The general thesis I want to defend in this paper is the following: the knowledge by acquaintance with an indeterminate object is not sufficient to guarantee the naming of this object because the acquaintance with it is not sufficient to guarantee neither its identification nor its future reidentification. If I am right in defending this thesis, then it should be accepted that the reference made by demonstrcttives depends on primitive elements with predicative function. Now, if this point about demonstratives (which Russell called logical proper names) could be established with some plausibility, important supports for the rigid designation's thesis about proper names would be lost. In this case, a moderate descriptivistic theory of proper names could be vindicated. I am interested on this last consequence of my argumentatian but I will not develop it here. What I intend to do is to reconstruct the Russell's theory of names, specially his theory of the logical proper names, to discuss the distinction between naming and describing and than to argue against the referential privilege of demonstratives.