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Philosophy of Language

A Unified Theory of Names

John Justice

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ABSTRACT: Theoreticians of names are currently split into two camps: Fregean and Millian. Fregean theorists hold that names have referent-determining senses that account for such facts as the change of content with the substitution of co-referential names and the meaningfulness of names without bearers. Their enduring problem has been to state these senses. Millian theorists deny that names have senses and take courage from Kripke's arguments that names are rigid designators. If names had senses, it seems that their referents should vary among possible worlds. However, the Millians have the enduring problem of explaining the apparent cognitive content of names. I argue that Mill's original theory, when purged of confusion, provides word-reflexive senses for names. Frege failed to notice senses of this particular sort. Moreover, it is these senses that account for names' rigid designation. When the views of Mill and Frege are understood as complementary, the problems that have faced the divided theorists of names vanish.

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The division of terms into connotative and nonconnotative is, according to Mill, one of the distinctions that "go deepest into the nature of language." (1) The importance of this distinction was reaffirmed by Saul Kripke in Naming and Necessity. Kripke followed Mill in holding that proper names must be understood as nonconnotative. To insist on this classification was, on Kripke's view, to reject the powerfully supported view of names that originated with Frege. (2) Since the publication of Kripke's lectures theories of names have come to be thought of as divided into two opposing types-Fregean and Millian.

This opposition of theories has impeded the development of a satisfactory theory of names. Mill's reflections on the nature of proper names are mistakenly taken to be incompatible with Frege's independently developed theory; and, consequently, the compelling support for Mill's view is mistakenly seen as evidence against Frege's.

That Frege's theory is incompatible with Mill's classification of names as nonconnotative may appear to be undeniable. The central tenet of Frege's view is that, in addition to the reference of a name, there is its sense, "wherein the mode of presentation [of the referent] is contained." (3) Mill, in seeming contrast, asserts that proper names lack connotation. If sense had to be understood as connotation, then the views would be contradictory. If, on the other hand, senses could be divided into the connotative and the nonconnotative, then the fact that names have senses would not entail that they have connotations; and acceptance of Mill's classification need not entail rejection of Frege's theory.

I will argue that Mill and Frege are both right — that names have nonconnotative senses. The views of these two theorists can be reconciled — without violence to either. All that is wanted for a unified Millian and Fregean theory of names is clarification where confusion was introduced by Mill, and completion where a crucial fact was overlooked by Frege.


Mill's distinction between connotative and nonconnotative terms needs clarification. Mill presents his division as one between terms that do two things and terms that do one thing only:

A non-connotative term is one which signifies a subject only, or an attribute only. A connotative term is one which denotes a subject, and implies an attribute. (4)

Mill uses 'signifies' and 'denotes' interchangeably, so the difference between the two types, as it is here presented, is that the connotative term does something in addition to what the nonconnotative term does. This presentation of the connotative term as doing something more turns out not to be justified by Mill's subsequent explanation.

First, what is it that the two types of term have in common? In Mill's varying terminology they both "signify," "denote," "stand for," or are "names of" the things of which they can be truly predicated. To use Mill's own examples, both 'Socrates' (a nonconnotative term) and 'virtuous' (a connotative term) denote Socrates. We can truly say of this man both that he is Socrates and that he is virtuous. What connotative and nonconnotative terms have in common is that they each have a range of correct application — an extension.

How do terms of these two types differ? They differ in the ways in which they come to have their extensions. The connotative term 'virtuous' applies to Socrates, and others, "in consequence of an attribute which they are supposed to possess in common, the attribute which has received the name of virtue." (5)

By contrast, the nonconnotative concrete term 'Socrates' and the nonconnotative abstract term 'virtue' apply to the man and the attribute respectively in consequence of these terms' having been bestowed on these individuals to be "simply marks used to enable those individuals to be made subjects of discourse." (6) The attribute in consequence of which a nonconnotative term applies is not one that is independent of the term; rather it is just the attribute of bearing the term as a "mark" (name).

Mill's explanation makes it clear that this difference in the conditions of application is the crucial difference between the terms. A connotative term is one that applies to an individual because of some term-independent attribute that the individual possesses. A nonconnotative term is one that applies to an individual simply because the term has been bestowed on it as a label. One consequence of this distinction is that a connotative term may be either general or singular depending on whether the attribute that "gives the name" is shareable, but a nonconnotative term will always be a singular term applying just to the individual that bears the term as a proper name.

But what can be made of the claim with which Mill introduced his distinction — that connotative terms do something more than nonconnotative terms? The extra that they are said to do is to "imply an attribute." This is, of course, not something that connotative terms do independently of denoting. They denote just those individuals that have the "implied" attributes. To predicate a connotative term is to ascribe an attribute.

However, nonconnotative terms also denote only in virtue of certain attributes. They denote just the individuals that bear the terms as names. Consequently, to predicate a nonconnotative term is to ascribe the attribute of bearing the term as a name.

Mill, though, insists that nonconnotative terms lack something that connotative terms have. He regards connotation as information or signification; and he says, "the only names of objects which connote nothing are proper names; and these have, strictly speaking, no signification." (7) However, there is confusion somewhere; for he has to admit that it is informative to be told of a town that it is York. He tries to dismiss this by saying that it is no information except that 'York' is its name. (8) He contrasts it with the information that the town is built of marble. Here, says Mill, is "what may be entirely new information." However, the identification of the town as York may as easily be new information as the fact that it is built of marble.

The difference between the predication of the nonconnotative term and the predication of the connotative term is simply in the kind of information imparted. The first gives information of a relation between the town and the term itself — the town has the name 'York'; while the other gives term-independent information about the material used in the construction of the town. This difference in the kind of information expressed is precisely the difference between nonconnotative terms and connotative terms. The former apply to those things that have the attribute of having been labeled with the term. The latter apply to those things that possess some attribute other than bearing the term itself as a proper name.

Mill has indeed marked a distinction that goes deep into the nature of language; however, he was confused in his presentation of the distinction. There is nothing that a connotative term does in its predicative use that a nonconnotative term does not do; nor is there something that a connotative term has that a nonconnotative term lacks. They are both meaningful, information conveying, terms. Both sorts of term apply only to those individuals that satisfy certain conditions, and both will serve to assert that designated individuals satisfy those conditions.


Frege, unlike Mill, develops his theory initially only for singular terms, which, on his view, can never be predicates. Frege's theory is devised to account for the fact that replacing a singular term designating an object by another term designating the same object results in "statements of differing cognitive value." (9) That the morning star is the morning star is not doubted by anyone. That the evening star is the morning star is not known to everyone. There must be something about singular terms, other than their referents, that accounts for this difference in cognitive value.

Frege's solution is well known. In addition to its referent, a singular term has a sense. Its sense is a "mode of presentation" of the referent that "illuminates only a single aspect." (10) A term designates whatever object possesses the distinguishing aspect expressed as the term's sense. To give the sense of a term is to state the attribute that will determine the referent.

Frege's idea that singular terms have senses apparently provides the correct explanation for the observed differences in the cognitive values of sentences that differ only by substitution of codesignative terms. The exchanged terms need only to have different senses to yield sentences of different cognitive values, because the sense is an epistemic basis for identifying the referent.

However, there is a notorious difficulty — the senses of ordinary proper names. What is the sense of the name 'Aristotle'? It is at this crux that Frege's account falters. He cannot find a condition to be the sense of 'Aristotle', and in a footnote he makes the uncharacteristic, and unfortunate, suggestion that a name's sense may vary with its user. (11) Frege's theory of sense appears to work only for definite descriptions — not for names.

It is here that Mill's distinction between connotative and nonconnotative terms offers assistance — not opposition — to Frege's theory. Mill presented his distinction as one between two sorts of condition of application for general and singular terms used as predicates; however, the same distinction applies to the conditions of designation for singular terms. From the perspective provided by Mill, a definite description is a connotative singular term having as its sense some term-independent attribute. A proper name, in contrast, is a nonconnotative singular term having as its sense the attribute of having the term itself as a label. The sense of a proper name may be said to be word-reflexive. The name enters essentially into its own condition of designation.

Intuitively, this account of the senses of names is correct. The sense is the epistemic basis associated with a term for determining its referent. What has to be known to know the referent of 'Aristotle'? Clearly, one must know who bears the name. No other attribute is relevant.

Why did Frege not see that there are two sorts of sense — connotative (term-independent) and nonconnotative (term-reflexive)? The explanation is probably to be found in Frege's persistent conception of content as independent of language. Just after his footnote suggesting that a name may have various senses, Frege asserts that "the same sense has different expressions in different languages or even in the same language." (12) In another essay he comments that "for all the multiplicity of languages, mankind has a common stock of thoughts." (13) These passages suggest that Frege simply overlooked the fact that not all the properties of objects are independent of their relations to language. Consequently, it did not occur to him that a word could be essential to a sense, and that even in alternative expressions of the sense the word itself would have to be mentioned.


The unification of the semantic theories of Mill and Frege yields a theory of great explanatory power. Neither of the opposed theories has been able to accommodate the observed facts about names. Millian theories have generated puzzles out of the fact that names have cognitive content: the puzzle of the failure of substitutivity in epistemic contexts and the puzzle of meaningful names without bearers. Fregean theories have conflicted with the fact that names never change referents when the sentences in which they occur are taken as assertions about counterfactual situations. However, both of these phenomena — cognitive content and rigid designation — are immediate consequences of the unified theory.

Mill's followers are unable to explain the cognitive content of proper names because they think of them as having only extension. But Mill was confused. Nonconnotative terms do not lack meaning. The content of proper names is word-reflexive. A name designates the individual that has the attribute of being its bearer. Codesignative names cannot always be substituted one for another in epistemic contexts because each name expresses a distinct epistemic basis for identifying a referent. To know a planet as the bearer of 'Phosphorus' is not to know it by other names. Similarly, the meaningfulness of names without bearers results from the fact that each name expresses as its sense the condition of being the bearer of itself. That a name was introduced as a label for something that does not exist does not change the fact that the name itself now exists with its self-regarding condition of designation. It will have no bearer, and consequently it will determine no referent when it is used; but it will have a sense.

Frege's followers are unable to account for the fact that names never change referents with a change in the circumstance of evaluation because they think of a name's sense as an attribute independent of the name itself. A term-independent sense (a connotation) gives a singular term only an indirect, and ordinarily breakable, link to a referent. Except for uncommon cases, such as being the least prime, a connotation will be some attribute that could be exemplified by different individuals in different possible worlds. So a connotative singular term, i.e. a definite description, will typically be a nonrigid designator.

However, a nonconnotative term will always be not only singular but also rigid. Only the individual that was made the bearer at a name's origin can be its referent. Furthermore, the bearer of the name will be the referent at each circumstance of evaluation in which it exists. The bearer is not designated in virtue of any relation it has to other individuals in a circumstance. In particular, it is not picked out at a circumstance because it is given the name, or called by the name, in the circumstance. The bearer relation is just a two-place relation between name and bearer — not a three-place relation involving speakers. A name will designate its bearer at every possible world in which the bearer exists — not just at those worlds in which the name is used.


Two contrasting sorts of objection to this unified theory can be anticipated. Some will fear that the bearer relation is a circular means for determining a referent; but others will object that this relation, far from being trivially circular, is so stringent that it rarely exists.

Word-reflexive senses would certainly be circular ways to determine referents if they were to be understood in the way that has been criticized by Kripke. (14) 'Socrates' cannot mean 'the individual referred to by "Socrates"'. However, this is not the unified account. It is that 'Socrates' means 'the bearer of "Socrates"'. (15) This account will seem circular only if being the bearer is not distinguished from being the referent. A name gets a bearer at its origin, but only if the intended bearer exists. The bearer relation thus established is independent of any use of the name. A name gets a referent when it is used to refer, but only if it has a bearer and that bearer exists in the appropriate circumstance of evaluation. Being the bearer is a name's mode of presentation of a referent. Being the referent is an outcome of a referential use of a name.

The contrasting objection will be that word-reflexive senses are typically unsatisfiable. Nothing can be the bearer of a name that has multiple bearers; and, more often than not, names have multiple bearers.

It is not clear how people who hold this view that proper names are common to any number of individuals would wish to count names. In general, words are not individuated solely by phonetic form, i.e. by vocable. Linguists take words to be at least triples: <phonology, syntactic category, meaning>. (16) The phonetic form of those English words that are spelled by the sequence of letters b, a, n, and k is shared by words of different grammatical types and even by different words within single types. It would be a striking anomaly if there were no homonymy among proper names — if names were simply individuated by phonetic form.

The only temptation to such an otherwise counterintuitive claim arises out of the fact that different individuals have the same name. However, this fact does not entail that names are individuated by vocable. Sameness may as easily be identity of kind as numerical identity. Consider that it is true that many people eat the same food or drive the same car — meaning type of food and car. Similarly, many people have the same name in the sense that they have the same phonetic, and orthographic, kind of name. It is clear that distinct proper names could share phonetic and orthographic form. On the other hand, it is far from clear that the rigid designation of proper names could ever be satisfactorily explained if names were shared by different individuals in different possible worlds.

On the unified theory there arises no need to attempt ambitious accounts of how shared names could become singular and rigid in use. Names are truly proper, and they are individuated by their origins. Each name is custom-made to serve as a mark of an intended bearer. The vocable of a name may be chosen as homage or allusion to some other individual bearing that kind of name, but still the result will be a distinct name with its own origin, its own bearer, and its own history of occurrences.

The sense of a name that emerges from the unification of Mill's and Frege's thinking turns out to be neither circular nor rarely satisfied. It is precisely the sense that a name requires. Word-reflexive, or nonconnotative, sense is all the sense that a name needs in order to determine a referent — and all the sense that it can afford in order to determine the same referent in every circumstance. A name is a rigid designator just because it has nonconnotative sense.

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(1) John Stuart Mill, A System of Logic, 8th ed. (New York: Harper and Brothers, 1874), 34.

(2) Saul A. Kripke, Naming and Necessity (Boston: Harvard University Press, 1980), 26-27.

(3) Gottlob Frege, "On Sense and Meaning," in Translations from the Philosophical Writings of Gottlob Frege, 3d ed., ed. Peter Geach and Max Black (Totowa, NJ: Rowman & Littlefield, 1980), 57.

(4) Mill, 34.

(5) Ibid., 35.

(6) Ibid., 36.

(7) Ibid., 37.

(8) Ibid., 38.

(9) Frege, "On Sense and Meaning," 56.

(10) Ibid., 57-58.

(11) Ibid., 58n.

(12) Ibid., 58.

(13) Frege, "On Concept and Object," 46n.

(14) Kripke, 68-70.

(15) Note that 'the bearer of "Socrates"' is a rigid description, a connotative term, synonymous with the nonconnotative term 'Socrates'.

(16) Pauline Jacobson, "The Syntax/Semantics Interface in Categorial Grammar," in The Handbook of Contemporary Semantic Theory, ed. Shalom Lappin (Oxford: Blackwell Publishers, 1996), 90.

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