Most direct reference theories of proper names would seem to be committed to the following four theses:
1. A proper name denotes, designates, refers to, its nominatum directly without the mediation of any properties. There is no description or disjunction of descriptions satisfaction of which is necessary for a name to target its nominatum. Accordingly, ordinary proper names are not definite descriptions in disguise as Russell famously maintained. The reference of a name is not routed through its sense or any component of its sense. A name may have a sense, but if it does it won't play a role in determining whether the name has a referent and which referent it is.
2. Proper names are first introduced at a 'baptismal ceremony' in which an individual is singled out as the name's nominatum. For example, a black cat wanders into my yard and I dub him 'Max Black.' Peter Lupu reminds me that names can get attached to objects also by the use of reference-fixing definite descriptions.
3. The connection established between name and nominatum at the baptism is rigid: once name N is attached to object O, N designates O in every possible world in which O exists. On the DR theory, then, 'Socrates' designates Socrates even in possible worlds in which Socrates is not the teacher of Plato, the husband of Xanthippe, etc. This is because the reference of 'Socrates' is not determined by any definite description or disjunction such descriptions.
Indeed, the DR theory has the strange implication that the following is possible: none of the definite descriptions we associate with the use of 'Socrates' is true of him, yet the name refers to him and no one else. Well, if the sense of the name does not determine reference, what does? What makes it the case that 'Socrates' designates Socrates?
4. A speaker S's use of N refers to O only if there is a causal chain extending from S's use of N back to the baptism, a chain with the following two features: (a) each user of N receives the name from an
earlier user until the first user is reached; (b) each user to whom the name is transmitted uses it with the intention of referring to the same object as the previous user.
Problem: How is (1) consistent with (4)? Suppose I first encounter the name 'Uriel Da Costa' in a book by Leo Strauss. If I am to refer to the same man as Strauss referred to, I must use the name with the intention of doing so. Otherwise I might target some other Uriel Da Costa. It seems to follow that my use of 'Uriel Da Costa' must have associated with it the identifying attribute, same object as was referred to by Strauss with 'Uriel Da Costa.' But then the reference is not direct, but mediated by this attribute. (4) conflicts with (1).