External Relations, Causal Coincidence, and Contingency
External Relations, Causal Coincidence, and Contingency
Abstract and Keywords
Many contingent facts concern objects standing in relationships by accident, prominent among these being spatiotemporal relationships, often taken as the paradigm of external (irreducible) relational properties. In this chapter it is argued that while spatiotemporal relations are external to their relata, in that they are not determined by the mere existence or natures thereof, such relations reduce to internal relations between the processes upon which spatiotemporally related individuals ontologically depend. Assuming that processes are ontologically prior to individuals, it is argued that since processes have their spatiotemporal locations essentially, they are internally spatiotemporally related. Assuming relationism about spacetime, this chapter concludes that we do not need to posit relational truthmakers to account for true spatiotemporal predications. The contingency of spatiotemporal relations between individuals, and the existence of spatiotemporal coincidences, is accounted for in terms of the contingency of the relationship between concrete individuals and their sustaining processes.
7.1 Background Assumptions
Many contingent facts concern objects standing in relationships by accident, prominent among these being spatiotemporal relationships, often taken as the paradigm of externality in relations. Yet the ontological basis for these facts is elusive. The metaphysics of relations is an intricate area, and the metaphysics of spatiotemporal relations especially so. Nearly everything in the area is disputed and it is not clear that we are close to an adequate account of such relations. The ontological account I shall propose reveals an underlying tissue of internal relationships leaving little if any scope for real, irreducible, and basic external relations. In order to be as clear as possible about the background assumptions with which I shall be working, I will take a little time to set them out. They are naturalistic nominalism, and sufficient reason.
Naturalistic nominalism as I understand it here is the metaphysical speculation that all entities are spatiotemporal and particular. It can be contrasted with forms of Platonism which postulate abstract entities, including universals and mathematical objects, and immanent realism about universals, which postulates repeatable universals in rebus.
Sufficient reason is Leibniz’s principle according to which for any contingent truth, there is a reason why it is true. In certain simple cases, namely those of simple, positive, unanalyzable truths, the reason takes the form not of another truth but of an entity or entities whose existence is sufficient to render the proposition in question true. Such entities are truthmakers for the proposition. Not all contingent truths have truthmakers,1 but there is always in principle a (p.114) story about why they are true in terms of the existence and non-existence of certain entities, or entities of a certain kind, though we are often, even usually, not in a position to tell this story in detail.
A third position to which I am strongly attracted and which I shall be assuming, but of whose truth I am less confident, is relationalism about space and time: that space and time are not independently existing substantial entities. If they were, this paper would have to be rather different. I am not advancing a positive story about what space and time are, only denying that they are substance-like, so a more accurate, less committal but uglier term for this negative view would be ‘anti-substantivalism’.
The kind of truths for which we shall be seeking sufficient reasons concerns where things are with respect to one another. For example on 18 June 1815 two European statesmen of different generations, Napoleon and Bismarck, were approximately 500 kilometres from one another. What entities are there required to be in order that this proposition be true? To anticipate the outcome, I shall be arguing for two things: that contingent spatiotemporal truths do not require external relations as a basic kind of entity, that the more fundamental relational truths behind such contingencies are internal; and secondly, that the contingency attaching to such truths has as its primary source the contingent existence of events and processes, including those that sustain enduring objects like Napoleon and Bismarck.
7.2 Relational Predications: Internal, Weakly External, Strongly External
For reasons that coincide with those mentioned by Jonathan Lowe elsewhere in this volume, I am not happy with talk of external and internal relations. I do not think there are any items in ontology that are to be called internal relations. I will therefore effect a semantic ascent and relocate the internal/external distinction among predications. Let a predication P(a, b, c,…) be about the several particulars a, b, c,…. Having more than one slot to be filled by nominal expressions for particulars, it is appropriate to call such a predicate ‘relational’. Call such a predication internal if its truth is necessitated by the mere existence of the objects denoted, which we call the terms of the predication. The terms are (jointly) truthmaker for the predication. So the only way in which the predication could have been false is if one or more of the terms had failed to exist. For example, the truth that John and Mary are numerically different is necessitated by the mere existence of John and Mary.
Call a relational predication external if it is not internal. It is weakly external if its truth is necessitated by the existence of the terms and the ways they as a matter (p.115) of fact intrinsically (non-relationally) are, their factual natures. For example, that John is taller than Mary is true because of how tall John is and how tall Mary is. Had John been shorter and/or Mary been taller, the predication could have been false. If the predication is false, it could have been true had the terms existed and been intrinsically different in at least one way. A relational predication is strongly external if the existence and factual natures of the terms do not necessitate its truth. For example that John and Mary are at a certain time spatially next to one another (proximate with no macroscopic body between them, like sitting next to one another on a sofa) is not necessitated by how John and Mary are then, but by where they are then, which is not a matter of their factual natures: these natures could have been the same and yet the two not have been next to one another at that time.
7.3 Relations as Something Objective in the World
In the case of true strongly external predications, we may raise the question as to what, if anything, makes them true. There are a number of proposals that have been made, including the factualist proposal we find in Bertrand Russell, the existence of a state of affairs (Russell calls it a ‘fact’) linking the terms with a relational universal. However, for reasons detailed elsewhere, I reject both universals and states of affairs.2 That does not mean objective or real relations are ruled out. If they exist, then the best candidate status for them is that of being a relational trope.3 A trope is a particular which depends for its existence on another particular which is not a part of it. The dependence is specific or rigid dependence on this other particular. A relational trope is one which is dependent on two or more particulars, neither of which is a part or it or of one another.
One example of a relational trope of which I am reasonably confident is the collision of two bodies. If John collides with Mary in the corridor at 10 a.m., the collision is an event which cannot exist without both John and Mary, neither of whom is part of the other, and since it is categorially impossible for an event to be part of a thing like John or Mary, the collision is a relational trope. The collision makes a later utterance of the sentence ‘John collided with Mary’ true. Of course there could have been a different collision between John and Mary, then or at another time, that made the same utterance true. For example, perhaps they collided elsewhere ten minutes earlier, or they might have collided elsewhere at 10 a.m. This particular collision does in fact make the predication ‘John collided with Mary’ true (taking account of the tense, it must be an utterance made after (p.116) 10 a.m.), but others could have done so and indeed other ones perhaps do make it true. This is because the predication, as Ramsey and later Davidson pointed out, is not atomic but has the truth-conditions of a doubly existentially quantified predication:
There was a collision between John and Mary at some time before now.
Notice that this is a symmetrical relational predication. Non-symmetric relational predications present additional problems that I am deliberately avoiding here.
If there are relational predications that can only be true because of the existence of relational tropes, then relations (qua tropes) are something to which this (nominalistic) account is ontologically committed. However if the truth of contingent relational facts can be accounted for without invoking relations as something objective in the world, we are not so committed.
7.4 Contingent Relational Facts
I am using the term ‘fact’ here not in the sense of Russell as standing for a category of entity but in Frege–Ramsey fashion as a synonym for ‘truth’. It is generally accepted, and I too shall accept, that some facts are contingent. Contingent facts stand in need of an account as to why they are true. Such an explanation need not in my opinion always call for truthmakers, because I am not a truthmaker maximalist. For example each of these truths: that there are no unicorns, that I am not now in San Francisco, that John did not collide with Mary yesterday, and that there are fewer than a hundred people now in this room, is not true because something exists, but is true by default because nothing exists that, were it (or they) to exist, would make it false.4 However some predications mean in such a way that in order to be true, some thing or things have to exist, either particular named things, or things of a certain kind. These things are necessary for the predications to be true, and whosoever assertively utters such a predication is thereby (wittingly or unwittingly) committed to the existence of such things. Most obviously, to assert an existential predication is to be committed to the existence of a thing or things making such a predication true. Not all cases of commitment in this way commit us to truthmakers for the predication in question. For example whoever asserts, as Kant did,5
(p.117) There are narwhals but no unicorns
is committed to narwhals, but these are not truthmakers for the predication because their existence, while necessary, is not sufficient for the truth of the conjunction, the second conjunct of which is a negative existential.
• Barack Obama was not in London on 3 October 2012
• Barack Obama was in Denver, Colorado on 3 October 2012
• SS Andrea Doria collided with MS Stockholm on 25 July 1956
• Asteroid 2012 KT42 did not collide with Earth on 29 May 2012
• On 29 May 2012 Asteroid 2012 KT42 was 14,000 kilometres from Earth
• Asteroid 2012 KT42 is (on 29 May 2012) approximately 7 metres in diameter
all appear to be true, contingent, relational, and strongly external. They are all concerned, in whole or in part, with spatial relationships, in particular, with where certain things are in relation to one another at certain times. It is such relationships that provide the best example of relational truths that appear to call for real relations as their truthmakers. Qua true, we look for why; qua contingent, we look to factors in the real world for the answer; qua relational they concern several things, and qua strongly external the answer does not turn solely on the existence or factual natures of their terms. They are thus among the best candidates for convincing us that real relations exist.
7.5 The Theoretical Unsettledness of Space and Time
The examples turn on spatial and temporal relationships, which are strong candidates for real external relations. However, space, time, and spacetime are notoriously intricate and unresolved areas in ontology. Disputes among proponents and opponents of relationalism and substantivalism on the one hand, and, in the philosophy of time, eternalism versus various species of real tensedness—presentism, growing block, moving spotlight, and pruning tree theories—are rife and involved. The physics of space and time is far from a settled matter: whether spacetime is discrete or continuous, finite or infinite, fundamental or emergent, are all matters of ongoing discussion and speculation. So there is no promise that we are yet close to a satisfactory answer as to whether the best metaphysics of space and time delivers us good arguments for fundamental relations, since we have no assurance such a metaphysics is yet at hand. Nor is this simply a matter of dim philosophers being unable to keep up with physics. The standard big (p.118) theories of physics, namely relativity and quantum theories, pull in different directions as to how they treat space and time. So it pays not to be dogmatic, but to attempt an account of relations which finesses the uncertainty.
7.6 Space, Time, and Causation
Relationalist accounts of space and time have traditionally been hampered by questions as to the possibility of spatiotemporal vacua, that is, places and times without real content, whether spatial vacua, regions without anything in them, or temporal vacua, times when nothing happens. If such things are possible, spacetime would appear to exist independently of its contents. Fortunately, it appears that there is no empty spacetime, so the question does not realistically arise.
There are a number of reasons for thinking that the best available account of the nature of spacetime has to bring in causation. The directional earlier–later asymmetry of time, or in relativistic terms, the asymmetry of the ordering of two events in timelike separation, has been explicated in terms of causal connectibility by Reichenbach, Grünbaum, van Fraassen, and others.6 According to this view, two loci L and M are in timelike separation, with L before M, if and only if it is physically possible for an event at L to cause an event at M. I consider this to be basically correct. I would only strengthen the position to say that L and M are not merely causally connectible, which begs the question as to the status of the modal operator, but actually connected, some event at L causing some event at M. Again it is the plenary nature of spacetime which appears to allow this. Questions of whether there can be time travel then turn on whether there can be causal loops. My own view is that there cannot, but a more irenic position would be to say that the direction and topology of time follows wherever the direction and topology of causation goes. If causation curls back on itself, or goes backwards, so does time.
I am assuming that the relata of causal relations are events, individually or severally (the latter to take account of multiple partial causes). It is then not unreasonable to suppose that when an event or collective of several events C causes another event e to occur, that the relationship between the one or several causes and the effect is internal. (I am using ‘exist’ and ‘occur’ interchangeably in this context.) Given that all of C exist, and that e exists, it is not metaphysically possible for C and e all to have existed and C not to have been the cause of e. From the point of view of the effect e, it could not have occurred and not have been caused by C. From the point of view of C however, it is not the case that if all of C exist, so must e. For it is possible for all of C to exist but in addition some impeding factor f to exist which prevents any event (p.119) like e from happening, or which makes C cause an event of a different kind. To take an old example, striking a match on a suitable surface in the presence of oxygen may cause the match to ignite, but not if the match is wet. If the match does ignite, the striking etc. are the cause of the igniting. The absence of an inhibiting or modifying factor is not itself a further event. So it seems not unreasonable that causation is internal to its terms, and hence that there is no need for an additional ontological element of causing, over and above the events involved. Certainly, as Hume pointed out, we never observe any such thing. But to endorse the internality of causation is not to reduce causation to constant succession or anything else. Causation is a fundamental, irreducible feature of the world whereby some things’ happening make other things happen. There is simply no additional item called the making.7
The causal account of time allows us to deduce the existence of spatial extendedness from that of time, as follows. If there were no spatial separation, i.e. all events were together, then all causes would take effect without delay, so all events would be simultaneous. But there is temporal separation, therefore there must be room for causes to travel or propagate. Conversely, if there is spatial separation, and there are processes in space, then there is temporal separation because of the finite speed of causal propagation. Perhaps both a spread-out unchanging universe and an enduring spaceless universe are conceivable, but neither is compatible with what we know about our causal universe, and neither is to be taken seriously in metaphysics, which is difficult enough already without exploring the merely conceivable.
7.7 Things and Processes: How Related
The contingent, external relationships of things in space and time remains a datum to be explained, but the things in question are not clearly the metaphysical last word as occupants of space and time. Consider, by way of contrast to the everyday Aristotelian–Strawsonian ontology of bodies, an ontology like that of Whitehead in which events and processes are ontologically prior to things. Natural science aside, there is a good metaphysical reason for looking with some favour on this ontology. This is the problem of truthmakers for temporally specific existence statements. Take the contingently true statement:
Bismarck and Napoleon were both alive on 18 June 1815.
What makes it true that the forty-six-year old Napoleon and the six-week old Bismarck were both (contingently) alive on this day? Not the mere existence of (p.120) these two individuals, because either or both could have died earlier: Napoleon at one of his battles such as Borodino or Leipzig, Bismarck of an infantile malady in his first month. Yet both would have existed in the sense of having been something rather than nothing. The only kinds of item connected with either European statesman that could have necessitated their existence on that day were vital processes such as breathing, the heart beating, and so on, which have two important characteristics: they were of a sort naturally necessary for their bearers to be alive then; and they essentially took place when and where they did and not at another time. These processes combined together to constitute processes sufficient to sustain a life, and occurring on that day, are truthmakers for the contingent truth above. If that is so, then the existence of a continuant such as Napoleon is dependent on there being some such processes sustaining him at some time. Not that any one of these processes is individually essential to Napoleon. Rather, he is generically dependent on there being some such processes. Since processes other than those which did sustain him at the time might have sustained him at the time, and these might have happened elsewhere, Napoleon’s actual whereabouts on the (for him and many others) fateful day of 18 June 1815 are contingent and accidental to him.
For it to have been Napoleon who was alive at the Battle of Leipzig in 1813 and the same person who was still alive on the day of Waterloo there must have been a succession, indeed an uninterrupted and continuous succession, of sustaining vital processes. The relationships among these processes are not causal in the sense that the earlier ones cause the later, but there are myriad strands of causation running through them, like threads in a rope. Adopting Kurt Lewin’s concept of genidentity,8 we can say that later phases of the total sustaining process are genidentical with earlier (and vice versa). Genidentity is an equivalence relation, and the ontologically derivative invariant that is identical throughout the phases is the enduring object, Napoleon Bonaparte, for example.9
If then enduring objects are ontologically secondary to processes, this means that the ontologically prior processes have a closer tie to their spatiotemporal locations than the invariant endurants (continuants) they sustain. The processes actually sustaining Napoleon on 18 June 1815 had to be where and when they were, but there is no necessity that those actual processes had to take place: Napoleon’s genidentity train might have stopped, or have been diverted elsewhere, meaning that it was contingent where Napoleon was on that day.
(p.121) 7.8 Causal Coincidence: Examples and Significance
That the location of enduring things at a time is contingent despite the locational essentialism of their sustaining processes means that it is not naturally or causally necessary that the lives of such things, as what in fact sustains them, take the course they do. This view is incompatible with causal determinism, and the question arises as to what form this causal indeterminism takes. While not discounting the role of quantum indeterminacy, as an underlying background and source of a good part of the indeterminacy that affects any macroscopic item, it does not appear to be the source of the more coarse-grained macroscopic indeterminacy that has Napoleon on 18 June 1815 engaged in battle south of Brussels and not quietly sipping wine on Elba, or already dead. To explain this we need other concepts.
Consider an unexpected chance meeting, such as one I had on 26 July 2012 with a Dublin colleague at the Turin railway station. We call that a coincidence, and the word is apt for several reasons. But what does such a coincidence consist in? We say things like: it was unplanned; we didn’t intend to meet; we each just happened to be there at the same time for different reasons, and so on. What these sayings amount to is this. The location of myself at the Turin station at that time was due to a sequence of events involving conference attendance and my chosen route. The location of my colleague there and then was due to a completely distinct sequence of events involving attendance at a quite different conference in a different city on a different topic and calling for a return to a different final destination. Our paths crossed by chance. The coincidence (co-incidence) is just that: the coming together of two causal sequences of events that were causally unconnected until the time at which they intersected, after which they continued in a merged sequence for a while (we sat together and talked on the train from Turin to Milan).
Here is another more widely appreciable example, albeit fictitious. In the 1880 novel Ben-Hur by Lew Wallace, the hero Judah Ben-Hur, alerted by the noise caused by the entry into Jerusalem of his childhood friend Messala, now a Roman military leader, leans on the parapet of his house roof, to see what is going on. He happens to lean on a roof parapet tile which is loose and which, thus dislodged, falls into the street, causing Messala’s horse to shy and throw him. As a result, Ben-Hur is arrested and sent to the galleys. The causal coincidence here is not the connection between the hubbub of Messala’s arrival and Ben-Hur’s going to the parapet to look, which are clearly linked, but the event of his leaning on the tile as Messala is passing, and the independent and prior long slow process of weathering which had caused the tile to come loose enough to be easily dislodged.
(p.122) Causal coincidences abound, and how we as agents deal with them help to define our characters, and the space they leave for alternatives in responding to them is most characteristic of our freedom. (Messala has Ben-Hur tried though he knows him to be innocent of any bad intent towards himself.)
The prior causal independence of the two or more causal chains merging in a coincidence is not absolute, because there must be something to the chains’ being first apart and then together. Our different journeys led both my colleague and me towards the Turin station, and our converging paths in space took the trajectories they did because of our spatial separations at successive times. For A to be 20 kilometres from B at a given time is for the fastest causal signals from A to B or vice versa to take two-thirds of a hundred-thousandth of a second to pass between them. But we pronounce the causal chains independent not because they lack all connection, but because any causal connections between them are so miniscule and swallowed up in the background of causal processes bathing the objects in question that they are negligible by several orders of magnitude. Only when my colleague and I were standing opposite one another a couple of metres apart, and looking with concomitant surprise and recognition at each other, did the mutual causal influences achieve sufficient prominence to constitute a coincidental merger. We then entered into conversation, and sat together on the train to Milan. Had we passed at a distance of 3–4 metres without noticing one another, the spatiotemporal coincidence would have been the same, but the events as affecting our personal histories that day would not.
Coincidence does not entail unpredictability or indeterminacy per se: heavenly bodies on a collision course may be set to collide and be predicted to collide long in advance, even though their prior interactions are weak, so when they do collide, or perhaps shortly before, the two hitherto weakly linked causal chains merge. As a matter of fact however, most coincidences are unpredictable because of the complexity of the situations in which the chains merge. The motions of large heavenly bodies are notoriously easy to predict by comparison with, say, the weather, or stock-market fluctuations.
Considerations of the ontological relation between things and processes have shifted the explanation of spatiotemporal contingency from the spatiotemporal relations themselves between things, to the indetermination affecting the continued existence of enduring things as sustained by processes. Were the processes all we had to consider, then contingency of this sort would be edged out: if locational essentialism is right, the processes that in fact happen must happen where they do, and the processes’ own spatiotemporal relationships turn on the typically more effete processes that actually link them according to the background causal account of spacetime. Where contingency enters in is that it is not (p.123) determined by any current state of the world exactly which processes will succeed and replace those of that current state. Indeterminism is correct. That covers the causal indeterminacy of quantum theory, and while on the intermediate scale of smallish bodies like ours the modest variations of quantum indeterminacy may be smoothed out, longer periods and larger distances allow events to occur which are in significant spacelike separation, which not only allows causal chains to be separated enough to allow of coincidences later, but also mean that small-scale indeterminacies can add up and result in the highly contingent spatiotemporal distribution of matter and energy we find in the world. No one watching the wind shake the leaves of trees in a forest, the waves breaking upon the shore, or the movements of pedestrians on a busy street, can reasonably doubt that there is genuine contingency at play in all the myriad coincidences that are continually occurring at all scales.
7.9 Contingency and Spatiotemporality
So while we have an explanation of sorts as to why there is contingency in the spatiotemporal distribution of things, we are still looking for plausible truthmakers for contingent truths about where enduring things are when. The when part is straightforward: such and such vital processes sustain the enduring thing then, and have their time of occurrence essentially. Likewise the location of these processes is essential. So consider again Napoleon at Waterloo and Bismarck at Schönhausen on that same day in 1815. They are sustained by causally independent but simultaneously unfolding sequences of vital processes, which have their locations essentially, and therefore would appear to have their spatial separation essentially. The existence of these Napoleon processes and these Bismarck processes are truthmakers for truths about their relative spatial positions at that time. The contingency turns on the circumstance that it is these processes and not others that as a matter of fact are sustaining these individuals then. The mere existence of the two human beings, even their existence at that time, is not sufficient for the truths about their spatial relationship, but that they do in fact exist at that time is due to their respective contingently constituting processes, and where and when these are is in each case essential to them, so that their spatial relationship is internal, while the spatial relationship between their constituted continuants, Napoleon and Bismarck, is external to those two gentlemen, though based on internal relations.
In the light of this, it appears there is no need for additional real relations connected with spatial position. Note that we have not eliminated relational (p.124) truths by this account. Two real events or processes do stand in spatiotemporal relationships of several kinds to one another, concerning distance, angle, and mutual relations to third objects, relationships which admit of quantitative and geometric description. The vast network of such relationships is what underlies our complex and sophisticated account of space and time. In that account our descriptive tools, typically various kinds of geometry and their mathematical representation in analysis and vector theory, and more recently in geometric algebra, accustom us to treating locations as if they were entities in their own right (points, regions, etc.) standing in structural relationships, but a relationalist will (I think correctly) consider this a derivative matter. The spatiotemporal relationships among events and processes are of their own kind, but they supervene or come on the back of the events and processes. Given that these and these events and processes take place, that is why they are spatiotemporally distributed thus and so. The distribution is not the same as the processes, but it comes with them as part of the package and is determined by them. That is what relationalism is. The (very many) processual inhabitants or occupants of spacetime are severally and jointly sufficient for the many truths about their spatiotemporal relationships, and no additional real relations are required in the truthmaking role.
It is tempting for mathematical reasons to treat spacetime as an independent substantial whole lacking independent parts, its parts being dependent on it, and the metrical and geometric relationships among different points and regions as internal structural relations among these dependent parts. This turns on the notions of part and of structure, both of which themselves require explication in terms of relations, but again in this case it is arguable that both the part–whole relationship and the structural relationships are internal. This seems to point in the same direction. Relational structure is mirrored in the mathematical structures that are used to model spacetime and since in any mathematical structure all the relationships are internal, we can get the relational ideology without any ontological overhead.
The problem with taking the mathematics as the source of the relationality is that it puts the cart before the horse. Any mathematical structure qua mathematical structure has all its relationships internally, precisely because it is mathematical and its nature is independent of whether or not it is applied, instantiated, or realized in reality. But only some mathematical structures are realized and others are not, and the answers as to which ones are realized turn on independently existing features of that to which the mathematics is applied. For the mathematics to be apt it is required that the mathematical structure be isomorphic to the independent structure, so that the direction of fit is (p.125) mathematics to world and not vice versa. The mathematics is there to serve the natural science, not the other way around.
The doctrine of internal relations was employed in the late nineteenth century by British Hegelians to underpin their ontology of absolute idealism. That we have found our way to a not dissimilar position should not be taken to imply that we endorse either the monism or the idealism of that metaphysic.10 There are many natural objects, and most of the truths concerning them, relational or not, are overwhelmingly objective and mind-independent. That they are here conjectured all to be true solely on the basis of the existence of pluralities of non-relational particulars may be surprising, perhaps even troubling, but is, I think, neither inconsistent nor idealist.
7.10 Incidental Advantages: Regress and Directionality
There are two final positive ontological payoffs accruing to the denial of real relational particulars. The first is that there is no way in which Bradley-style regresses of the relations relating relations to their terms can arise, because there are no relations (whether as universals or particulars). When things stand to one another in a certain way, the ontology discloses nothing but internal relatedness, and this prevents any regress from getting started.
The other payoff concerns a more recent controversy about whether relations are directional or not, started by Kit Fine and continued in particular by Fraser MacBride and Joop Leo.11 Briefly, the issue is whether a relation which is not symmetrical has its directionality built into it or not. There are several mutually incompatible competing positions. The issue is typically raised for universals, but it applied to particulars as well. Take two people A and B and consider whether (at a certain time) A faces B or not, and the separate and independent question whether B faces A or not. All four combined cases are possible, so if the positive cases were made true by relational tropes of facing, there would have to be two of them in case A and B face one another, because either could face the other and not vice versa, and indeed the situation can change over time. It then raises the question (which is generalizable to other non-symmetric relations) how the trope making it true that A faces B differs from the trope making it true that B faces A. If there are no relational tropes, the problem does not arise. Of course that (p.126) does not obviate us of the necessity to explain in what the distinction consists, assuming it has an ontological account. Indeed it may be more difficult to do so, because generally to give ontological accounts gets harder, the fewer the entities are at one’s disposal. Ockham’s Razor is wielded at a price. But the problem does not arise as one about the directionality of relations.12
(7) For further discussion of the internality of causal relations, see the chapters by Lowe, Heil, and Yates in this volume.
(12) Thanks to two anonymous reviewers for constructive suggestions for improvement.