Just how, following, you will we determine ‘real causation using the architectural equations framework?
(8) A varying Y counterfactually hinges on a variable X into the a design if the and just in case it is actually the case you to X = x and you can Y = y there exist viewpoints x? ? x and you will y? ? y such that substitution brand new picture having X which have X = x? efficiency Y = y?.
A varying Y (distinct from X and you can Z) are advanced between X and you will Z when the and only in the event it belongs to particular station ranging from X and you will Z
Of course, so far we just have something we are calling a ‘causal model, ?V, E?; we havent been told anything about how to extract causal information from it. As should be obvious by now, the basic recipe is going to be roughly as follows: the truth of ‘c causes e (or ‘c is an actual cause of e), where c and e are particular, token events, will be a matter of the counterfactual relationship, as encoded by the model, between two variables X and Y, where the occurrence of c is represented by a structural equation of the form X = xstep one and the occurrence of e is represented by a structural equation of the form Y = men seeking couples y1. That would get us the truth of “Suzys throw caused her rock to hit the bottle” (ST = 1 and SH = 1, and, since SH = ST is a member of E, we know that if we replace ST = 1 with ST = 0, we get SH = 0). But it wont get us, for example, the truth of “Suzys throw caused the bottle to shatter”, since if we replace ST = 1 with ST = 0 and work through the equations we still end up with BS = 1.
Better make it because of the provided how SEF works together with cases of later preemption such as the Suzy and Billy circumstances. Halpern and you will Pearl (2001, 2005), Hitchcock (2001), and you may Woodward (2003) all provide more or less a comparable therapy of late preemption. The answer to the treatment is the utilization of a particular procedure for testing the current presence of a good causal family relations. The procedure is to search for an important techniques hooking up this new putative cause-and-effect; suppress the dictate of their non-inherent surroundings of the ‘cold men and women land because they actually are; following subject the brand new putative end up in to help you a great counterfactual try. Therefore, eg, to evaluate if or not Suzys tossing a rock caused the package so you’re able to shatter, we should evaluate the process powering off ST owing to SH in order to BS; hold fix within their genuine really worth (which is, 0) the latest varying BH that is extrinsic to this procedure; right after which wiggle the latest variable ST to see if they alter the value of BS. The very last actions involve researching the newest counterfactual “In the event that Suzy hadnt tossed a rock and you can Billys rock hadnt strike this new bottle, brand new container do not have smashed”. It is possible to see that this counterfactual holds true. Alternatively, when we do the same techniques to test whether or not Billys organizing a stone was the cause of container so you can shatter,we are expected to look at the counterfactual “If Billy hadnt tossed his material and you will Suzys rock had hit brand new bottle, the brand new bottles would not shattered”. So it counterfactual try not the case. Simple fact is that difference in the fact-values of these two counterfactuals that explains the point that it was Suzys stone tossing, and never Billys, that caused the bottles so you can shatter. (A similar concept try designed in Yablo 2002 and you will 2004 regardless if not in the structural equations build.)
Hitchcock (2001) presents a useful regimentation of this reasoning. He defines a route between two variables X and Z in the set V to be an ordered sequence of variables <X, Y1,…, Yn, Z> such that each variable in the sequence is in V and is a parent of its successor in the sequence. Then he introduces the new concept of an active causal route: