So far we have considered a wide range of issues to do with time. In the background of much of this discussion has been the concept of causation. Indeed, for each of the main areas of philosophical interest in the notion of time, causation has some role to play. In this chapter we turn our attention to understanding this intriguing notion. We will draw a rather broad (and somewhat artificial) distinction between two very general theories of causation, before looking at the relationship between causation and time.
The two major theories of causation discussed in contemporary philosophy are process theories of causation and counterfactual theories of causation. We will have more to say about both theories in due course; for now, however, it is useful to place these two theories on a kind of ‘metaphysical spectrum’, from the most substantive to the least substantive theories of causation.
At one end of the spectrum we have process theories. These are the most substantive theories of causation in so far as they treat causation as a kind of physical process that is available for empirical investigation in the ordinary way. Process theories are substantive because they treat causation as something to be discovered, just like any other thing that we might seek to investigate scientifically.
At the other end of the spectrum we have counterfactual theories of causation. These theories are the least substantive in so far as they don’t treat causation as any kind of physical process. Indeed, it is compatible with a counterfactual theory of causation that causation obtains in the complete absence of any physical process whatsoever. On this view, causation is analysed chiefly in terms of the truth or falsity of counterfactual conditionals: claims of the form ‘if X had not been the case, Y would not have been the case’.
This way of carving up the space of theories of causation has one chief limitation: it doesn’t cover all of the theoretical approaches to causation that there are. The advantage of dividing the terrain into process and counterfactual theories is that it produces a fairly straightforward narrative that helps us to see a lot of what is at stake in debates over causation. Because the truth should never get in the way of a good story, we will keep the division, but with the understanding that it is not supposed to be a completely accurate representation of the philosophy of causation.
Process theories of causation have a fairly long tradition in the history of Western thought. Contemporary process theories of causation have their roots in mechanistic theories of causation, which rose to prominence in the wake of the unprecedented scientific success of Newton’s Principia Mathematica. For the first time in history, it seemed that humanity had tamed the heavens. The motion of the stars and the planets in our solar system had been given a detailed and precise mathematical characterisation that produced predictions of incredible accuracy. The picture of the universe that Newton paints is like the inner workings of a clock, with every gear and lever set on the tension of every other, to produce an exact and unrelenting process. An account of what it is for one thing to cause another follows very naturally from this picture of the universe.
One of the chief insights of Newton’s picture is that what we really need to explain is deformations in motion. Everything in the universe is continuing on some path or other, and will do so unless impinged on by an external force. The concept of causation ‒ which appears to be the very engine of this kind of change ‒ is mechanistic in nature. According to this very basic mechanistic account, causation is ‒ to put it somewhat crudely ‒ a matter of things bumping into one another. Causation occurs when an object that is minding its own business, heading through the universe in a straight line, is struck by something and is then forced to change its motion in some respect.
In other words, according to a mechanistic theory of causation, P causes Q when P brings about a change in Q’s motion. Causation, then, just is the alteration of the motion of one thing by another. Mechanistic theories of causation such as this have clear limitations. Chief among these is the fact that a great deal of causation has nothing to do with motion. When Sally touches a hot stove and burns herself, the burn that Sally receives is not a result of motion. It is, rather, the result of the transference of energy. Similarly, when the path of an asteroid is altered in virtue of the gravitational field of a nearby sun, it is not because the motion of the sun induced a change in the motion of the asteroid. It is, rather, the unmoving gravitational field of the sun that changes the asteroid’s direction.
Mechanistic theories of causation, then, are no good. But they do preserve a core insight, one that many process theories seek to develop. That insight is that causation is an empirical phenomenon. Motion can be measured and detected, as can changes in motion. Inertia is well defined and understood, as is velocity. All of these are straightforwardly encoded in a working mechanics, such as Newton’s. Causation, then, is within the purview of empirical investigation.
Recent process theories of causation take this core insight and develop it further. Just as early process theories had their roots in the best mechanics of the time ‒ Newton’s ‒ contemporary process theories have their origins in the best mechanics of our time ‒ Einstein’s. The basic idea behind contemporary process theories is to treat causation as a matter of objects in constant motion interacting in some manner. Because, in Einstein’s theory, every object can be considered to be in motion relative to some frame of reference, every object has the capacity to exert a causal influence.
According to one prominent process theory, a causal process is a causal interaction between two persisting objects, and a causal interaction involves the transference of a ‘mark’ from one object that is persisting in this manner to another. We can think of a mark transfer as a local modification of one object, by another. Suppose that a chalk-covered white billiard ball hits a red billiard ball, leaving a white chalk mark on it. That is a paradigmatic instance of mark transfer: we can see the mark ‒ the chalk ‒ that is transferred from one object to the other.
Contemporary process theorists take the idea of mark transfer and provide a concrete account of what marks are, and thus what mark transference involves. According to contemporary process theories, a mark is a conserved quantity. Mark transference, then, is the transference of some conserved quantity or other. A conserved quantity is any quantity that obeys the laws of conservation. The contemporary process theorist relies on our best science to tell us what conserved quantities are. Candidates, however, include mass, energy, momentum and electric charge.
The contemporary process theorist provides a two-part definition of causation. First, they define a causal interaction as follows:
CQ1 A causal interaction is an intersection of world lines which involves exchange of a conserved quantity.
Then they define a causal process in terms of conserved quantities:
CQ2 A causal process is a world line of an object which possesses a conserved quantity.
Note that a ‘world line’ is just a trajectory through spacetime: a path from one spacetime point to another, where any two adjacent spacetime points in the path are light-like or time-like separated from one another (they are at a null or negative spatiotemporal distance to each other and thus one can get from one spacetime point to the other by travelling at a speed that is at or below the speed of light).
The basic idea is that causation occurs when two objects meet in spacetime (this is what happens when their world lines intersect), and one object transfers some conserved quantity to the other. Since there are a variety of conserved quantities, this idea can account for a wide variety of causal processes, from burning one’s hand on a hot stove to one billiard ball causing another to change direction (or to be covered in chalk). And notice that the account does all of this in a scientifically upstanding and empirically tractable manner. Our best mechanics is used to define causation, and then causation is analysed in terms of empirically discoverable features of the world; features that obey important scientific laws (the conservation laws).
Unfortunately, as we shall now see, all process theories face a serious problem. Suppose that Sara buys a new plant. She affectionately names the plant Bertie. Sara tends to her plant dutifully, showering it with love, attention and, most importantly, water. One day, however, Sara goes on holiday and forgets to organise for someone to stop by and water her plants. Sadly, Bertie dies. It seems very plausible to say that Sara caused Bertie’s death by failing to water her beloved plant. And yet, every process theory of causation currently on the market has trouble delivering that straightforward result.
Why? Well, let’s go through the reasoning. According to the contemporary process account outlined in the previous section, causal interactions occur only when the world lines of two objects meet and, when they do, a conserved quantity is transferred from one object to the other. So for Sara to cause Bertie’s death at, say, spacetime point P ‒ the exact time and place of Bertie’s final breath ‒ Sara would need to be located near enough to P to interact with Bertie. But suppose that Sara has gone on holiday to the USA and Bertie lives (and dies) in Australia. Well, then Sara and Bertie’s world lines do not meet at P and so Sara can’t cause Bertie to die. More generally, there just is no conserved quantity that is transferred from Sara to Bertie and so no causal process linking the two.
The problem, in its most general form, is this. Sara’s failure to water Bertie is not, itself, an event, or a physical phenomenon. It is, rather, the absence of an event, or the absence of a physical phenomenon. Bertie’s death is, however, a physical phenomenon: it is a spatiotemporally located event. According to all versions of the process theory of causation, in order for there to be causation between Sara and Bertie there must be a physical process of some kind linking an absence (Sara’s failure to water) with a presence (Bertie’s desiccated corpse). But processes don’t connect absences with presences. They always connect existing physical phenomena, one to the other. So it would seem that there simply cannot be a physical process connecting the cause with the effect in this case. It follows that no process theory can do any better than the account outlined in the previous section. All such theories will fail to account for the causal relationship between Sara and her beloved Bertie.
The process theorist has a number of responses available to her to solve the problem. None of them seem very good. First, the process theorist might simply bite the bullet. Yep, Sara does not cause Bertie’s death. So what? To see why this type of response won’t do, it suffices to consider a structurally analogous case. Consider Sam. Sam has a child he affectionately names ‘Rudolph’. Sam tends to his son dutifully, showering him with love, attention and, most importantly, food. One day, however, Sam goes on holiday and forgets to organise for someone to look after Rudolph and feed him. Sadly, Rudolph dies. It seems very plausible to say that Sam caused Rudolph’s death by failing to feed his beloved son. And yet, every process theory of causation currently on the market has trouble delivering that straightforward result.
Now, suppose that the process theorist tells us to simply bite the bullet on this case. Yep, Sam is not a cause of Rudolph’s death. So what? Suppose, further, that Sam is arrested and charged and brought before the judge for his negligence. If the process theorist is right, then Sam did not cause Rudolph’s death. But on the plausible assumption that it is necessary for being responsible for an event E, that one is at least a partial cause of E, then it follows that Sam is not responsible for Rudolph’s death ‒ not morally, and not legally. That’s preposterous: of course Sam is responsible for Rudolph’s death (just try the ‘but the process theory of causation is true’ defence in a court of law and see how far it gets you!). But if Sam is responsible for Rudolph’s death, then he must be causally implicated in that death somehow. The process theorist’s denial that Sam is causally involved in the death looks troubling indeed.
One might take a ‘divide and conquer’ approach to this type of problem. The process theory of causation, the process theorist might argue, is a theory of causation that is fit for service in scientific contexts only. It does not work outside of very particular empirical situations, involving the transference of conserved quantities. To be sure, there is some other notion of causation that is broader than this purely scientific one, but the process theory is just not in the business of analysing that broader concept. The approach is a ‘divide and conquer’ approach because, in essence, the process theorist is recommending the sub-division of the concept of causation into two distinct concepts: one fit for service inside a legal context, and one fit for service inside a scientific context.
Whether this divide and conquer response works depends a bit on what it is that we are trying to do. If we are trying to give an account of causation regardless of the particular context in which a causal notion is used, then the process theory is not up to that task. If, however, we are trying to give an analysis of a peculiarly scientific concept of causation, then perhaps the process theory will do. Our view is that the goal of developing a theory of causation is, or at least should be, the more general one of analysing causation wherever it arises. The more localised project is not really a project of understanding causation. It is, rather, a project of understanding something like physical interaction inside science, or empirical influence as constrained by conservation laws or something along those lines. That project is of limited philosophical interest. The more interesting project, and the one that will really help us to understand what causation is, is the more general project. So it is a rather severe limitation of the process theory if it is just not up to the task.
The next option available to the process theorist is to reify absences. What does this mean? Well, recall the general form of the problem facing the process theory: the failure to water Bertie is the absence of an event; Bertie’s death is not. Processes can’t link presences to absences. But presumably that’s because absences are not a part of the inventory of the universe. There is no ‘thing’ that corresponds to the failure of Sara to water Bertie. But what if there were such a thing? What if the failure was as much a spatiotemporally located object as was the death? In that case there would be no problem in linking the two things via some physical process or other.
This response to the general problem is costly. For it requires adding peculiar entities ‒ absences ‒ into our inventory of what exists. Such things cry out for a metaphysical account of their nature. But providing such an account looks hard indeed. Moreover, even if such an account could be given, the resulting theory would offend against parsimony in the extreme. For there is an infinite number of things that fail to exist, or to obtain. Once we open the door to some of these, it is difficult to see why we shouldn’t countenance them all. Our account of the world would become bloated with these new objects. Worse still: once we have let these absences into the world, how do we stop them from being causally efficacious? For consider, it is not just Sara’s failure to water the plants that brings about Bertie’s death. Everyone on Earth failed to water the plants as well. If all of these various failures are things that exist it is difficult to see why they shouldn’t also be causally implicated in Bertie’s death. But that seems bizarre. Consider again the case of Sam and Rudolph. Everyone on Earth failed to feed Rudolph. So should we all go to prison? Even the judge sitting on the case? No; something has gone wrong.
The process theorist is not done yet. She might deny that absences are things, but nonetheless maintain that there is some process implicated in the relationship between Sara and Bertie. Think of it this way: there is a range of physical processes that bring it about that Bertie dies. We should think of the absence of watering not as the lack of a process, but as the initiation of a process which eventually kills Bertie. The process, in this case, being the process of desiccation. So while it seems natural to say that it is Sara’s failure to water Bertie that kills him, what actually occurs is that Sara sets another process off ‒ a process of heating by leaving Bertie in a hot room, or a process of wilting that is brought about by leaving Bertie in the sun ‒ and so on, and it is these processes that link Sara to Bertie’s death. In short, talking of Sara’s failure to water Bertie as the cause of his death is a metaphorical way of identifying some underlying process that Sara does, in fact, bring about.
The trouble with this solution is that the general problem under consideration can be reconstructed for these other processes. Without going into details, just about every physical process involves two things at some point: excitation, whereby something is forced to happen, and inhibition, whereby something is prevented from happening, and this prevention in turn brings something else about. So when we heat the room in which Bertie lives, this heating in turn inhibits certain things from happening inside Bertie, such as the process of cellular respiration inside Bertie’s cells. The lack of cellular respiration then brings about Bertie’s death. In order to fully specify the process that is responsible for Bertie’s death, a process that Sara initiates, we will be forced to once again call upon causation by some absence or other inside the relevant process that we have appealed to.
Now, we could try and make the same move with this second case of causation by absence, namely: find a third process to reinterpret the causation by absence, and treat the causation by absence as a kind of metaphor. But right down to the sub-atomic level we find processes of inhibition occurring. So it is very doubtful that we can find a scale at which, for every case of causation by an absence, there is a process that fully accounts for the causation in the relevant situation and that features no inhibition of any kind. In short, the universe seems to feature causation by absences at the most fundamental levels, making it very difficult to treat all statements of causation as metaphorical ways of specifying some underlying process.
This exhausts the standard solutions to the problem of causation by absence facing the process theory. In what follows we turn our attention to counterfactual theories of causation which, among their many virtues and vices, manage to provide an easy solution to the problem of causation by omission.
As we have already noted, modal claims deal with possibility and necessity. A counterfactual is a unique kind of modal claim. The easiest way to gain a sense of what a counterfactual is, is to look at some examples. So consider the following:
[1] If Trump had not won the 2016 US election, Clinton would have.
[2] If the 2016 referendum in the UK had received a majority of remain votes, the UK would not have decided to leave the European Union.
A counterfactual tells us what would or might have happened, had something that in fact occurred, not occurred; or if something that did not occur, had occurred.
A counterfactual theory of causation seeks to build causation around claims such as the above. Such theories attempt to analyse the causal relationship between distinct events in terms of counterfactual relationships between claims about those events. We start by defining a notion of counterfactual dependence as follows:
Counterfactual Dependence: A counterfactual depends on B just when
[i] if it were not the case that A, then it would not be the case that B, and
[ii] if it were the case that A then it would be the case that B.
To understand this definition it is useful to consider a very basic example. Suppose that Sara strikes a match and lights it. Now consider the two events: E1, Sara striking the match, and E2, the match lighting. E2 counterfactually depends on E1 when two counterfactual claims are true, namely:
[3] If E1 had not occurred, then E2 would not have occurred.
[4] If E1 had occurred, then E2 would have occurred.
We know that the second counterfactual is true, very roughly, because we can look to see what actually happened. Given that Sara struck the match and her striking the match was followed by a lighting, we have good reason to suppose that [4] is true (we will sharpen this up in due course). The first counterfactual is more difficult to evaluate. But here’s the basic idea. First, we imagine a situation that is just like the world we live in, except that in that world Sara doesn’t strike the match. Based on what we know about science and the laws of nature, we then run the scenario forwards in our minds to see what happens with the lighting of the match. If the match does not light, then we have reason to suppose that [3] is true. If the match lights anyway, then we should think that [4] is false (this will also be made more precise in a moment).
We can use the basic notion of counterfactual dependence outlined above and formulate it into a first-pass theory of causation, as follows:
CF Theory of Causation: ‘X causes Y’ is true iff there is a causal chain leading from X to Y consisting of events A, B, C … such that C depends counterfactually on B, B depends counterfactually on A and so on.
Here’s the basic idea. Consider two events, E1 and E2. E1 causes E2 when there is a chain of events linking the two such that any two adjacent links in that chain stand in a relation of counterfactual dependence. So consider, again, Sara and her match lighting. As before, let E1 be the event of Sara striking the match and let E2 be the event of the match’s lighting. In between E1 and E2 there is a sequence of events:
A: The match head heats up.
B: The material on the match head combusts.
C: The match head catches fire.
E2 counterfactually depends on C: if the match head had not caught fire, then the match would not have lit. Similarly, C counterfactually depends on B: if the material on the match head had not combusted, the match head would not have caught fire. B, in turn, counterfactually depends on A: if the match head had not heated up, then the material on the match head would not have combusted. Finally, A counterfactually depends on E1: if Sara had not struck the match, the match head would not have heated up.
Using this basic model, it is easy to extend the counterfactual theory of causation to handle a great many of the cases of causation in which we are interested. One of the important features of the counterfactual theory is that it can handle all of the cases of causation invoked by the process theory of causation, and then some. Processes of the kind that process theorists are interested in can be modelled using chains of counterfactual dependence, where each step in the chain specifies a particular event ‒ a localised happening in spacetime ‒ and where any two spatiotemporally adjacent steps stand in a relation of counterfactual dependence.
But while the counterfactual theory of causation can handle instances of process-based causation, it does not demand the existence of processes linking cause and effect for causation to occur. And therein lies the chief advantage of the counterfactual theory: it is flexible enough to handle causation no matter what in the world underlies the causal facts in question. Because of this the counterfactual theory of causation is capable of handling causation by absence with ease.
To see this, suppose, once again, that Sara goes on holiday and neglects to water her beloved Bertie. To fit this case into a counterfactual theory of causation, we begin by identifying the sequence of events that leads from Sara’s failure to water Bertie to Bertie’s unfortunate demise. We can imagine that the sequence of events goes something like this:
E1: Sara fails to water Bertie.
A: Bertie becomes dehydrated.
B: Photosynthesis in Bertie’s cells ceases.
C: Bertie’s cells cease respiration.
E2: Bertie dies.
Having identified the relevant sequence of events, we then chain the events together with relations of counterfactual dependence, like so:
[1] If Sara had watered Bertie, Bertie would not have become dehydrated.
[2] If Bertie had not become dehydrated, photosynthesis in Bertie’s cells would not have ceased.
[3] If photosynthesis in Bertie’s cells had not ceased, Bertie’s cells would not have ceased to respire.
[4] If Bertie’s cells had not ceased to respire, Bertie would not have died.
Because these four counterfactuals are true, there is a causal chain leading from E1 to E2 of the kind required by the counterfactual theory of causation. Because there is a chain of the relevant kind, it follows that Sara caused Bertie’s death.
One of the nice things about the counterfactual theory of causation is that it treats causation by absence in just the same way as it treats any other kind of causation. In every case a chain of counterfactuals is used to establish a causal chain linking cause with effect, a causal chain that underwrites causation.
It would seem then that the counterfactual theory of causation has a lot to recommend it. Before looking at some of the difficulties that the counterfactual theory of causation faces, it is important to dig down into the details of the view a bit more. In particular, it is important to say a bit about how we determine whether a counterfactual conditional is true.
As we have seen, a counterfactual is a kind of if/then statement: it is a conditional. But it is not like the usual kind of if/then statement that we encounter in a first-year logic course. That kind of if/then statement has the following truth conditions: the statement ‘if A then B’ is true just when either A is false, or B is true.
The truth conditions for a counterfactual conditional are more complicated. To understand the conditions, we need the concept of a possible world. Recall that a possible world is just a way that the entire universe could be: it is a complete specification of a possibility. For present purposes it will be useful to imagine our universe floating in a sea of bubbles, where each bubble is a self-contained cosmos that differs from our universe to greater or lesser degrees. Each such cosmos is a possible world.
The next thing we need is the concept of a similarity ordering. In particular, we need the idea that possible worlds can be ordered with respect to the actual universe in terms of how similar those worlds are to the actual universe. The most similar worlds to the actual world are the closest possible worlds. The most dissimilar possible worlds to the actual world are the furthest possible worlds.
Using these two notions, we are now in a position to state a first-pass semantics for counterfactual conditionals. Here it is:
Analysis 1: For any counterfactual of the form ‘if it were that A, then it would be that B’, that counterfactual is true just when some possible world in which both A and B are true is closer to the actual world than any possible world in which A is true and B is false.
To see how Analysis 1 works it is useful to apply it to a particular case. Suppose, again, that Sara strikes a match and the match lights. Now, consider the counterfactual dependence of the lighting of the match on Sara’s striking, as enshrined in the following conditional:
[5] If Sara had not struck the match, the match would not have lit.
[5] is true when there is some possible world in which Sara does not strike the match and in which the match does not light that is more similar to the actual world than any world in which Sara does not strike the match and the match lights anyway. The thought, then, is that the counterfactual is true when it is more of a departure from actuality when Sara does not strike and the match lights anyway than when Sara does not strike and the match does not light. Intuitively, the counterfactual is true: if we imagine a scenario in which Sara does not strike the match, then, assuming that the world is exactly like our world in all other respects leading up to the striking, there won’t be anything else available to light the match in lieu of Sara’s striking. So the match won’t light.
So far we have looked at a basic counterfactual theory of causation, and have provided an overview of the semantics for counterfactual conditionals. Let us now consider the chief problem facing a counterfactual theory of causation. The central problem for a counterfactual theory of causation concerns a phenomenon called pre-emption. Pre-emption tends to occur when, for some causal chain, there is a back-up system in place, ready to kick in if the main causal chain fails. There are many ways to formulate a problem based on pre-emption, but we will focus on just one to give a flavour for the difficulties that back-up systems pose.
Suppose Sara and Emma are throwing rocks at a bottle. Sara throws, and then Emma throws, just after Sara does. Sara’s rock gets there first at the last second, striking the bottle and smashing it. Emma’s rock whizzes through the debris field. But for the accuracy of Sara’s throw, Emma’s would have done the job.
It seems clear that Sara’s throw caused the smashing of the bottle. Unfortunately, the counterfactual theory of causation cannot deliver that result. In order for it to be the case that Sara caused the smashing of the bottle, there must be a chain of events leading from Sara’s throw to the smashing such that any two adjacent events in that chain stand in a relation of counterfactual dependence. Let us model the chain, roughly, as follows:
E1: Sara throws the rock.
A: Sara’s rock flies through the air towards the bottle.
B: Sara’s rock strikes the bottle.
E2: The bottle smashes.
For Sara to be the cause of the smashing, each of the counterfactuals in the following sequence must be true: if Sara had not thrown the rock, Sara’s rock would not have flown through the air towards the bottle; if Sara’s rock had not flown through the air towards the bottle, Sara’s rock would not have struck the bottle; if Sara’s rock had not struck the bottle, the bottle would not have smashed.
The last counterfactual in this sequence is false, because of Emma’s throw. It is just not true that if Sara’s rock had not struck the bottle, then the bottle would not have smashed. That’s because if Sara’s rock had somehow missed the bottle, Emma’s rock would have still been on target and would have hit the bottle. In other words, it is not true that some world in which Sara’s rock does not strike the bottle and the bottle does not smash is closer than any world in which Sara’s rock does not strike the bottle and the bottle smashes anyway. That’s because, in the relevant world in which Sara’s rock does not strike the bottle, Emma’s rock strikes the bottle instead, and the bottle smashes regardless.
So the counterfactual theory yields the result that Sara does not cause the bottle to break. The problem is quite a general one: whenever there is a back-up system of the kind just described, the chain of counterfactual dependencies needed to establish causation is undermined by the back-up.
Now, you might think that the problem posed by pre-emption is not all that deep. After all, there is a physical process linking Sara’s throw to the smashing of the bottle, and there is no such process linking Emma’s throw to the smashing of the bottle. It might be thought, then, that there is scope for a proponent of the counterfactual theory of causation to avoid the problem by leaning on some of the resources made available by the process theory of causation. But there are two problems with this response. First, when the counterfactual theorist makes use of the resources available to the process theorist she opens herself up to the problems posed by absence causation (just imagine the Sara and Emma story recast in terms of causation by absence). Second, even if the counterfactual theorist can somehow make use of the process theorist’s picture of causation to solve the problem posed by pre-emption, there are nastier versions of the problem that can be formulated. Can you think of one?
We have before us two prominent theories of causation: process theories of causation and counterfactual theories of causation. In this final section we will turn our attention to the relationship between causation and time.
Let us call causation that goes backwards in time ‘retro causation’. As we shall see later on, time travel scenarios seem to require backwards in time causal influences. For instance, suppose that Tim steps into a time machine on Tuesday and steps out of the time machine on the previous Monday. Tim’s stepping into the time machine causes his exit from the time machine. His entrance into the time machine, however, occurs after his exit. So the causal influence in virtue of which Tim brings it about that he travels through time must be moving in the future-to-past direction, which is the opposite direction from the one in which causation typically moves.
That time travel requires retro causation is undeniable. What is less clear is how the two theories of causation considered thus far fare with respect to accommodating causation of this kind. At first glance, it seems that the counterfactual theory of causation has an advantage over the process theory of causation. As we have already seen, the counterfactual theory of causation requires no physical processes to underlie causal influence. Its ability to easily handle causation by absence is a testament to this fact. This seems to be a benefit in the present context because backwards causation, if cast in process terms, would seem to require a process that goes backwards in time.
The trouble is that such backwards in time processes appear to be unlikely. Even in a fully relativistic spacetime, the background metric structure of the universe seems to have a causal direction built into it. This is not to say that backwards in time processes are impossible. They are clearly possible. There are solutions to Einstein’s field equations (the equations that underlie general relativity) that permit processes of this kind. But even though such processes are possible, the universe has to have a very particular structure in order for such processes to arise.
That backwards in time processes are unlikely is not in and of itself a problem. The problem is that the process theory of causation defines causation in process terms. So the process theory of causation has built into it the idea that backwards in time processes are unlikely. The counterfactual theory of causation, by contrast, does not seem to have the same implication, since it does not tie causation so directly to processes.
Ultimately, however, both the process theory and the counterfactual theory have the same scope ‒ limited as it is ‒ to accommodate backwards in time causation. Both the process theory and the counterfactual theory tie causation to the laws of nature. The process theory does this indirectly, by tying causation to processes that are, presumably, law-governed. The counterfactual theory does this directly, by using the laws of nature as a basis for evaluating counterfactuals. As discussed in Chapter 5, the laws of nature display deep symmetries when it comes to time. These deep symmetries suggest that, in so far as the laws of nature are concerned, causation should be possible in both the past-to-future direction and the future-to-past direction. Which is to say that the laws of nature provide no in principle reason to suppose that retro causation can’t happen.
Moreover, in so far as there is a temporal asymmetry to be found, it seems to be more to do with the distribution of matter and energy within spacetime which, in turn, is a function of the past hypothesis: the idea that the boundary conditions of the universe display low entropy. It is plausibly because of this distribution, combined with statistical mechanics, that we see the types of asymmetries that we do. More carefully, in so far as processes that go backwards in time are unlikely, it is because of statistical mechanics in combination with the past hypothesis. But these rather global constraints that make backwards in time processes unlikely really extend to all causal influences; it really has nothing to do with physical processes per se. Causal influences that go against the entropic grain of the universe, as it were, are unlikely. This low probability affects the process theory and the counterfactual theory of causation equally. In both cases, the laws of nature plus the boundary conditions of the universe make retro causation a difficult affair. Ultimately, then, neither of the two theories that we have looked at boasts much of an advantage when it comes to accommodating the kind of causal influences needed for time travel.
Is time reducible to causation? There are really two distinct issues one might have in mind in asking this question. One is the broad question of whether we can reduce temporal relations to causal relations. The second is a narrower question of whether we can reduce temporal directionality to causal directionality. We have already considered this second question in Chapter 5, so we will not further consider that issue here. Instead, we turn to the broader question of whether temporal relations (i.e. time itself) might be reducible to causal relations (i.e. causation).
First: what it would it take to reduce time to causation? Well, presumably, we would need to take a particular theory of what causation is and, with respect to that theory, show that time itself can be identified with whatever causation turns out to be. Achieving a reduction of this kind is going to be easier if we use a counterfactual theory of causation. That’s because the process theory of causation, at least as that theory has been outlined here, presupposes a spatiotemporal structure as the backdrop against which causation is defined. Which is to say that causation is analysed partly in terms of time. If we were to then try and reduce time down to causation, the resulting reduction would result in a deep and unpleasant circularity: causation exists because time exists, and time exists because causation exists. Not all circles are bad, but this one looks unpleasant. For it is an explanatory circle: time partly explains causation and causation explains time. This violates plausible constraints on explanation, namely that explanation is not symmetrical in this manner.
Even if such a reduction is possible, why would anyone want to reduce time to causation in this fashion? We can see at least three reasons. The first is an appeal to Ockham’s Razor. If we can reduce time to causation, then we have fewer aspects of the universe to try and explain. In particular, if we can reduce time to causation then we might be able to use whatever explanations we have available of causal asymmetries ‒ the fact that retro causation seems unlikely, while ordinary causation is commonplace ‒ to explain temporal asymmetries, thus reducing the explanatory tasks we are required to complete by one.
Second, by reducing time to causation in this manner we may gain a better understanding of what time is and how it works, an understanding that can then be brought back into physics. For instance, if time is reduced to causation, then that would seem to fit neatly with the causal sets approach to quantum gravity discussed in Chapter 4. Even if we can’t fit the resulting picture of time and causation into an existing theory, we may nonetheless still gain some insight into how time works, since it will inherit whatever properties causation has.
Third, the reduction of time to causation brings with it the potential to provide an explanation of temporal flow. As we saw when discussing the dynamic theory of time and the various difficulties it faces, there are many different ways of characterising the flow of time. What we didn’t really consider, however, is that some of these ways of understanding the flow of time stand in need of explanation. Consider, for instance, the flow of time as it is understood within the growing block theory of time. According to the growing block theory, the flow of time involves the gradual coming into existence of new slices of reality. But exactly what is the mechanism behind this coming into existence of new slices? What makes the flow of time happen? The reduction of time to causation presents us with a potential answer to this question. The process just considered, whereby new slices of reality come into existence, is a causal process, and so as a process it is just like any other case in which some entity is brought into existence via a causal influence. Of course, whether or not this is a viable picture of time overall remains contentious.
Ultimately, whether it is possible to reduce time to causation depends upon whether or not causation itself is grounded in, or based on, temporal notions. We need to use a theory of causation that does not, itself, build time into the analysis of causation. Since the counterfactual theory of causation doesn’t build time directly into the way in which causation is analysed, it is more amenable to the kind of reduction under consideration. But if the counterfactual theory of causation doesn’t build time into its analysis of causation, then this opens up an intriguing possibility: instead of reducing time down to causation, can we simply eliminate time altogether without thereby also eliminating causation? Can there be causation in a timeless world? Let us briefly consider this possibility.
The chief challenge in disentangling time and causation is to give an account of causation that does not somehow presuppose temporal notions. In principle, at least, the counterfactual theory of causation looks like a good bet in this respect. As we have already seen, the counterfactual theory of causation analyses causal relations in terms of chains of counterfactual dependence. A great deal of the work in developing this theory, then, is being done by the underlying counterfactuals. Counterfactuals, however, are not essentially temporal. Indeed, there appear to be many counterfactuals that don’t involve temporality at all, or at least do not depend on time for their truth or falsity. For example, consider the following counterfactuals:
If the molecular structure of the diamond had not been a covalent network lattice, the diamond would not have had the same hardness.
If the inverse square law of gravitation had been an inverse cube law, galaxies would not have formed.
If the neural structure of Sally’s brain were different, she would not have an experience of pain.
Each of these counterfactuals appears to be true, or at least plausible (perhaps subject to being worked out in a bit more detail). And yet while these counterfactuals are about things that happen in time, or things that exist in time, the actual truth of the counterfactuals does not seem to be essentially linked to time.
To see this, let us imagine a timeless universe. As we discussed in Chapter 4, we will suppose a timeless universe to be one that lacks even a C-series (and hence also lacks a B-series and an A-series). In such a universe there may be a number of three-dimensional spatial configurations. Each of these corresponds to a complete specification of the location of every particle that there is, plus all of the inter-particle distances. One could think of these (very roughly) as being each of the physically possible ways of distributing all the particles in our universe, at a time. Importantly, however, these spatial configurations are not connected by any temporal relations whatsoever. There is, as it were, no proper or correct way to order these configurations into a temporal ordering. No spatial configuration is earlier than another; no spatial configuration is later than another; nothing is simultaneous with anything else, since all spatial configurations are purely spatial: they have no internal temporal relations either. If you were to think of the spatial configurations as being like pieces of a jigsaw puzzle, then this is equivalent to the claim that there is no right way to fit these pieces together to form a unified picture.
Now, let us take one of these spatial configurations. In that spatial configuration, let us suppose, there is a diamond with a covalent network lattice. The first counterfactual above seems to be true of the diamond even though there is no time in the universe under consideration. If we were to imagine a similar timeless world in which the diamond in the relevant spatial configuration lacks a covalent network lattice structure, then it seems plausible that the diamond would not be as hard in that situation. Similarly, take the full range of spatial configurations and suppose that gravity across the relevant spatial configurations is governed by an inverse square law, or at least appears to be: in so far as there is any gravitational relationship between objects in space, the gravitational fields in a given spatial configuration always obey an inverse square law. Now, suppose we consider a sequence of spatial configurations in which gravity is obeying an inverse cube law. Again it seems plausible that the structure of the spatial configurations would be wildly different. It doesn’t seem out of order to suppose that these spatial configurations won’t feature any galaxies. Finally, take a spatial configuration in which Sally exists, and the neural structure of her brain is thus and so. Now, consider a nearby timeless world in which the neural structure of Sally’s brain is different. Then it would be plausible to suppose that she would be having a different experience.
Now, we recognise that this last example (and perhaps the gravitational example as well) may seem a bit strange. If there is no time in the imagined world, how can be Sally be experiencing anything. Isn’t time a precondition for experience? Perhaps. But that question is somewhat orthogonal to the point we are trying to make. The point is just this: there can be counterfactual relationships between low level phenomena – such as neural states or molecular structures – and high level phenomena that appear, in principle at least, detachable from temporal notions.
All we have shown thus far is that counterfactuals can be true even in worlds without time. That is a far cry from showing that a theory of causation can be given that does not presuppose time. It does, however, at least provide a glimmer of hope towards completing that larger project. For if counterfactual dependence itself is not essentially temporal, then there may be a way to analyse causation in terms of counterfactual dependence whereby the resulting analysis does not make essential use of time.
The chief challenge to developing a counterfactual theory of causation along these lines is to show that all of the cases of causation that we know and love – the types of things that motivate the development of a theory of causation in the first place – can be recovered using a notion of counterfactual dependence that is not essentially temporal.
In this chapter we have asked whether we might be able to reduce time to causation, and in Chapter 5 we asked whether we might be able to reduce the direction of time to the direction of causation. Both of these questions, and our discussion of causation at the beginning of this chapter, reveal something important. We have largely assumed that causation itself is directed. That is, we have assumed not only that, typically, causes temporally precede their effects (causation is temporally asymmetric), but also that causation goes from cause, to effect. We very naturally think of causation as directed, in the same way that we naturally think of time as directed: as going from earlier, to later. If causation is, indeed, directed in this way, then the temptation to try to reduce some aspect of temporality to causation is inevitable: for we can hope to get the direction of time from the direction of causation. (Alternatively, we could try to get the direction of causation from the direction of time, by noting that causes are, by their very nature, the things that happen earlier in time than do effects.)
It is, however, worth noting that just as there are some who reject the contention that time has a direction ‒ namely C-theorists ‒ there are also those who reject the contention that causation has a direction. Though these are distinct views they are quite naturally paired together. Just as C-theorists think that, really, there is simply a temporal ordering of events, but no temporal direction to those events, the analogous view about causation is that there are causal connections between events, but no causal direction. We can think of the latter as the view that causation is like the glue between events. The glue is real: it really does hold events together. But there is no sense in which the glue goes from one event (the cause) to another (the effect). Still, just as C-theorists think there is a mere appearance as of time having a direction, an appearance that is, in part, the result of our particular local environment and our particular psychologies, so too on this view of causation there is an appearance as of causation being directed. And, again, this will likely be explained by our particular psychological features and our epistemic goals. In both cases the idea is that the world itself is entirely symmetrical with respect to time and causation. It is just that our particular orientation in the world is such that we experience it as asymmetrical: as directed from earlier to later, from cause to effect.
It is important to notice that even if causation is not directed, this does nothing to defang the objections to timeless theories that we have already encountered. For it does not immediately help to show how to make sense of causation in the absence of time, since it still seems that we need a C-series ordering of events to make sense of causation, even if causation itself is undirected. But it is a C-series ordering of events that we are lacking in a timeless world, and so the resources with which to generate an account, even an account of undirected causation, are still meagre.
In this chapter, we have provided a potted overview of the metaphysics of causation. There is a great deal more to say about causation than has been outlined here. Theories of causation are legion, and we have really only focused on two prominent theories. These two theories, and the debate between them, do however structure much of the contemporary discussion surrounding the metaphysics of causation. The key points we have covered in this chapter may be summarised as follows:
(1) Contemporary process theories analyse causation in terms of the transfer of conserved quantities between interacting objects in spacetime.
(2) Process theories of causation have difficulty accommodating causation by omission.
(3) Counterfactual theories of causation analyse causation in terms of chains of counterfactual dependencies.
(4) Counterfactual theories can handle cases of causation by omission, since counterfactual dependence does not require the existence of any physical processes.
(5) Counterfactual theories of causation have difficulty accommodating pre-emption, which involves the existence of causal back-up systems that undermine counterfactual dependence.
(6) Process theories and counterfactual theories of causation perform equally well when it comes to accommodating retro causation.
(7) Counterfactual theories of causation appear to be better suited to reducing or eliminating temporal relations.
(8) Causation, like time, may be undirected; there may be a causal analogue of the temporal C-series.
i. Outline one version of the process theory of causation. Identify three problems for that theory. Try to find a solution for each problem.
ii. Consider the problem of causation by omission. Do you think that this is a serious problem for the process theory or do you think that it can be overcome?
iii. Break into three groups: the prosecution, the defence and the evaluation. Put the counterfactual theory of causation on trial. Let the prosecution argue that the counterfactual theory is false, let the defence defend the counterfactual theory, and let the evaluation declare a winner. Take it in turns to argue until a verdict has been reached.
iv. Can you see a way to modify the counterfactual theory of causation so as to avoid the problem of pre-emption? Defend your proposal.
v. Can you think of any other ways to order worlds in terms of similarity? Are any of these better than using our ‘gut feelings’?
vi. Consider the idea that causation is undirected. Can you foresee any problems for this view of causation?
Absence
The lack of an event.
Conserved Quantity
A quantity in physics that obeys the laws of conservation, e.g. energy.
Counterfactual
A modal claim about what would or might have happened had something that actually occurred not occurred, or had something that actually did not occur, occurred.
Counterfactual Dependence
An event E counterfactually depends on an event E* when if E had not occurred E* had not occurred and if E had occurred E* would have occurred.
Ockham’s Razor
A principle of methodology; the simpler theories are more likely to be true.
Pre-emption
A case of causation in which there is a back-up system operating.
Retro Causation
Causation of an event at t by an event at some time t+ after t.
Spatial Configuration
A complete specification of all of the particles in the universe at a time, including all inter-particle distances.
World Line
A trajectory through spacetime.