Causation and necessity

We can distinguish two types of causal statements: general causal statements and singular ones. General statements relate types of phenomena (for instance: smoking causes cancer), whereas singular causal statements connect individual occurrences (for example: the cause of the sinking of the Titanic was that it collided with an iceberg). While the two categories of causal claims are undoubtedly related, their relation is not straightforward. It may seem that general causal statements of the form “Phenomenon A causes phenomenon B” can be reduced to the following singular claim: “For all x, if x is of type A, then x causes some y of type B”. But this won’t work. From the fact that smoking causes cancer it does not follow that every smoker will suffer from cancer. General causal claims are very often statistical only, and their truth is typically hedged by the ceteris paribus condition. On the other hand, if we wanted to define singular causal claims of the type “x causes y” with the help of the general formula “The type of phenomena A to which x belongs causes the type of phenomena B containing y”, we would encounter an immediate problem connected with the fact that each individual event can be classified into many distinct types. In the following we will restrict our analysis to singular claims only, and therefore we will interpret causation as a relation between individual objects.
It may be useful to start an analysis of causation from the following questions:

(1) What are the relata of the causal relation?
(2) What are formal properties of the causal relation?
(3) What is the temporal relation between a cause and its effect?

(1) Typically three categories of objects are regarded as being capable of standing in the causal relation: things, events and facts. One natural way of speaking about causal links seems to identify causes as things. For instance, we can say that John smashed a window glass with a stone, and a car hit a pedestrian. This suggests that causes are things (John, car) while effects are events (shattering the window, hitting the pedestrian). But clearly this is an oversimplified way of speaking. If John is busy talking on the phone, there is no shattering, although the purported cause (John) is still present. If the car is parked in a garage, no pedestrian is in danger of being hit by it. Strictly speaking, it is not John but his throwing the stone that causes the breaking, and it is not the car but its particular movement that causes the hitting of the pedestrian. This observation leads to the most commonly accepted conception of causation, according to which both causes and effects are events (throwing the stone – shattering the glass, movement of the car – hitting the pedestrian).

However, some philosophers insist that this account is too restrictive, as it does not make room for cases of negative causation. Sometimes it seems natural to single out absences of events rather than events themselves as causal factors contributing to a given effect. We say that the lack of attention of the driver was a cause of the crash, and that the absence of sprinklers contributed to the fire. But there are no negative events (in Kim’s conception, events are property attributions, but it is customary not to admit negative properties). In order to admit negative causation (sometimes also called causation by omission) it is proposed that causes and effects be facts, not events. Facts are just ontological counterparts of true statements, so there is no problem with the assumption that there are negative facts corresponding to negative statements. But critics point out that negative causation is really not necessary, and moreover that admitting it opens the door to many unintuitive cases of spurious causation. It may be claimed that underlying every case of apparent negative causation there is an instance of positive causation (for instance the driver’s lack of attention could have been actually his talking on the phone). And we tend to dismiss statements of the sort “The fact that I had not been struck by lightning caused me to survive” if there was no reason to expect that the lightning was imminent.

(2) It should be clear that the causal relation is not reflexive (there are events that don’t cause themselves). But is it irreflexive (no event is a cause of itself)? That depends. If we admit the possibility of causal loops (as in time travel), and we agree that causality is transitive, then there may be cases of self-causation (x causes y and y causes x, therefore x causes x). Similarly, causality is not symmetric, but it is open to debate whether it is asymmetric (if there are causal loops, clearly it is not asymmetric). The case for transitivity looks plausible enough, but recently this feature of causality came under attack. Some philosophers point out that there are cases which seem to violate the transitivity requirement, such as the following one. A bomb had been planted at the door of a politician’s house, but luckily it was spotted by the security and defused. It is natural to assume that the placing of the bomb was a cause of its defusing (if there hadn’t been a bomb, there wouldn’t have been the act of defusing), and the defusing of the bomb causes the politician to survive. But it is unnatural to say that the placing of the bomb was a cause of the politician’s survival (clearly the counterfactual “If the bomb had not been planted, the politician would not have survived” is false).

(3) It is typically assumed that a cause happens earlier (or, at least, not later) than its effect. But, again, if we want to admit that it is conceptually possible to have backward causation, we have to reject this requirement.

The main question we have to ask now is “What is causation?”. Answers to this question can be given in the form of a reductive analysis, explicating the causal relation in terms of some more fundamental concepts. We will start with the most famous reductive analysis of causation given by David Hume. Hume observes that it is an uncontroversial fact that causation displays the following two properties: the cause and the effect are contiguous in space and time (they “touch” each other), and the cause temporally precedes the effect. Actually, both claims can be questioned. The issue of temporal precedence has been already mentioned in point (3). As for the contiguity, at best it can be applied to direct causes only. Clearly there is a temporal and spatial gap between my act of hurling the stone and the smashing of the window. But it can be claimed that there has to be a chain of events contiguous in space and time leading from the throwing to the breaking. Still, this does not seem to be conceptually necessary. There is nothing inconsistent in considering causal links acting at a distance with no intermediate stages. Actually, this is how gravitational interaction between massive bodies can be assumed to work in Newtonian mechanics. So it looks like the two conditions proposed by Hume are not necessary for causation to occur. But we have to agree with Hume that they are not sufficient either, for there are plenty of events following one another which are not causally connected.

Hume then asks, what should be added in order to have a sufficient condition for the presence of a causal link. One typical response is that the cause has to be necessarily linked with its effect, or in other words, that if the cause occurs, the effect must occur. But Hume famously questions this. Firstly, he notices that the purported necessity cannot be of the logical kind, for no contradiction arises from the supposition that a given event does not produce its expected effect. I can imagine without contradiction the stone magically passing through the glass, or bouncing off it. But perhaps the necessity connecting causes and effects is of a different kind (nomological, or physical). Hume’s response is that no such necessity is given to us in sensory experience. We never perceive two events as connected, only as conjoined.

Clearly, Hume’s criticism of the necessary character of causation has its roots in his version of empiricism. Hume insists that every meaningful concept should be traced back to some sensory experience (‘impression’). But this requirement may be seen as overly restrictive. Hume’s radical empiricism does not square well with modern science which commonly postulates the existence of unobservable objects and properties. According to Hume’s criterion, along with the notion of necessity we should abandon such concepts as that of atoms, electrons, electromagnetic field, etc., as they cannot be supported by any direct sensory data either. On the other hand, more moderate versions of empiricism can in principle accommodate the notion of a necessary causal link, if it is treated as a theoretical concept used to make empirical predictions and explain observable facts.

Reading:

B. Garrett, "Causation", pp. 53-66, What is this thing called metaphysics?

Events

Events constitute a separate category of spatiotemporal objects which is different from the category of things. The main difference between events and things lies in their different ways of existing in time. Things, according to the common intuition, persist in time, while events happen, occur, or take place. Things are continuants, while events are occurents. This difference can be explained as follows. Compare the battle of Waterloo, which is an event, with Napoleon, a thing. Both Napoleon and the battle of Waterloo coexisted during a certain period of time, but at each moment of the battle Napoleon was fully present, while only a small part of the battle takes place at a given moment. Events are not repeatable – they occur as a whole only once – but things exist at different times without losing their identity. (It has to be added though that there are non-standard conceptions of how things persist in time, according to which at a given moment of time only a part of the thing is present, exactly as in the case of events. We will talk more about this later.)

Events are ubiquitous in natural language, as well as in the language of philosophy and of science. We talk without hesitation about battles, treaties, births, deaths, weddings, earthquakes etc. In philosophy events are typically considered as arguments of the causal relation. It is also common to talk about mental events. In physics events of coincidence play an important role in relativity theory, while measurements constitute the foundation of quantum mechanics. It is difficult to imagine a language which would not make reference to events. And yet some philosophers deny that events exist as a separate category of entities. To counter this claim, Donald Davidson has suggested a linguistic argument in support of the admission of events into one’s ontology. Consider the following sentence: (1) Jones slowly buttered a piece of toast with a knife in the kitchen at midnight. It is quite obvious that from this sentence we can logically derive several consequences, for instance that Jones buttered a piece of toast, that Jones buttered a piece of toast at midnight, or that Jones did something with a knife in the kitchen at midnight. And yet it is extremely difficult to formalise these valid inferences within standard first-order logic when we assume that the variables of our language range over things only. For example, the statement “Jones walked slowly” is formalised as P(a), where P represents the complex predicate “walks slowly” and a stands for the name “Jones”. But this method of interpretation treats the sentence “Jones walked” as containing a new predicate “walks” (Q) different from the adverbially modified expression “walks slowly”, and therefore cannot account for the unquestionable entailment between the two sentences (formula Q(a) cannot be logically derived from P(a)).

Davidson suggests that we should rephrase the above sentences in a language containing reference to events. The initial sentence (1) can be interpreted as follows: “There is an x such that x is a buttering of a piece of toast, x is done by Jones, x is done slowly, x is done with a knife, x is done in the kitchen, x is done at midnight”. By eliminating some elements of the multiple conjunction we can easily obtain required logical consequences, such as “There is an x such that x is a buttering of a piece of toast, and x is done by Jones” (“Jones buttered a piece of toast”), or “There is an x such that x is done by Jones, x is done with a knife, x is done in the kitchen and x is done at midnight” (“Jones did something with a knife in the kitchen at midnight”).

Accepting events as part of our ontology requires that we be able to give some criteria of identity and difference for them. When are two events numerically identical? One possible answer may be that the sufficient and necessary condition for the identity of events is their spatiotemporal coincidence. But there are convincing examples of numerically distinct events which nevertheless coincide in space and time. A typical example is that of a metal sphere which simultaneously rotates around its axis and heats up. The events of rotating and of heating up are clearly numerically distinct, and yet they occupy the same region of spacetime. One way of saving this intuition is to adopt Davidson’s causal criterion of identity: events x and y are numerically identical iff x and y have the same causes and the same effects. Clearly the rotation of the sphere and its heating up have different causes, and different effects (for instance the former causes the sphere to flatten a bit due to the centrifugal forces, while the latter causes it to expand uniformly). But there is one big problem with Davidsonian criterion – it is namely circular. Let us suppose that we have events x and y of which we don’t know yet whether they are identical or distinct, and let us suppose that x is caused by another event u, while y is caused by w. For simplicity’s sake we assume that x and y don’t stand in causal relation to any other events. Now, in order to decide whether x = y, we have to verify whether their causes u and w are one or two events. But to do that we have to apply Davidson’s criterion again, and this requires that we know whether x and y are identical (as they are effects of u and w). Here the circle closes, and apparently we have no way of solving our initial problem.

However, it turns out that under certain assumptions it is actually possible to decide in each case the issue of identity for a group of events using Davidson’s criterion. Here I follow the suggestion made by Leon Horsten. Suppose that we have a graph containing points representing descriptions of events (not events themselves!) and arrows representing causal relation. Moreover, let us assume that our graph satisfies the condition of completeness, i.e. for each pair of events e and e’, if e is a cause of e’, then each description of e is connected by an arrow with each description of e’. Under this assumption it turns out that each graph satisfying Davidson’s criterion is solvable, i.e. for each two descriptions it is decidable whether they refer to one or two distinct events. However, it may be pointed out that the assumption of completeness is too strong (if a graph is complete, this fact by itself already fixes some identity relations). A more reasonable assumption is that of semi-completeness: for all events e and e’, if e is a cause of e’, then each description of e is connected by an arrow with some description of e’. But it can be showed that semi-complete graphs are not always solvable, and therefore the problem of circularity remains.

Jaegwon Kim proposed a different interpretation of events as property exemplifications. More specifically, an event for Kim is a triple <a, P, t>; where a is an object, P is a property, and t is a time at which a possesses P. From this definition it follows that two events are identical iff they happen on the same object, at the same time, and they involve the same property. The last requirement ensures that the rotation and the heating of the sphere are numerically distinct. But Kim’s conception has several controversial consequences. First of all, it multiplies events beyond what is ordinarily acceptable. If Jones is walking slowly, his walking and his walking slowly constitute two distinct events (actually, there are as many different events of walking involved as there are ways to describe the individual style of Jones’ walking). This fact can actually threaten the analysis of logical inferences proposed by Davidson and sketched above, as in each sentence we are talking about a different event. Moreover, according to Kim’s approach it is an essential feature of an event that it occurs on a given object, at a given time, and that it involves a given property. From this it follows that my lecture on ontology given on Wednesday, February 17, at 11:30 could not have been given by someone else, could not have been a rock concert, and could not have started five minutes later. Especially the last consequence seems to be rather controversial. Other criticism of Kim’s conception is based on the observation that events can involve more than one object (relational events) or no object at all (spontaneous excitations of vacuum predicted in quantum field theory).

Event-ontologies are based on the assumption that events are the fundamental kind of objects and that other categories of objects can be reduced to events. According to one type of event-ontology, things are just sequences of events. A person, for instance, is a collection of all events from his/her birth to the death. It is worth noticing that such a reductive definition cannot be accepted by Kim, for in his conceptions events are defined in terms of things, so there would be obvious circularity. Alternatively, we could interpret events as consisting of properties and moment of time only, or we could rely on Davidson’s criterion, provided that its own circularity problem could be overcome.

Readings:

E.J. Lowe, Chapter 12 "Actions and events", pp. 214-231, A Survey of Metaphysics.
M.J. Loux, "Facts, states of affairs, and events", pp. 142-150, Metaphysics. A Contemporary Introduction.