 Intuitively, this is what is going on: If \(X = x^*\) is an actual cause of \(Y = y^*\) then there has to be at least one directed path from \(X\) to \(Y\). \(\bZ\) will consist of variables that lie along some (but not necessarily all) of these paths. (If \(X\) is a direct cause of \(Y\), then \(\bZ\) can be empty.). F-G requires that \(X = x^*\) raises the probability of \(Y = y^*\) in the sense that interventions that set \(X\) to \(x^*\) result in higher probabilities for \(Y = y^*\) than interventions that set \(X\) to \(x'\). Specifically, \(X = x^*\) must raise the probability of \(Y = y^*\) when we also intervene to set the variables in \(\bW\) to their actual values. \(\bW = \bw^*\) is like a background context of the sort discussed in  Section 2.4,  except that \(\bW\) may include some variables that are descendants of \(X\). Moreover, \(X = x^*\) must raise the probability of \(Y = y^*\) in conjunction with any combination of variables in \(\bZ\) being set to their actual values. The idea is that the probabilistic impact of \(X\) on \(Y\) is being constrained to flow through the variables in \(\bZ\), and at every stage in the process, the value of the variables in \(\{X\} \cup \bZ\) must confer a higher probability on \(Y = y^*\) than the baseline probability that would have resulted if \(X\) had been set to \(x'\).