 How, then, might we define ‘actual causation’ using the structural equations framework? We’ll get there by considering how SEF deals with cases of late preemption such as the Suzy and Billy case. Halpern and Pearl (2001, 2005), Hitchcock (2001), and Woodward (2003) all give roughly the same treatment of late preemption. The key to their treatment is the employment of a certain procedure for testing the existence of a causal relation. The procedure is to look for an intrinsic process connecting the putative cause and effect; suppress the influence of their non-intrinsic surroundings by ‘freezing’ those surroundings as they actually are; and then subject the putative cause to a counterfactual test. So, for example, to test whether Suzy’s throwing a rock caused the bottle to shatter, we should examine the process running from ST through SH to BS; hold fix at its actual value (that is, 0) the variable BH which is extrinsic to this process; and then wiggle the variable ST to see if it changes the value of BS. The last steps involve evaluating the counterfactual “If Suzy hadn’t thrown a rock and Billy’s rock hadn’t hit the bottle, the bottle would not have shattered”. It is easy to see that this counterfactual is true. In contrast, when we carry out a similar procedure to test whether Billy’s throwing a rock caused the bottle to shatter,we are required to consider the counterfactual “If Billy hadn’t thrown his rock and Suzy’s rock had hit the bottle, the bottle would not shattered”. This counterfactual is false. It is the difference in the truth-values of these two counterfactuals that explains the fact that it was Suzy’s rock throwing, and not Billy’s, that caused the bottle to shatter. (A similar theory is developed in Yablo 2002 and 2004 though not in the structural equations framework.)