nothing to worry about.
(For further discussion of presentism, see
 section 6.) 
 But unless there are independent reasons for accepting presentism
(see the separate entry on
 time),
 it seems like a drastic response to the problem of change.



Less radically, endurantists may claim that objects change by standing
in different relations to different times. There is no absolute fact
of the matter regarding the ripeness of the banana: instead, the
banana bears the *being-unripe-on* relation to Monday, and the
*being-overripe-on* relation to Friday.  (Alternatively,
perhaps the banana possesses two compatible properties,
*being-unripe-on-Monday*, and
*being-overripe-on-Friday*.) There's no mystery in an
object which bears apparently incompatible relations to different
things: you are bigger than the Mona Lisa, and smaller than the
Louvre, but metaphysicians don't puzzle over how you can be both
bigger-than and smaller-than. Those who oppose this relational view of
changeable properties claim that it's just too relational: the
banana seems to lose all its intrinsic nature. We may also worry that,
as with the temporal parts account, it's not clear whether
anything really changes on this picture: the banana always stands in
the same relations to the various times.



(For further discussion see the separate entry on
 intrinsic vs. extrinsic properties,
 especially section 1.1.)



A third endurantist account of change is adverbialism. Change is
puzzling because it seems that a single object (like the banana) both
has and doesn't have a single property (like
*being-unripe*). The adverbialist idea is that, instead of
subdividing the object into temporal parts (the banana-on-Monday and
the banana-on-Friday), or subdividing the property (into
*being-unripe-on-Monday* and *being-overripe-on-Friday*),
we should subdivide the way in which the object has the property. The
banana has the property *being-unripe* in a Monday way, and it
fails to have that same property in a Friday way. (Adverbialism is
so-called because it focuses on ways of having properties: an adverb
tells you about the way something is done.) Objections to adverbialism
focus on whether this relativisation of ways things have (or
'instantiate') properties can explain change without
simply raising further problems about the nature of instantiation.



In summary, then, those who believe in temporal parts seem to have a
nice explanation of change to hand. But those who reject temporal
parts also have a range of options, none of which seems decisively to
have been ruled out. (For further discussion, see the separate entries
on
 change
 and on
 singular propositions
 .)



There have been a number of challenges to the idea there is any
genuinely metaphysical 'problem of change'; this is
sometimes diagnosed as a problem arising from confusions about tensed
language. However, there is no consensus about what the consequence
would be if there were no metaphysical problem of change: should we
default to endurance, or to perdurance, or should we conclude that the
contrast between these two positions is also somehow illusory? 



**Suggested Reading**: It's a good idea to start
with Lewis (1986a, pp. 203-4), who coins the phrase
'problem of temporary intrinsics', argues that none of the
endurance theories of change are satisfactory, and sets out the
perdurance account of change. Wasserman (2006) surveys the debate; see
also Wasserman (2010). McTaggart (1927, sections 315-6), Simons
(1987), Mellor (1998, section 8.4), McCall and Lowe (2009), and
Oderberg (2004) argue that variation between temporal parts is not
genuine change (Oderberg 2004 is also sceptical as to whether there is
any genuine puzzle here). For a response see Heller (1992), then
Lombard (1994) in return. Botterell (2004) also criticises the
temporal parts account of change; Sattig (2002, 2003) objects to the
perdurantist and stage accounts of predication; see also Hansson
Wahlberg (2009, 2010), Lombard (2006) and Perovic (2019); Giberman
(2017) argues against endurantist accounts of change. For the
presentist account of change, see Merricks (1994), Hinchliff (1996),
Zimmerman (1998a), and Fiocco (2010); Rettler (2012) makes other
connections between the metaphysics of persistence and of time. van
Inwagen (1990a) advocates a relations-to-times view of temporary
properties, as do Wasserman (2003) and Mellor (1981), although Mellor
(1998) has a different account, in terms of fact-constituents;
Effingham and Melia (2007) defend the view against objections from
Sider (2001). For discussion of Lewis's objection to the
relations-to-times view, see MacBride (2001) and Rodriguez-Pereyra
(2003); for a related objection see Browning (1988). Rychter (2008)
discusses what it is to have a property atemporally. Lowe (1987),
Johnston (1987) and Haslanger (1989b) all propose versions of
adverbialism. For discussion of these, see Lewis (1988; 2002), Lowe
(1988b) and Lombard (2003). Miller and Braddon-Mitchell (2007) defend
both adverbialism and relations-to-times against objections; see also
Bottani (2016). Rea (1998b) argues that consideration of change does
not favour perdurantism. For stage theory see Sider (2000; 2001,
section 4.6). Hawley (2001, chapter 1) also advocates stage theory,
and discusses most of the issues covered in this section. Alternative
accounts of change are mooted by Ehring (1997; 2001), Simons (2000a),
MacBride (2001), Parsons (2001), and Brower (2010). Klein (1999)
argues that neither endurance nor perdurance theories permit genuine
change; see also Meincke (2019). In various ways, Rychter (2009),
Hansson (2007), and Hofweber (2009) argue that there is no genuine
problem of change; Raven (2011) argues that there is, whilst Einheuser
(2012) gives a nuanced assessment. Eddon (2010a) argues that the
problem cannot give us purchase on which theory of persistence to
adopt.


## 4. Coincidence



We usually assume that two different things can't be in the same
place at the same time: how could there be room? But certain puzzle
cases challenge this assumption. These puzzles are of interest in
their own right, but they feature in this article because, as with the
problem of change, perdurantists have argued that believing in
temporal parts is the best way to solve the puzzles. And, as with the
problem of change, endurantists may reply that temporal parts
don't help, or that there is a perfectly good endurantist
alternative, or both.


### 4.1 Temporary Coincidence



In some puzzle cases it seems that two objects occupy the same place
at the same time, but not forever: one or both of them exist either
before or after the period of coincidence. For example, suppose you
take a lump of clay, and by moulding and shaping it create a statue,
which you place proudly on a plinth. What's on the plinth? Well,
the statue is. Is the original lump of clay also on the plinth? It
seems so: you didn't destroy or even damage the lump of clay
just by changing its shape. So are there are two statue-shaped things
on the plinth, a statue and a lump of clay? On the one hand it seems
daft to count these as two different objects. But on the other hand
they do seem different: the lump of clay is older than the statue, for
example, and perhaps it makes sense to describe the statue as
'well-made' or as 'yet another derivative bit of
art-as-therapy', while the lump of clay is neither well-made nor
derivative: it was just dug out of the garden. These differences
suggest that the lump of clay and the statue are two different things,
occupying the same place at the same time.



This argument is sometimes expressed using Leibniz's Law, the
principle which says that if objects differ in their properties, they
cannot be one and the same thing. Leibniz's Law should be
distinguished from the more controversial Principle of the Identity of
Indiscernibles, which says that if objects share all their properties,
they must be one and the same thing. (See the separate entry on the
 identity of indiscernibles.)



Similar examples of temporary coincidence can arise when objects gain
or lose parts. Tibbles the cat is made of the usual catty parts,
including a tail, and a tail-complement, i.e., all of Tibbles except
for her tail. A tail-complement is a slightly strange object, but
it's rather like a torso, i.e., all of an animal except for its
limbs and head. Tibbles has a whimsical owner, who names the
tail-complement 'Tib'. One eventful day, Tibbles loses her
tail in an accident: she shrinks to become exactly the same size and
shape as Tib. On the one hand it seems daft to count Tibbles and Tib
as two different objects after the accident. But on the other hand
they do seem different: Tibbles has been a cat for years, unlike Tib,
and Tibbles is her owner's favourite animal, while perhaps we
cannot say this of Tib. These differences suggest that, after the
accident, Tibbles and Tib are two different things occupying the same
place at the same time.



(Related problems about cats and their parts are dealt with in the
separate entry on the
 problem of the many.)



What have these puzzles about temporary coincidence got to do with
temporal parts? If we accept that statues, lumps of clay, cats, tails
and tail-complements all have temporal parts, then we can tell a
coherent story about these cases. This should tempt us to believe in
temporal parts, unless endurantists can come up with a good story of
their own. Let's look at the perdurantist and endurantist
stories in turn.



Central to the perdurantist account of temporary coincidence is the
claim that, while it is bizarre to think that two distinct objects
could entirely coincide, there is nothing bizarre about two objects
partially coinciding by sharing a part, and nothing bizarre about an
object partially coinciding with one of its own parts. Recall the
example of you and your conjoined twin. If you share a hand, there is
no puzzle about how you can both be in the same glove without jostling
for space: you and your twin partially coincide by sharing a part. And
think of your left foot: there is no mystery about how you and your
foot can both be in the same sock, nor about how you can be partially
in the same place as your own foot. According to perdurantists, cases
of temporary coincidence involve objects which partially overlap by
sharing temporal parts, or objects which partially overlap because one
is a temporal part of the other (we can think of this as a limiting
case of sharing parts).



Think of the lump of clay and the statue. Suppose you formed the lump
out of smaller bits on Monday, made it into a statue on Wednesday,
then smashed the thing to pieces on Sunday. According to
perdurantists, the lump of clay is a week-long four-dimensional
object, and the statue is a five-day-long four-dimensional object.
Indeed, the statue is a temporal part of the lump of clay, composed of
some of the instantaneous temporal parts which compose the lump. Now,
how many statue-shaped things are on the plinth on Thursday? Well, the
lump of clay and the statue both have a temporal part sitting on the
plinth on Thursday, so they're both partially on the plinth on
Thursday. But neither the lump nor the statue is wholly there on the
plinth on Thursday. This explains both our intuition that
there's only one object there (there's just the one
arty-looking temporal part at any given moment) and our intuition that
the statue and the lump are different objects with different
properties (they occupy different four-dimensional regions).



Much the same can be said for Tib and Tibbles. Tib and Tibbles are
both long-lasting four-dimensional objects, according to
perdurantists. Before the accident, at any given moment a temporal
part of Tib is a spatial part of a temporal part of Tibbles. After the
accident, Tib and Tibbles share temporal parts. But there's no
mystery as to how Tib and Tibbles can coincide after the accident yet
still be different things: neither the whole Tib nor the whole Tibbles
is there, just some of their shared temporal parts.



Objections to the perdurance account of temporary coincidence focus on
more general (alleged) difficulties for perdurantism; on whether the
account can generalise to cope with all coincidence problems (see
 section 4.2);
 and on whether it can explain why we are happy to call the statue but
not the lump 'well-made' or 'derivative'.
There are also specific objections to the perdurance account of cases
of temporary coincidence which involve people (see
 section 9
 for these). What can endurantists come up with instead?



One popular endurantist option is simply to accept that two different
objects can wholly occupy exactly the same location at the same time.
This view is sometimes called the 'standard account' of
coincidence. The relationship between wholly-coinciding objects is
often called 'constitution', and so the slogan of the
standard account is 'constitution is not identity'. The
lump of clay constitutes the statue, so they do not have to jostle for
space, but they are distinct objects, so they can differ in their age,
in whether they are derivative, and so on. (Beware: the
similar-sounding 'composition is not identity' usually
represents the quite different view that a whole is not identical to
its several parts.)



The examples we have seen so far involve coincidence between objects
of different kinds: a cat and a tail-complement, a statue and a lump
of clay. According to some versions of the standard account,
constitution is always a one-way relationship: the lump constitutes
the statue, but not vice versa. Accounts without this restriction can
be sympathetic to coincidence between objects of the same kind. This
may occur, for example, if objects of the same kind can
'merge' without losing their identity, or if what looks
like a single object can 'divide' into two of the same
kind (some versions of the 'ship of Theseus' problem have
this form). The most intriguing imagined cases of fusion and fission
involve people, and will be discussed briefly in
 section 9.
 (The claim that same-kind coincidence is impossible is sometimes
called 'Locke's thesis'.)



Opponents of the standard account make the following objections: it
requires just too many objects (a particular problem in vague cases,
see
 section 5);
 it entails that when a 1kg statue is constituted by a distinct 1kg
lump, the result ought to weigh 2kg; and, most seriously, it fails to
explain how two distinct objects, made of the same parts and matter,
arranged in the same way and at the same place and time, can be
distinct objects with different properties. How could all these facts
about the arrangement of parts fail to fix the facts about the
whole?



Defenders of the standard account make various responses. 
Regarding the 'too many objects' accusation, some point
out that perdurantists require even more objects when you count up all
the temporal parts, some attempt to establish principled limits on how
many objects are required, and others simply accept the
multitude.  After all, it's not so bad having all those
objects when you realise they don't all need separate locations.
The response to the objection about mass turns on an analogy with
ordinary parts and wholes: your various internal organs and limbs
weigh several kilos each, but we wouldn't expect these to show
up on the scales in addition to your total body mass, since you are
made of the same stuff as your organs and limbs. Likewise, supposedly,
although the lump and the statue are distinct 1kg objects, we
shouldn't expect these to show up separately on the scales,
since they are made of the same stuff.



Explanations of how coinciding objects can have different properties
vary with different versions of the standard account. Some claim that
coinciding objects share all their parts (and are parts of one
another). Others claim that, for example, the arm of the statue is not
part of the lump of clay, although there may be an arm-shaped lump of
clay which constitutes the statue-arm and is part of the bigger lump
of clay. But a couple of themes recur in defences of the standard
account: first, there is an attempt to shift the burden of proof. Why
*expect* all the properties of a composite object to be
determined by the identity, properties and interrelations of its
present parts? Second, there is the point that, although the standard
account entails that objects made of the same parts may differ, there
is no arbitrariness here. Not every object made of suitably-arranged
particles of clay is a lump of clay, for some are statues, but
whenever there are suitably-arranged particles of clay, there is a
lump of clay.



Those who find these explanations unsatisfactory and thereby reject
the standard account needn't become perdurantists, however, for
there are several less-popular endurantist accounts of temporary
coincidence. Perhaps identity can be temporary: the statue and the
lump are identical once the statue exists, although the lump was not
always identical to the statue; Tib and Tibbles begin as
non-identical, and become identical. This proposal requires us to
change our views of identity, and of the connection between identity
and sharing of properties. Or perhaps objects can be destroyed more
easily than we had realised: the lump of clay ceases to exist when the
statue is created (it is replaced by a new, statue-shaped lump of
clay, made from the same clay particles); the cat's
tail-complement ceases to exist when it is separated from the
tail.



Or perhaps we should be more restrictive about the kinds of object we
accept into our ontology. After all, a tail-complement seemed like a
dubious object from the beginning, and if there is no such thing as
Tib, we don't have to explain what relationship holds between
Tib and Tibbles (we may grandly deny that cats have 'arbitrary
undetached parts'). Similarly, perhaps it is a mistake to think
that there literally are such things as statues and lumps of clay, as
opposed to mere quantities of stuff or pluralities of particles.
Restrictive ontologies come in different strengths: accepting only
partless objects and living organisms; accepting only partless objects
and those composite objects which are 'greater than the sum of
their parts'; accepting only partless objects; accepting only
'stuff' or matter and not objects at all; accepting only
'proper' objects and not quantities of stuff. 
Difficulties here include reconciling such radical claims with our
everyday beliefs, and, for the more moderate versions, ensuring that
each and every possible case of coincidence really has been ruled
out.



Further discussion of these and other options can be found in the
separate entry on
 relative identity.


### 4.2 Permanent Coincidence



The cases discussed so far involve objects which seem to coincide for
a while, yet fail to coincide at other times at which at least one of
them exists. Perdurantists claim that temporarily-coincident objects
are not wholly coincident: their non-coincident parts lie in the past
or future. But other puzzle cases seem to involve
permanently-coincident objects: even perdurantists have to accept that
permanently-coinciding objects wholly coincide.



Suppose that, instead of first forming or digging up the lump of clay
then later moulding it into a statue, you make the two halves of the
statue separately, then create both statue and large lump in one fell
swoop, by sticking the halves together. Later, you petulantly smash
the thing into pieces, destroying statue and lump simultaneously.
Here, it seems that the lump of clay and the statue coincide at every
moment at which either exists, yet they seem to be distinct objects
because they differ in how they could have been: for example, the
statue could have been made of a different lump of clay, but the lump
could not. Talk of temporal parts doesn't help here: lump and
statue share all their temporal parts, and differ only in their modal
features (in how they could have been different).



Can perdurantists accept that the lump and statue are distinct,
coinciding objects? In principle, yes, but this would be strategically
unwise: accepting the possibility of complete coincidence without
identity leaves perdurantism with no advantage over the standard
endurantist account of coincidence. Perdurantists are better advised
to claim that the statue and the lump of clay are one and the same
object, then come up with some explanation of why they appear to have
different properties. We may say that the object in question could,
*qua* statue, have been made out of a different lump of clay,
but could not, *qua* lump, have been made out of a different
lump of clay. There are various ways of explaining what the
'*qua*' clauses are doing in this peculiar claim,
and perhaps the most popular explanation involves counterpart theory,
a controversial theory about our talk of possibilities. Objections
here turn either on problems for counterpart theory, or else on
whether a satisfactory theory of how we talk about actual things can
ever be compatible with this view.



Endurantists are in a happier position regarding permanent
coincidence: whatever solution they have adopted in response to
temporary coincidence will also handle permanent coincidence (although
adjustments are necessary in some cases).



**Suggested reading**: This is a large field, but Rea
(1995) provides a helpful overview, and the papers collected in Rea
(ed.) (1997) are a useful next step. Sider (2001, chapter 5) and
Hawley (2001, chapters 5 and 6) also survey this area, both from a
temporal-parts perspective. Korman (2015: chapter 11) and Sattig
(2015: chapters 3 and 5) provide more up-to-date entry points to the
debate. The standard account is advocated or discussed sympathetically
by Doepke (1982), Baker (1997), Fine (2000; 2003), Johnston (1992),
Robinson (1985), Levey (1997), Lowe (1983; 1997; 2003), Moyer (2006),
Oderberg (1996), Rea (1997), Simons (1985; 1986; 1987; 1997), Yablo
(1987), Thomson (1983; 1998), Paul (2006) and Wasserman (2002);
critics include Olson (1997), Heller (2000), Hughes (1997a; 1997b),
Lewis (1971), Noonan (1993) and Burke (1992). Gilmore (2007) argues
that endurance theorists can handle coincidence by paying attention to
the appropriate notion of spatiotemporal location; Eagle (2010a)
criticises this argument, and Gilmore (2010) responds, followed by
Eagle (2010b). McGrath (2007a) argues that temporal parts views suffer
the same difficulties as the standard account; Hawley (2008) discusses
this further, whilst Hawley (2005) explores related issues; see also
Donnelly (2016). Moyer (2009) argues that coincidence is neutral
between endurance and perdurance; in response, Eddon (2010) defends
perdurance; Rychter (2011) also defends perdurance here. Sattig (2008)
argues that perdurantists cannot combine coincidence with informative
identity criteria. Temporary identity is advocated by Baxter (1989)
and Gallois (1990; 1998). The claim that objects can be very easily
destroyed is advocated by Burke (1994a; 1994b; 1997a; 1997b) and Rea
(2000), and critically discussed by Carter (1997), Denkel (1995), Lowe
(1995b), Noonan (1999b), Olson (1997a), Zimmerman (1997) and Zammiello
(2001). Restrictive ontologies are discussed by Chisholm (1973), Elder
(1999), Merricks (2000; 2001), Olson (1996; 1997b), van Inwagen (1981;
1990b), and Zimmerman (1997; 1995); Sidelle (1998) explores a number
of interesting options, as does Needham (2010). Walters (2019) draws
connections with debates in mereology. It's hard to avoid
Wiggins (1980; 2001). The classic discussion of permanent coincidence
is Gibbard (1975). Temporal-parts accounts of permanent coincidence
include Noonan (1988; 1993; 1999a). Counterpart theory is advocated by
Lewis (1986, chapter 4). Magidor (2016) argues that the arguments
discussed in this section cannot settle the endurance-perdurance
debate. A more formal approach to problems concerning change of parts
can be found in the separate entry on
 mereology,
 especially in section 3.2; further discussion can also be found in
the separate entries on
 material constitution,
 on
 relative identity
 and on
 ordinary objects.


## 5. Vagueness



(The so-called 'argument from vagueness', sometimes
invoked in support of temporal parts, is discussed in
 Section 8
 below.)



Vagueness, or indeterminacy, seems to be a feature of our everyday
experience of persisting things, and it creates problems which,
according to temporal parts theorists, can best be solved by accepting
that things have temporal parts. As with the problems of change and of
coincidence, endurantists may criticise the temporal parts solution to
this problem, provide solutions of their own, or both.



Vagueness often occurs at the beginning and ending of existence. It is
notoriously controversial whether there is a precise moment at which
human people begin to exist, and if so when that moment is. But most
of us will have a grey area at the end of our existence, a few
seconds, a few minutes, or even longer during which we seem to be
neither clearly alive nor clearly dead. More mundanely, formation and
decay are gradual processes for many kinds of object, both natural and
artificial: think of a lake or haystack which gradually comes into
existence, or a building or a rock formation which slowly crumbles
away. Let's call this phenomenon 'fuzzy temporal
boundaries'.



Indeterminacy can also arise when objects intermingle in a way which
seems to leave it clear that they survive the process, but unclear
which object is which. Suppose you remove about half the parts from
the bicycle your uncle gave you, about half the parts from the bicycle
your aunt gave you, and switch them over. Afterwards, you have two
bicycles, each half-made of parts that used to be in the bicycle your
uncle gave you, and half-made of parts that used to be in the bicycle
your aunt gave you. Which post-repair bicycle is the one your uncle
gave you, and which the one your aunt gave you? There seems to be no
clear fact of the matter. Let's call this phenomenon
'radical disruption'.



In their bare essentials, the two types of indeterminacy are the same
(and it is possible to construct cases of intermediate types). In each
case, we are not sure how to pin down the career of an object. In
fuzzy-boundary cases, we don't know which of many overlapping
career paths an object follows (one which begins earlier, or later?);
in radical disruption cases, we don't know which of (at least)
two intersecting career paths an object follows.



Typical temporal parts theorists argue that such indeterminacy results
from a mismatch between human language and temporarily-coincident
objects (of the sort discussed in
 section 4.1).
 Take a building which slowly crumbles away to nothing. According to
most temporal parts theorists, there are very many
'nested' four-dimensional objects involved in this
process, some of which end before others do. We are unclear about when
the building ceases to exist because our use of language just
doesn't determine which of these many four-dimensional objects
is 'the building'.



Likewise, in radical disruption cases like that of the bicycles,
perdurantists typically recognise a number of different
temporarily-coincident four-dimensional objects. Suppose the bicycle
your uncle gave you starts off made of parts *A* and parts
*B*, and the bicycle your aunt gave you starts off made of parts
*C* and parts *D*. After the switch-around, you have a
bicycle made of parts *A* and parts *C*, and a bicycle made
of parts *B* and parts *D*. Perdurantists recognise (at
least) the following four-dimensional objects:


1. something that begins with *A* and *B*, then continues
with *A* and *C*;
2. something that begins with *A* and *B*, then continues
with *B* and *D*;
3. something that begins with *C* and *D*, then continues
with *A* and *C*;
4. something that begins with *C* and *D*, then continues
with *B* and *D*.



Before the switch-around, objects (1) and (2) temporarily coincide, in
the place where you keep the bicycle your uncle gave you, and objects
(3) and (4) temporarily coincide, in the place where you keep the
bicycle your aunt gave you. After the switch-around, objects (1) and
(3) coincide, and objects (2) and (4) coincide. When we initially
talked about 'the bicycle your uncle gave you', there was
no fact of the matter as to whether we were talking about (1) or (2).
And (1) and (2) end up in different places after the switch-around,
which is why we don't know what to say about the final location
of the bicycle your uncle gave you.



From a typical perdurantist perspective, apparent indeterminacy in
persistence arises from our fumbling failures to deal with the
multitude of precise four-dimensional objects around us. This account
of indeterminacy is not a consequence of perdurance theory alone: as
well as the claim that ordinary things have temporal parts, it
involves the claim that there are many more persisting things than we
recognise in ordinary life. It is possible to believe in temporal
parts without accepting this second claim but, as we will see in
 section 8,
 most perdurantists do accept the second claim. The typical
perdurantist story also involves a theory of vagueness which traces it
to our use of language; it is not compulsory for perdurantists to
think about vagueness in this way, but many do adopt this
'linguistic' or 'semantic' approach to
vagueness.



Objections to the typical temporal parts account of indeterminacy in
persistence turn on the sheer number of temporarily coincident objects
required to make the story work; or on independent objections to the
language-based account of vagueness (see the separate entry on
 vagueness);
 or on particular objections to telling such a story about
indeterminacy involving people (see
 section 9).



What can endurantists say about indeterminacy in persistence? 
One option is to mimic the perdurantist temporary-coincidence account,
but without the temporal parts. That's to say, endurantists
could claim that there are very many wholly-present coincident
building-like objects where the building stands, each of which ends at
a slightly different moment from all the others. This multiplicity,
together with our loose talk, accounts for the unclarity in when the
building ceases to exist. Likewise, endurantists could recognise
objects (1)-(4), just as perdurantists do, but claim that each
is wholly present whenever it exists. This strategy is unpopular,
because temporarily-coincident enduring objects can seem worse than
temporarily-coincident perduring objects: temporarily-coincident
endurers are wholly coincident, unlike temporarily-coincident
perdurers. Endurantists may want to recognise some temporarily
coinciding things (see
 section 4.1),
 yet stop short of the multitudes which would be required to explain
fuzzy boundaries.



A second endurantist option is to accept that sometimes there just are
no precise facts of the matter about the temporal boundaries and
careers of objects, because the world itself is sometimes
indeterminate. This is the claim that there can be worldly
('ontic', or 'metaphysical') vagueness. (A
worldly-vagueness option is also available to perdurantists, and might
be attractive to those who want to avoid commitment to a multitude of
temporarily-coincident four-dimensional objects. But typical
perdurantists adopt the
temporary-coincidence-plus-linguistic-vagueness account outlined
above.)



Many people recoil at the thought that the world itself could be vague
or indeterminate, perhaps because they believe that indeterminacy must
be a result of mismatch between what is represented (the world), and
what does the representing (thought or language). Even those who
don't mind a bit of worldly vagueness may have reason to reject
worldly vagueness in persistence, because this amounts to worldly
vagueness in identity: it's vague whether the original bicycle
your uncle gave you is identical with the bicycle you now ride to
work. Worldly vagueness in identity is thought to be especially
problematic, because all identity is self-identity, and it's
hard to see how there could be any vagueness in self-identity.



Third, endurantists could claim that we speak precisely, that there
always are determinate facts of the matter about the identity,
existence and careers of objects, but it's just that sometimes
we can't tell what these facts are. (This involves an
'epistemicist' account of vagueness.) This claim could be
developed in one of two ways. In the case of the crumbling building,
for example, endurantists could claim that there is a single
building-shaped object with an unknown final moment. Or they could
claim that there are very many temporarily-coincident building-like
objects, each with a different final moment, that we refer to just one
of these when we say 'the building' but we do not know
which. (Again, perdurantists may adopt one of these epistemicist
strategies, but typically do not.)



Objections here may turn on problems for the epistemicist view of
vagueness in general; on the oddity of insisting that, for example,
there is an exact number of molecules which a building can lose before
it stops existing (on the first version of the view); or on objections
to multitudinous temporary coincidents (on the second version of the
view).



Finally, endurantists could adopt a restricted ontology, as some do in
response to temporary coincidence. If there aren't really any
such things as bicycles, buildings or lakes, just particles moving
around and interacting, then there are no issues to resolve about the
careers and identities of bicycles, buildings or lakes. As before, the
main difficulty here is in reconciling our everyday beliefs with a
sufficiently restricted ontology: after all, people and even
fundamental particles seem sometimes to be indeterminate. (Again, it
is open to perdurantists to adopt a restricted ontology, but typically
they do not.)



In summary then, both perdurantists and endurantists can adopt various
responses to apparent vagueness in persistence; which they choose
depends in part upon their more general views about the nature of
vagueness. Typical perdurantists posit temporary coincidence between
objects, and a failure on our part to talk determinately about any one
of these. Endurantists could make the same claim, but typically do
not. A temporary-coincidence view could instead be paired with an
epistemic account of vagueness, and our failure to know which object
we're talking about. Alternatively, vagueness may be either
attributed to objects themselves, and their failure to have
determinate careers, or else to our failure to know what careers they
have. A radical option is to deny that any genuine object is involved
(thus restricting ontology). In different ways, all of these options
are available to perdurantists and endurantists alike, but the costs
and benefits differ.



**Suggested Reading**: For a way into the general debate
about vagueness, try Keefe and Smith (eds.) (1997), and the separate
entry on
 vagueness.
 Stalnaker (1988) is a particularly nice discussion of vague
persistence.  Issues discussed in this section are covered in
more detail by Hawley (2001, chapter 4). Temporal parts accounts of
vague persistence are defended by Sider (2001, section 4.9) (Sider
presents a distinctive argument which will be discussed in
 section 8)
 and Heller (2000); these are criticised by Lowe (2005). Romerales
(2008) compares perdurance and stage theory on this front. Endurantist
worldly vagueness is defended by van Inwagen (1988; 1990b) and
discussed by Cowles (1994), Garrett (1991), and Hirsch (1999). The
classic argument against worldly vagueness in identity can be found in
Evans (1978) and Salmon (1981). Heller (1996) objects to worldly
vagueness of all kinds. Hudson (2000) defends an epistemicist temporal
parts theory. Williamson (1994, chapter 9) discusses an epistemicist
account of vague objects. Haslanger (1994) considers multitudes of
coinciding endurers, and Sosa (1987; 1999) looks kindly upon the idea,
as does Kurtsal Steen (2010). Further discussion can also be found in
the separate entries on
 ordinary objects
 and on
 identity.



## 6. Time and Temporal Parts



As well as disagreeing about whether persisting things have temporal
parts, philosophers disagree about the nature of time itself. Does
time flow? Are the past and the future as real as the present?
Philosophers also disagree about the connection between these
disagreements: does taking a certain view about the nature of time
commit you to any particular view about the existence of temporal
parts? What about vice versa?



You can find a more detailed discussion of the nature of time
elsewhere in this encyclopedia (see the separate entry on
 time).
 The most relevant debate for our purposes turns on whether distant
times are like distant places. For example, people, objects and places
in Antarctica exist, even though they are far away (if you are reading
this in Antarctica, please adjust the example). It can be difficult to
communicate with distant places, and they may be less important to us
than our immediate surroundings, but they exist nevertheless. What
about eighteenth-century people, objects and times? Does David Hume
exist, despite being far away in time? Or is it more reasonable to say
that Hume used to exist, but now does not exist?  Eternalists
believe that past and future things exist, just like present things.
Presentists, in contrast, believe that distant times are not like
distant places: things in distant places exist, but things at distant
times do not. According to the intermediate 'growing
universe' theory, past and present things exist, but future
things do not.



What connection is there between the eternalism-presentism debate, and
the debate about temporal parts? It's natural to suppose that
presentists should be endurantists, claiming that things are wholly
present whenever they exist. If you don't believe in either the
past or the future, there's nowhere and nowhen for any
'missing' parts to be. This argument from presentism to
endurantism needs some work, however. Presentists think that only the
present exists, but they're happy for us to talk about the
causes of the First World War, about next week's seminar, or
about David Hume. Although Hume does not exist, it's right to
say that David Hume wrote *An Enquiry Concerning Human
Understanding*, and wrong to say that David Hume wrote *The
Feminine Mystique*. Presentists worth their salt provide a story
about what makes certain statements about the past and the future
right, and others wrong. Can presentists claim that, although past and
future temporal parts of the banana do not exist, the banana did have
temporal parts in the past, and will have other temporal parts in the
future? This takes us back to the question of how to define
'temporal part' (see
 section 2),
 and it raises a methodological issue: should 'temporal
part' be defined in such a way that presentists can believe in
temporal parts, or not?



Well, perhaps presentists should reject temporal parts and so be
endurantists. Must eternalists, who believe in the past and the
future, accept temporal parts and so be perdurantists? Or are
eternalists free to choose between endurantism and perdurantism? 
One reason to think that eternalists should believe in temporal parts
is that without them they may have difficulty explaining how things
change. How can you both know about theories of persistence (tomorrow)
and fail to know about theories of persistence (yesterday)?
Presentists don't seem to have a problem here: your failure
yesterday to know about theories of persistence just doesn't
exist. But eternalists are committed to the existence of your two
apparently-conflicting states. If eternalists accept temporal parts,
they have a neat explanation at hand: your yesterday temporal part
doesn't know about theories of persistence, but your tomorrow
part does know about theories of persistence. But if eternalists
reject temporal parts, then the two apparently-conflicting states are
states of one and the same thing (you), and it's not obvious how
to resolve the conflict. So perhaps eternalists should believe in
temporal parts, and, conversely, those who reject temporal parts
should be presentists. This argument succeeds only if eternalists
really can't explain change without believing in temporal parts
(see
 section 3).



If we could establish that things have temporal parts if and only if
the past and the future exist, this would raise a number of issues.
First, should we attempt to establish a theory of persistence, and
then let this dictate our theory of time? Or should we start with the
theory of time? (See
 section 7
 for an argument from physics against presentism and thus, perhaps,
against endurantism.) Or can we somehow establish both at once?
Second, tying the dispute about persistence to the dispute about time
makes trouble for anyone who thinks that one of the disputes is
genuine but the other is merely a verbal disagreement. And, third,
since presentism and eternalism seem clearly to be incompatible, if
each compels a different account of persistence, then there
can't be 'mixed' worlds in which some things perdure
and others endure (a peculiar consequence, since most endurantists
think that processes perdure).



Attempts to connect debates about time with debates about persistence
have focused on the disagreement between eternalists and presentists.
But there is another dispute about time which may have some bearing on
whether things have temporal parts. Eternalists agree that past,
present and future times all exist, but they disagree amongst
themselves as to whether there are important ontological differences
between the three categories. Advocates of the 'A-theory'
of time argue that the flow of time pushes events from one ontological
status to another (presentists are usually taken to be A-theorists
too). But advocates of the 'B-theory' of time think that
there is no important ontological difference between past, present and
future, and that there is no such thing as 'the flow of
time'. There is some tendency to think that the A-theory is more
hospitable to endurantism, and the B-theory more hospitable to
perdurantism, but there is no consensus on this matter.



Finally, considerations about the possibility of time-travel have been
used to argue both for and against the existence of temporal parts;
these arguments connect with debate about whether we should approach
persistence as an issue about parthood and/or as an issue about
location. For more on this debate, see section 4.2 of the separate
entry on
 Time Travel,
 and section 6.3.5 of the separate entry on
 Location and Mereology.



**Suggested Reading**: Earlier discussions of temporal
parts paid close attention to analogies and disanalogies between space
and time: e.g. Taylor (1955), Meiland (1966); Butterfield (1985)
reflects on these. Lombard (1999) and Brogaard (2000) argue that
presentism is compatible with perdurantism, while Merricks (1995) and
Hestevold and Carter (2002) argue that presentism compels endurantism.
Benovsky (2009) takes an even-handed approach. Merricks (1995) and
Hinchliff (1996) argue that eternalism rules out endurantism, because
of the problem of change; see the suggested reading at the end of
 section 3
 for endurance-friendly eternalist accounts of change. Lowe (1998a)
argues for a connection between theories of time and theories of
persistence. Markosian (1994) attempts to formulate the
endurance-perdurance debate in a way which is independent of the
eternalism/presentism debate. Mellor (1981; 1998) and Johnston (1987)
combine eternalism and endurantism, whilst Ingthorsson (2009) opposes
this combination, and Pezet (2019) favours endurance with presentism.
Tallant (2018) argues that presentism is incompatible with each of
perdurantism, endurantism, and stage theory; responses include Baron
(2019), Noonan (2019), Iaquinto (2019), and Hochstetter and Hess
(2020). For discussion of the relationship between the A/B-theory
debate and the debate about persistence, see Butterfield (1985),
Oaklander (1992), Wilson (1955), and Carter and Hestevold (1994).
Parsons (2005) highlights a semantic problem for B-theory
perdurantists. Barker and Dowe (2003) criticise endurantism by drawing
on rival theories of time; McDaniel (2003) and Beebee and Rush (2003)
respond, provoking Barker and Dowe (2005); see also Benovsky (2009a).
Following Sider (2001), Effingham and Robson (2007) argue that
endurantism cannot account for the possibility of time travel, as does
Simon (2005), whilst Miller (2006a) defends endurantism; Gilmore
(2007) and Effingham (2011a) argue that time travel is a problem for
perdurantism. See also Effingham (2010) and Daniels (2014). Wasserman
(2017: chapter 6) sets this discussion in the context of wider debates
about time travel; Proetti and Smid (2019) are sceptical about time
travel arguments here. See also Mooney (2019a, 2019b), Valaris and
Michael (2015). Gilmore et al (2016) consider other connections
between the metaphysics of time and debates about persistence.


## 7. Special Relativity and Temporal Parts



Didn't Einstein show that space and time are basically the same
thing? It's true that Einstein's two theories of
relativity radically altered our scientific picture of space and time,
although it is more controversial what consequences the theories have
for metaphysics. (See section 3 of the separate entry on
 being and becoming in modern physics
 for more detail on this issue.) It is the Special Theory of
Relativity (STR) which has had most impact on the debate about
temporal parts: three quite different arguments have been proposed,
each of which purports to show that STR lends support to the
perdurantist claim that things have temporal parts.



For our purposes, the key feature of STR is its claim that, for many
pairs of events, there is no absolute fact of the matter as to which
event, if either, happened first, or whether both occurred at the same
time. The question of precedence has different answers according to
different frames of reference, and there are no grounds for selecting
any single frame of reference as the one which gives the
'real' answer. This means that, for many events, there is
no absolute fact of the matter as to whether they are occurring in the
present, in the past or in the future. (If they were occurring now,
they'd be occurring simultaneously with your reading this
sentence, but there's no absolute fact of the matter about this
simultaneity issue.)



A first argument from STR to perdurantism goes as follows: STR shows
space to be much like time, objects extend in space by having spatial
parts, so objects persist through time by having temporal parts. 
But this argument is weak: although STR does show space to be like
time in some respects, the theory does still differentiate between
spatial and temporal dimensions. Even if it did not, we would need
some further reason to believe that persistence must be just like
spatial extension.



A second argument from STR to perdurantism proceeds via the debate
about time (see
 section 6).
 According to STR, for many events there is no absolute fact of the
matter as to whether those events are simultaneous with now.
That's to say, at any moment, there is no absolute fact of the
matter as to which events are present. This makes life difficult for
presentists, who claim that only present events exist. If STR thereby
rules out presentism, and if endurantism requires presentism in order
to explain change (see
 section 3),
 then STR rules out endurantism: things have temporal parts. But not
all endurantists agree that they must be presentists, and not all
presentists agree that their view is undermined by STR.



A third argument from STR to perdurantism does not rely on the claim
that STR is out-and-out incompatible with endurantism. Instead, the
claim is that STR highlights a phenomenon which can better be
explained by perdurantists than by endurantists. To understand the
phenomenon, imagine a three-dimensional cylindrical chocolate cake
which you want to cut up into two-dimensional pieces (you've got
a lot of friends). If you cut only at right angles to the length of
the cake, then each piece will be circular. But if you cut at a
different angle, then each piece will be oval. The cylindrical shape
of the cake explains the shapes of the various pieces produced by
cutting at various angles.



Now imagine a four-dimensional object, cut into three-dimensional
timeslices. In a non-relativistic world, there's only one way to
do this, because there's only one way to divide up events into
groups of simultaneous events: it's like cutting the cake at
right-angles. But, by relativising simultaneity to reference frames,
STR gives us lots of different ways to cut the four-dimensional object
into three-dimensional slices, just as there are lots of different
angles at which to cut the cake. The shape of the three-dimensional
slices you get by cutting in different ways, from the perspective of
different reference frames, can all be explained by the shape of the
four-dimensional object you're cutting up.



Endurantists don't think there is any four-dimensional object to
do this explaining job. There are only the three-dimensional slices,
which are just the single, persisting three-dimensional object (each
slice is that object, at a different time). STR tells us that the
persisting thing has different three-dimensional shapes with respect
to different reference frames. The different shapes in different
reference frames are correlated, but according to the endurance
theorist there is no 'underlying' four-dimensional object
to explain these correlations. Endurantists may respond by questioning
the need for explanation here.



In short, while the general ambience of modern physics may seem more
friendly to perdurance than to endurance theory, it is remarkably
difficult to devise any conclusive argument from physics to temporal
parts.



More recent concerns have focused on how the various theories of
persistence can be formulated within a relativistic framework: can we
sustain a distinction between temporal and spatial parts, or should we
think in terms of spatiotemporal parts? 



**Suggested Reading**: Balashov (2011) is an advanced
overview of these issues, Hawley (2009) is much more introductory, and
Gilmore (2008) is a very useful middle ground; Balashov (2008) is a
more technical paper which attempts precise definitions of the rival
theories of persistence against a relativistic backdrop. Broad (1927,
chapter 2) is an early discussion of the links between perdurantism
and STR; see also Quine (1960, p. 172); Rea (1998b, section 1.1)
responds. Mellor (1981) argues that STR is compatible with
endurantism, while Mellor (1980) argues that the General Theory of
Relativity is also compatible with endurantism, contrary to Nerlich
(1979). Balashov (1999; 2000a) argues that perdurantism can better
explain relativistic phenomena. Balashov (2002) argues that STR
favours perdurantism over stage theory; Balashov (2000b) raises
further problems for endurantism, while Gilmore (2002) responds,
followed by Balashov (2005a); Gilmore (2006) develops a relativistic
version of endurance theory. Hales and Johnson (2003) weigh in against
endurance theory; see also Hales and Johnson (2007), and Schmidt
(2015). Further installments include Balashov (2009), Sattig (2006),
Miller (2004), Harrington (2005), Gibson and Pooley (2006). See also
Hudson (2005) and Balashov (2010) for book-length treatments of this
and related topics. McCall and Lowe (2003) argue for an STR-friendly
notion of the flow of time. Davidson (2013). Balashov (2014), and
Calosi (2015) exchange arguments about four-dimensional shapes in
relativistic contexts. Pashby (2013) argues that quantum objects lack
temporal parts, see also Pashby (2016); Gomori and Szabo (2019)
discuss the persistence of the electromagnetic field .


## 8. Relations Between Temporal Parts



Suppose we accept that ordinary persisting things have temporal parts.
What can we say about the relations which hold between those temporal
parts? For example: must the different temporal parts of a single
object lie along a smooth trajectory through space and time, or can
objects jump about instantaneously, or pop out of and back into
existence? Similar questions also arise for endurantists, and not all
perdurantists answer these questions in the same way, but for the most
part perdurantists do agree on a particular type of answer to these
questions. This is because perdurantism is very often held in
conjunction with two other doctrines: the doctrine of universalism,
and that of Humean Supervenience.



Universalism is the view that any collection of objects whatsoever has
a sum, an object they compose. Thinking just of the present moment,
this entails that there is an object composed right now of your left
ear, the front fork of your bicycle, and the Louvre. If you think
about all times, and imagine that ordinary things are made of
instantaneous temporal parts, then you can see that universalist
perdurantists believe in quite an extraordinary number of objects. Any
combination of temporal parts of any objects from any times, no matter
how scattered and disparate, composes an object. So there is an object
made of your maternal grandmother's wedding ring on the day she
was married, your right ear yesterday and a brief temporal part of an
electron in the year 2525. (Universalism is sometimes called
'unrestricted mereology', 'unrestricted
composition' or 'unrestricted fusion';
'fusion' means 'sum'. For more on
universalism, see the separate entry on
 mereology,
 especially section 4.2.)



There are a number of reasons why perdurantists typically adopt
universalism  First, the claim that there is a large number of
nested four-dimensional objects is central to the most common
perdurantist account of vagueness in persistence (see
 section 5).
 The building doesn't seem to have a clear last moment of
existence because there are very many coinciding building-shaped
four-dimensional objects, each of which ends at a slightly different
moment, and it is vague which of these is 'the building'.
Whether its role in this story is a reason to accept universalism
depends upon the strength or weakness of alternative accounts of
vagueness in persistence.



Second, it often seems that whether or not an object survives a
certain kind of change is in some sense conventional, or up to us.
Many believe that we set the standards for how many repairs you can
make to your bicycle without destroying it, and that whether or not a
person can survive massive memory loss is partly a matter of what we
mean by 'person'. How things persist seems sometimes to be
a matter of what kind of classifications we choose to use. A radical
version of this suggests that physical objects come into and out of
existence when we decide they do. This sounds mysterious: how could we
have such powers? But the combination of universalism and perdurantism
permits a less radical version of the view: there are lots of
four-dimensional objects which share temporal parts with the wheeled
thing in your bike shed, and it's up to us which one of those
counts as a 'bicycle'. Similarly, perhaps it's up to
us which of the multitude of four-dimensional objects count as
'people'. 



Third, perdurantists who reject universalism seem committed to giving
an account of the difference between collections of temporal parts
which have a sum, and collections which do not. But such accounts seem
to permit borderline cases, in which it's not clear whether a
certain collection has a sum. And borderline cases look like cases in
which it is not clear whether a certain object (the sum of those
parts) exists or not. And many find such vagueness in existence
unacceptable. Objections to this argument turn on whether
non-universalists really have to give such an account, and on whether
vague existence really is unacceptable.



This third type of argument for universalism has also been used to
argue directly for the existence of temporal parts. Roughly speaking,
instead of asking which temporal parts have a sum, we ask which
matter-filled regions exactly contain objects. Unless we agree that
they *all* do, we will get into trouble with borderline cases,
as in the previous paragraph. But if every matter-filled region
exactly contains an object, then even three-dimensional matter-filled
regions exactly contain objects. So the world is full of instantaneous
objects: these look very like temporal parts. This argument is now
often known as the 'argument from vagueness'. Objections
here include those mentioned in the previous paragraph; we might also
question whether the instantaneous objects are really temporal
parts.



However they argue for their position, perdurantists who are also
universalists have an easy answer to some questions about what paths
objects may take through space-time: *any* series of
object-stages composes an object. It is certainly interesting to ask
which of those objects are bicycles, or ships, or people, but these
now look like questions about the classification of objects, rather
than questions about persistence.



The other doctrine which usually goes along with perdurantism is
Humean Supervenience. This is the claim that, roughly speaking, facts
about which intrinsic properties are instantiated at which points
determine all the facts there are. There are no irreducibly holistic
facts. In conjunction with perdurantism, this entails that all the
facts about a given persisting object supervene upon intrinsic facts
about its briefest temporal parts. That's to say, if you fix
what's happening at each moment, you've fixed everything.
This sounds pretty plausible, but it turns out that it's rather
difficult to reduce facts about motion, for example, to suitable
moment-by-moment facts.



There are various responses to this difficulty. Endurantists are not
usually tempted by Humean Supervenience, since they are committed to
facts about identity between objects wholly existing at different
times, and these identity facts are not easily reducible to
moment-by-moment facts. So some take the difficulty for Humean
Supervenience to be a reason for adopting endurantism. Some
perdurantists stick with perdurantism, but reject Humean
Supervenience. Instead, they accept that some facts about persisting
objects cannot be reduced to facts about their briefest temporal
parts; they may accept, for example, that causal relations between
earlier and later parts are irreducible in this way. Finally, some
perdurantists insist that the supposed facts which seem to cause
problems for Humean Supervenience are not real facts after all.



**Suggested Reading**: Lewis (1986a, pp. 212-3),
Heller (1990, section 2.9), Jubien (1993, section 2.2), Quine (1981,
chapter 1), Rea (1998a) and Hudson (2000) argue for universalism; van
Inwagen (1990b, section 8), Markosian (1998), Merricks (2001) and
Varzi (2003) object in various ways. Balashov (2007a) discusses
universalism and stage theory; Campdelacreu (2010) responds. Sosa
(1999) investigates the options for endurantist universalism, whilst
Miller (2006) develops an endurantist 'universalism' based
on constitution rather than parthood; see also Inman (2014). Sider
(1997; 2001, section 4.9) develops the 'argument from
vagueness' via universalism to temporal parts; Koslicki (2003)
is critical, while Sider (2003a) responds. Further discussions of
Sider's argument include Balashov (2005), Nolan (2006),
Markosian (2004), Sider (2004), Miller (2005a), Varzi (2005), Noonan
(2010), Magidor (2015) and Eagle (2016b). Korman (2010) provides an
overview of this debate, with further references. Hirsch (1982) is an
extensive, rewarding discussion of criteria of persistence. Humean
Supervenience is articulated by Lewis (1986b, pp. ix-x), and discussed
by Loewer (1996). The problem about motion is raised by Armstrong
(1980), and addressed by Robinson (1989) Hawley (1999; 2001, chapter
3), Zimmerman (1998b; 1999), Callender (2001), Sider (2001, section
6.5), Lewis (1999), Teller (2002) and Butterfield (2006), while
Jaskolla (2017) makes intriguing connections between this debate and
panpsychism. Butterfield (2005) raises many interesting connections
between the physics of motion and the metaphysics of persistence, see
also Pashby (2016). Balashov (2003a, 2003b, 2010), Hudson (2002,
2003), Effingham (2011) and Torre (2015) discuss issues about
restricted composition and laws of nature. Haslanger (1994) discusses
the connection between endurance and Humean Supervenience; Hawley
(2015) discusses links between persistence, temporary intrinsics and
Humean Supervenience in Lewis's work. Oakes (2004) raises causal
difficulties for perdurantism without relying on HS. Magidor (2016)
argues that much of the debate around perdurance and endurance looks
very different when we notice implicit assumptions about universalism;
see also Miller (2008) and Varzi (2007). Della Rocca (2011) argues
that endurantists must adopt an implausible kind of anti-reductionism
about persistence; Baker (2013) responds.


## 9. Do People have Temporal Parts? And Other Special Cases.



Issues about the persistence of people are the subject of an entire
encyclopedia article in their own right (see the separate entry on
 personal identity),
 but it is worth highlighting points where the arguments discussed in
earlier sections have special consequences for personal survival.
People have various distinctive features: we have moral status, we
have mental properties like reasoning and being conscious, and we are
associated in an intimate but somewhat puzzling way with living
organisms.  Moreover, most of us seem to have a special concern
for our own future, and are willing to limit current pleasures like
smoking, shopping, and not writing encyclopedia articles, because we
believe that sacrifices made now will benefit us in the future. We
also feel a distinctive kind of pride or shame about our own past
actions, and are bound by our own past promises but not by those of
other people.



Is there room for these distinctive features within the different
theories of persistence? It has been suggested that only endurantists
can justify our willingness to make sacrifices for our future selves,
to act upon the plans formulated by our past selves, and to rely upon
the evidence gathered by our past selves . The idea is that these
activities make sense only if a present person is identical to her
past and future selves. Perdurantists may respond in one of two ways.
First, they may argue that it is the whole, identical,
four-dimensional person who makes sacrifices, acts upon plans and
reasons from evidence, via the activities of her temporal parts.
Alternatively, they may accept that it is short-lived temporal parts
which act, sacrifice and reason, but that past- and future-regarding
actions can be justified by the intimate relations between distinct
temporal parts of the same person. Stage theorists must take this
second route, for they claim that the person just is a brief stage,
who takes responsibility for the actions of her past counterparts, and
acts to benefit her future counterparts.



There are a number of issues about coincidence involving people. For
example, it seems that we human people at least coincide with human
organisms. You occupy the same location as a human organism right now,
but it seems that you differ in various ways: the organism may have
existed since conception, and will go on until biological death, but
some believe that the person does not come into existence until the
organism is relatively well-developed, and that the person may cease
to exist before biological death, by entering a persistent vegetative
state. You also seem to differ from the organism regarding
what's possible: perhaps you could have been a robot, or a
disembodied intelligence, whereas the organism could not.



Certain puzzle cases also seem to suggest that a person might divide
into two: suppose that, as a result of philosophical confusion on the
hospital ethics committee, a doctor is permitted to remove the two
halves of your brain and implant them into two different (brainless)
bodies. On one understanding of this process, each of the resulting
people has a good claim to be you. Is this a reason to think that two
coincident people were walking around together before the operation,
and that they have only now been separated?



Moreover, it seems that people are prone to indeterminacy, just like
crumbling buildings and bicycles: some people have gradual endings,
and sometimes, in stories at least, a person can undergo such a
traumatic change that it's not clear whether the same person
exists after the change.



We saw a number of ways of dealing with coincidence and indeterminacy
more generally, in
 section 4
 and
 section 5.
 But any talk of either partial or total coincidence involving people
can seem problematic, because of concerns about the use of
first-person pronouns (who does your 'I' refer to before
your brain-splitting operation, if there are two of you?), and about
multiplying conscious entities (could two people have literally the
same headache? if you merely coincide with a human organism, are you
sure it's you who has the headache, and not the organism?).
It's not clear, however, whether we should revise our theories
of persistence as a consequence of these problems, or whether we
should revise our ideas about people. This 'too many
thinkers' problem is discussed in more detail in the entry on
 personal identity.



The 'too many thinkers' problem looms even if we just
consider two entities, the person and the organism, but it
proliferates if we adopt a combination of perdurantism and
universalism (as discussed in
 section 8).
 On such a view, there seem to be a multitude of person-like entities
sitting in your chair right now, each with slightly different
start-dates and end-dates. Perdurantists may argue that only the
longest-lived of these is really a person, and that the others are
mere temporal parts of a person, but opponents resist this move.



People are especially interesting, but metaphysical questions about
persistence have been raised for objects of various other kinds,
including musical works, social entities such as institutions or
groups of people, and biological species. It is often controversial
what sort of entities these are - material objects, abstract
types, processes, sets? - and so it is also controversial how
far the arguments discussed above, which focus on material objects,
are relevant to these special cases. Useful articles elsewhere in this
Encyclopedia include
 Philosophy of Music,
 Philosophy of Theater,
 Biological Individuals,
 and
 Social Ontology.



Finally, this article has focused on debates about temporal parts
within philosophy, with a dash of physics. However temporal parts are
also significant within applied ontology, where they may feature
within the conceptual schemes adopted by computer scientists,
biologists and others to represent information systematically.



**Suggested Reading**: There is a huge literature on
personal identity, but everyone should read Williams (1973) and Parfit
(1971; then 1984 part 3 (at least)). Work on people which is informed
by the broader debate about persistence includes Lowe (1996), Olson
(1997; 2007), Merricks (2001), Baker (2000), Hudson (2001), Noonan
(2003b), Tappenden (2011), Langford (2016), Oyowe (2016). Lewis (1976)
and Hudson (1999) provide perdurantist accounts of people, while
Merricks (1999b) advocates endurantism, and Brueckner (2009) responds
to Merricks; Patrone (2017) advocates stage theory. Haslanger (1992)
argues that rational enquirers must endure; Rosenkrantz (2005) argues
from self-knowledge to endurance; Prosser (2006) uses the nature of
experience to explain away the appeal of endurantism in general;
Parsons (2015) argues from the nature of experience to stage theory,
see also Smith (2010); Brink (1997) discusses self-concern in a
perdurantist framework; Broome (1991 chapter 11) discusses connections
between theories of persistence and utilitarianism; Braddon-Mitchell
and West (2001) argue that stages are primary. Other questions of
ethics and self-concern are addressed by Olson (2010), Tognazzini
(2010), Taylor (2013), Miller (2014, 2015), Mullins (2014), and Briggs
and Nolan (2015). Duncan (2015) argues from the temporal extendedness
of thought to the falsity of certain views about personal persistence.
Dietz (2020) argues that temporal parts can be agents, whilst
Hochstetter (2015) argues that stages cannot act. Rimmel (2018) argues
that tensed belief creates difficulties for perdurantists. Hedden
(2015) challenges many standard assumptions about the connection
between personal persistence and rationality. Special concerns about
coincidence involving people, including 'too many
thinkers' are discussed by Noonan (1999a), Merricks (2003),
Olson (1997a), Shoemaker (1999), Sider (2003b), Sutton (2014),
Johnston (2016, 2017), Kovacs (2016, 2019), Kaiserman (2019), Eklund
(2019), and Longenecker (2019). Burke (1997b), Ehring (1995), Heller
(2000), Roache (2010), Wasserman (2005) and Demarest (2016) are also
relevant. 



Dodd (2004), Thomasson (2004), Caplan and Matheson (2006), Tillman
(2011), Aliyev (2017), Moruzzi (2018), Alward (2019), Friedell (2020)
discuss the persistence of musical works. Slater and Varzi (2007),
Jansen (2008), Hansson Wahlberg (2014a), Epstein (2015 ch.12), Hawley
(2017), Faller (2019), Hansson Wahlberg (2019), and Wilhelm (2020)
discuss the persistence of social entities. Merkouris (2014) discusses
the persistence of legal treaties. Reydon (2008) discusses biological
species. Nicholson and Dupre eds. (2018) is an open-access collection
including many interesting articles about the persistence and broader
metaphysics of biological entities, from a 'process'
perspective. A final very special case: Baber (2002) discusses
God's temporal parts; for discussion see the entry on
 the Trinity.
 There are many resources on applied ontology at the Buffalo Ontology
Site (see Other Internet Resources), whilst Bittner, Donnelly and
Smith (2004) explicitly discusses endurance and perdurance in an
applied ontology context.