Given the continuing interest in the question of the semantic status of names and the impressive evidence for something like a Millian theory of names, the problem posed by non-referring or empty names is often thought to be among the most difficult and important problems currently facing philosophy of language. It is hard to disagree. Harder to accept, however, is the all-consuming focus on empty names. It
can be shown, I think, that empty or non-referring definite descriptions give rise to a related problem on the most plausible theories of definite descriptions, including Russell’s. Furthermore, this new problem is one that ought to concern Millians. For not only are Millians among the most ardent supporters of Russell’s theory of definite descriptions (although not, of course, as applied to names), but this new problem also affects certain Millian-friendly descriptivist solutions to the problem of empty names (ones that uphold a Millian story about names but allow definite descriptions to do duty for empty names in problem contexts). In short, there is a problem of empty descriptions that is also a problem for Millianism. The present paper describes this problem, shows why Millians should be worried, and provides a Millian-friendly solution. The concluding section draws some lessons about how all this affects Millianism and the problem of empty names.