Counterfactual theory of causation

Now we have to say a couple of words about the relation of closeness (or similarity) between possible worlds. Formally, it is a two-place relation relativised to the actual world: “world w1 is more similar to the actual world than world w2”, and it is assumed to possess standard properties, such as asymmetricity, transitivity and linearity, plus minimality (the actual world is closer to itself than any other world). But what properties of possible worlds should be taken into account when evaluating their relative similarity with respect to the actual world? Let us observe that two aspects of similarity can be taken into account: similarity with respect to individual facts and similarity with respect to laws. It may seem that the similarity with respect to laws should be seen as more important than the similarity with respect to individual facts, and consequently that a world with laws different than those in the actual world should be seen as more distant than any world with the same laws but different individual facts. But this assumption leads to unintuitive consequences, as Lewis points out. Suppose that we are working under the assumption of determinism, i.e. the assumption that the complete state of the world at a given moment t, together with the laws, uniquely determine all the later states. From this it follows that if we consider a world w which differs from the actual world at a moment t, and has all the actual laws, w would have to differ from the actual world at all moments preceding t. But this implies the following counterfactual: “If I sneezed now, the state of the universe would be different at any past moment t”. Counterfactuals for which the antecedent describes an event happening later than the event described by the conditional are called “backtracking”. Lewis maintains that backtracking counterfactuals are usually considered incorrect in standard discourse. In his approach backtracking counterfactuals come out false even under determinism, because possible worlds in which a small violation of laws (“a miracle”) makes it possible for the antecedent-event to occur are usually closer to the actual world than the worlds in which the differences in individual facts stretch infinitely into the past. The world in which we evaluate the counterfactual “If I sneezed at t, then ...” is exactly identical with the actual world up to moment t, when a small miracle occurs making it possible for me to sneeze.

Let us return to the analysis of causation done with the help of counterfactual conditionals. The elimination of backtracking counterfactuals advocated by Lewis solves the main problems affecting the regularity approach: the problem of mixing up causes and effects and the problem of how to distinguish causal relations from the common cause correlations. If an event x of type A causes an event y of type B, the counterfactual “If y had not happened, x would not have happened beforehand” is not (typically) true, because it is a backtracking counterfactual. To evaluate it, we take a possible world which is identical with the actual one up to the moment when y is supposed to occur, and in such a world x happens, but a small miracle prevents y from happening. Regarding the common cause case in which A causes B and then C, it is not true that if B hadn’t occur, C would not have occurred, because A would still be present, causing C to happen. The elimination of B is achieved again not by eliminating its cause A via a backtracking counterfactual (which would eliminate C as well), but by assuming a small miracle which happens just before B and makes it disappear.

But Lewis’s account of causation has its own share of troublesome cases. The identification of the causal relation with the relation of counterfactual dependence between distinct events leads to difficulties with the cases of pre-emption. Suzie’s throw is clearly a cause of the bottle’s shattering, and yet there is no counterfactual dependence between the two events, due to the presence of Billy and his stone. And the counterfactual “If Suzie hadn’t thrown her stone, Billy would have thrown his” is a normal, forward-looking counterfactual which does not require backtracking. Lewis’s response to this case is the following modification of the definition of causal relation. Event x is a cause of event y iff there are events x1, x2, ..., xn such that x1 is counterfactually dependent on x (meaning that if x hadn’t happened, x1 would not have happened), x2 is counterfactually dependent on x1, ..., and y is counterfactually dependent on xn. In the pre-emption case this modification works as follows. We pick an event X between the act of throwing the stone and the shattering such that at its moment Billy has already given up on his throw (this event may be that the stone is flying to its target at a certain speed). Now we can observe that X is counterfactually dependent on Suzie’s throw (if she hadn’t thrown, her stone would not have been flying towards the target), while the shattering is counterfactually dependent on X (if X hadn’t happened, the bottle would not have shattered). The crucial assumption is again that no backtracking is allowed, for we cannot accept that if Suzie’s stone hadn’t been flying, Billy would have thrown his stone). Lewis’s modification has one more advantage: it ensures that the causal relation is transitive (as we remember, the relation of counterfactual dependence is not transitive).

However, Lewis’s analysis faces more threats from modified cases of pre-emption. Suppose that in the Suzie and Billy case Billy has actually thrown his stone, but Suzie’s stone has reached the bottle first, thus pre-empting Billy’s throw. In this case, known as late pre-emption, Lewis’s improved analysis still gives the wrong answer, because there is no moment during the flight of Suzie’s stone at which we could say that if there had been no stone, the bottle would not have shattered. Another troublesome case is called “trumping pre-emption”. A major and a sergeant both shout the same order to a soldier. The soldier obeys, but given the military hierarchy it looks like it was the major’s order and not the sergeant’s which caused the soldier’s action. But there is no counterfactual dependence: if the major’s had not given the command, the soldier would have obeyed the sergeant’s order.

Lewis considered several possible corrections to his approach in order to deal with the problems of late pre-emption and trumping pre-emption. One possibility is to adopt a conception of events whose identity conditions are so strict that even a small modification produces a numerically distinct event (such events are called ‘fragile’). If the shattering of the bottle is a fragile event, then the shattering produced by Billy’s stone is numerically different from the shattering brought about by Suzie’s stone (the stones are flying from slightly different directions, with slightly different speeds, etc.). Thus it is true that if Suzie’s throw had not occurred, this particular shattering would not have occurred (although a similar one would have replaced it). Notice that the fragile character of events is supported in Kim’s conception, according to which events are differentiated by properties, and quantitative properties can be close in value and yet numerically distinct. But an undesirable consequence of this solution is that now plenty of insignificant background conditions will become causes of a given event. Even a gust of wind counts as a cause of the shattering, because it certainly, although minimally, affected the trajectory of the stone, so it is true that if there had been no gust of wind, there would have been no actual shattering, but a very similar yet numerically distinct one. On the other hand, the solution based on the assumption of fragility may be defended against this objection, if we observe that the purported cause (the gust of wind) is itself a fragile event. Hence, the counterfactual assumption that there was no gust of wind can be made true by assuming that the gust of wind was slightly different, and given that the dependence of the stone’s trajectory on the wind is very weak, it is natural to expect that a slight change of the strength of the wind would produce no discernible differences in the qualities of the shattering.

But even the fragility solution is unable to cope with the following counterexample. Suppose that at a point where the railway tracks split two terrorists plan an attack on a coming train. One of them operates the switch, sending the train on a dead end track and causing a train wreck. The second terrorist acts as a back-up, in case the first one does not carry out the sabotage. Clearly, there is no counterfactual dependence: if the first terrorist had not moved the switch, the second one would have acted and the train would have crashed. But the counterfactual dependence cannot be restored even if we assume that all events are fragile. The train wreck is identical regardless of which terrorist moves the switch, or when exactly the switch is moved, or how the switch is moved. The reason is that the characteristic of the train wreck depends solely on the properties of the train and its travel (speed, brakes, etc.), and not the manner in which the switch is moved.

Reading:

E.J. Lowe, Chapter 10, "Counterfactuals and event causation", A Survey of Metaphysics, pp. 174-191.