Consider a system of ‘neurons’ such as that presented in Fig.  1 .

Thus in Fig.  1 , neurons A and C fire.

Figure  1 depicts a case of (early) preemption: C’s firing causes E to fire, but if C hadn’t fired, A’s firing would have caused E to fire.

We can use the causal structure depicted in Fig.  1 to provide an informal explanation of how structural equations approaches to causation work.

The account of Yablo (2002) works similarly.

It may be that the particular pattern of dependence represented in a neuron diagram such as Fig.  1 is in place, in part, because of additional factors that are being held fixed in the background.

It may be that the particular pattern of dependence represented in a neuron diagram such as Fig. 1 is in place, in part, because of additional factors that are being held fixed in the background.

In Pearl’s terminology, a variant must have the same mechanisms as the original causal structure.but which may vary with respect to which objects or systems engage in the default or deviant behaviors.

If an object or system has more than one deviant behavior, it may also differ with respect to which deviant behavior it engages in.

Figure  2 represents a reduction of the causal structure depicted in Fig.  1 .

For example, in the causal structure represented in Fig.  1 , C’s firing is a cause of E’s firing, because in the reduction depicted in Fig.  2 , C fires, E fires, and E would not have fired if C had not fired.

Hall’s treatment of the cases of preemption and symmetric overdetermination shown in Figs.  1 and 3 was successful because in both cases it is possible to eliminate the backup causal process by substituting default behaviors for deviant behaviors.