 Some of the fundamental work concerns epistemology: e.g., the issue of whether a sentence like ‘Hesperus = Phosphorus’ is a posteriori as well as necessarily true. Would the above considerations in favor of distinguishing assertoric from ingredient sense  undermine Kripke’s ideas here, at least, even if the considerations do not undermine Kripke’s ideas about modality? That seems unlikely. On the contrary, the claim that names, though rigid, share the semantic content of descriptions seems likely to vindicate Kripke’s claims about the epistemic status of statements like the above, if anything. That is because one could say that ‘Hesperus’ and ‘Phosphorus’ differ in assertoric content (in an extended sense, applied to designators rather than statements) but they do not differ in ingredient sense or modal content. Because they do not differ in ingredient sense or modal content, being rigid designators for the same thing, ‘Hesperus = Phosphorus’ is necessarily true. Because they do differ in assertoric content, ‘Hesperus = Phosphorus’ is a posteriori; ‘Hesperus = Hesperus’, by contrast, is a priori since both occurrences of ‘Hesperus’ have one and the same assertoric content. So descriptivism of this sophisticated sort suggests one means to retain Kripke’s epistemic claims. Anti-descriptivism in the form of direct reference, by contrast, is incompatible with at least one interpretation of the claim that ‘Hesperus = Phosphorus’ is “a posteriori”,  because on the theory of direct reference, ‘Hesperus’ and ‘Phosphorus’ just share the same content, end of story: so ‘Hesperus = Phosphorus’ shares the same content as ‘Hesperus = Hesperus’, which is a priori just in virtue of content (again, on one interpretation of the claim that the statement is “a priori”).