highest-ranking officer. Both a sergeant and a major issue the order to march, and the soldiers march. Let us put aside the morals that Schaffer attempts to draw from this example (with which we disagree; see [Halpern and Pearl 2005] and [Hitchcock 2010]), and consider only the modeling problem. We will presumably want variables S, M, and A, corresponding to the sergeant's order, the major's order, and the soldiers' action. We might let S **= 1 represent the sergeant's giving the order to march**
and S = 0 represent the sergeant's giving no order; likewise for M and A**. But this**
would not be adequate. If the only possible order is the order to march, then there is no way to capture the principle that in the case of conflicting orders, the soldiers obey the major. One way to do this is to replace the variables M, S**, and** A by variables M′, S
′ and A′that take on three possible values. Like M, M′ **= 0 if the**
major gives no order and M′ **= 1 if the major gives the order to march. But now**
we allow M′ **= 2, which corresponds to the major giving some other order.** S
′ and A′ **are defined similarly. We can now write an equation to capture the fact that if** M′ **= 1 and** S
′ = 2, then the soldiers march, while if M′ **= 2 and** S
′ **= 1, then the**
soldiers do not march.

The appropriate set of values of a variable will depend on the other variables in the picture, and the relationship between them. Suppose, for example, that a hapless homeowner comes home from a trip to find that his front door is stuck. If he pushes on it with a normal force then the door will not open. However, if he leans his shoulder against it and gives a solid push, then the door will open. To model this, it suffices to have a variable O **with values either 0 or 1, depending on** whether the door opens, and a variable P**, with values 0 or 1 depending on whether**
or not the homeowner gives a solid push.

On the other hand, suppose that the homeowner also forgot to disarm the security system, and that the system is very sensitive, so that it will be tripped by any push on the door, regardless of whether the door opens. Let A **= 1 if the alarm goes off,** A = 0 otherwise. Now if we try to model the situation with the same variable P**, we**
will not be able to express the dependence of the alarm on the homeowner's push.

To deal with both O and A, we need to extend P **to a 3-valued variable** P
′**, with**
values 0 if the homeowner does not push the door, 1 if he pushes it with normal force, and 2 if he gives it a solid push.

These considerations parallel issues that arise in philosophical discussions about the metaphysics of "events".6 **Suppose that our homeowner pushed on the door with**
enough force to open it. Is there just one event, the push, that **can be described** at various levels of detail, such as a "push" or a "hard push"? This is the view of Davidson [1967]. Or are there rather many different events corresponding to these different descriptions, as argued by Kim [1973] and Lewis [1986b]? And **if we take** the latter view, which of the many events that occur should be counted as causes of the door's opening? These strike us as pseudoproblems. We believe that questions 6**This philosophical usage of the word "event" is different from the typical usage of the word in**
computer science and probability, where an event is just a subset of the state space.