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We caletter find straightaway, but not, that people cant straightforwardly identify causation having counterfactual dependence as outlined inside (8) a lot more than
Exactly how, then, you’ll we define ‘actual causation by using the architectural equations framework?
(8) An adjustable Y counterfactually hinges on an adjustable X when you look at the good model when the and just in case it is really the circumstances one X = x and Y = y and there exists values x? ? x and you can y? ? y such that substitution the new picture to have X with X = x? efficiency Y = y?.
A varying Y (distinct from X and you may Z) are advanced between X and Z in the event that and only when it is part of certain channel between X and you may 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 hookup dating in Chico of the form Y = 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 happen by considering just how SEF works closely with instances of late preemption such as the Suzy and you may Billy circumstances. Halpern and you may Pearl (2001, 2005), Hitchcock (2001), and you can Woodward (2003) every bring roughly an identical remedy for late preemption. The answer to their treatment solutions are the aid of a particular procedure for analysis the clear presence of an excellent causal loved ones. The procedure is to search for a built-in process linking this new putative cause and effect; suppress the latest influence of its low-built-in landscaping by the ‘freezing those people land as they are really; following subject the fresh new putative result in in order to a great counterfactual sample. Very, such, to test whether Suzys throwing a stone was the cause of package to help you shatter, you want to see the procedure powering of ST because of SH in order to BS; hold enhance in the its actual worthy of (that’s, 0) the brand new changeable BH that is extrinsic compared to that process; immediately after which action new changeable ST to see if it transform the value of BS. The very last strategies involve contrasting the counterfactual “In the event that Suzy hadnt thrown a rock and you may Billys rock hadnt struck the brand new container, the newest package would not have smashed”. It is easy to notice that which counterfactual is valid. In contrast, as soon as we manage a similar procedure to evaluate if Billys tossing a rock caused the bottle so you’re able to shatter,we are expected to consider the counterfactual “In the event the Billy hadnt tossed his rock and you can Suzys material got struck the latest package, the container wouldn’t smashed”. This counterfactual is not the case. This is the difference in the truth-opinions of the two counterfactuals which explains the point that it was Suzys material putting, and never Billys, one was the cause of container to shatter. (The same concept is created in Yablo 2002 and you will 2004 even in the event outside of the architectural 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:
