# Causality

## Counterfactual Dependence

In his Enquiry Concerning Human Understanding (1748) Hume stated briefly another way to view causality. He said that an object is the cause of another when "if the first object had not been, the second never had existed" (1975 ed., p. 146). This view has been articulated into a theory of causality by David Lewis. Lewis (1986) defined causality in terms of the counterfactual dependence of the effect on the cause: the cause is rendered counterfactually necessary for the effect. For instance, to say that the short-circuit caused the fire is to say that if the short-circuit had not happened, the fire would not have ensued. To be more precise, Lewis defined causality by reference to a causal chain of counterfactually dependent events, where a sequence of events (C, E, E, …) is a chain of counterfactual dependence if and only if E counterfactually depends on C, E counterfactually depends on E, and so on. This move is meant to enforce that causation is a transitive relation among events (that is, if C causes E and E causes E, then C causes E). As Lewis put it: "one event is a cause of another if and only if there exists a causal chain leading from the first to second" (p. 167). Statements such as "if C had happened, then E would have happened" are called counterfactual conditionals (another example, "if this sugar cube had been in water, it would have dissolved") for they state what could or could not have happened, under certain circumstances. But it has been notoriously difficult to specify the conditions under which counterfactual conditionals are true or false. Lewis articulated a rather complicated logic of counterfactual conditionals, which was based on the idea that, besides the actual world, there are also other possible worlds, which can be deemed more or less similar to the actual. A chief but not inviolable criterion for judging the similarity among worlds was taken to be whether the same laws of nature govern the worlds under comparison.

Though it is still one of the main contestants, this view of causality faces important difficulties. A chief among them comes from cases of causal overdetermination, where there are two factors each of which is sufficient to bring about the effect, but none of them is necessary, since even if the one was not present, the other factor would ensure the occurrence of the effect. For instance, two rocks are simultaneously thrown at a bottle and they shatter it. They both caused the shattering, but the effect is not counterfactually dependent on either of them, since if the first rock had missed the bottle, the other would have still shattered it. So there is causality without the cause being counterfactually dependent on the effect.

Here is a billiard-ball lying on the table, and another ball moving towards it with rapidity. They strike; and the ball, which was formerly at rest, now acquires a motion. This is as perfect an instance of the relation of cause and effect as any which we know, either by sensation or by reflection. Let us therefore examine it. 'Tis evident, that the two balls touched one another before the motion was communicated, and that there was no interval betwixt the shock and the motion. Contiguity in time and place is therefore a requisite circumstance to the operation of all causes. 'Tis evident likewise, that the motion, which was the cause, is prior to the motion, which was the effect. Priority in time, is therefore another requisite circumstance in every cause. But this is not all. Let us try any other balls of the same kind in a like situation, and we shall always find, that the impulse of the one produces motion in the other. Here therefore is a third circumstance, viz., that is a constant conjunction betwixt the cause and effect. Every object like the cause, produces always some object like the effect. Beyond these three circumstances of contiguity, priority, and constant conjunction, I can discover nothing in this cause. The first ball is in motion; touches the second; immediately the second is in motion: and when I try the experiment with the same or like balls, in the same or like circumstances, I find that upon the motion and touch of the one ball, motion always follows in the other. In whatever shape I turn this matter, and however I examine it, I can find nothing farther.(pp. 649–650)

SOURCE: David Hume, Abstract to A Treatise of Human Nature. Published by Hume anonymously in 1739.