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A Physical Argument Against Composition
1.
© ï Philosophical
Writings Proceedings of the Fifteenth Annual British Postgraduate Philosophy Conference A PHYSICAL ARGUMENT AGAINST COMPOSITION Jonathan Erhardt â 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 Hudsonâs 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 Balashovâs 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 âcompositionâ as an abbreviation for âsynchronic compositionâ.
2.
Jonathan Erhardt 33 ©
ï Philosophical Writings 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 âSRâ for âspecial relativityâ: [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 âCOâ for âcompositionâ: [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 âCCâ for âcriterion of compositionâ: [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
3.
34 A Physical
Argument Against Composition © ï Philosophical Writings 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: âWhat do you have to do to some objects to get them to compose something â to bring into existence some further thing made up of those objects? Glue them together or what?â7 The answer according to CC is âThatâs right! Or you could use screws and boltsâ. 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 âIDâ for âidentityâ: [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 âPHâ for âphysicalityâ: [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: âWhen 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.â 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.
4.
Jonathan Erhardt 35 ©
ï Philosophical Writings 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
5.
36 A Physical
Argument Against Composition © ï Philosophical Writings kilometres. Therefore O will move at a speed of one million kilometres per second. Thatâs 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 âmomentâ. 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
6.
Jonathan Erhardt 37 ©
ï Philosophical Writings 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.
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38 A Physical
Argument Against Composition © ï Philosophical Writings 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 Balashovâs 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 weâre 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.
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ï Philosophical Writings light (if travelling at all)! Since this claim is â without some empirical criterion for immanent causality â 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
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Argument Against Composition © ï Philosophical Writings 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. Letâs 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 âMicro-immanent causality is fundamental and strictly governed by the laws of physics, whereas its macroscopic counterpart is derivative and may be loose (in Bishop Butlerâs sense) because, in the end, it owes its worth to an underlying theory of synchronic compositionâ (Balashov 2003b, pp. 26-7). From here itâs 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.
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ï Philosophical Writings 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: âTemporal Parts and Superluminal Motionâ in Philosophical Papers 32:1, pp. 1-13. Balashov, Yuri, 2003b: âRestricted Diachronic Composition, Immanent Causality, and Objecthood: A Reply to Hudsonâ in Philosophical Papers 32:1, pp. 23-30. Hudson, Hud, 2002: âMoving Faster than Lightâ 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 âarranged x-wiseâ; see van Inwagen 1990, pp. 105-109. Trenton Merricks suggests a reading of this idiom which differs from van Inwagenâs: âAtoms 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 atomsâ composing a statue would non-trivially supervene.â (Merricks 2003, p. 4) 13 I am very grateful to Dominik Aeschbacher, Hud Hudson, Simon DĂŒrr, Matthias Egg, Alexandru Marcoci, Pendaran Roberts, Dean Zimmerman and Tobias ZĂŒrcher for discussing the argument with me and providing valuable comments. Iâm also grateful to the audience at the BPPA 2011 conference for their questions and feedback.
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Argument Against Composition © ï Philosophical Writings Sider, Theodore, 2009: âOntological Realismâ 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: âWhen are Objects Parts?â in Philosophical Perspectives 1: Metaphysics (ed. James Tomberlin). Atascadero: Ridgeview, pp. 21-47.
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