A Physical Argument Against Composition

©  Philosophical Writings
Proceedings of the Fifteenth Annual British Postgraduate Philosophy Conference
A PHYSICAL ARGUMENT
AGAINST COMPOSITION
Jonathan Erhardt – University of Bern
Abstract
Following the lead of Hud Hudson and Yuri Balashov, I formulate an
argument against the thesis that objects arranged in a particular way
compose a further object. I present a number of assumptions from the areas
of physics, ontology and mereology. I then argue on the basis of a thought
experiment that these assumptions yield a contradiction. I suggest that the
best way to avoid this contradiction is to deny that simple objects ever
compose anything. We should accept the thesis of mereological nihilism.
Introduction
Hud Hudson has argued for the truth of the following conditional:
If the conjunction of a rather liberal view of diachronic identity, four-
dimensionalism and some other background assumptions is true, then
there are certain physical objects that move faster than light.1
Since
Hudson accepted the metaphysical antecedent of this conditional, he
concluded via modus ponens that there are indeed objects that move at
superluminal speeds. Yuri Balashov accepted Hudson's conditional but
turned the argument on its head and concluded via modus tollens that
there is something wrong with Hudson’s liberal view of diachronic
identity.2
In this paper I develop a new version of Hudson's conditional: I
argue that the conjunction of any sensible view of diachronic identity,
some background assumptions plus either three- or four-dimensionalism
leads to the possibility of superluminal objects. I then accept Balashov’s
modus tollens argument and argue that we should give up one of
thebackground assumptions, that of synchronic composition.3
The argument can be presented as a set of five propositions that
yield a contradiction when applied to specific states of affairs. In the first
1
Hudson 2002.
2
Balashov 2003a.
3
In this paper I will use the term ‘composition’ as an abbreviation for ‘synchronic
composition’.

Jonathan Erhardt 33
section I present this set of propositions. In the second section I propose a
thought experiment and argue that it allows us to deduce a contradiction
from these five propositions. The third section is a short analysis of the
problem. The final section is dedicated to possible ways to avoid the
contradiction and a defence of one specific way of avoiding it, namely by
giving up composition.
Five Propositions
The first proposition is often thought to be a consequence of the
special theory of relativity.4
We can call this ‘SR’ for ‘special relativity’:
[SR] For every object O, if O is a physical object, then O does not travel
at superluminal speeds.
The next proposition is the common sense view that there can be
such things as composed objects, i.e. objects with other objects as their
parts. Like SR, this is widely accepted among metaphysicians. This
proposition does not entail any particular criterion of composition. Let us
call this ‘CO’ for ‘composition’:
[CO] For every object O1, O2, … and On, if O1, O2 and On are arranged
in a particular way, then O1, O2, … and On compose a further object O.
The third proposition is what I take to be the most restrictive
criterion of composition we can combine with CO without making the
resulting view of composition highly implausible. More liberal criteria
combined with CO might still yield plausible views of composition; more
restrictive criteria on the other hand will lead to a view that entails that
many things we take to be composed objects in everyday life are not
really composed objects after all. Let us call this proposition ‘CC’ for
‘criterion of composition’:
[CC] For every object O1, O2, … and On, if O1, O2, … and On are
arranged in such a way that every object is either directly or via
intermediate objects attached to every other object, such that they
communicate any force applied to any of them, then they compose a
further object O.5
4
See Hudson 2002, p. 1; Balashov 2003a, p. 1.
5
This criterion seems problematic for a number of reasons. First, most objects interact with
each other through the four forces of nature and therefore communicate force, even if there
is a great distance between them. Second, the process of communicating force is something
that takes time and this brings additional complications for a criterion of synchronic

34 A Physical Argument Against Composition
Something like CC seems to be what most of us tacitly assume in
making statements about composition in everyday life.6
It offers a very
straightforward answer to a question asked by Peter van Inwagen: ‘What
do you have to do to some objects to get them to compose something – to
bring into existence some further thing made up of those objects? Glue
them together or what?’7
The answer according to CC is ‘That’s right! Or
you could use screws and bolts’.
The fourth proposition is a statement about diachronic identity.
Most people who accept the existence of composed objects would also
subscribe to some criterion of diachronic identity that allows the same
object to exist at different moments. Instead of providing a full-blown
criterion of diachronic identity I want to settle for an uncontroversial
statement about identity. This statement can be formulated without
appeal to either three-dimensionalist or four-dimensionalist vocabulary.
If we avoid any appeal to endurance or perdurance we can use the same
statement in both metaphysical frameworks. We just have to cash it out
in the appropriate vocabulary once we have decided which metaphysical
view we want to accommodate. We can call this proposition ‘ID’ for
‘identity’:
[ID] Every composed physical object O survives replacement of a
quarter of its parts at a time.8
The last proposition is nothing more than a statement of the
commonly accepted view that composed objects are paradigm cases of
physical objects. Let us call it ‘PH’ for ‘physicality’:
[PH] For every composed object O, if O has only physical objects as
parts, then O is a physical object.
composition. I will use CC anyway because I am not familiar with a more successful
formulation of a criterion of composition.
6
It is also very similar to the criterion suggested by Spinoza in his definition after §13,
Lemma III in Part II: ‘When a number of bodies of the same or different magnitude form
close contact with one another through the pressure of other bodies upon them, or if they
are moving at the same or different rates of speed so as to preserve an unvarying relation of
movement among themselves, these bodies are said to be united with one another and all
together to form one body or individual thing, which is distinguished from other things
through this union of bodies.’ Spinoza 2002 [1677], p. 253.
7
See Sider 2009 with references to van Inwagen 1987, 1990.
8
Perhaps there are some composed physical objects, such as brains, for which ID is not
true. We can ignore this complication as long as ID is true for the type of object in the
thought experiment.
Nothing important depends on the fraction used here. We could use any number less
than 1, say 1/1,000,000. We would just have to adjust the thought experiment accordingly.

Jonathan Erhardt 35
Each of the five propositions on its own as well as their ensemble
seem quite innocent at first. In the next section I want to argue that they
yield a contradiction.
A Thought Experiment
Think about the black and grey boxes in the following illustration
as representations of huge metal objects. The width of each object is
around one million kilometres. Their height and depth is very small, only
around ten centimetres each. Countless such objects are aligned to form
something like a huge path through the universe. Any two adjoining
boxes are attached to each other by some mechanism. Imagine that one
day the huge path is broken because whoever built the objects decided to
move four adjoining boxes downwards by just about eleven centimetres.
Those four objects are still attached to one another, but there is a small
distance between them and the rest of the path. Since those four objects
(call them O1, O2, O3 and O4) satisfy CC, they compose a further object
O. Now imagine that every second one metal box on one side of O is
detached from the intergalactic path and moved down to align perfectly
with O. On the other side of O an object is detached from O and moved
upwards to align it with the path. The moved boxes are then again
attached to their neighbors. This step is repeated every second.
Figure 1: illustration of the thought experiment
What happens is the following. Every second part of O is detached
and replaced by another part. But this new part is not attached at the
place of the old piece; it is attached on the other side of O. This
replacement will result in another composed object because CC is
satisfied. The resulting composed object will still be O: only a quarter of
the parts of O have been replaced at a time and therefore ID ensures that
O will survive this replacement. After every cycle (each cycle taking one
second) the object O will have moved to the left by one million

kilometres. Therefore O will move at a speed of one million kilometres
per second. That’s more than three times the speed of light.
But this contradicts SR, since PH assures that O is a physical
object. Thus the five propositions yield a contradiction when applied to
the state of affairs described in the thought experiment. Note that no
appeal to any assumptions specific to three- or four-dimensionalism was
necessary to deduce the contradiction.
Movement Through Assimilation
What causes this problem is that CO, CC and ID allow for
movement through assimilation. The parts of O do not move themselves
(before they are moved vertically they are detached from O and therefore
cease to be parts of O according to CC), but O moves because it
assimilates new parts while it loses old parts. It is a rather unusual way of
moving, but not unlike the movement of a caterpillar drive (the obvious
difference however being that the segments of the chain remain the same
because they are being transported back on the top of the track). This
way of moving seems to be rather useless, but this does not change the
fact that it is allowed by CO, CC and ID, all propositions to which most
adherents of composition would subscribe.
Looking for a Way Out
There are various ways to respond to this contradiction. I will start
with what I take to be an initially attractive but rather problematic option:
we could deny ID. We then have to propose a more restricted statement
about survival of partial replacement. A way to get a more restricted
statement is by claiming that objects survive only a fifth or a sixth (or
any other amount) of their parts at a time, but not more. But this does not
help. The thought experiment could be modified to take this into account
by assuming that O consists of more than four objects. Another way to
formulate a more restrictive statement is by specifying what is meant by
‘moment’. We could propose that an object can survive replacement of a
quarter of its parts per four seconds. This would prevent O from moving
at superluminal speeds. But once again the thought experiment could be
amended: we simply have to quadruple the width of the boxes. Given the
immense size and age of the universe we could adjust the thought
experiment to new versions of ID for a long time. The adherent of
composition should find this dialectic unattractive. Once they put too

Jonathan Erhardt 37
much distance between their restrictive version of ID and the common
sense formulation of ID, they will face the charge of arbitrariness. Why
should this version of ID be true? It is as far away from common sense as
the denial of composition (i.e. the rejection of CO).
Balashov has argued for this way of avoiding a contradiction.9
He
proposed a statement of restriction of diachronic identity of composed
objects (or in his four-dimensionalist terminology: diachronic
composition), which is based on immanent causality.
[ID*] Objects that are not connected by immanent causality do not
diachronically compose anything.
This statement of restriction is incompatible with ID. If ID* is true then
there are cases where objects do not survive replacement of a quarter of
their parts at a moment. Therefore adopting ID* amounts to denying ID.
In which situations do objects not survive replacement of a quarter
of their parts according to ID*? To answer this question we have to
explicate a bit further what it means to move at superluminal speeds.
Figure 2: a Minkowski space-time diagram
Figure 2 shows a Minkowski space-time diagram. At the center is
an event O with a light cone separating events that are spacelike related
to O from events that are timelike related to O. If an object O moves at
superluminal speed, then it will have a worldline like W that reaches
outside its absolute past. The object will then be related spacelike to itself
9
Balashov 2003b, p. 25.

at other locations in spacetime. But it is widely accepted that it is a
consequence of the theory of relativity that only events in the absolute
past of an event O can causally influence O.
If immanent causation resembles ordinary causation in this respect,
then there will be no immanent causation between events that are related
spacelike. But if immanent causation is a necessary condition for identity
(as ID* suggests), then an object O with a worldline reaching outside its
absolute past cannot exist. Therefore, according to ID*, whenever
survival of replacement of a quarter of the parts of an object would result
in superluminal motion, the object does not survive this replacement.
This means that we can merge ID and ID* into ID**:
[ID**] Every composed physical object O survives replacement of a
quarter of its parts at a time, unless this would result in O moving at
superluminal speed.
It therefore seems as if Balashov’s modification of ID will do the
job and avoid the contradiction. But is it a good solution? There are at
least two problems with this solution. The first problem has already been
mentioned: this move is subject to the charge of arbitrariness. In what
sense is adopting ID* arbitrary (it is after all motivated by a physical
theory)? It seems to me that the only reason for adopting ID* is to avoid
the contradiction. ID** makes it clear that we’re adding an ad hoc clause
to ID in order to deal with the thought-experiment. There is no theory-
internal motivation for adopting ID*, nothing within the common sense
idea of composition or diachronic identity of composed objects gives us
any reasons to prefer ID* over ID.10
The second problem is this: endorsement of ID* without some
empirical criterion for immanent causality leads to the problem that we
are no longer in a position to falsify SR by observing superluminal
objects. To see why this is so, let us imagine that an alien spacecraft has
been observed which has been traveling through the galaxy at
superluminal speeds. Certainly we would be tempted to give up or
modify the theory of special relativity. But ID* would make this
unnecessary, for this spacecraft might, according to ID*, not be one
spacecraft but a series of spacecrafts, each travelling below the speed of
10
I think this can be illustrated if we adjust the thought-experiment in such a way that O is
composed of 1,000,000 parts. We can then reformulate ID** accordingly: Every composed
physical object O survives replacement of 1/1,000,000th of its parts at a time, unless this
would result in O moving at superluminal speed. It seems to me that we would intuitively
reject this version of ID** as absurd; every physical object O survives replacement of
1/1,000,000th of its parts at a time full stop.

Jonathan Erhardt 39
light (if travelling at all)! Since this claim is – without some empirical
criterion for immanent causality – not open to empirical investigation, it
would be logically impossible to falsify SR by empirical observations
like this. We therefore need some empirical criterion to avoid this strange
result.
Balashov suggests that we might use the idea of mark transmission
to find out whether objects are immanent-causality related. Mark
transmission itself is observable and can therefore help us to determine
empirically whether we have observed one spacecraft travelling at
superluminal speeds or a series of spacecrafts. But this suggestion leads
to further problems when applied to our thought experiment.
Imagine that we apply blue colour to the object O at t0. This color
is going to serve as our mark. If an observer sees the blue color at t1 (after
O has moved according to the thought experiment), then we have
successfully transmitted the mark and O is still the same object according
to ID*, and mark transmission as a criterion for immanent causality. We
then let O go through three cycles of replacement as described in section
three. At t1 our object O still has one quarter of its colour, one element
bears our mark and it will be visible to observers of O. It seems like we
have successfully transmitted a mark and therefore (according to ID*
combined with mark transmission as a criterion for immanent causality)
O is still the same object. And yet O has already travelled at superluminal
speed. The contradiction has not been solved. Does this mean that ID*
fails as a criterion? Perhaps not, maybe we have to be more specific
about how we measure the mark at t1.
Figure 3: measuring the mark at t1

The grey object in figure 3 represents O with its spatial extension
and its (interpolated) movement through three cycles between t0 and t1.
The darker square on O represents what remains of the blue mark at t1.
The illustration suggests that it matters where on O we measure at t1 in
order to determine whether the mark has been transmitted. Let’s first
assume we measure at m2. As seen from m2, the mark has been applied
outside the absolute past of the observer. Accordingly the mark has not
been transmitted and we will conclude that the object in front of us is not
identical with the initial object O. If we measure at m1 on the other hand,
some of the mark has been applied inside the absolute past (the area
marked with a dark shade of grey) and we will observe that the mark has
been transmitted. Depending on our choice of measurement (m1 or m2)
we end up with a different verdict about the diachronic identity of O. But
each verdict is not just a verdict about some part of O, it is a verdict
about O itself! It seems to me that the most elegant way to avoid this
measurement problem is to restrict the criterion to point-like objects, i.e.
objects without spatial extension. But then it is no longer a solution for
our present case. I therefore conclude that avoiding the contradiction by
giving up ID is either unattractive or unsuccessful.11
Another option would be giving up CC while retaining CO. This
option has some of the same problems as giving up ID. CC is already a
rather restrictive criterion of composition and in everyday life we are
often a lot more liberal (look at that cloud in the sky, for example).
Opting for a more restrictive version of CC will once again invite either
revision of the thought-experiment or the charge of arbitrariness.
We could also simply drop SR but I take it that only few will be
tempted to take this road. Instead we might perhaps think about giving up
PH. I think there are two arguments against giving up PH. If we endorse
CC and CO, we think that there are many composed objects consisting of
physical parts. But if we deny PH, then these objects are not physical
objects. This amounts to denying physicalism. There may be many good
reasons to deny physicalism, but the problem in question does not seem
to be one of them. Composed objects such as tables, chairs, and ships are
thought to be paradigm-cases of physical objects.
11
Balashov suggests that ‘Micro-immanent causality is fundamental and strictly governed
by the laws of physics, whereas its macroscopic counterpart is derivative and may be loose
(in Bishop Butler’s sense) because, in the end, it owes its worth to an underlying theory of
synchronic composition’ (Balashov 2003b, pp. 26-7). From here it’s a small step to give up
CC and CO. If macroscopic immanent causality is loose and we want to deny that in
ontology anything is ever loose, then we can insist that there are no composed objects. This
leaves us with immanent causality simpliciter.

Jonathan Erhardt 41
The second argument against giving up PH is based on
considerations about logical supervenience. It seems highly plausible that
composed objects (if they exist) supervene logically on their parts. It
seems logically impossible that there are atoms arranged chair-wise but
no chair.12
If we deny PH then we have to accept that non-physical
objects can logically supervene on physical objects. This is a high price
to pay. Because of this I think we should not deny PH.
What is left is giving up CO, which entails giving up CC: we can
deny that objects ever compose anything. All that exists are simple
objects, basic stuff, elementary particles. This is the thesis of
mereological nihilism. This option does not seem ad hoc: mereological
nihilism has not been developed to avoid this contradiction. It just
happens that this theory fits perfectly with the predictions of special
relativity. I think this is the hallmark of a good theory (e.g. genetics and
evolutionary theory). And neither does this option suffer from any of the
other objections above. I conclude that we should therefore adopt
mereological nihilism.13
Bibliography
Balashov, Yuri, 2003a: ‘Temporal Parts and Superluminal Motion’ in
Philosophical Papers 32:1, pp. 1-13.
Balashov, Yuri, 2003b: ‘Restricted Diachronic Composition, Immanent
Causality, and Objecthood: A Reply to Hudson’ in Philosophical
Papers 32:1, pp. 23-30.
Hudson, Hud, 2002: ‘Moving Faster than Light’ in Analysis 62:3, pp.
203-205.
Merricks, Trenton, 2003: Objects and Persons. Oxford, New York:
Oxford University Press.
12
Peter van Inwagen introduced the idiom ‘arranged x-wise’; see van Inwagen 1990, pp.
105-109. Trenton Merricks suggests a reading of this idiom which differs from van
Inwagen’s: ‘Atoms are arranged statuewise if and only if they both have the properties and
also stand in the relations to microscopia upon which, if statues existed, those atoms’
composing a statue would non-trivially supervene.’ (Merricks 2003, p. 4)
13
I am very grateful to Dominik Aeschbacher, Hud Hudson, Simon Dürr, Matthias Egg,
Alexandru Marcoci, Pendaran Roberts, Dean Zimmerman and Tobias Zürcher for
discussing the argument with me and providing valuable comments. I’m also grateful to the
audience at the BPPA 2011 conference for their questions and feedback.

Sider, Theodore, 2009: ‘Ontological Realism’ in Metametaphysics (ed.
David J. Chalmers, David Manley and Ryan Wasserman). Oxford,
New York: Oxford University Press, pp. 384-423.
Spinoza, Baruch, 2002 [1677]: Ethics in Complete Works (ed. Michael L.
Morgan and Samuel Shirley). Indianapolis: Hackett, pp. 213-382.
Van Inwagen, Peter, 1990: Material Beings. Ithaca, London: Cornell
University Press.
Van Inwagen, Peter, 1987: ‘When are Objects Parts?’ in Philosophical
Perspectives 1: Metaphysics (ed. James Tomberlin). Atascadero:
Ridgeview, pp. 21-47.

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