The Standard Theory of Reference
“Reference” has many senses, and a common understanding of the word derives from an early mistranslation of the Frege’s term Bedeutung.4 A common and pre-theoretical definition is that a term refers when it signifies which thing we are talking about in making a statement.5 “Reference” I shall characterize as what happens when we refer, and I shall use the terms “identification” and “designation” as synonymous for the most part with “reference.” Reference is what singular or definite terms do, and what common or indefinite terms don’t. The name “Socrates” in “Socrates is running” tells us which person is said to be running, or (in philosophical jargon) tells us which individual satisfies the predicate “is running.” Singular terms contrast with common terms, which do not specify who satisfies the predicate. “Some philosopher is running” is true if at least one of Socrates, or Plato, Aristotle, and so on is running, no matter which one. Thus, “some philosopher” does not refer. Or suppose it did, for example, to Socrates. Then, “it is not the case that some philosopher is running” would be true when Socrates is not running, even if it is the case that some other philosopher, say Plato, is running, which is absurd.
The standard theory of reference, sometimes called “direct reference,” is primarily a theory about proper names. It involves two assumptions. The first is the nondescription assumption, that a proper name has no connotation or descriptive sense that determines its reference. As Abelard argued, the accidental properties connected with some description can hardly enter into the imposition of the signification of the name, or the name would change its meaning through time. “Socrates was called Socrates before he became a musician, and will be so called after he ceases to be the son of Sophroniscus [i.e., after Sophroniscus dies].”6 More recently, Kripke has said much about this. The second assumption is what Devitt calls the semantic presupposition 7 that there are no other possible candidates for a name’s meaning other than a descriptive meaning, or the bearer of the name itself. If both assumptions are correct, the meaning of a proper name is none other than the bearer itself, that is, the name is merely a tag or label for its bearer, and has no other significance.
These two assumptions (nondescription and semantic presupposition) are of crucial importance to the theoretical framework of classical (i.e., the twentieth century) semantics, entailing as they do that sentences with empty names cannot express propositions. In that framework, the truth conditions or proposition (or information content) expressed by a sentence, relative to a context, are compositionally determined by the semantic values or referents of the terms in the sentence.8 The structure and components of the proposition mirror the structure and components of the sentence expressing the proposition. To understand a sentence we have to grasp its truth conditions: the way the world has to be if the sentence is true, but the truth conditions are determined by the referents of the words in the sentence, including the referent of any proper name. Hence, we cannot understand what is expressed by the sentence unless the words, including any proper names, have a referent. As Evans, in his exposition of Frege, says:
The Proper Name “John” has the role of introducing an object, which is to be the argument to the function introduced by the concept-expression “ξ is wise”—a function which maps all and only wise objects to the value True. Thereby, and only thereby, is the sentence determined as having a truth-value, and, therefore, as having the significance of a complete sentence—something capable of being used alone to make an assertion.9
When a sentence contains an empty name, the name cannot introduce an object as argument to the function, the function has no value, that is, no truth value, and the sentence cannot express a thought or a proposition. Evans again, quoting Frege:
The sentence “Leo Sachse is a man” is the expression of a thought [Ausdruck eines Gedankens] only if “Leo Sachse” designates [bezeichnet] something.10
The standard theory also entails that the existence of a bearer is presupposed, rather than asserted, by a subject-predicate sentence containing a proper name. As Frege argues, the negation of “Kepler died in misery” is not “Kepler did not die in misery, or the name ‘Kepler’ has no significance,”11 that is, “Kepler died in misery” is not a conjunction of the statements that “Kepler” is significant and that Kepler died in misery.12 According to the standard theory, it is presupposed rather than asserted that that the name “Kepler” is significant, hence (because the name signifies the bearer) it must be presupposed that the bearer exists.
A further corollary of the standard theory is that there can be only one reason for a proper name sentence being false, namely that the predicate does not apply to the subject. Hence, on that theory, there can be only one form of negation for proper name subject-predicate sentences, namely wide scope or sentential negation. If “Moses was a prophet” is false, it is because Moses existed but was not a prophet. This corollary is reflected in the standard notation of the predicate calculus: the negation “Fa” is “~Fa.” On the standard theory, proper names are not descriptive, or properly speaking, are not predicable, a predicable being an expression that yields a proposition about something if we attach it to an expression, that is, a singular term, which stands for, that is, designates or refers to, what we are forming the proposition about.13 As Geach says:
To Frege we owe it that modern logicians almost universally accept an absolute category-difference between names and predicables; this comes out graphically in the choice of letters from different founts of type for the schematic letters of variables answering to these two categories.14
A predicable can be empty if nothing has the property it expresses, for example,” round square.” Frege explains that a common name like “planet” has no direct relation to the Earth. You can understand the concept it signifies without anything falling under the concept, for a predicable is not intrinsically about any object. “If I utter a sentence with the grammatical subject ‘all men,’ I do not wish to say something about some Central African chief wholly unknown to me.” But a proper name cannot be empty. “A proper name that designates nothing is illegitimate (unberechtigt).”15
Thus, on the standard theory, reference is a relation between a linguistic expression, such as a proper name, and an extralinguistic item, the object that an author (or speaker) uses the expression to write (or talk) about, and so is an extralinguistic or word-world relation.16 The co-reference between the names “God” in the first line of the Quran, and in “The second word of the Quran refers to God,” is explained by means of an external relation to a third item, namely God himself. We understand that the first token signifies God, that the second token signifies him also, and thereby understand that the two tokens co-refer. The co-reference takes place only because the tokens both “hit” the same object in external reality. According to the standard theory, “reference” is primary, co-reference is secondary.
The standard theory of reference, which begins with Frege,17 contrasts with the traditional “Aristotelian” semantics, which it supplanted at the end of the nineteenth century. In Aristotelian semantics, there is also a distinction between proper names and common terms. At the beginning of chapter 7 of the Perihermenias, Aristotle says that some “things,” that is, terms, are universal, others singular. He has in mind the distinction between a common term (“man”) and a proper name (“Callias”). A universal or common term is that which by nature can be predicated of (κατηγορεῖσθαι) different individuals, such as Socrates and Callias.18 A proper name is what can be predicated of only one individual. Following Aristotle, scholastic logicians like Peter of Spain claimed that a singular term is suited by nature (aptus natus) to be predicated of (i.e.,