I investigate two intuitions regarding the reference of proper names and natural kind terms that have received significant attention in the philosophy of language, and I discuss the role that they have played in modeling communicative exchanges using the two-dimensional framework in the views defended by Robert Stalnaker, Frank Jackson, and David Chalmers. I call the first intuition the uniform extension intuition: the intuition that proper names and natural kinds refer uniformly across worlds. This means that a proper name uniformly refers to the same individual--namely, the individual to which it refers at the actual world--across all worlds at which refers to anything at all, and a natural kind term uniformly refers to all and only samples of the same kind--namely, the same kind to which it refers at the actual world--across all worlds at which it picks out anything at all. I call the second intuition the contingent extension intuition: had the world turned out differently in the relevant respect(s), the extensions of the relevant expressions would have differed accordingly. This means that, for example, had the kind that we've been calling water turned out to be, say, XYZ, `water' would have referred to XYZ. An attraction of the two-dimensional framework is that it allows us to accommodate both of these intuitions.

I argue that using the two-dimensional framework to model communicative exchanges allows for what I call the problem of informativity: the problem of modeling the impact of an assertion on the state of a conversation. I argue that there is a class of assertions for which Stalnaker's, Jackson's, and Chalmers's views do not accurately model the way that the assertion changes the state of the conversation. I offer a general framework of a solution to the problem as it arises on their accounts, and then give two interpretations of that framework: the first serves as a solution for Stalnaker's account, and the second serves as a solution for Jackson's and Chalmers's accounts. I conclude by discussing the consequences for each view of adopting the proposed solution for that account.