 Fourth, counterpart theory offers a way to accept haecceitistic intuitions without subscribing to haecceitism. Lewis assumes that all truths supervene on qualitative truths: no two worlds agree in all qualitative respects, while disagreeing with respect to who plays which roles. A world of two-way eternal recurrence might look like a counterexample: intuitively, we could have lived in any of the epochs of such a world; these seem to be distinct possibilities, but they do not correspond to any qualitative difference. Lewis suggests that the different epochs really do represent different possibilities for us, because we have counterparts in each of them. Here, too, Lewis invokes multiple counterparthood relative to the same counterpart relation. (See Lewis 1986e, 230–5.)