 Returning to Pearl, and following his framework, let us represent the proposition that the value of \(X\) has been set by an intervention to some particular value, \(x_0\), by means of a “\(\do\)” operator \((\do(X=x_0)\), or more simply, \(\do x_0)\). It is important to understand that conditioning on the information that the value of \(X\) has been set to \(x_0\) will in general be quite different from conditioning on the information that the value of \(X\) has been observed to be \(x_0\) (see Meek and Glymour 1994; Pearl 2009). For example, in the case in which \(X\) and \(Y\) are joint effects of the common cause \(Z\), and \(X\) does not cause \(Y\), \(P(Y/X=x_0) \ne P(Y)\); that is, \(Y\) and \(X\) are not independent. However, \(P(Y/\do(X=x_0) = P(Y)\); that is, \(Y\) will be independent of \(X\), if the value of \(X\) is set by an intervention. This is because the intervention on \(X\) will break the causal connection from \(Z\) to \(X\), so that the probabilistic dependence between \(Y\) and \(X\) that is produced by \(Z\) in the undisturbed system will no longer hold once the intervention occurs. In this way, we may capture Menzies’ and Price’s idea that \(X\) causes \(Y\) if and only if the correlation between \(X\) and \(Y\) would persist under the right sort of manipulation of \(X\).