 Further, even if rigidity does follow from anti-descriptivism, anti-descriptivism does not follow from rigidity: so rigidity’s work is not limited to that of direct reference. We have seen that descriptive designators may be rigid: e.g., world-indexed designators. But rigidity performs much of the same work on these as on arguably nondescriptive expressions like names. For example, ‘The evening star in α = the morning star in α’ would seem to be a necessarily true, a posteriori statement whose necessity and aposteriority cannot be explained in terms of the nondescriptive nature of the designators flanking the ‘=’ sign.