 A second general issue, related to the one just described, concerns the sense, if any, in which interventions must be “possible” and the bearing of this on the truth of the associated causal claims. Returning to the notion of intervention associated with Pearl above, note that this notion says nothing about whether there is an actual or even possible causal factor that might accomplish the kind of surgical modification Pearl describes. We may if we wish represent such an intervention \(I\) by means of arrow directed into the variable \(X_i\) that is intervened on which breaks all other arrows directed into \(X_i\) (and Pearl sometimes uses this representation) but both the \(I\) variable and this arrow seem dispensable. We could instead just think of \(X_i\) as set to some new value in the arrow-breaking or equation replacement manner described above, with no further restrictions on when such a setting operation is possible (or when it is permissible or legitimate to invoke it). I will call this a setting intervention. This contrasts with an alternative conception of interventions and their connection to causal claims according to which the truth of a claim like “\(X\) causes \(Y\)” requires that interventions on \(X\) must be “possible” in some non-trivial sense of this notion, which then must be specified. (In other words, the truth of “\(X\) causes \(Y\)” requires both that \(Y\) changes under an intervention on \(X\) and that this intervention be possible.) When a possibility condition of this sort is imposed, I will say we are making use of a possibility constrained notion of intervention. Use of this notion raises the difficult question of how the relevant notion of possibility should be understood. I will suggest below that the best way of making sense of this notion is in terms of some notion of conceptual or mathematical (or if you like, “metaphysical”) coherence—roughly speaking, the issue is whether there is an appropriately empirically grounded theoretical/mathematical apparatus that allows for a coherent description of the possible intervention in question and allows us to determine what would happen if the intervention were realized. In some cases (see below) such a description may be available even though the intervention in question may not be physically  possible.[2]  Recognizing obvious worries about the clarity of this notion of possibility (which in my view should be acknowledged by defenders of this notion), one might think that it is preferable to always employ the setting notion in formulating an interventionist account. However, as we shall see, formulations in terms of the “possibility constrained” notion have appealing features (they seem to do a better job of capturing the truth conditions for some causal claims) and a number of writers seem to rely on such a conception. 