If A(x) is a predicate satisfied by exactly one x, then we write Ix.A(x) for that object x. The operator I is called a descriptor. The author reviews the various treatments of descriptors in the literature, pointing out that the problem each treatment faces is ''what to do with Ix.A(x) when \(\exists !xA(x)\) is not (yet) known''. The obvious answer is that it is undefined. The technical contribution of the paper is to show that this obvious answer can be formalized. The author bases his formalization on Scott's E-logic, and shows that ''partial descriptors'' can be added to such a theory conservatively. In a final section, he considers theories with function variables and quantification. In that case descriptors are not conservative, since they yield axioms of choice; but he shows that is all they yield. The paper is very clearly written and to the point.