Theories of Causation

Every account of causation has to say what the striking of a match has that its mere accompaniment by the lighting lacks. The first pass found that regular succession is not enough, and that asking what would have happened otherwise does better. Philosophers have since built four families of theory on those two ideas, and they have tested them against a small set of cases that have become the standard proving ground. A theory that survives the cases is doing something right. A theory that does not has usually shown, by exactly where it fails, what it was missing.

Hume and the regularity theory

The theory descends from David Hume's Enquiry concerning Human Understanding (1748). Hume looked for the necessary connection that a cause is supposed to have with its effect and found no impression of it. We observe the striking and then the lighting; we do not observe a tie between them. What we have is a habit of mind formed by seeing the pair together many times. His official definition of a cause is therefore an object followed by another, such that all objects like the first are followed by objects like the second.

On this view the regularity does all the work. John Stuart Mill refined the idea, and J. L. Mackie in "Causes and Conditions" (American Philosophical Quarterly, 1965) gave it its most careful form. Ordinary causes, Mackie noticed, are neither sufficient nor necessary for their effects. A short circuit causes a fire, but it needs flammable material nearby, and the fire might have had a different cause. So he proposed that a cause is an insufficient but non-redundant part of an unnecessary but sufficient condition. The short circuit is one ingredient in a complex of conditions that is enough for a fire, and it is not redundant within that complex, because without it the rest would not suffice. Another complex, such as a dropped cigarette together with other ingredients, could have done the job in its place.

This is the necessary-and-sufficient condition vocabulary of the first pass put to work. It handles a good deal, and it explains why we single out the short circuit and not the oxygen: the oxygen was there whatever happened.

The theory has two persistent difficulties.

The second difficulty is that the theory is silent about single cases. A cause that occurs once, in a situation that never recurs, would have no regularity to fall under, unless some very general law is assumed to stand behind it. Yet we are confident that a particular crack in a particular girder caused a particular bridge to fall.

The counterfactual analysis

Hume's second definition, which he gives in the same breath as the first, is of this kind, and it was long treated as an afterthought. David Lewis revived it in "Causation" (Journal of Philosophy, 1973). Lewis's version asks whether the nearest situations in which the cause is absent are also situations in which the effect is absent. If the match had not been struck, would it have lit? Almost certainly not, so the striking caused the lighting.

This answers the barometer. If the barometer had read differently, the storm would still have come, so the reading is not a cause of the storm. It also handles direction. If the storm had not come, the barometer would still have fallen, since the pressure still dropped, so the storm does not cause the fall. The theory is also about single cases, which a regularity theory is not. And it fits what we say when we assign blame: the driver caused the accident if, had they not driven that way, it would not have happened.

Two points about the details. The comparison is with the nearest situations in which the cause is absent. It is not a comparison with every way things might have gone, since in some distant situation the effect could occur through another route. And the analysis concerns whether the effect would have occurred, which makes it sensitive to the whole of the background, so a theory of causation built on it inherits the difficulty of saying which background matters.

Overdetermination and preemption

Two kinds of case show that counterfactual dependence is neither necessary nor sufficient for causation in the way the analysis needs.

A firing squad of two shoots a prisoner at once, and each bullet strikes the heart at the same instant. Had the first rifleman missed, the prisoner would still have died. Had the second missed, the same. So the death does not depend on either shot, and the counterfactual analysis says neither shot caused it. That is the wrong answer: both caused it. Some philosophers bite the bullet and say that overdetermination cases are rare and the intuitions unreliable, but the general lesson stands. Dependence is not required for causing.

The more damaging case is a different one.

The difference from overdetermination matters. In overdetermination the two causes both act. In preemption only one acts, and the other is cut off, but the effect still does not depend on the one that acted, because the backup stands ready. The counterfactual analysis wrongly denies that the preempting cause is a cause.

Two versions need separating. In early preemption, the backup is cut off before the effect occurs. An assassin shoots the target, and a second assassin, who would have shot had the first held back, sees the shot fired and stands down. The target's death does not depend on the first assassin's shot, since the second would have killed him. But Lewis had a response. Look at the intermediate events: the bullet leaving the barrel, the bullet in flight, the bullet entering the heart. Each of these depends on the one before, since by then the second assassin has already stood down, and the death depends on the last of them. Causation, he said, is the chain of such dependences. The first shot causes the death because there is a chain of counterfactual dependence from one to the other. The second assassin is not a cause, because he never fired and no process runs from him to the death.

In late preemption, the backup is not cut off until the very moment of the effect, and the chain solution fails. Suzy and Billy throw rocks at a bottle. Suzy's rock arrives first and shatters it. Billy's rock was flying true and would have shattered the bottle a moment later, and it passes through the place where the bottle was. The shattering does not depend on Suzy's throw, since Billy's would have done it. There is also no intermediate event in Suzy's chain on which the shattering depends: Billy's rock is on its way at every stage, and no stage in Suzy's process is needed to produce the breaking when Billy's would have produced it a moment later.

Probabilistic causation

The approach starts from the observation that many causal relations are not deterministic. Smoking causes lung cancer, but most smokers do not develop it and some non-smokers do. A regularity theory has to say that smoking is not a cause, because it is neither necessary nor sufficient. A counterfactual theory has trouble too, since a smoker with cancer might have got it anyway. The probabilistic account says that smoking raises the chance of cancer. Patrick Suppes developed this in A Probabilistic Theory of Causality (1970), building on the work of I. J. Good and Hans Reichenbach.

Reichenbach had noticed the importance of common causes. If A and B are correlated, and neither causes the other, a common cause C often explains why. Falling air pressure produces both the barometer reading and the storm, so the two are correlated, and once the pressure is held fixed the reading tells you nothing more about the storm. The pressure is then said to screen off the correlation. This gives a way to separate spurious correlations from real causes: a real cause raises the probability of the effect even when everything else relevant is held fixed.

The account has its own failures. Germund Hesslow raised the best-known one in "Two Notes on the Probabilistic Approach to Causality" (Philosophy of Science, 1976). Birth-control pills can cause thrombosis directly, yet pregnancy also causes thrombosis, and the pills prevent pregnancy. For some groups the net effect can be that taking the pills lowers the probability of thrombosis. The pills are a cause of thrombosis that does not raise its probability. The relation is real, but it is hidden by the way the effect travels by two routes, and the simple probability-raising criterion does not see it.

The deeper problem is that probability-raising does not itself say what is happening. Probabilities are associations, and associations need an explanation in terms of causal structure. Nancy Cartwright pressed the point in "Causal Laws and Effective Strategies" (Noûs, 1979): the probabilities alone do not say which variables to hold fixed, and answering that already requires causal information. The probabilistic approach can therefore not stand alone, which is the opening for the next account.

Interventionism

James Woodward developed this in Making Things Happen (2003), drawing on the work in computer science and statistics by Judea Pearl in Causality (2000) and by Peter Spirtes, Clark Glymour and Richard Scheines. The thought is practical. Causes are what we can use to bring about effects, and the test of whether X causes Y is what would happen to Y if X were set by an experimenter.

The barometer case is the clearest illustration. If we move the needle by hand, the storm does not change. If we lower the air pressure, the needle moves and the storm comes. An intervention is a change that affects the target only through the variable intervened on, which is why moving the needle by hand shows nothing about the weather: it is not tied to the weather at all. This separates the barometer from the pressure without any appeal to temporal order.

The account is also at home with probabilistic relationships. The probabilistic link between smoking and cancer is a link that holds under intervention. Take a population and set the smoking variable, and the cancer rate shifts. Hesslow's case is handled by noticing that the two routes can be represented separately, and that an intervention on the pills would show both effects.

Its relation to preemption is worth stating plainly. Interventionism is best at type-level claims, such as smoking causes cancer, and these are not what Suzy and Billy are about. For one actual event it needs an extra step: hold fixed that Billy's rock in fact never reached the bottle, and ask whether an intervention on Suzy's throw changes the shattering. That is the route taken by structural equation approaches, which the advanced tier takes up. It works, but it adds machinery that a simple intervention test does not contain.

What the tests teach

The four accounts are better seen as responses to one another than as rivals picking at random.

The regularity theory fixes on the idea that causation is a pattern and fails on the barometer and on single cases. The counterfactual analysis fixes on dependence, answers the barometer and singular causation, and fails on overdetermination and late preemption. The probabilistic account repairs the problem of indeterminism, and fails because probability-raising needs a causal structure to be read correctly. The interventionist account takes that structure as its starting point, at the cost of giving up the project of a reduction.

Preemption has a particular role. It is a case where everything about the physical situation is clear, and the verdict that Suzy's throw is the cause is not in doubt, and yet counting the relations of dependence fails to deliver it. That makes it a test of whether an account captures the actual process by which the effect came about, rather than only what would have happened under other conditions. Overdetermination is subtler: there the verdict itself is less clear, and philosophers divide over whether to revise the intuition or the theory.

One further point is useful to take away. The accounts differ about what causation is for. The regularity and probabilistic theories take it to be a feature of the world's pattern. The counterfactual theory takes it to be a feature of what depends on what. Interventionism takes it to be a matter of what can be done. A philosopher who thinks the central point of causal talk is explanation will favour different examples from one who thinks it is blame, or prediction, or control, and the case-by-case argument often hides this disagreement about purposes.

Causes seem to push events along, and if every event is pushed, it is natural to ask what room is left for choice, which is the question of the next article.