Carroll J.W., Markosian N. An Introduction to Metaphysics

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Material objects 189

surely the truth about this other possible world is simply that its physical

objects (and laws of nature) are very different from our own.

This thought experiment involving an exotic possible world suggests

a different approach to understanding physical objects. For the objects

we considered in this imagined world were strange, but they were never-

theless located in space, and it is probably for that reason that we ﬁnd it

plausible to call them physical objects. If so, then perhaps we should say

that physical objects are objects with spatial locations.

The spatial location account of physical objects has some very intuitive

consequences. It counts such ordinary macroscopic objects as humans,

rocks, planets, and stars as physical objects. It also counts their smaller

parts, including molecules, electrons, and quarks. In addition, the spatial

location account declares such things as numbers, properties, functions,

and sets to be non-physical, and that too seems plausible.

one worry that can be raised concerning this account, however, involves

such shady objects as shadows, sensations, specters, mirror images, hal-

lucinations, and apparitions. All of these putative objects seem to have

spatial locations, but it doesn’t seem right to call any of them a physical

object.

A second objection to the spatial location account is that it seems to

require a sharp distinction between space and time. As seen in Chapter 7,

there is a sizeable movement among metaphysicians to treat the three

dimensions of space and the one dimension of time as four intrinsically

similar dimensions of the world; and anyone who is sympathetic to that

movement will not want to make having a spatial location be the dis-

tinguishing mark of the physical. But (as also seen in Chapter 7) there is

still considerable opposition to the space-and-time-are-intrinsically-alike

movement, and those who take space and time to be fundamentally differ-

ent will not mind the spatial location account implying as much.

Another main objection to the spatial location account concerns the

possibility of spatially unextended minds that nevertheless have spa-

tial locations. For many ordinary people, as well as such philosophers as

locke and descartes, want to deﬁne ‘mind’ as roughly synonymous with

‘non-physical, thinking substance’; but some who accept this deﬁnition

This view is endorsed by Hobbes in Part II, Chapter VIII of his Concerning Body (con-

tained in Hobbes, Metaphysical Writings), and defended in Markosian, “What Are

Physical objects?”

An Introduction to Metaphysics190

of ‘mind’, and say that they believe in minds, also believe that minds can

have spatial locations.

(Such a person might say, for example, that your

mind is currently located at a certain point inside your brain.) Anyone who

likes this way of thinking about the mind will ﬁnd the spatial location

account of physical objects unacceptable.

There is, however, another spatial account of physical objects that

might appeal to such a person. descartes and others have suggested that

what characterizes physical objects is not that they have spatial locations

(since, it is suggested, non-physical minds can also have spatial locations)

but, rather, that they have spatial extension (where an object is spatially

extended if it occupies more than a single point in space). endorsing this

account of physical objects would allow a person to maintain, for example,

that your mind is a non-physical (because unextended) object that is located

at a certain point inside your brain.

The main cost of the spatial extension account of physical objects is that

it entails that all point-sized things are non-physical. Thus, for example,

if our current physical theories are correct, then many (perhaps even

all) of the particles that compose the macroscopic objects around us are

non-physical objects. For according to current theories those particles are

point-sized things.

8.3 The Special Composition Question

A lot of the questions we will consider in the next two sections have to do

with a branch of metaphysics called mereology, which is concerned with

a cluster of issues surrounding the part-whole relation. These issues have

received a lot of attention from philosophers in the last eighty years or so,

and especially in the last thirty years. The main question that sparked the

recent ﬂurry of activity within the philosophical community was raised

by Peter van Inwagen in Material Beings. Van Inwagen’s book is concerned

with the notion of “composition” – roughly, the forming of a whole by two

or more parts. Here is how van Inwagen deﬁnes this notion.

x overlaps y =df there is a z such that z is a part of x and z is a part of y.

See, for example, locke, An Essay Concerning Human Understanding; and descartes,

Meditations on First Philosophy.

Van Inwagen, Material Beings, p. 29.

Material objects 191

The xs compose y = df (i) the xs are all parts of y, (ii) no two of the xs overlap,

and (iii) every part of y overlaps at least one of the xs.

Note that the only mereological term taken as primitive in these deﬁni-

tions is ‘part’. Note also that in keeping with tradition in discussions of

mereology, van Inwagen uses ‘part’ in such a way that each thing is auto-

matically a part of itself. But we can distinguish between parts in general

and ‘proper parts’, where a proper part of x is understood to be a part of x

that is not identical to x. (Thus the philosophical concept of a proper part

no doubt corresponds more closely to the common-sense notion of a part

than does the broader philosophical notion of a part.)

Now, intuitively, there are many cases in which some xs compose a further

object. For example, it’s natural to think that all of your cells compose your

body, and also natural to think that four legs and a tabletop can compose a

table. But it’s equally plausible to think that there are many cases in which

some xs fail to compose a further object. For example, it’s very natural to

think that your underwear and the eiffel Tower do not compose anything.

If there are cases in which some xs compose something, and also cases in

which some xs fail to compose anything, then it makes sense to ask, What

is the general rule governing when composition occurs and when it doesn’t

occur? This is the question that van Inwagen raised in Material Beings, and t hat

sparked the recent ﬂurry of activity on the mereology of physical objects.

Here is a variation on van Inwagen’s more precise way of asking this

question.

The Special Composition Question (SCQ)

What necessary and jointly sufﬁcient conditions must any xs satisfy in

order for it to be the case that there is an object composed of those xs?

It’s important to understand that SCQ is not asking for an analysis of the

concept of composition. For we already have such an analysis: it is stated

in the above deﬁnition of ‘the xs compose y’. Instead, SCQ is asking for

some interesting, non-analytic principle about the way (if any) in which

other properties and relations are (necessarily) linked up with the relation

of composition. That is, SCQ is asking for a way of ﬁlling in the blank in

For van Inwagen’s characterization of the question, and an explanation of plural

quantiﬁcation (i.e., the use of expressions like ‘for any xs’), see section 2 of Material

Beings.

An Introduction to Metaphysics192

the following sentence schema: for any xs, there is an object composed of those

xs iff

--------

8.4 Contact and Fastening

You might think that SCQ is an easy question to answer. For example,

you might think that whenever some xs are collectively in contact with

one another, there is an object composed of those xs, and also that cases

of composition always involve the relevant objects being in contact. Van

Inwagen calls this view Contact.

Many people, upon ﬁrst learning of SCQ, are initially drawn to this

proposal. And, indeed, if you consider certain cases, such as the cells that

make up your body, and the parts of your kitchen table, Contact seems to

give some very plausible results. But what if you happen to bump into a

stranger on the subway? Is there all of a sudden a new object that pops into

existence when this happens? (An object that just as quickly pops out of

existence when you and the stranger separate?) or consider the particles

that make up an atom. They are extremely small, and they’re separated

by relatively large expanses of empty space. So they are not in contact.

But does it follow that there is no object composed of those particles? Are

there no atoms after all?

These last two examples suggest both that mere contact is not enough

for composition (as in the subway case), and also that genuine contact is

not a requirement for composition (as in the case of the particles that

compose an atom). The examples also seem to support a different relation

as the key to composition: for you and the stranger on the subway are

never really stuck together, whereas the subatomic particles, although

not in contact with one another, are nevertheless bound together by very

powerful forces. Perhaps, then, being collectively fastened together is

necessary and sufﬁcient for composition.

Van Inwagen calls this view

Fastening, and, perhaps even more than Contact, it has a great deal of

initial appeal.

There may be problems with giving a satisfactory account of what it means to say

that some objects are fastened together. (See in this regard van Inwagen, Material

Beings, pp. 56–7, and Markosian, “Brutal Composition.”) But let us set those problems

aside.

Material objects 193

one objection to Fastening, raised by van Inwagen, concerns the follow-

ing kind of example.

Suppose that you and van Inwagen shake hands,

and that right at that moment, your ﬁngers and his become paralyzed

in such a way that you and he are fastened together. Then according to

Fastening, there is a new object in the world, composed of the two of you.

But (says van Inwagen, and presumably many people will agree) this is

the wrong result: we cannot increase the number of objects in the world

merely by paralyzing handshakers in this way.

Advocates of Fastening will no doubt disagree, and will likely claim

that there is no harm in admitting the existence of the relevant object (the

thing composed of you and van Inwagen while you are stuck together), but

acknowledging that we would normally ignore it when counting objects.

In any case, here is another problem for Fastening. Being fastened

together is a multigrade relation that comes in degrees.

So which degree

of fastenation among some objects is sufﬁcient for their composing a fur-

ther object? Any speciﬁc answer we give is likely to seem arbitrary; why

should a degree of 0.5 (on a scale from 0 to 1), say, or 0.6478592, rather than

just a tiny bit more or less, be the dividing line between cases of compos-

ition and cases of non-composition?

8.5 Nihilism

Some of the above considerations against Contact and Fastening suggest

the following line of thought. You can rearrange the smallest parts of the

world, piling some up over here, separating others out over there, but

you cannot thereby change the total number of objects in the world, any

more than you can change the number of objects that exist by rearranging

grains of sand in the desert.

Merely sticking some small pieces together,

or painting them the same color, or deciding to think of them as compos-

ing something, does not bring anything new into existence.

If this is right, then there are far fewer objects in the world than we

ordinarily think. For if this is right, then it is never the case that two or

Van Inwagen, Material Beings, pp. 57–8.

A multigrade relation is one that can relate different numbers of objects. Two objects

can be fastened together, but so can three objects, or four, etc.

Van Inwagen makes some similar remarks, on behalf of the Nihilist (see below), in

section 13 of Material Beings.

An Introduction to Metaphysics194

more objects compose a further object. Following van Inwagen, we can

call this view Nihilism. According to Nihilism, the only material objects in

the world are “mereological simples” – objects without any proper parts.

Nihilism certainly has its advantages. For one thing, unlike many other

answers to SCQ, Nihilism is a clean and elegant view. For another thing,

with fewer objects in your ontology, you may have fewer metaphysical

problems to deal with. (For example, you won’t face problems like those

raised below by the example of Theseus’s ship.)

Still, Nihilism does face some objections. The main one is just that the

Nihilist’s ontology contains too few objects. According to Nihilism, there

are no atoms, molecules, rocks, dogs, chairs, planets, or stars; and that

goes against what most of us believe.

There is a method for dealing with this objection, however, that is avail-

able to the Nihilist, namely, the paraphrasing approach that van Inwagen

has developed in response to a similar objection to his own view (which

we will consider shortly). Here’s the idea. Suppose we’re in a situation in

which it would be natural to say that there is a chair in the corner. Then

according to the Nihilist, the sentence ‘there is a chair in the corner’ is,

strictly speaking, false. But still, the Nihilist can say, there is something

in the ballpark that is true, namely, the sentence ‘there are some simples

arranged chair-wise in the corner’. And since we have this true paraphrase

of the sentence that it would be natural to say is true, we can accommo-

date our intuitions on this matter, while still claiming that ‘there is a

chair in the corner’ is (strictly speaking) false.

It is an interesting question whether this paraphrasing strategy pro-

vides the Nihilist with an adequate reply to the objection that his or

her ontology contains too few objects. Are our intuitions satisﬁed by the

claim that in ordinary circumstances a sentence like ‘there is a chair in

the corner’ is false, but may be paraphrased into a sentence that is true?

There is potentially a further difﬁculty facing the Nihilist who opts for the para-

phrasing strategy. (The difﬁculty is raised in Sider, “Van Inwagen and the Possibility

of Gunk.”) Suppose it turns out that there are no mereological simples. That is, sup-

pose it turns out that every physical object is composed of further physical objects, so

that it is “parts all the way down”. Then even when it appears that there is a chair in

the corner, it will never be the case that there are some simples arranged chair-wise

in the corner. Perhaps the upshot is that the Nihilist may have to fall back on such

paraphrases as ‘there is some stuff arranged chairwise in the corner’. For more on

stuff see 8.11 below.

Material objects 195

or is it a fatal blow to Nihilism that it entails that such sentences are

always false?

In any case, here is a further objection that can be raised against

Nihilism: what about you? You think, and from that it seems to follow, by

Cartesian reasoning, that you exist. Yet you don’t appear to be a mereo-

logical simple. So where in the Nihilist’s ontology do you ﬁt in?

8.6 Van Inwagen’s Proposed Answer

Consideration of this last objection to Nihilism might lead us to think as

follows. What is most plausible about Nihilism is the idea that it is very dif-

ﬁcult to increase the number of objects in the world merely by rearranging

the simples that already exist. (of course, this must be weighed against the

implausibility of claiming that there are no atoms, molecules, rocks, dogs,

chairs, planets, or stars.) But what is especially implausible about Nihilism

is what it entails about us, namely, that we either don’t exist or else are

mereological simples. What is needed, then, is an answer to SCQ accord-

ing to which there are a limited number of composite objects – enough to

include we humans, and perhaps other things that are sufﬁciently like us,

but not so many as to include rocks and chairs.

Van Inwagen offers such a view in response to the SCQ.

The basic idea

behind van Inwagen’s view is that there are both simples and composites,

but the composites are limited to living organisms. The two main back-

ground concepts on which his view is based are the notion of a life, and the

notion of the activity of some xs constituting a particular event.

A life is what you think it is: a special kind of event, of which your life

is an example. lives can be short or very long, and they tend to resemble

certain other events (like hurricanes, tornados, and riots) in important

respects: they persist over time, they can range over a large area, and

they both take things in and expel objects that have been caught up in

them.

Closely related to this last point (regarding the manner in which a life

both takes in objects and also expels objects that have been caught up in

Van Inwagen raises this objection in more detail in Material Beings, sections 8

and 12.

Van Inwagen, Material Beings, especially section 9.

An Introduction to Metaphysics196

it) is the notion of a life (or any event, for that matter) being constituted

at a time by the activity of some speciﬁc objects at that time. Thus, for

example, an avalanche might be constituted, at any given time while it is

occurring, by the activity of a certain group of rocks, and your life is right

now constituted by the activity of a certain group of subatomic particles.

(The very same particles, as it happens, that it would be natural to say com-

pose your body right now.)

Here then is van Inwagen’s view (which we will call Van Inwagen’s Proposed

Answer, or VIPA): for any xs, those xs compose a further object iff the activ-

ity of the xs constitutes a life. According to this view, there are just two

kinds of physical object in the world: mereological simples and organisms.

one main objection that can be raised against VIPA is similar to the

above objection to Nihilism: the view entails that there are no atoms, mol-

ecules, rocks, bicycles, or planets. And we already know from our discus-

sion of Nihilism in 8.5 what van Inwagen’s reply to this objection will

be: paraphrasing, in the manner discussed above.

Meanwhile, another main objection to VIPA, having to do with the view

entailing the possibility of “ontological vagueness”, will be raised below.

But ﬁrst we’ll look at another approach to answering SCQ.

8.7 The Serial Response

Contact and Fastening yield some counterintuitive results, and Nihilism

is much more restrictive than common sense about the number of mater-

ial objects in the world. Meanwhile, VIPA gets good results regarding liv-

ing organisms, but not when it comes to inanimate objects. But perhaps

the problem with all of these different views is that they fail to take into

account that whether some xs compose something can depend a lot on

what exactly the xs are like. For it is natural to think that the way in which

some subatomic particles compose an atom is very different from the way

in which some molecules form a rock or the way in which some cells com-

pose a living body.

If we take this idea into account in formulating an answer to SCQ, we

will want to identify a series of different types of object, and for each such

type we will want to specify the conditions under which some objects

of that type compose something (without assuming that these conditions

must remain constant for all types of object).

Material objects 197

In order for us to have a more precise way of characterizing this response

to SCQ, consider the following sentence schema:

Series

Necessarily, for any non-overlapping xs, there is an object composed of the

xs iff either the xs are F1s and related by R1, or the xs are F2s and related

by R2, or … the xs are Fns and related by Rn.

Now, the view in question, which we will call The Serial Response to SCQ, says

that there is a correct answer to SCQ, but that it is an instance of Series.

Perhaps the biggest objection to The Serial response is simply that no

one has yet offered a speciﬁc instance of Series in response to SCQ. It has

also been suggested that The Serial response compounds problems with

standard moderate answers to SCQ. For The Serial response ﬁrst requires

us to identify the different types of object (F1, F2, and so on) that are rele-

vant to composition. And then The Serial response requires us to ﬁnd not

just one relation that we can say is both necessary and sufﬁcient for com-

position (and hence immune to counterexample), but one such relation for

each of the types of object (the Fns) that we have identiﬁed as relevant to

composition.

8.8 Universalism and the argument from vagueness

We turn now to an argument that has been suggested by david lewis and

reﬁned by Theodore Sider, and that seems to have some persuasive force

against views like Contact, Fastening, VIPA, and The Serial response to

SCQ.

The problem, as lewis sees it, is that we tend to think that com-

position is restricted to cases in which some xs are adjacent, are fastened

together, contrast with their environment, and act jointly. or anyway,

the more some objects satisfy these intuitive desiderata, the more we are

inclined to think they compose something.

Compare van Inwagen’s discussion of “series-style” answers to SCQ in section 7 of

Material Beings. Compare also the view proposed by rosenberg in “Comments on

Peter van Inwagen’s Material Beings,” as well as the “Finite Serial response” discussed

in Markosian, “Brutal Composition.” (The two objections that follow are from “Brutal

Composition.”)

See lewis, On the Plurality of Worlds, pp. 212–13; and Sider, Four-Dimensionalism,

chapter 4, section 9.

An Introduction to Metaphysics198

But these intuitive desiderata, says lewis, are vague; they come in

degrees. Which means that if we try to use them to generate an answer to

SCQ, then we will have to say that it can be a vague matter whether some

particular xs compose anything. And that, says lewis, is no good:

The only intelligible account of vagueness locates it in our thought and

language. The reason it’s vague where the outback begins is not that

there’s this thing, the outback, with imprecise borders; rather there are

many things, with different borders, and nobody has been fool enough to

try to enforce a choice of one of them as the ofﬁcial referent of the word

‘outback.’ Vagueness is semantic indecision.

lewis’s preferred account of vagueness is sometimes called The Linguistic

Theory of Vagueness. Here is how VIPA, to take one example, seemingly runs

into trouble with this theory of vagueness. As van Inwagen points out, in

many cases it is probably an indeterminate matter whether a certain sub-

atomic particle is caught up in a certain life. (For example, suppose you

have just taken a sip of water. Then many of the H

o molecules [and their

atoms and particles] that you have just ingested will soon be incorporated

into your life, but are right now in a sort of halfway state between being

caught up in your life and not being caught up in your life.) So VIPA has

the consequence that it can be an indeterminate matter whether a certain

object is a part of a certain other object. And this means that, contrary to

The linguistic Theory of Vagueness, there can be “ontological vagueness”

or genuine vagueness in the world.

According to Contact, there are (or at least can be) both cases in which

some objects compose a further object and cases in which some objects

fail to compose a further object. The same thing is true of Fastening, VIPA,

and many other answers to SCQ. Van Inwagen calls answers to SCQ accord-

ing to which there can be both cases of composition and also cases of

non-composition “moderate” answers to that question, and they can be

contrasted with what he calls “extreme” answers.

There are two extreme answers. one of them is Nihilism, which we

have already considered, and the other one is called Universalism (aka

Unrestricted Composition). According to Universalism, composition is auto-

matic; whenever there are some (non-overlapping) xs, there is an object

lewis, On the Plurality of Worlds, p. 213.