## 1. The Puzzles



Puzzles of material constitution played an important role in the
development of philosophy and continue to be a source of much debate
today. Here, we introduce four of the most famous puzzles.



*The Debtor's Paradox*. The ancient playwright Epicharmus
tells the tale of a poor but resourceful debtor. When approached for
payment, the man responds with a riddle. If you add a pebble to a
collection of pebbles, you no longer have the same number. If you add
a length to a cubit, you no longer have the same measure. In the same
way, if you add a bit of matter to an existing portion of matter, you
no longer have the same entity. Since man is nothing more than a
material object whose matter is constantly changing, we do not survive
from one moment to the next. The debtor concludes that he is not the
same person who incurred the debt, so he cannot be held responsible
for the payment. The exasperated creditor then strikes the debtor, who
protests the abusive treatment. The creditor expresses sympathy, but
points out that he cannot be held accountable for the assault. After
all, material change has already taken place so, by the debtor's
own line of reasoning, the guilty party is no longer present. The
scene is intended to be comedic, but the argument is no laughing
matter. The man who incurred the debt was constituted by one portion
of matter, M1. The man who is approached for payment is
constituted by a distinct portion of matter, M2 (let us
assume, for the sake of argument, that M2 consists of
M1, together with some new matter). If constitution is
identity, then the debtor's reasoning is sound: the man
approached for payment is not the man who incurred the debt. More
generally, this version of the argument would show that it is
impossible for material objects to survive the addition of any new
parts. (Note: the claim that constitution is identity should not be
confused with the thesis of "composition as identity". On the latter
view, see Section 8 of the entry on
 identity.)



*The Puzzle of Dion and Theon*. The Stoic philosopher
Chrysippus asks us to consider the case of Dion and Theon, where Dion
is a normal human being and Theon is a large part of Dion consisting
of everything but Dion's right foot. Suppose now that the right
foot is removed. Theon obviously survives the operation, for his parts
remain completely unchanged. But, in that case, it seems as if Dion
does *not* survive the operation, for otherwise we would have
two people in the same place at the same time. Hence, Dion does not
survive the loss of his foot. More generally, the argument would show
that material objects cannot survive the loss of any constituent
parts. (A modern version of the puzzle, due to Peter Geach, concerns
Tibbles and Tib, where Tibbles is a cat and Tib a cat-part consisting
of everything but Tibbles's tail.)



*The Ship of Theseus Puzzle*. The ancient historian Plutarch
recounts the story of the famous ship of Theseus, whose parts were all
gradually replaced as they wore down. The resulting ship was
eventually displayed in Athens, where philosophers debated whether it
was still the original ship of Theseus, despite having none of the
original parts. In the modern era, Thomas Hobbes added a further twist
to the story. Suppose that a custodian collected the original planks
as they were removed from the ship and later put them back together in
the original arrangement. In this version of the story, we are left
with two seafaring vessels, one on display in Athens and one in the
possession of the custodian. But where is the original Ship of
Theseus? Some will say that the ship is with the museum, since ships
can survive the complete replacement of parts (provided, at least,
that the change is sufficiently gradual). Others will say that the
ship is with the custodian, since ships can survive being disassembled
and reassembled. Both answers seems correct, but this means that, at
the end of the story, the ship of Theseus is in two places at once.
More generally, the argument suggests that it is possible for one
material object to exist in two places at the same time. We get an
equally implausible result by working backwards. After all, there are
clearly two ships at the end of the story, but both ships were also
around at the beginning, for the reasons just given. So, at the
beginning of the story, there were two ships of Theseus occupying the
same place at the same time--one of which would go on to the
museum and one of which would end up with the custodian.



*The Puzzle of the Statue and the Clay*. Various ancient
philosophers, including Aristotle, pointed out that statues seem to
differ in important respects from the portions of matter from which
they are made. Suppose that, on Monday, a sculptor purchases an
unformed lump of clay, which he names 'Lump'. Suppose
further that, on Tuesday, the artist sculpts the clay into the form of
the biblical king David and names his statue 'David'. It
is tempting to say that, in this case, there is only one object in the
sculptor's hands--David *just is* Lump. But, on
reflection, this identification is problematic, since Lump and David
seem to differ in many respects. For example, Lump existed on Monday,
whereas David did not. Moreover, Lump could survive being squashed
tomorrow, whereas David could not. However, this would imply that Lump
and David and numerically distinct entities, since Leibniz's Law tells
us that numerical identity requires qualitiative sameness. The upshot,
once again, is that it is possible for two material objects to exist
in the same place at the same time.



These four puzzles differ in details, but raise a common problem. (A
fifth
 puzzle--the problem of the many--raises
 significantly different issues and is dealt with in a separate
entry.) We will focus on the case of the statue and the clay, and we
will formulate the puzzle as follows:


1. David did not exist on Monday (but does exist on Tuesday).
2. Lump did exist on Monday (and also exists on Tuesday).
3. If (1) and (2), then David is not identical to Lump.
4. [So] David is not identical to Lump.



The premises of the argument are plausible, but the conclusion is
problematic, for it implies the possibility of *spatially
coincident objects*--something that we ordinarily take to be
impossible.



Generally speaking, there are five possible replies to this puzzle.
First, one could simply accept (4) and admit that David is not
identical to Lump. We consider this response in sections 2 and 3,
where we discuss *the constitution view* of David Wiggins
(1968) and *the temporal parts theory* of David Lewis (1976).
Second, one could deny (1) by either denying the existence of David or
by insisting that David existed on Monday. We consider these responses
in section 4, where we discuss the *eliminativist* views of
Peter Unger (1979), Peter van Inwagen (1990), and Roderick Chisholm
(1979). Third, one could deny (2) by either denying the existence of
Lump (as the eliminativist does) or by claiming that Lump does not
survive being shaped into a statue. We consider this second option in
section 5, where we discuss the *dominant kinds view* of
Michael Burke (1992). Fourth, one could deny (3) by rejecting the
standard formulation of Leibniz's Law. We consider this response
in section 6, where we discuss *the relative identity theory*
of Peter Geach (1967). Fifth and finally, one could respond to the
paradox by insisting that the underlying issues are in some sense
verbal, so that there is no fact of the matter about which premise (if
any) is false. We consider this response in section 7, where we
discuss the *deflationist* views of Rudolf Carnap (1950) and
others. (For an alternative survey of these issues, along with a
collection of relevant papers, see Rea 1987.)



Note that, while our focus throughout will be on material objects,
similar problems arise for other kinds of entities, including events,
properties, and groups--see, for example, Pfeifer (1989),
Shoemaker (2003), and Uzquiano (2004a).


## 2. Coincident Objects



The most popular reply to the puzzle of material constitution is to
embrace the conclusion: Lump and Statue exist at the same place at the
same time, but differ in their historical and modal properties, so it
is possible for there to be two material objects in the same place at
the same time. This view is sometimes referred to as *the
constitution view* since it holds that the statue is constituted
by, but not identical to, the lump of clay from which it is formed. In
a slogan: *constitution is not identity* (Johnston 1992).
Constitution is distinguished from identity insofar as it is an
*asymmetric* relation--Lump constitutes Statue, but not
*vice versa*. Constitution is also taken to be a
*dependence* relation--as David Wiggins (1968, p. 91) puts
it, the statue "consists in" and is "nothing over
and above" the lump of clay. (For more on the nature of
constitution, see Wasserman 2004.)



The constitution view is extremely popular, having been defended by
Wiggins (1968), Doepke (1982), Lowe (1983, 1995, 2003), Simons (1985),
Yablo (1987), Oderberg (1996), Baker (1997, 2000, 2002), Thomson
(1998), Shoemaker (1999), Fine (2003), Koslicki (2008), and many
others. Indeed, the view is so common, it is sometimes called
"the standard account" (Burke 1992). Why not join the
crowd?



"Just try to walk through a wall," quips the skeptic.
"Two things can't be in the same place at the same
time!" We will call this *the impenetrability objection*,
since it appeals to the common idea that impenetrability is the mark
of the material (Descartes 1641 [1993, p. 13]).



The constitution theorist has a ready reply to the this objection.
Unlike you and the wall, David and Lump share the same parts, and this
*material coincidence* explains how they are able to occupy the
same place at the same time (Wiggins 1968). Material coincidence also
helps to answer another common complaint. Suppose that Lump weighs
10lbs. David will obviously weigh the same. So why don't you get
a reading of 20lbs. when you place both on the scale? (Lewis 1986, p.
252) Answer: because the two objects share the *same* weight as
a result of sharing the same parts (Zimmerman 1995, p. 89, fn. 57).
Here it is important to note that we do not determine the weight of a
wall, for example, by summing up the weight of its bricks *and*
its constituent molecules, since that would involve counting some parts
more than once. According to the constitution theorist, weighing David
and Lump would involve the same kind of double-counting.



Material coincidence may explain how spatial coincidence is possible,
but what about material coincidence itself? On the face of it, the
claim that different things can be made up out of the exact same parts
is no more plausible than the claim that different things can be
located in the exact same place. We will call this *the
extensionality objection*, since it appeals to the common idea
that wholes are individuated by their parts in the same way that sets
are individuated by their members.



One obvious response to this objection is to reject extensionality
(Thomson 1983). However, this move comes at a cost since it requires
giving up on classical
 mereology.
 A second response is to deny that objects like David and Lump share
*all* their material parts. For example, Baker (2000, p. 81)
suggests that David's nose is a part of David, but not a part of Lump.
A third response is to grant that coinciding objects share all their
*material* parts, while insisting that they differ in some
*non*-material aspect (see, for example, Rea 1998, McDaniel
2001. Paul 2002, Koslicki 2008, and Brower 2014). The most familiar
version of this view traces back to Aristotelian idea that material
objects are compounds of matter and form (see
 Aristotle's metaphysics).



Whether or not David and Lump share all the same parts, it is clear
that they share many of the same properties. Both have the same
weight, the same size, and the same shape. Indeed, the two seem to be
perfect duplicates, right down to their sub-atomic structure. But this
raises a puzzle: how could duplicates of this kind differ in their
temporal properties, persistence conditions, and the like? We will
refer to this as *the grounding objection* since it appeals to
the common idea that such properties must be grounded in more basic
features of an object. (For different statements of this worry, see
Simons 1987, pp. 225-6, Heller 1990, pp. 30-2, Burke 1992,
Zimmerman 1995, pp. 87-8, and Olson 2001. The objection is
sometimes put in terms of
 supervenience,
 but, as Bennett 2004 points out, supervenience is importantly
different from
 grounding.)



The natural response to this objection is to appeal to differences in
*kind* (Wiggins 1980). Lump can survive being squashed or
rolled into a ball, for example, since Lump is a mere lump of clay.
David, however, is a statue, and statues cannot survive changes of
these kinds. This response, however, pushes back the explanatory
challenge: how could intrinsic duplicates like Lump and David differ
in kind? One option would be to appeal to *relational*
differences. For example, Lynne Rudder Baker suggests that
David--unlike Lump--is a statue because it is essentially
related to an artworld--it is the sort of thing that is admired,
reviewed, and discussed (Baker 2000, pp. 35-46). The problem is
that this seems to get things backwards, for it is natural to say that
David is admired, reviewed, and discussed *because it is a
statue* (rather than a mere lump of clay). A related idea is to
explain the difference in kind by appealing to differences in
*historical* facts (Burke 1992, p. 15). For example, one might
say that Lump is a mere lump of clay because it was created by a
claymaker whose intent was to create a lump, whereas David was created
by a sculptor whose intent was to create a statue. One worry for this
line of response is that it cannot be extended to every case of
constitution. For example, Alan Gibbard (1975) asks us to imagine a
case in which an artist sculpts a statue of the biblical giant Goliath
in two pieces--bottom and top--and then brings those pieces
together, simultaneously creating a statue ('Goliath') and
a new piece of clay ('Lumpl'). The next day, the artist
smashes the statue to bits, simultaneously destroying both the statue
and the lump. The crucial feature of this case is that Lumpl and
Goliath share *all* of their historical properties and appear
to stand in the *same* relations to everything else around
them. For example, both are created at the same time, by the same
person, with a single set of intentions. Both are put on display in
the same galleries and gazed upon by the same patrons. Both are
destroyed at the same time, in exactly the same way. In short, Lumpl
and Goliath seem to share all their relational properties while still
differing in kind, in which case the explanatory challenge remains
unanswered. (For recent discussions of this issue, see DeRosset 2011,
Einheuser 2011, Sutton 2012, Saenz 2015, and Koslicki 2018.)



At this point we have reviewed the three most common complaints about
the constitution view: the impenetrability worry, the extensionality
objection, and the grounding problem. A fourth and final concern is
what we might call *the anthropic objection* (see, for example,
Sosa 1987, Sider 2001, pp. 156-8, and section 2.5 of the entry
on
 ordinary objects.)
 So far, we have focused on the question of whether two material
objects--like David and Lump--could exist at the same place
and time. But why stop at *two*? Consider the *mereological
sum* of David and Lump's material simples. Those simples existed
long before David or Lump came into existence, so the sum would appear
to be another object in addition to the statue and the lump. But why
stop at *three*? Consider the *instatue* that coincides
with David whenever that statue is indoors and then goes out of
existence whenever David is taken outside (cf. Hirsch 1982, p. 32).
There is also the tablestatue (that exists when and only when the
statue is on a table), the litstatue (that exists when and only when
the statue is in the light), the dinnerstatue (that exists only when
the statue's sculptor is eating dinner), and so on. Ernest Sosa
(1987) refers to this multiplication of entities as "the
explosion of reality".



Defenders of the constitution view may try to run from the explosion
and insist that there are only two (or three, or four) objects in the
same place at the same time. But what could justify this exclusionary
attitude? Granted, we do not normally *concern* ourselves with
instatues, litstatues, and the rest. Ordinary English does not even
have sortal terms for *discussing* these entities. But these
are facts about our interests and linguistic decisions. Why should we
think that there is a correspondence between the *sortal terms*
in our language and the *kinds of objects* in the world? One
way to explain this correspondence would be to claim that reality is
determined, in some sense, by our conceptual scheme. But the
constitution view is normally offered as an *alternative* to
anti-realist views of this kind. Perhaps, then, the constitution
theorist should accept Sosa's explosion and say that our
inattentiveness does not exclude things like instatues and litstatues
from the realm of being? Perhaps all of those objects exist at the
same place at the same time, sharing the same parts and the same
matter (Yablo 1987, Bennett 2004, Hawthorne 2006, Fairchild 2019)?
Perhaps. But this brings us very close to adopting a different view
of material constitution. It is to that view that we now turn.


## 3. Temporal Parts



Consider the case of Interstate 5. I-5 runs through Washington,
Oregon, and California, but the road is not wholly present in any of
those states. Rather, I-5 exists in different states by having
different road segments in each--there is the Washington segment
of I-5, the Oregon segment, etc. According to the *temporal parts
theory* (or *four-dimensionalism*), persistence through
time is exactly like *that.* (Quine 1953, Lewis 1976, Sider
2001) Just as roads exist at different places by having distinct
spatial parts at those places, material objects exist at different
times by having distinct *temporal parts* at those times. In
the case of David Lewis, for example, there is the 1970s segment, the
1980s segment, and so on. More formally, we can say that *x* is
a temporal part of *y* at (or during) *t* if and only if
(i) *x* is a part of *y* at (or during) *t*, (ii)
*x* overlaps everything that is a part of *y* at (or
during) *t*, and (iii) *x* exists only at (or during)
*t* (Sider 2001, p. 60).



Consider now the case of U.S. Route 29, which runs from the western
suburbs of Baltimore to Pensacola, Florida. As U.S. 29 passes through
Charlotte it becomes Tyson St.--a street wholly located within
the state of North Carolina. The two roadways in this case are not
identical, but they are *partly* identical, for Tyson St. is
identical to a proper part of U.S. 29. According to the temporal parts
theorist, the case of the statue and the clay is similar. Lump exists
for some period of time and then "turns into" David. If
the sculptor is unsatisfied with her work and squashes the statue,
then Lump--but not David--continues to exist, in which case
David is nothing more than a proper temporal part of Lump.



There are, of course, various arguments for and against this view.
(See the entry on
 temporal parts.)
 Here, we focus on the relevance of the doctrine to the puzzles of
material constitution and, in particular, to the challenges facing the
constitution view.



*The impenetrability objection*. The first problem for the
constitution view was that it allowed for two material objects to
exist in the same place at the same time. The temporal parts theorist
avoids this objection for he will say that, whenever Lump and David
exist, there is a single object that exactly occupies the relevant
location--a temporal part that is shared by both David and Lump.
Of course, those two objects will be *partly* present at the
same location, but this is no more problematic than two roads being
partly present at the same place by sharing a common road segment.



*The extensionality objection*. The second problem for the
constitution view was that it allowed for two objects to be composed
of all the same parts. The temporal parts theorist avoids this problem
in the case of the statue and the lump, since he will say that those
objects share some, but not all, of the same temporal parts. Of
course, those objects will have all the same parts *when they both
exist,* but this is no more problematic than two roads sharing all
the same parts *where they overlap*.



*The grounding objection*. The third challenge for the
constitution theorist was to identify a ground for the different
features of coinciding objects. The same challenge can be put to the
friend of temporal parts. In the case of the statue and the clay, for
example, we have two objects that are perfect duplicates whenever they
both exist--in virtue of what, then, do they differ with respect
to their temporal properties, persistence conditions, and so on? The
temporal parts theorist could follow the constitution theorist in
claiming that the relevant objects differ in kind, for example, in
virtue of their historical properties or he could simply insist that
the difference in kind is grounded in the fact that the two objects
have different temporal parts (Wasserman 2002).



*The anthropic objection.* The last worry for the constitution
view was that it postulated an unexplained correspondence between the
sortal terms in our language and the kinds of objects in the world.
The temporal parts theorist avoids this worry as well. On the standard
four-dimensionalist picture, persisting objects are ultimately
composed of instantaneous temporal parts and, for any collection of
these parts, there is a further object that they compose (Quine 1960,
p. 171). For example, there is an object composed of all and only the
temporal parts of David *when that statue is indoors*. This
would be what we earlier called an "instatue". There is
also an object composed of all and only the temporal parts of David
*when that statue is in the light*. This is what we earlier
called a "litstatue". In this way, the temporal parts
theorist finds a place for all of the objects introduced earlier, and
thereby avoids an implausible correlation between the sortal terms of
our language and the kinds of objects in the world. (Of course, some
people think that this solution is worse than the problem--see,
for example, Markosian 1998, p. 228, Elder 2008: 440, and Korman 2015:
Chapter 4.)



Unfortunately, the temporal parts solution cannot be extended to the
case Lumpl and Goliath since those objects exist at all of the same
times and thus share the same temporal parts. The four-dimensionalist
who accepts extensionality will therefore be forced to conclude that
Lumpl is identical to Goliath. This, however, is problematic, since
those objects seem to differ in their modal properties. Lumpl, for
example, could survive beings squashed, whereas Goliath could not.



The most popular reply to this worry is due to David Lewis (1971,
1986), who defends a *counterpart theory* of *de re*
modal ascriptions. According to Lewis, ordinary objects like Goliath
exist in only one possible world, but have *counterparts* at
other worlds that serve as truth-makers for *de re* modal
ascriptions. Crucially, whether or not something counts as a
counterpart of Goliath (for example) will depend on what respects of
similarity are at issue. Since the name 'Goliath' is associated with
the kind *statue*, a sentence like "Goliath could survive being
squashed" will normally be true (relative to a context) just in case
Goliath has some *statue*-counterparts that survive squashing
(i.e., some counterparts that survive squashing *as statues*).
Presumably, there are no such counterparts, so that sentence will
express a falsehood. Meanwhile, the name 'Lumpl' is
associate with kind *lump of clay,* so a sentence like "Lumpl
could survive being squashed" will be true just in case Lumpl has a
*lump*-counterpart that survives being squashed. Presumably,
there are some such objects at other worlds, so that sentence will
express a truth. Moreover, this will be the case even if the temporal
parts theorist is correct and a single object is picked out by both
'Lumpl' and 'Goliath'. The key point is that
the phrase 'could survive being squashed' expresses different
properties when combined with these names, so Leibniz's Law has
no application. (For objections to counterpart theory, see Fara and
Williamson 2005.)



One worry for this response is that it cannot account for apparent
non-modal differences between Lumpl and Goliath. For example, Kit Fine
(2003) argues that Lumpl, but not Goliath, might be
*well-made*, and that Goliath, but not Lumpl, might be
*Romanesque*. Since these are not modal ascriptions,
counterpart theory has no application. As a result, it is unclear what
the temporal parts theorist is to say about apparent differences of
this sort. (For more on this issue, see the exchange between Fine
2006, Frances 2006, and King 2006.)


## 4. Eliminativism



The simplest way of avoiding the puzzles of material constitution is
to deny the existence of some of the objects that give rise to those
problems. For example, if one claims that there are no such things as
statues and lumps of clay, then there is no threat of having a statue
and a lump of clay in the same place at the same time.



This kind of eliminativism is often associated with Peter Unger
(1979), who (at one time) defended the thesis of *mereological
nihilism*. Nihilism is the view that there are there are no
composite objects (i.e., there are no objects with proper
parts--only atoms exist). On this view, there are no statues,
animals or any other macroscopic object made up out of smaller parts.
Since the nihilist denies the existence of statues in general, he will
deny the existence of the particular statue, David. Hence, he will
reject the very first premise of the original argument for coincident
objects. He will also reject the second premise of that argument,
since he will deny the existence of the relevant lump. (Note that
Unger's use of 'nihilism' differs slightly from its
current meaning--see van Inwagen 1990, p. 73.)



The nihilist makes two main claims, both of which can be challenged.
First, there is the negative thesis that there are no composite
objects and no statues in particular. The most common reaction to this
claim is an incredulous stare. For many, the existence of composite
objects is a Moorean fact, more certain than any premise that could be
used to argue against it. The nihilist may reply that we can make
sense of our statue-talk by paraphrasing it into claims about simples.
For example, instead of saying that there is a statue on the table, we
can say that there are some simples arranged "statuewise"
on top of some other simples arranged "tablewise".
Similarly for other talk of statues, ships, and other composite
objects. (For more on this paraphrasing strategy, see van Inwagen
1990, chapter 10. For worries, see O'Leary-Hawthorne and Michael
1996, Uzquiano 2004b, and McGrath 2005.) This brings us to the
nihilist's positive thesis that there are material simples. This
claim can also be challenged. After all, it was once thought that
chemical atoms were fundamental particles, until the discovery of
protons and neutrons. And it was thought that protons and neutrons
were mereological simples, until the discovery of quarks. One might
think it is possible for this process goes on without limit, in which
case our world would be *gunky* (i.e., it would have no simples
as proper parts). The problem is that this possibility is inconsistent
with nihilism, which seems to imply that a material world must contain
material simples (Sider 1993, Zimmerman 1996, Schaffer 2003).



A second version of eliminativism is associated with Peter van Inwagen
(1990), who defends the view that living objects are the only
composite objects. This view is closely related to nihilism, but has
one notable advantage--it allows for the existence of human
persons. For example, in the case of Dion and Theon, van Inwagen will
say that Dion exists at the beginning of the story, since the activity
of the relevant simples constitutes a life (the life of Dion). But van
Inwagen will deny that Theon exists, for the activity of the relevant
simples only constitutes a *part* of Dion's life at that
time. Of course, the activity of those same simples constitutes a life
after Dion's right foot is removed, at which point the simples
come to compose Dion. More generally, van Inwagen denies the existence
of what he calls "arbitrary undetached parts":



*The Doctrine of Arbitrary Undetached Parts* (DAUP): For every
material object *m*, time *t*, and regions
*r*1 and *r*2, if *m*
occupies *r*1 at *t* and
*r*2 is a sub-region of *r*1, then
there is a part of *m* that occupies *r*2 at
*t*. (cf. van Inwagen 1981, p. 123)




Let *m* = Dion, *t* = a pre-operation time,
*r*1 = the region occupied by Dion at *t*,
and *r*2 = the region corresponding to all of Dion
except for his right foot at *t*. If DAUP were correct, then
Theon would exist, for it would just be the proper part of Dion that
occupies *r*2 at *t*. Van Inwagen denies the
existence of Theon, so he rejects the general principle as well. (For
more on DAUP and material constitution, see van Inwagen 1981, Olson
1995, and Parsons 2004.)



Van Inwagen's version of eliminativism is subject to the same
objections raised against nihilism, but it also faces problems of its
own. Here is one worry. There are borderline cases where it is vague
whether or not the activity of some simples constitutes a life
(consider, for example, the question of when, exactly, a person's life
comes to an end). But, if it is vague whether the activity of some
simples constitutes a life then, according to van Inwagen, it is vague
how many objects exist. But it cannot be vague how many objects exist,
since cardinality claims can be made in a part of language where
nothing is vague. Suppose, for example, that there are exactly
one-million simples and that it is vague whether or not the activity
of those simples constitutes a life. Now consider the numerical
sentence that asserts the existence of (at least) one-million and one
objects. (A *numerical sentence* is a first-order sentence
asserting the existence of some objects. For example, the numerical
sentence that there exist at least two objects is:
[?]*x*[?]*y*(*x* [?] *y*).) If
van Inwagen is correct, then it is indeterminate whether or not the
relevant numerical sentence is true, in which case one of the
constituent expressions--'[?]',
'*x*', '*y*', '~',
'='--must be vague. Yet philosophers have claimed
that the terms of first-order logic do not admit of borderline cases.
(For a more detailed presentation of this argument, see Lewis 1986,
pp. 212-213, Sider 2001, pp. 120-132, and section 2.2 of
the entry on
 ordinary objects.
 For potential replies, see Hirsch 2002b, Liebesman and Eklund 2007,
and van Inwagen 1990, Chapter 13.)



A third version of eliminativism is often associated with Roderick
Chisholm (1973), who defends the doctrine of *mereological
essentialism*: for any *x* and *y*, if *x* is
a part of *y* then, necessarily, *y* exists only if
*x* is a part of *y*. This doctrine is an
"eliminativist" view insofar as it denies the existence of
mereologically ductile objects. For example, in the Ship of Theseus
case it is natural to think that there is a ship which survives the
replacement of at least some of its parts. The essentialist's
response to the paradox is to deny this apparent truism. In the same
way, the Debtor's Paradox and the Puzzle of Deon and Theon only
arise on the assumption that human persons can gain and lose parts.
The essentialist solves these puzzles by rejecting this assumption.
The Puzzle of the Statue and the Clay remains problematic, however,
for that example involved a change in shape, rather than a change in
parts. In order to respond to this puzzle, the essentialist must
endorse an additional principle: for any *x*s and for any
*y*, if the *x*s compose *y* then, necessarily,
the *x*s exist only if they compose *y*. This thesis
says that the whole is essential to the parts, so that whenever you
have the same parts, you have the same whole. The defender of this
thesis will say that, in our earlier case, Lump exists on both Monday
and Tuesday, for the same clay parts are there on both days. The same
is true of David. The parts that compose David on Tuesday are present
on Monday, in which case the first premise of the earlier argument is
false--David *did* exist on Monday. In that case, the
defender of mereological essentialist is free to identify David and
Lump and thereby avoid any commitment to coincident objects.



Viewed from one perspective, the essentialist's picture can seem
intuitive. When one rearranges the dining room furniture, one does not
bring new furniture into existence--one simply brings existing
furniture into a new arrangement. In the same way, rearranging the
material contents of the universe does not bring new material objects
into existence--it simply puts existing objects into new
arrangements. Thus, when the artist sculpts the lump of clay she gives
that object a new form, but does not create a new object. Viewed from
another perspective, however, this picture seems completely absurd,
for it implies that if we annihilate a single particle of David, the
entire statue will be destroyed. More frightening still, if we
annihilate a single particle from your body, then *you* will no
longer exist. The mereological essentialist may reply that, if we were
to annihilate a particle from David, there would still be a statue
left in its place--call it *David\**. David\* would not be
*identical* to David, but it would be very similar. For
example, it would have roughly the same mass, the same shape, and the
same location. In Chisholm's terminology, this would be a
"statue-successor" of David, and the existence of this
successor gives us a loose sense in which "the statue"
survives. Here is a second worry for the essentialist, focusing on the
idea that the whole is essential to the parts. Imagine that the artist
who sculpted David becomes dissatisfied with her work and squashes the
statue while preserving all the bits of clay. If the whole is
essential to the parts, then it would follow that David (the thing
that was previously composed of those parts) still exists. But this
seems absurd--statues cannot survive being squashed. We get an
equally absurd result in the opposite direction. David's parts
existed prior to the sculpting, so David itself existed prior to the
sculpting. But how can a statue exist before it is sculpted? The
eliminativist might reply that the thing which is (currently) a statue
existed prior to the sculpting, but it was not (then) a statue. In
this sense, at least, we can say that the statue did not exist prior
to sculpting. Similarly, the thing which is (currently) a statue may
survive being squashed, but it will not (then) be a statue. So, in
that sense, the statue will not survive the squashing. (For more
details on this paraphrasing strategy, see Chisholm 1976, chapter
3.)


## 5. Dominant Kinds



In the previous section, we examined various ways of resisting the
first premise of our original argument*--*the claim that
*David did not exist on Monday*. Let us now turn our attention
to the second premise: *Lump did exist on Monday*.
Eliminativists like Unger and van Inwagen will reject this premise,
since they deny the existence of objects like Lump. But there are
other accounts that reject this premise as well. One such theory is
the *dominant kind view* defended by Michael Burke (1994,
1997a, 1997b).



Burke begins with the assumption that there is a single object present
on Tuesday. For the moment, let us call this object "Rex".
Burke assumes that Rex is both a lump of clay and a statue. This is a
perfectly natural assumption, but it is also problematic. As we have
seen, kinds are associated with different persistence conditions. For
example, unlike the kind *statue*, the kind *lump of
clay* is associated with the property of *being able to survive
squashing.* Now consider the following principle: for any object
*o* and kind *K*, if *o* is a *K*, then
*o* has the persistence conditions associated with *K.*
(Burke 1994, p. 598) If this principle is correct, then we have a
problem. Rex is both a lump of clay and a statue, so the principle
tells us that it is able to survive squashing and that it is not.
Burke concludes that the proposed principle is false--it is
possible for an object to be a *K* without having the
persistence conditions associated with that kind. In particular, Burke
claims that Rex is a statue and a lump of clay, but it only has the
persistence conditions associated with one of those kinds. Which one?
Burke answers that, in general, an object has the persistence
conditions associated with its *dominant* kind. What is a
dominant kind? Burke answers that, in general, an object's
dominant kind is the kind that "entails possession of the widest
range of properties" (Burke 1994, p. 607). For example, if
something is a lump of clay, then it must have certain
*physical* properties. If something is a statue, on the other
hand, then it must have both physical *and* aesthetic
properties. In this sense, *statue* entails a wider range of
properties than *lump of clay*. Hence, *statue*
dominates *lump of clay*. Rex therefore has the persistence
conditions associated with the kind *statue*. Rex, in other
words, is just David. What about Lump? In the original story, the name
'Lump' is introduced for the lump of clay that exists on
Monday. At that point there was no statue, so Lump's dominant
kind is simply *lump of clay*. Let us now introduce the name
'Lump\*' for the lump of clay that exists on Tuesday. The
lump of clay that exists on Tuesday is also a statue (Lump\* is David,
i.e., Rex), so Lump\*'s dominant kind is *statue*. Hence,
Lump [?] Lump\*. On Burke's view, the process of sculpting a
lump of clay into a statue destroys one object (a mere lump of clay)
and replaces it with another (a statue). The resulting statue is also
a lump of clay, but it is numerically distinct from the lump of clay
with which we began. Burke concludes that Lump exists on Monday, but
does not exist on Tuesday. Hence, the second premise of the original
argument is false.



The dominant kinds view has several advantages over the eliminativist
accounts. Most notably, the dominant kinds view recognizes the
existence of ordinary objects like statues and lumps of clay and
allows for these objects to gain and lose parts. However, some of the
objections raised in previous sections apply to Burke's view as
well. For example, the anthropic objection from section 2 can also be
raised against the dominant kinds view (Sider 2001, p. 165). In
addition, the view faces problems of its own.



First, there is the objection from commonsense. According to Burke,
sculptors can destroy lumps of clay by doing nothing more than
reshaping them in accordance with certain artistic intentions. In
fact, given certain theories of what constitutes an artwork, the
sculptor doesn't even have to do that much. Suppose that an
artist takes a liking to a particular rock in his yard. He gives it
the title *Rocky* and invites art critics to admire his new
work of art. If this is all it takes to create an artpiece, then this
is all it takes to destroy a rock. After all, the rock at the
beginning of the story has *piece of rock* as its dominant
kind, while the rock at the end has *piece of art* as its
dominant kind. Hence, the latter rock is numerically distinct from the
former--the original rock is no more. This seems absurd. Burke
replies by appealing to ambiguity (1994, 596-7). According to
him, 'the rock' could denote *the rock* (a singular
object) or *the rocky stuff* (the matter that constitutes that
object). On the first reading, the rock from the beginning of the
story is *not* the same as the rock at the end (since there is
a new dominant kind). But, on the second reading, the rock from the
beginning of the story *is* the same as the rock at the end
(since it is the same matter throughout). Burke claims that this is
enough to satisfy the demands of commonsense. (For more on mass terms
and the distinction between stuff and things, see the entry on
 the metaphysics of mass expressions.)



A second problem concerns Burke's account of dominance. Burke
claims that one kind dominates another when it entails a wider range
of properties. This seems to get the current case correct, for there
is a natural sense in which *statue* entails a wider range of
properties than *lump of clay*. But other cases are less clear.
Take, for example, the case of a performance artist who poses his own
body to form a statue. The relevant object is both a person and a
statue. The kind *statue* entails having certain aesthetic
properties, but does not entail having any mental properties. The kind
*person* arguably entails having certain mental properties, but
does not entail having any aesthetic properties. But, in that case,
neither kind dominates the other, so Burke's account seems
incomplete. (For further discussion of this worry, see Rea 2000.)



A final problem for the dominant kinds view is that it cannot be
extended to all cases of constitution. For example, in the Ship of
Theseus case, we seem to have two ships in the same place at the same
time. Since there is a *single* kind at issue in that case, the
question of dominance does not arise and Burke's account cannot
help. (For further examples of this kind, see Fine 2000.)


## 6. Relative Identity



In the previous two sections, we discussed various ways of challenging
the first two premises of the argument for coincident entities. Let us
now turn our attention to the third and final premise: *If David
did not exist on Monday and Lump did exist on Monday, then David is
not identical to Lump*. The premise follows from Leibniz's
Law: for any *x* and *y*, if *x* is identical to
*y*, then *x* and *y* share all of the same
properties. The denial of Leibniz's Law therefore provides one
way of resisting the final premise of the argument.



The denial of Leibniz's Law is sometimes associated with Peter
Geach (1962, 1967), who defends a view called *the relative
identity theory*. Geach's central thesis is that there is no
relation of absolute identity--identity is always *relative to
a* *kind*. Thus, we can say that David is the same
*statue* as Lump and we can say that David is the same *lump
of clay* as Lump, but it makes no sense to say that David is the
same as Lump *simpliciter*. The consequent of the third premise
is therefore nonsense, like saying 'David is not taller
than'. More generally, Geach rejects the standard formulation of
Leibniz's Law as incomplete, since it includes a non-relativized
identity predicate. In this way, the relative identity theorist is
able to block the third step of the argument for coincident
objects.



Geach makes many interesting claims about the behavior of relative
identity relations. For example, he claims that it is possible for
*a* to be the same *K* as *b*, but not the same
*K*\*, where '*K*' and
'*K*\*' are sortal terms denoting distinct kinds.
Take, for example, the Debtor's Paradox. In that case, we have
an earlier portion of matter, M1, and a later portion of
matter M2. According to Geach, M1 is not the
same portion of matter as M2, but it is the same person. In
this way, he is able to allow for the persistence of persons through
changes in parts. (See the entry on
 relative identity
 for more details.)



The relative identity theorist may deny the standard formulation of
Leibniz's Law, but there is significant pressure to accept
*some* version of that principle since it seems to capture a
central fact about identity. An obvious suggestion is to offer a
relativized version of Leibniz's Law: for any *x* and
*y*, if *x* is the same K as *y*, then *x*
and *y* share all of the same properties (where 'K'
is a sortal denoting a kind). If Geach's relative identity
relations do not conform to this law, one might worry that they are
not *identity* relations at all. And here we have a potential
problem. Take the case of David and Lump. As we have seen, some
philosophers want to say that David is both a statue and a lump of
clay (it is not a *mere* lump of clay, since it is also a
statue, but it is still a lump of clay). Lump is obviously a lump of
clay. Since there is only one lump of clay on Tuesday, David must be
the same lump of clay as Lump. But then, by the relativized version of
Leibniz's Law, David and Lump must share all of the same
properties. This, once again, seems false. Lump existed on Monday, but
David did not, so there is at least one property that Lump has and
David lacks. In response, the relative identity theorist might appeal
to another component of Geach's view. Geach suggests that proper
names are always associated with kinds. For example,
'David' is associated with the kind *statue* and
'Lump' is associated with the kind *lump of clay*.
Taking a cue from the counterpart theorist (section 3), the relative
identity theorist may go on to claim that this association creates
opaque contexts when we ascribe modal properties. Take, for example,
the following pair of statements:


1. Lump existed on Monday.
2. David existed on Monday.



The relative identity theorist could say that (1) is true if and only
if there was a *lump of clay* on Monday which is the same lump
of clay as Lump. (2), on the other hand, is true just in case there
was *statue* on Monday which is the same statue as David. Given
these truth conditions, (1) is true and (2) is false, for there was a
lump of clay on Monday (the same lump of clay as Lump), but no statue.
More importantly, on this analysis the predicates in (1) and (2)
express different properties, in which case the relativized version of
Leibniz's Law has no application. So, one cannot move from (1)
and the negation of (2) to the conclusion that Lump and David are
distinct lumps of clay.



A second worry for Geach is that it seems as if the relative identity
theory cannot solve all of the puzzles with which we began. Take, once
again, the Ship of Theseus Puzzle. In that case, we have the original
ship of Theseus (A), the museum's ship (B), and the
custodian's ship (C). The problem is that B seems to be the same
ship as A, which seems to be the same ship as C. If the *same ship
as* relation is transitive, we get the absurd conclusion that B is
the same ship as C. The relative identity theorist might deny
transitivity, of course, but this would give us another reason to
suspect that relativized identity relations are not really
*identity* relations at all (Gupta 1980).



A third and final worry for Geach concerns his denial of absolute
identity. As many commentators have pointed out, this denial has
drastic implications for logic, semantics, and set theory. To take
just one example, consider the set theorist's axiom of
*extensionality*: for any sets *A* and *B*, if
*A* and *B* have the same members, then *A* is
the same set as *B*. Let *A* be David's unit set
and let *B* be Lump's unit set. Is *A* the same
set as *B*? The relativist must reject this question as
ill-formed. It makes no sense to ask whether *x* and *y*
are the same members, since this requires a notion of absolute
identity (intuitively, 'member' does not denote a genuine
kind, so 'same member as' does not express a relative
identity relation). As a result, the relative identity theorist must
deny extensionality, which throws set theory into jeopardy (Hawthorne
2004).


## 7. Deflationism



Imagine a debate between two friends over whether or not boats are
ships. One party points to a rowboat and says, "That boat is a
ship. After all, a ship is a vessel that floats on water and the
rowboat is obviously a vessel that floats on water." The second
party disagrees: "A ship is a sufficiently *large* vessel
that floats on water and the rowboat is not sufficiently large. So the
boat is not a ship." Clearly, there is something defective about
this debate. First, there are two "candidate meanings" for
the predicate 'ship'--namely *a vessel that floats
on water* and *a sufficiently large vessel that floats on
water*. Second, neither of these candidate meanings is more
"natural" than the other--unlike 'water'
or 'electron', the predicate 'ship' does not
correspond to a natural kind in the world. Third, the two parties to
the debate agree on all of the "non-ship" facts--in
particular, both parties agree that the rowboat is a vessel, that it
floats on water, and that it is relatively small in size. Given these
points, it is tempting to say that the two parties agree on all of the
*facts* and that their dispute is *merely verbal*. Note
that this conclusion is consistent with the view that one of the
parties is actually mistaken. Suppose, for example, that *semantic
externalism* is correct and the meanings of our terms are
determined, in part, by overall use (see the entry on
 externalism about mental content).
 In that case, the first party to our debate is presumably mistaken,
since English-speakers do not use the term 'ship' for rowboats. Still,
there is a sense in which the debate is verbal, for there is a
possible language ("English\*") that (a) employs a
different, equally natural meaning for 'ship', (b) is
adequate for describing all of the facts, and (c) is such that the
first party's statements would be true in that language. Thus,
we might say that the real dispute between the two parties is over
whether or not English is English\*. And that is clearly a verbal
dispute.



Some philosophers have suggested that the debate over material
constitution is defective in exactly the same way. There is no genuine
dispute between Lewis and Unger, for example, over whether or not
statues exist. Both parties agree on all of the relevant
facts--e.g., that there are simples arranged statuewise. And both
parties agree that there are two possible languages
("Lewis-English" and "Unger-English") where
the sentence "Statues exist" comes out true in one and
false in the other. So the only disagreement is over whether English
is Lewis-English or Unger-English. In other words, the debate is
merely verbal. This kind of *deflationist view* is often
associated with Rudolf Carnap (1950), Hilary Putnam (1987) and, more
recently, Eli Hirsch (2002a, 2002b, 2005). The issues raised by
deflationism are extremely complicated; here, we will limit ourselves
to a few initial observations. (For a longer introduction to these
issues, see Chalmers, Manley, and Wasserman 2009. For an extended
defense of deflationism, see Thomasson 2015.)



In the imagined dispute, we know exactly what the disputed term is
('ship') and exactly what the relevant candidate meanings
are (*a vessel that floats on water* and *a sufficiently
large vessel that floats on water*). In the actual dispute between
Lewis and Unger, matters are not so clear. One might suspect that the
disputed term in this case is the predicate 'statue', but
it turns out to be fairly difficult to specify the relevant candidate
meanings. For example, we might say that, in Lewis-English,
'statue' simply means *a collection of simples arranged
statuewise*. Whether or not that is a plausible interpretation of
what Lewis means depends in part on the meaning of
'collection' (Sider 2009, pp. 388-90). In any case,
it is even more difficult to specify an appropriate candidate meaning
for 'statue' in Unger-English. More importantly, even if
we are able to specify the relevant candidate meanings, we will not
have succeeded in showing that the general dispute between Lewis and
Unger is verbal, for the dispute can be brought out without using the
predicate 'statue' (or any non-logical predicate, for that
matter). Consider, for example, a world that contains one-million
simples arranged statuewise and nothing else. And consider the
numerical sentence (see section 4) which asserts the existence of at
least one-million and one things. Lewis and Unger will disagree over
the truth of that sentence. But that sentence contains only logical
vocabulary. Hence, if the two parties are really talking past each
other, then they must assign different meanings to one or more of the
logical constants.



The most plausible suggestion is that Lewis and Unger assign (or, at
least, intend to assign) different meanings to the existential
quantifier, '[?]' (as well as quantificational phrases
like 'there are', 'there is', and
'some'). And, indeed, this is where deflationists have
focused their attention. Putnam, for example, writes that "[T]he
logical primitives themselves, and in particular the notions of object
and existence, have a multitude of different uses rather than one
absolute 'meaning' " (1987, p. 71). This
thesis--that there are many meanings for the existential
quantifier that are equally natural and equally adequate for
describing all the facts--is often referred to as "the
doctrine of quantifier variance" (Hirsch 2002b). What exactly
are the candidate meanings in question? Once again, matters are not so
clear. Lewis could, of course, simply interpret Unger to be using a
*restricted* quantifier that ranges only over simples. On that
interpretation, Unger speaks truthfully when he utters the sentence
"Statues do not exist", since there are no statues among the simples.
The problem with this interpretation is that it seems manifestly
implausible, given that Unger will insist that his quantifiers are to
be understood as unrestricted. Even more worrying is the question of
how Unger is supposed to interpret Lewis. He cannot, for example, say
that Lewis is using a less restrictive quantifier, for that would be
to say that there are things (that Lewis's quantifier ranges
over) that do not exist (by Unger's own lights). Unger could,
perhaps, take a more holistic approach and interpret Lewis's
assertion of 'Statues exist' to mean *there are some simples
arranged statuewise*. More generally, Unger could interpret Lewis
by replacing singular quantifiers over composites with plural
quantifiers over simples, and by replacing each predicate of
composites with an irreducibly plural predicate of simples. Once
again, we should expect protest--Lewis will reject the proposed
translation and insist that he is using singular quantification when
he asserts the sentence 'Statues exist'.



These initial observations bring out one disanalogy between the
ontological dispute and paradigm verbal disputes. In the earlier
argument over whether or not boats are ships, the proposed
translations are *friendly*, since the first party will admit
that he uses 'ship' to mean *a vessel that floats on
water* and the second will grant that he uses 'ship'
to mean *a sufficiently large vessel that floats on water*.
Given this disambiguation, the dispute will evaporate. The
deflationist's proposals are instead *hostile*, for
neither Lewis nor Unger will accept the deflationist interpretation
offered by his opponent (Sider 2009, section 5). This does not mean
that the ontologists' debate is non-verbal, but it does mean
that the issues involved here are more complicated than those in
paradigm verbal disputes. (For recent work on quantifier variance, see
Thommason 2016, Finn and Bueno 2018, Hirsch and Warren 2019, Sud and
Manley 2020, and Eklund forthcoming.)