Exactly how, next, might we explain ‘genuine causation by using the architectural equations framework?
(8) A changeable Y counterfactually utilizes an adjustable X in the an excellent model when the and only if it is truly the circumstances you to X = x and you will Y = y there exists beliefs x? ? x and you can y? ? y in a way that substitution the brand new formula to have X that have X = x? yields Y = y?.
A varying Y (unlike X and you may Z) are advanced anywhere between X and Z in the event that and simply in the event it belongs to certain route anywhere between 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 = x1 and the occurrence of e is represented by a structural equation 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, hookup apps for married people 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.
Really get there by considering just how SEF deals with instances of late preemption for instance the Suzy and Billy situation. Halpern and Pearl (2001, 2005), Hitchcock (2001), and Woodward (2003) the give about the same treatment of late preemption.