 Paull and Sider’s isolation principle does the job. Consider again the worlds w1 and w2 that Petrie described. Petrie purported to describe the worlds in full. Thus, P and S are presumably supposed to be intrinsic properties. It follows from the isolation principle that there is a world w3 that contains an isolated duplicate of x—call it “z”—and a world w4 that contains an isolated duplicate of x*—call it “z*.” As Paull and Sider note, these worlds will be as follows: