PROPER NAMES AND DESCRIPTIONS

A singular term is an expression whose semantic function, when used in a particular context, is to refer to (denote, designate)—that is, to stand for—a single thing. A definite description is a singular noun phrase beginning with the definite article "the" or with a possessive noun or pronoun, as "the author of Waverley " and "my brilliant career." Proper names, such as "Shakespeare" and "London," are generally classified along with definite descriptions, individual variables, pronouns, and some other indexicals as singular terms. A French speaker who utters the words "Londres est jolie " asserts the same thing as an English speaker uttering "London is pretty." The thing asserted is a proposition, that London is pretty. The fundamental semantic role of a declarative sentence is to express (or to contain ) a proposition (q.v.), which is the semantic content of the sentence. The proposition that Sir Walter Scott is ingenious has some component in common with the proposition that Scott is ingenuous, because both of these are directly about Scott, and some other component again in common with the proposition that Shakespeare is ingenious. These two proposition components are separately correlated with the proper name "Scott" and the predicate "is ingenious." The proposition component semantically correlated with an expression is the expression's semantic content. The principal philosophical controversy regarding proper names (and other singular terms) concerns the question: What are their semantic contents? The theories of John Stuart Mill (1806–1873), Bertrand Russell (1872–1970), and Gottlob Frege (1848–1925) provide rival answers.

1. The Naive Theory and the Millian Theory

One natural theory of semantic content is the naive theory, whose main theses are: (i) the semantic content of any singular term, as used in particular context, is its referent (bearer; the individual referred to); (ii) any semantically contentful expression refers to its semantic content; and (iii) the proposition semantically contained in a sentence is a complex, structured entity whose constituents are the semantic contents of expressions making up the sentence, typically the simple (noncompound) component expressions. (The theory may allow particular sorts of exceptions, as for example those generated by the use of quotation marks.) On the naive theory the proposition contained in "Shakespeare is ingenious" is a singular proposition —composed partly of things such as properties, relations, and concepts, and partly of the very individual(s) the proposition is about. By contrast, a (purely ) general proposition is made up exclusively in a certain way of the former sorts of entities. On the naive theory, semantic content and reference collapse into one.

Definite descriptions pose a difficulty for the naive theory because they contain proper parts with semantic content. In A System of Logic (1893), Mill proffered a variant of the naive theory on which the proposition contained in "The author of Waverley is ingenious" is composed of something involving the attribute of authorship of Waverley in place of Scott himself. Mill distinguished between denotation (referent) and connotation. A general term ("concrete general name") was said by Mill to "denote" the class of individuals to which the term applies. Mill used the term "connotation" for a semantic content consisting of attributes or properties. General terms were held to have both denotation and connotation. According to Mill, definite descriptions also have both connotation and (typically) denotation, whereas proper names have only denotation. Mill's theory strongly suggests a systematic modification of the naive theory. The central theses of the Millian theory are: (i) the semantic content of any simple (noncompound) singular term is its referent; (ii) any expression refers to its extension; and (iii) the semantic content of a typical contentful compound expression (e.g., a definite description) is a composite entity whose constituents are the semantic contents of expressions making up the compound expression, typically the simple component expressions. (Mill's actual theory was somewhat more complex, but also somewhat less plausible.)

2. The Puzzles

The naive and the Millian theories give rise to philosophical puzzles concerning substitution and nonreferring names. Frege's puzzle arises from certain sentences, especially identity sentences. The sentence "Hesperus is Phosphorus" (or "The Evening Star is The Morning Star"), by contrast with "Hesperus is Hesperus," is informative. Its semantic content apparently extends knowledge. It is also a posteriori and synthetic. Yet according to both the naive theory and the Millian theory, the semantic contents of both sentences are composed of the same components, evidently in precisely the same way. Those theories thus ascribe the same semantic content to both sentences. In his early work, Begriffsschrift (1972 [1879], §8), Frege proposed solving this puzzle by reading the predicate for numerical identity as covertly metalinguistic: It was held that "Hesperus is Phosphorus" contains a substantive proposition concerning the names "Hesperus" and "Phosphorus," to the effect that they are co-referential. There are serious difficulties with this account, however, and Frege came to reject it. Most significantly, the account fails to solve the general problem of which "Hesperus is Phosphorus" is a special case. Unless the theory is part of a more sweeping proposal concerning all expressions and not just that of identity predicates, there is no explanation for the analogous difference in epistemic and semantic status between "Hesperus is a planet if Phosphorus is" (synthetic a posteriori ) and "Hesperus is a planet if Hesperus is" (analytic a priori ).

A second puzzle is the apparent failure of substitution in special contexts, especially those of propositional attitude. Jones may sincerely and reflectively assent to "Hesperus appears in the evening sky" and sincerely and reflectively dissent from "Phosphorus appears in the evening sky," even while fully grasping their semantic content. This appears to violate the classical logical rule of Leibniz's law, or the substitutivity of equality. Both the naive theory and the Millian theory treat "Jones believes that Hesperus appears in the evening" and its substitution instance "Jones believes that Phosphorus appears in the evening" as having the same content, and therefore also the same truth-value.

A further nest of problems concerns sentences involving nonreferring proper names. The sentence "Sherlock Holmes is addicted to cocaine" clearly has content. Yet on both the naive theory and the Millian theory, the semantic content of any sentence will lack a necessary component if any contained name lacks a referent. It is evident, moreover, that this sentence (taken as a statement of real fact, rather than as a statement made from within the fiction) cannot be counted literally true. But, it seems, neither can its negation—"Sherlock Holmes is not addicted to cocaine"—be truly uttered. This seems to violate the classical law of excluded middle. These puzzles are especially pressing with regard to negative existentials, such as "Sherlock Holmes does not exist." This sentence is true if and only if "Sherlock Holmes exists" is false, and therefore, it would seem, if and only if the referent of "Sherlock Holmes" lacks existence. Yet the negative existential itself implies that the name does not so much as have a referent. How, then, can it be true? Indeed, how can it have any content at all?

3. Russell's Theory of Descriptions

Russell's semantic theory (post-1904) is a supplement to the naive theory. Russell employed propositional functions in lieu of attributes. A propositional function assigns to any objects in its domain a singular proposition concerning those objects. Russell's general theory of descriptions, or of what he called "denoting phrases," consisting of a noun phrase preceded by a determiner such as "all" or "some," assigns a content to sentences in which they figure while denying that the determiner phrases themselves are meaningful units. The theory analyzes sentences of both the Aristotelian A form, "Π(all S )" (e.g., "All millionaires are wealthy"), and the I form, "Π(some S )," where Π is a monadic predicate. (More generally, Π may be the result of filling all but one of the argument positions of an n -adic predicate, n ≥ 1.) The A form is analyzed as "For everything x, if x is a S, then Π(x )"—more colloquially as, "Everything is such that: if it is a S, then Π(it)" ("Everything is, if a millionaire, then wealthy"). The complex predicate "is such that: if it is a S, then Π(it)" stands for a certain propositional function, whereas the quantifier "everything" stands for a higher-level propositional function, which assigns to any first-level propositional function, F, the proposition that F is "always true"—that is, the proposition that F yields a true proposition for each and every argument.

Russell analyzed "Π(some S )" as "Something is such that: it is a S and Π(it)"—wherein the complex predicate "is such that: it is a S and Π(it)" stands for a certain propositional function said to be "sometimes true"—that is, to yield a true proposition for at least one argument. An English phrase of the form "all S " thus corresponds to the incomplete string, "everything is such that: if it is a S, then it … ," and a phrase of the form "some S " corresponds to the incomplete string, "something is such that: it is a S and it.…" Russell called phrases of either form incomplete symbols. The sentences in which such phrases figure have content, though the phrase, in and of itself, does not contribute a proposition-component to the proposition expressed. As Russell put it in "On Denoting," "denoting phrases have no meaning in isolation."

The introduction of a quantifier ("everything," "something") into the analysis gives rise to ambiguities analogous to that of "every boy kissed a girl" when the simple Aristotelian sentential form occurs within the scope of a governing operator, such as "not," "necessarily," or "Jones believes." Thus, on Russell's general theory of descriptions, a sentence of the form "not Π(all S )" (e.g., "All millionaires are not wealthy") may be analyzed by giving the indefinite description "all S " primary occurrence (over "not"), yielding: "Everything is such that: if it is a S, then not-Π(it)." This reading is equivalent to the Aristotelian E form, "Π(no S )." Alternatively, and nonequivalently, "not Π(all S )" may be analyzed by giving the phrase "all S " secondary occurrence, yielding the reading, "Not everything is such that: if it is a S, then Π(it)." (The latter analysis—equivalent to the Aristotelian E form—is obtained by letting the negation in "not Π(all S )" govern the entire A form, not just its predicate Π.) Similarly, "Jones believes Π(some S )" may be analyzed as "Something is such that: it is S and Jones believes that Π(it)" (primary occurrence), or alternatively, and nonequivalently, as "Jones believes: that Π(some S )" (secondary).

In most cases, only one of the two readings is plausibly intended (as with "Jones believes some husbands are bachelors"). If the simple Aristotelian A or I form occurs with two or more governing operators, the number of readings is compounded. For example, "Jones believes some millionaires are not wealthy" may be analyzed alternatively, and nonequivalently, as: (i ) "Someone is a millionaire and Jones believes he/she is not wealthy" (wide scope ); (ii ) "Jones believes: that someone is both a millionaire and not wealthy" (intermediate scope ); or (iii ) "Jones believes: that no one is both a millionaire and wealthy" (narrow scope ).

The central tenet of Russell's theory of definite descriptions is that a description such as "the author of Waverley " (used in the sense of "the sole author of Waverley ") is semantically equivalent to the corresponding uniqueness-restricted existential quantifier "some unique author of Waverley," in the sense of "something such that it, and nothing else, wrote Waverley." The restricted quantifier falls under the purview of Russell's general theory of descriptions. On Russell's theory, then, "the author of Waverley " corresponds to the string "Someone is such that: he or she uniquely wrote Waverley and he or she … ," making definite descriptions also "incomplete symbols" which have "no meaning in isolation." The words "The author of Waverley is ingenious" are not directly about Walter Scott, but about the complex propositional function, being a unique author of Waverley who is also ingenious, expressing that this function yields a true proposition for at least one individual. There is nothing that the phrase "the author of Waverley " contributes on its own to this proposition.

As with "some S," sentences that position a definite description within governing operators yield multiple readings. For example, "Jones believes the author of Waverley is not ingenious" may be analyzed alternatively, and nonequivalently, as: (i) "Someone uniquely wrote Waverley and Jones believes he is not ingenious"—that is, Jones believes of Waverley 's sole author that he is not ingenious (wide scope ); (ii) "Jones believes: that someone both uniquely wrote Waverley and is not ingenious"—that is, Jones believes that whoever wrote Waverley single-handedly is not ingenious (intermediate scope ); or (iii) "Jones believes: that no one both uniquely wrote Waverley and is ingenious" (narrow scope ). The wide-scope reading is consistent with Jones's belief not involving a conception of Scott as sole author of Waverley. The narrow-scope reading attributes a belief that is consistent with Waverley not having a sole author.

A definite description is said to be proper when there is someone or something that uniquely answers to the description, and is improper otherwise. Russell artificially, and misleadingly, extended Mill's term "denotation" to the semantic relation that obtains between a proper definite description and the individual uniquely described, even though a definite description is supposed not to be a singular term. He might instead have called this relation "simulated denotation." Russell retained the term "meaning" for semantic content.

Both the Millian theory and Russell's theory deny that the individual that uniquely answers to a definite description is itself a component of the content of sentences involving the description. Those theories are able to solve the puzzles in the special case where the terms involved are definite descriptions rather than proper names, by reading sentences involving definite descriptions as containing propositions involving corresponding attributes or propositional functions. In particular, Russell's claim that definite descriptions are not singular terms, but quantificational constructions, blocks substitutivity of equality, which is applicable only to singular terms, from licensing the substitution of "the first Postmaster General" for "the inventor of bifocals" in the secondary-occurrence reading of "Jones believes that the inventor of bifocals was clever." (By contrast, the envisioned substitution is indeed licensed by logical principles, including substitutivity as applied to variables, when the sentence takes on its primary-occurrence reading.)

Russell handled the same difficulties in the case of proper names (and such devices as demonstratives) through his thesis that names are ordinarily not used as "genuine names" (singular terms). Instead they were held to be "disguised" or "abbreviated" definite descriptions. The proposition expressed by a sentence involving a typical name is to be analyzed in accordance with Russell's theory of descriptions. This blocks substitution in sentences such as "Jones believes that Hesperus appears in the evening." Russell acknowledged the possibility of "names in the strict, logical sense" (logically proper names), which function in accordance with the naive theory. The class of admissible semantic contents for usable genuine names was severely limited by Russell's principle of acquaintance, that every proposition one can grasp must be composed entirely of constituents with respect to which one has a special sort of intimate and direct epistemic access, (direct ) acquaintance. This restriction seems sufficient to prevent the puzzles from arising with logically proper names. (Russell did not countenance genuine names lacking a referent. Curiously, he claimed that singular existential and negative existential statements involving genuine names are without meaning. It would have been better to say that such sentences are always trivially true and trivially false, respectively.)

4. Frege's Theory of Sinn and Bedeutung

In his classic paper, "Über Sinn und Bedeutung " (1892), Frege abandoned the naive theory in favor of a richly elegant philosophy of semantics, which extends the Millian theory's two-tiered semantics for definite descriptions and predicates to include all meaningful expressions. (Like Mill, and unlike Russell, Frege counted definite descriptions as singular terms.) Frege distinguished between the referent (Bedeutung ) of an expression and its sense (Sinn ). The sense of an expression contains a purely conceptual manner of presenting the name's referent. Individuals that are not themselves senses—such as persons and even their sensations—cannot be constituents of a genuine Fregean sense. Furthermore, the sense of a singular term secures the term's referent. An expression's sense is a conception of something, and the expression's referent, if there is one, is whatever uniquely fits the concept. The reference relation is thus the relative product of a purely semantic relation (that between an expression and its sense) and a nonlinguistic relation (that between a sense and the object that fits it). Third, the sense of an expression is the semantic content. Expressions having the same sense must have the same referent, but importantly, expressions having the same referent may differ in sense. Frege illustrated his notion of sense by means of three lines that intersect in a single point. Then the phrases "the point of intersection of a and b," "the point of intersection of a and c," and "the point of intersection of b and c " converge in reference but diverge in sense.

The observation that proper names have a sense, as distinct from the referent, is tailor-made to solve both Frege's Puzzle and the problem of how sentences involving nonreferring names can have content. Frege's solution to the substitution problem is more complex. Crucial to Frege's theory are the principles of extensionality and compositionality. They hold that the referent or sense, respectively, of a complex expression is a function of the referents or senses, respectively, of the component expressions. In the latter case Frege spoke metaphorically of the sense of a constituent expression as a part of the sense of the complex expression, so that the sense of the whole is composed of the senses of the parts.

Thus, if a constituent expression is replaced by one having the same sense, the sense of the whole is preserved, whereas if a constituent expression is replaced by one having the same referent but a different sense, the referent of the whole is preserved even though the sense is not. In particular, Frege held as a special case of extensionality that a compound expression having a nonreferring part must be nonreferring ("Sherlock Holmes's older brother"). Frege argued, using extensionality, that the cognitive value (Erkenntniswerte ) of a sentence is not the referent of the sentence, but is fixed by its sense, and that the referent of a sentence is one of two truth values, truth and falsity ("the true" and "the false"). Because a sentence refers to its truth-value, and a sentence involving a nonreferring name itself refers to nothing, such a sentence as "Sherlock Holmes is addicted to cocaine" is neither true nor false. (Frege held that the sentence presupposes, without asserting, that Sherlock Holmes exists.)

Frege argued that certain expressions create a special context in which subordinate expressions do not refer to their customary referent. When occurring within quotation marks (for example, in "direct discourse" reporting the words used by a speaker) an expression refers to itself. Analogously, expressions occurring subordinate to operators such as "Jones believes that" and "Jones said that" (the latter occurring in "indirect discourse" reporting the content of a speaker's utterance) refer to their ungerade (indirect, oblique) referent, which is the customary sense. Extensionality is to be understood as requiring the validity of substituting for a name in a sentence any expression having the same referent in that same position. (Scattered remarks suggest that Frege might have applied his doctrine of semantic shifting also to the problem of negative existentials.)

5. The Theory of Direct Reference

Despite a fundamental disagreement over the matter of singular propositions, there is common ground between Russell and Frege in regard to ordinary proper names. Both held a strong version of the theory that names are descriptional. On their view, if "St. Anne" is analyzable as "the mother of Mary," it must be analyzable even further, because "Mary" is also supposed to be descriptional. But even "the mother of the mother of Jesus" must be in this sense further analyzable. If "α" is a nondescriptional singular term referring to Mary, then it may be said that the description "the mother of α" is descriptional relative to Mary. A thoroughly descriptional term is one that is descriptional but not descriptional relative to anything. The orthodox theory, shared by Russell and Frege, is the theory that proper names and similar devices are either thoroughly descriptional or descriptional relative only to items of direct acquaintance. Frege held the stronger thesis (which is retained by contemporary variants of Frege's theory, such as that of John Searle) that proper names are thoroughly descriptional. Any departure from the stronger thesis would constitute a rejection of fundamental Fregean theory.

In recent philosophy the orthodox theory has been forcefully challenged, most notably by Keith Donnellan (1972), David Kaplan, Saul Kripke (1972, 1979), Ruth Barcan Marcus, and Hilary Putnam. These philosophers favor the theory of direct reference, which holds that proper names (and similar devices) are nondescriptional. Importantly, this theory does not deny that particular names may exhibit any or all of the three aspects of a Fregean sense mentioned in the previous section. What is denied is that the conceptual representation carried by a name secures the referent. But the direct-reference theory is significantly stronger than a simple denial of Russell's doctrine that ordinary names are abbreviated definite descriptions. The theory holds that names are not even similar to definite descriptions. An immediate consequence is that a great many definite descriptions fail to be thoroughly descriptional or descriptional relative only to items of direct acquaintance, because many contain names of ordinary individuals.

Three main kinds of arguments have been advanced in favor of the direct-reference theory. The modal and epistemological arguments are due chiefly to Kripke. Suppose for simplicity that the name "Shakespeare" simply means "the English playwright who wrote Hamlet, Macbeth, and Romeo and Juliet." If the orthodox theory of names is correct, then the sentence, "Someone is Shakespeare iff he is an English playwright who is sole author of Hamlet, Macbeth, and Romeo and Juliet," should express a necessary, a priori truth. On the contrary, however, it might have come to pass that Shakespeare elected to enter a profession in law instead of becoming a writer. Furthermore, it is possible, and is not ruled out solely by semantic reflection, that Francis Bacon should go on to write these plays. These intuitions are supported by a complementary intuition: that "Shakespeare" continues to refer to the same person even with respect to nonactual possible worlds in which Shakespeare lacks the distinguishing characteristics that people actually use to identify him—that is, even in discourse about such a counterfactual scenario. One important consequence of the direct-reference theory is that any proper name is a rigid designator (Kripke)—that is, it designates the same thing with respect to every possible world in which that thing exists and does not designate anything else with respect to other possible worlds.

One example of the semantic arguments for the direct-reference theory comes from Donnellan: According to the orthodox theory, the semantic content of the name "Thales" is determined by a description such as "the Greek philosopher who held that all is water." But suppose that the man referred to by writers from whom the use of the name "Thales" derives never genuinely believed that all is water but was thought to, owing to some error or hoax, and that, by coincidence, there was a Greek hermit who did hold this bizarre view, though he bears no historical connection to anyone. Contrary to the orthodox theory, the name "Thales" would nevertheless refer to the first of the two. This argument seems to reveal also that the surrounding settings in which speakers find themselves, and not merely the concepts evoked in them, are crucial to determining the referents of the names they use. In a word, the securing of a referent for a name is a contextual phenomenon. Donnellan and Kripke have provided partial accounts of the securing of a referent for a name by means of historical chains of communication. Putnam has given a similar account of certain terms designating something by means of a "division of linguistic labor." Because of these accounts the direct-reference theory is sometimes called the causal theory of reference.

6. The Millian Theory Reconsidered

What, then, is the semantic content of a name? It is tempting to answer that it is, or at least includes, a descriptive or conceptual "mode of presentation." Although this proposal does not require that the associated mode of presentation secure the referent, it faces some of the same difficulties as the orthodox theory. A more general difficulty arises because the variations of the argument from Frege's Puzzle against the naive theory and the Millian theory can be mounted against a wide variety of theories of semantic content, including Frege's. The general strategy involved in that argument, however, seems to involve an error. This might be demonstrated through an application to a situation involving expressions for which it is uncontroversial that semantic content is exactly the same.

Suppose that foreign-born Sasha learns the words "ketchup" and "catsup" by actually consuming the condiment and reading the labels on the bottles. Suppose further that, because of his idiosyncratic experience, Sasha comes to believe that the substances so named are different condiments sharing a similar taste, color, and consistency. Whereas "Ketchup is ketchup" is uninformative for Sasha, "Catsup is ketchup" is informative. It would be a mistake, however, to conclude that "catsup" and "ketchup" differ in semantic content for Sasha. The terms are perfectly synonymous in English; indeed, they are arguably the same English word. Most English speakers learned one in a sort of ostensive definition, and the other as a strict synonym (or as an alternative spelling) of the first. If either may be learned by ostensive definition, then both may be—witness Sasha. This discredits the original argument from Frege's puzzle.

One important consideration favoring the Millian theory over the orthodox theory comes by consideration of individual variables. Consider the following propositional-attitude attribution:

(1) The planet Venus is an individual x such that Jones believes that x is a star.

It is characteristic of this de re (as opposed to de dicto ) locution that it does not specify how Jones is supposed to conceive of Venus in believing it to be a star. The Orthodox Theorist contends that this is a result of the allegedly descriptional name "Venus" positioned outside of the scope of the nonextensional operator "Jones believes that," where it is open to substitution and to existential generalization. What is more significant, however, is that a nondescriptional singular term is positioned within the scope of the nonextensional context: the last occurrence of the variable "x " in (1). It follows by the principles of conventional semantics that (1) is true if and only if its component open sentence:

(2) Jones believes that x is a star

is true under the assignment of Venus as value for the variable. In turn, (2) is true under this assignment if and only if Jones believes the semantic content of the complement open sentence:

(3) x is a star

under the same assignment. But the fundamental characteristic of a variable with an assigned referent is that its semantic content is just its referent. This is precisely the point of using a variable rather than a definite description (such as "the first heavenly body visible at dusk") within the scope of an attitude verb in a de re attribution. If a variable with an assigned value had, in addition to its value, a Fregean sense, then (3) would contain a specific general proposition, under the relevant assignment. If (1) is to fail to specify how Jones conceives of Venus, the content of (3) under the assignment of Venus to "x " can only be the singular proposition about Venus that it is a star. If the open sentence (3), under the assignment of Venus as the value of "x," contains the singular proposition about Venus that it is a star, then so does the closed sentence "a is a star," where "a " is an individual constant that refers to Venus. It is not the variability of a variable, but its structural simplicity, that gives it the feature that the variable's semantic content, under an assignment of a referent, is just the assigned referent. (An exactly parallel argument proceeds using pronouns in place of variables, using "The planet Venus is such that Jones believes that it is a star.")

It is important to note also that at least some aspects of the remaining puzzles would arise even in a language for which it was stipulated that the Millian theory is correct. Suppose, for example, that an authoritative linguistic committee that legislates the grammar and semantics of the language, and to which all speakers of the language give their cooperation and consent, decreed that proper names are to function exactly like the mathematician's variables, "x," "y," and "z," except that they are to remain constant. Ordinary speakers would presumably continue to regard co-referential names as not always interchangeable in propositional-attitude attributions. English speakers who use "ketchup" and "catsup" as exact synonyms may be inclined to assent to "Sasha believes that ketchup is a sandwich condiment, but he does not believe that catsup is." On philosophical reflection, however, it emerges that this expresses a logical impossibility. Similarly, speakers who agree to abide by the legislative committee's decree about proper names might for independent pragmatic reasons be led to utter or to assent to such sentences as "Jones believes that Hesperus appears in the evening, but he does not believe that Phosphorus does." Insofar as the same phenomena that give rise to the puzzles would arise even in the case of a language for which the Millian theory was true by fiat and unanimous consent (and do in fact arise with respect to such straightforward synonyms as "ketchup" and "catsup"), the puzzles cannot be taken as evidence against the Millian theory. A deeper understanding is needed of the puzzles, and a reexamination of the Millian theory in light of this deeper understanding.

See also Demonstratives; Indexicals; Quantifiers in Natural Language.

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Nathan Salmon (2005)