 One possibility would be for the intentionalist to dispute the above judgments and embrace the claim that the token uses of ‘that’ in (9) and (10) do in fact refer to the pictures of Kaplan and Carnap, respectively (see Radulescu (forthcoming) for a response along these  lines).  Most intentionalists have not gone down this route, however. Instead, they have either tried to restrict the range of intentions that count as properly ‘referential’, or else they have tried to impose certain limitations on when speakers’ intentions in fact determine reference. This first strategy has generally proceeded by appealing to certain considerations drawn from Paul Grice’s (1957) theory of meaning. The second, in contrast, has tended to try to derive the relevant constraints from the standing meanings of, or rules of use for, the impure indexicals and demonstratives. More recently, some philosophers have also tried combining these two approaches.