Full Idea
Summary: in favour of the descriptive theory of names are it gives you a mechanism for doing the referring (and Mill doesn't), we can identify two descriptions if there is one referent, and it allows us to question the existence of a referent.
Gist of Idea
Descriptive reference shows how to refer, how to identify two things, and how to challenge existence
Source
report of Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1) by PG - Db (ideas)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.28
A Reaction
If this problem is seen in terms of mental files (with labels and contents) this whole problem becomes a lot clearer. I take reference to be the action of a thinker, not a function of language.