Regularity theories of causation

Having rejected the postulate of the necessity of causal links, Hume replaces it with the condition of regularity. Paraphrasing his words, if x is a cause of y, each event that is similar to x is followed by an event similar to y. Thus, the complete definition of causation can look like this: x is a cause of y iff x is spatiotemporally contiguous with y, x temporally precedes y, and for all x’, if x’ is similar to x, then there is a y’ such that y’ is similar to y and y’ follows x’. One of the main difficulties with this definition is the notorious vagueness of the notion of similarity between events. If we interpret similarity as being identical in some respect, then it is plausible that every object is similar to every other object, and as a consequence the condition of regularity can never be satisfied. On the other hand, similarity conceived as identity in all respects (qualitative identity) collapses into numerical identity (given the PII), and therefore the condition of regularity reduces to the previous two conditions (contiguity and temporal precedence). The main challenge to Hume’s analysis is to characterize the notion of a relevant aspect with respect to which the similarity between events is interpreted. But even if this can be done, Hume’s analysis is open to serious criticism. Critics point out that there are cases of regular successions of events without a causal link. Days regularly follow nights, and yet there is no causal relation between the two. Similarly, if according to the timetable after the departure of train A train B regularly arrives at the station, this does not indicate that one causes the other. Note that typically the regular but not causal correlations can be explained with the help of a common cause (the succession of day and night is explained by the rotation of the earth, and the timetable acts as the common cause of both the departure of train A and the arrival of train B). So it can be concluded that Hume’s regularity approach has difficulties with distinguishing between direct causal regularities and regularities arising from a common cause.

Another group of counterexamples to the Humean analysis contains cases of causal links where no regularity is present. It is sometimes argued that causal links between unique events (for instance the Big Bang) don’t satisfy the requirement of regularity. Actually, they satisfy it but trivially, making all spatiotemporally conjoined unique events causally connected with each other. But it is unquestionable that in real life we make numerous causal claims where there is no underlying regularity. We say that the failure of brakes was a cause of the car crash, although not every failure of that sort leads to a crash. This clearly shows that Hume’s analysis is in need of serious corrections.

Neo-Humean approaches to causation try to eliminate some of its weak points. One of them is the nomological conception. According to it, an event x of type A is a cause of an event y of type B iff x and y occur in conditions C and there is a law of nature according to which if an event of type A happens in conditions C, an event of type B occurs. There are two main differences between this approach and Hume’s regularity account: the presence of background conditions C and the reference to laws of nature. The role of laws of nature is to eliminate accidental regularities, while the presence of conditions C should take care of the problem of the apparent lack of regularity of some causal links (the failure of brakes leads to an accident only in certain specific circumstances). But these additions to the regularity approach bring new problems. What are laws? Hume himself insisted that laws are nothing over and above mere regularities, but if that’s the case the addition of laws to the definition of causation does not constitute an improvement with respect to the old, Humean version. The introduction of conditions C creates a different problem. By a crafty selection of appropriate “conditions” we can make virtually any succession of events a causal one. It may be claimed, for instance, that the snapping of my fingers causes the lights to go out if we include in the appropriate conditions that someone turns off the switch at the same moment. Yet another objection is that there are laws which are not causal. Pascal’s law states that a gas exerts equal pressure in all directions, but it is not correct to say that the fact that the pressure in one direction equals p is caused by the fact that the pressure in the opposite direction is also p. Finally, most laws of physics are symmetric in time, but from this it does not follow that backward causation is a common fact.

One of the most sophisticated versions of the regularity approach is the conception of causation proposed by J.L. Mackie. Mackie notes that the notion of a cause is closely related to sufficient and necessary conditions, but a cause of x cannot be simply defined as a necessary or a sufficient condition of x. Let us consider Mackie’s example with a fire of a house being caused by a short circuit. The short circuit by itself is not sufficient for the house to burn down; other conditions have to be present, such as the presence of inflammable materials, of oxygen, the absence of automatic sprinklers and smoke detectors, etc. Generally speaking the short circuit is not necessary for the fire either, for fires can start in many different ways, for instance after a strike of a lightning bolt. But in the actual conditions the short circuit was necessary, because without it the conditions themselves would not have created the fire. (Mackie speaks in this case about a necessary condition post factum.) The short circuit is an INUS condition for the occurrence of the fire, where the acronym INUS stands for an Insufficient but Necessary part of an Unnecessary but Sufficient condition. A more precise definition of an INUS condition is as follows: A is an INUS condition for B iff there are conditions X and Y such that (AX or Y) is a necessary and sufficient condition of B, but neither A nor X is a sufficient condition of B. In our example A is the short circuit, B is the fire, X refers to all the conditions which together with A were sufficient for the fire to occur, and Y stands for a disjunction of all alternatives ways of starting a fire. In most cases a cause of an occurrence B is an INUS condition of B such that it occurred, and no alternative conditions Y were present (however, Mackie admits the possibility that a cause itself may be sufficient for its effect, or even sufficient and necessary – he refers to all such cases jointly as “at least” INUS conditions of B).

It has to be noted that some further restrictions on the causal condition A have to be introduced, otherwise Mackie’s analysis will lead to obviously incorrect conclusions. To see this, let us use the letter C to abbreviate the complete sufficient condition of B that was actually present, and let us select any fact S irrelevant to the occurrence of B that happened simultaneously with C (for instance the fact that when the fire started somebody walked past the house whistling “Ode to joy”). The formula [(S or C) and (not-S or C)] is logically equivalent to C, and hence if there is a condition Y such that (C or Y) is a necessary and sufficient condition of B, then {[(S or C) and (not-S or C)] or Y} is a necessary and sufficient condition of B too. But now observe that the condition (S or C) satisfies the requirement for an INUS condition of B. (S or C) is not sufficient for B, nor is (not-S or C), and yet their conjunction is sufficient (as it is equivalent to C). But it is highly unintuitive to pick the disjunction S or C as a cause of B. To eliminate cases like this it may be suggested that causes should not have the form of disjunctions of simple events.

An interesting element of Mackie’s conception is that he admits that causal claims are always made in a context. In order to account for this fact, he introduces the notion of a causal field. Let us consider as an example the case of a person going down with flu. The answer to the question “What caused this man to contract the flu?” depends on the context. If we consider as the causal field the set of all moments in his life, and ask why he contracted the disease at this moment rather than any other, then the correct answer may be that he was infected by influenza viruses. But we can also select as the causal field the set of all people who came into contact with influenza viruses, and we may be interested in selecting the factor which is responsible for the fact that some of them contracted the disease, while the others did not. Mackie introduces the causal field to his definition of a cause, assuming that the conditions characterizing this field are present when the cause is present.

Reading:

M.J. Loux, Chapter 6 "Causation", pp. 187-203, Metaphysics: A Contemporary Introduction.