 However, there are versions of the role-switching argument that do not rely on the cumulative effect of a series of small changes. Suppose we assume that Adam and Noah do not differ from one another in their essential properties; in other words, that all the differences between them are accidental (i.e., contingent) differences. It seems immediately to follow that any way that Adam could have been is a way that Noah could have been, and vice versa. But one way that Adam could have been is the way Adam actually is, and one way that Noah could have been is the way Noah actually is. So (if Adam and Noah do not differ in their essential properties) it seems that there is a possible world in which Adam plays the Noah role, and a possible world in which Noah plays the Adam role. But there is no obvious reason why a world in which Adam plays the Noah role and a world in which Noah plays the Adam role shouldn’t be the very same world. And in that case there is a possible world in which Adam and Noah have swapped their roles. This argument for the generation of a role-switching world does not rely on a series of small changes: all that it requires is the assumption that there is no essential difference between Noah and Adam: or, to put it another way, that any essential property of Noah is also an essential property of Adam, and vice versa. (See Mackie 2006, Ch. 2; also Adams 1979; cf. Dorr, Hawthorne, and Yli-Vakkuri 2021.)