The debate concerning the theory of reference was about which of two competing accounts, one based on the views of Frege and one based on the early views of Russell, is best able to explain how people, using language, are able to refer to things in the world and to communicate with each other. The debate involved a long-standing puzzle regarding so-called “identity” statements—i.e., statements consisting of two names or descriptions joined by is or are. The puzzle was how to account for the apparent informativeness of statements such as “Venus is the morning star,” in which the referents of the names or descriptions are the same. Because “Venus” and “the morning star” both refer to Venus, the statement “Venus is the morning star” must be equivalent in content to “Venus is Venus”—both statements say of a certain object, namely Venus, that it is Venus. But if the two statements say the same thing, how is it possible that one of them, “Venus is the morning star,” is informative—indeed, it represents a discovery made by astronomers in ancient Babylonia—whereas the other, “Venus is Venus,” is not?

Frege’s solution to the puzzle involves a tripartite distinction between a linguistic expression, its meaning, or sense (Sinn), and its referent (Bedeutung). The meaning of an expression, according to Frege, is what one can be said to grasp when one understands it and what the expression shares with its translations into other languages. The meaning determines the expression’s referent as the thing to which the meaning uniquely applies. Thus, the referent of “the morning star” is the planet Venus, because the meaning of “the morning star” uniquely applies to that planet. Accordingly, whereas “Venus” and “the morning star” have the same referent, their meanings are different, and this explains why “Venus is the morning star” is informative and “Venus is Venus” is not.

Russell’s solution to the puzzle is based on his theory of descriptions. As discussed above (see History of analytic philosophy: Bertrand Russell), Russell held that definite descriptions are not genuinely referring expressions, as are logically proper names, and that sentences containing them are logically equivalent to complex general statements containing existential and universal quantifiers. On this view, the sentence “Venus is the morning star” is logically equivalent to the complex statement “(i) There is a morning star, (ii) there is at most one morning star, and (iii) if anything is a morning star, then it is Venus.” Thus, “Venus is the morning star” is informative because it is equivalent to a complex statement that contains information about the morning star and its relation to Venus. In contrast, according to an early view of Russell (one in which ordinary proper names function logically as genuine names rather than as concealed descriptions), the sentence “Venus is Venus” says only that Venus is identical to itself.

A major difference between the Fregean and the Russellian accounts is that for Frege every referring expression, whether a proper name or a description, has both a meaning and a referent, whereas for Russell proper names have referents but no meanings. Consequently, within a Russellian semantics the connection between language and the world via proper names is direct, whereas for Frege it is indirect, taking place through the intermediation of the meaning of the name.

From the early 20th century, analytic philosophers were thus divided over whether reference is direct or indirect. In 1980 support for the direct-reference view was provided by the American philosopher Saul Kripke, who argued that proper names, unlike descriptions, were “rigid designators” that referred directly to the same object in every “possible world.” Thus, according to Kripke, although Aristotle was the teacher of Alexander the Great, it could have turned out that someone other than Aristotle was Alexander’s teacher. In linguistic terms the referent of “the teacher of Alexander the Great” is different in different possible worlds, and the sentence “Aristotle was the teacher of Alexander the Great” is therefore true in some possible worlds and false in others (i.e., it is a contingent truth). But whereas someone other than Aristotle could have been the teacher of Alexander the Great, no one other than Aristotle could have been Aristotle. In linguistic terms, once the referent of Aristotle is fixed in the actual world (i.e., once Aristotle is applied to Aristotle), the name Aristotle must refer to Aristotle in every possible world in which it refers at all, and the sentence “Aristotle is Aristotle” is therefore true in every possible world (i.e., it is a necessary truth). But if the referent of Aristotle is the same in every possible world, then it cannot be determined by means of a description such as “the teacher of Alexander the Great,” because the referents of such descriptions, as we have seen, are different in different possible worlds. Therefore, Aristotle and all other proper names refer directly to their bearers. Kripke was anticipated in this theory by the philosopher Ruth Barcan Marcus and joined by a large number of other thinkers, including Hilary Putnam, David Kaplan, Joseph Almog, and Howard Wettstein.

The Fregean side of the debate also had many supporters, chief among them the American philosopher John Searle. His view, following that of the British philosopher P.F. Strawson, was that to speak as if words by themselves refer is an oversimplification: it is not words that refer but people using words. What ultimately determines the referent of an expression is what the person who uses it on a particular occasion has in mind. Consider a particular use of the proper name Aristotle, as in an utterance of the sentence “Aristotle is intelligent.” As Kripke has shown, it cannot be assumed that the referent of Aristotle in this utterance is whoever was the teacher of Alexander the Great, because someone other than Aristotle might have been Alexander’s teacher . But from this fact it does not follow that Aristotle and other proper names refer directly to their bearers. Whether the referent of Aristotle in this utterance is Aristotle the philosopher or someone else (say, the speaker’s son) depends on what (or whom) the speaker has in mind. And what the speaker has in mind, according to Searle, must be something like a Fregean meaning or sense.

At the start of the 21st century, there was still no resolution of the dispute between the Fregean and the Russellian accounts. Both had their advocates, and the debate continued with highly sophisticated arguments on both sides.