In presenting his objections to descriptivism, Kripke assumes that both descriptions and names satisfy the general scheme that:

(R) The referent of ‘X’ is X

where ‘X’ is to be replaced by a name or a definite description. Kripke sees this as a point of agreement between himself and those (such as Russell) who adopt some version of descriptivism. But although it is likely that Russell would have accepted Kripke's (R), Donnellan (1966) had objected to Russell's theory of descriptions on the grounds that his theory incorrectly assumes (R) for definite descriptions. This led some philosophers to think that if Donnellan was correct in his objections to Russell's theory, which assumes (R), then Kripke's objections to descriptivism, which also assume (R), may fail to show that descriptivism is mistaken when Donnellan's position is taken into account. Donnellan did not view his objections to Russell's theory of descriptions as a reason for adopting descriptivism since he had independently offered a theory of names that is very similar to Kripke's (Donnellan 1972). So it is something of an irony that some would use Donnellan's distinction as an objection to Kripke.

Kripke does note this issue at the very beginning of Naming and Necessity, but claims that the points that Donnellan makes against Russell “have little to do with semantics or truth conditions” (NN: 25, n.3). In a later paper, “Speaker's Reference and Semantic Reference”, Kripke defends Russell's theory of descriptions against the objections of Donnellan and in the process draws certain methodological conclusions about certain types of questions and theories in the philosophy of language.