 One possible limitation of the notion of a setting intervention (or at least Pearl’s characterization of it) concerns the scope of the requirement that an intervention on \(X_i\) leave intact all other mechanisms besides the mechanism that previously determined the value of \(X_i^.\) If, as Pearl apparently intends, we understand this to include the requirement that an intervention on \(X_i\) must leave intact the causal mechanism if any, that connects \(X\)i to its possible effects \(Y\), then an obvious worry about circularity arises, at least if we want to use the notion of an intervention to characterize what it is for \(X_i\) to cause \(Y\). A closely related problem is that given the way Pearl characterizes the notion of an intervention, his definition  (C) of the causal effect of \(X\) on \(Y\), seems to give us not the causal contribution made by \(X = x\) alone to \(Y\) but rather the combined impact on \(Y\) of this contribution and whatever contribution is made to the value of \(Y\) by other causes of \(Y\) besides \(X\). For example, in the case of the regression equation \(Y = aX+U\), the causal effect in Pearl’s sense of \(X=x \textrm{on} Y\) is apparently \(P(Y) = ax + U\), rather than, as one might expect, just \(ax\). In part for these reasons (and for other reasons, described below), Woodward (2003) and Woodward and Hitchcock (2003) explore a different way of characterizing the notion of an intervention which does not make reference to the relationship between the variable intervened on and its effects. For Woodward and Hitchcock, in contrast to Pearl, an intervention \(I\) on a variable \(X\) is always defined with respect to a second variable \(Y\) (the intent being to use the notion of an intervention on \(X\) with respect to \(Y\) to characterize what it is for \(X\) to cause \(Y)\). Such an intervention \(I\) must meet the following requirements (M1–M4):