 This need not be a full retreat to a Fregean view for two reasons. The descriptive element may not suffice to pick out the kind (in the non-empty cases)—the implicit historical ostension of a sample may be necessary to fix reference. And the description itself may have non-Fregean features—it may have an indexical component, for example, a reference to the actual world, that a Fregean would deny. The retreat from pure Millianism (and a partial vindication of Mill’s own view of general terms, which Kripke rejected) need not undermine the claim that kind terms are rigid designators. Rigid designation does not require direct reference; complex theoretical expressions, such as ‘H2O’, may, as we saw, also be rigid designators.