Denotation (along with its counterpart, connotation) is considered, depending on the context, as either a characteristic or a function (i) of individual terms (what does the word “dog” denote?); (ii) of declarative propositions (the sentence “the dog barks” may denote a state of the world, that there is a dog barking—but, if “the dog” is taken as denoting a species—all dogs, that is—then it could denote a characteristic common to the entire canine race); (iii) of nominal phrases and definite descriptions (the phrase “the President of the Republic” may denote, depending on the context and the circumstances of its utterance, either the actual president currently in power or the role provided for in a constitution). In each of these cases we must decide whether the denotation has to do with the meaning, the referent, or the act of reference. To sum up, by denotation do we mean what is signified by the term, the thing named, or, in the case of propositions, what is the case or what is believed to be the case, inasmuch as it forms the content of a proposition?
For structural linguists, “denotation” is concerned with meaning. For Hjelmslev (1943) the difference between a denotative semiotic and a connotative semiotic lies in the fact that the former is a semiotic whose expression plane is not a semiotic, whereas the latter is a semiotic whose expression plane is a semiotic. Barthes (1964) too formulates his position basing himself on Hjelmslev and develops a fully intensional idea of denotation, according to which, between a signifier and a first (or zero) degree signified, there is always a denotative relationship.
In componential analysis, the term has been used to indicate the sense-relationship expressed by a lexical term—such as the term “uncle,” which expresses the relationship “father’s brother” (see, for instance, Leech 1974: 238). In other words, in structuralist circles, denotation, referring back to Frege’s (1892) distinction, is closer to Sinn than to Bedeutung, closer to meaning than to reference, and in Carnap’s (1955) terms has more to do with intension than with extension.
It is, however, Frege’s term Bedeutung that is ambiguous, and it should be replaced with Bezeichnung (which we may translate as “designation”), given that, in the vocabulary of philosophy, Bedeutung usually stands for “meaning,” whereas Bezeichnung stands for “reference, designation” and for denotation in the extensional sense. Husserl (1970), for instance, says that a sign signifies or means (bedeutet) a signified and designates (bezeichnet) a thing. This is why, in the most recent tradition of Anglo-Saxon semantics inspired by Frege, Bedeutung is often rendered with “reference” or “denotation” (see, for example, Dummett 1973). And so the usage of the structuralists is completely turned on its head.
In the field of analytic philosophy, the whole picture underwent a radical change with Russell’s essay “On Denoting” (1905), in which denotation is presented as different from meaning; and this is the direction followed by the entire Anglo-Saxon philosophical tradition. See, for instance, Ogden and Richards (1923) and Morris (1946), where it is said that when, for example, in Pavlov’s experiment, a dog reacts to the bell, food is the denotatum of the bell, while the condition of being edible is its significatum.
In this sense, an expression denotes either the individuals or the class of individuals of which it is the name, whereas it connotes the characteristics on the basis of which such individuals are recognized as members of the class in question. If we go on to substitute (see Carnap 1955) the pairing extension/intension for the pairing denotation/connotation, then denotation becomes a function of connotation.
But even if we establish that denotation stands for extension, it may refer (i) to a class of individuals, (ii) to an actually existing individual (as in the case of the rigid designation of proper names), (iii) to each member of a class of individuals, (iv) to the truth value contained in an assertive proposition (with the consequence that, in each of these fields, the denotatum of a proposition is what is the case, or the fact that p is the case).
Very reasonably, Lyons (1977: 2:208) proposed using the term designation in place of denotation, and using denotation in a neutral fashion, between extension and intension: in this sense “dog” would denote the class of dogs (or perhaps some typical member, or exemplar, of the class), while “canine” would denote the characteristic whereby we recognize that it is correct to apply the expression. His proposal did not meet with much favor, however, at least in the analytical koinè, and therefore the polysemous nature of the term persists.
9.1. From Mill to Peirce
The term denotation was used in an explicitly extensional sense by John Stuart Mill in his System of Logic (1843, I, 2, 5): “the word white, denotes all white things, as snow, paper, the foam of the sea, etc., and implies, or in the language of the schoolmen, connotes, the attribute whiteness” (emphasis in original).
Peirce was probably the first to realize that there was something that did not jibe in this solution, despite the fact that he himself always used denotation in this extensional sense. Let us see how he uses the term on various occasions:
the direct reference of a symbol to its objects, or its denotation (CP 1.559)1
a Rhematic Indexical Sinsign [is] really affected by the real camel it denotes (CP 2.261)
a symbol … must denote an individual and must signify a character (CP 2.293)
every assertion contains such a denotative or pointing-out function (CP 5.429)
signs are designative or denotative or indicative, in so far as they, like a demonstrative pronoun, or a pointing finger, “brutally direct the mental eyeballs of the interpreter to the object in question” (8.350)
Peirce was well aware that, as far as connotation went, Mill was not in fact following, as he claimed to be, traditional Scholastic usage. The Schoolmen (at least up until the fourteenth century) distinguished between significare (meaning) and appellare (naming), and did not use connotation in opposition to denotation, but as an added form of signification:
It has been, indeed, the opinion of all the students of the logic of the fourteenth, fifteenth and sixteenth centuries, that connotation was in those ages used exclusively for the reference to a second significate, that is (nearly), for a reference to a relative sense (such as father, brighter, etc.) to the correlate of the object it primarily denotes.… Mr. Mill has, however, considered himself entitled to deny this upon his simple authority, without the citation of a single passage from any writer of that time. (CP 2.393)
Peirce develops the same argument in CP 2.431, and he later points out that in the Middle Ages the most common opposition was between significare (to mean) and nominare (to refer to). He further observes how Mill uses—in place of the term significare—connotare, implicitly reserving denotare for designating, naming, or referring. Furthermore, he recalls a passage from John of Salisbury (Metalogicus II, 20), according to whom “nominantur singularia sed universalia significantur,” concluding that unfortunately “the precise meaning recognized as proper to the word ‘signify’ at the time of John of Salisbury … was never strictly observed, either before and since; and on the contrary the meaning tended to slip towards that of ‘denote’ ” (CP 2.434).
However, although Peirce lucidly realizes that at a certain point significare partially shifted from an intensional paradigm to an extensional one, he nevertheless fails to recognize that in ensuing centuries the term retains for the most part its intensional meaning. Thus, he accepts the fact that denotation is an extensional category (and took issue with Mill’s work only with respect to connotation), whereas it is precisely the term denotare that, initially used halfway between extension and intension, finally (and the terminus ad quem is in fact Mill) took over as an extensional category. Peirce does not indicate when this happened for the first time, and he fails to do so because the question was far from lending itself to a simple solution.
9.2. From Aristotle to the Middle Ages
Plato had already made it clear that by pronouncing a single term (say, “dog”) we can certainly signify a given idea, but only when we enunciate a proposition (such as “that dog barks”) can we say that something is the case, and hence say something is true or false.
As for Aristotle, in the famous passage in De interpretatione (16a et seq.), he outlines a semiotic triangle in which words are on the one hand linked to concepts (or to the passions of the soul) and on the other to things. Aristotle says that words are “symbols” of the passions, and by “symbol” he means a conventional and arbitrary expedient. It is also true, however, as we will see in what follows, that he claims that words may be considered as symptoms (semeia) of the passions, but he says so in the same sense that any and every verbal utterance may first of all be a symptom of the fact that its speakers have something on their minds. The passions of the soul,
