by Umberto Eco
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, on the other hand, are likenesses or icons of things. But, according to Aristotelian theory, things are known through the passions of the soul, without there being a direct connection between symbols and things. We name things and we mean their icons, that is, the corresponding ideas that the things arouse in our minds.2 To indicate this symbolic relationship, Aristotle does not employ the word semainein (which could almost be translated as “to signify”), though in many other circumstances he uses this verb to indicate the relationship between words and concepts (see Figure 9.1).
Figure 9.1
For Aristotle too, as for Plato, single terms taken in isolation do not make any statement about what is the case. They merely “mean” a thought. Sentences or complex expressions on the other hand also mean a thought; but only a particular kind of sentence (a statement or a proposition) asserts a state of affairs that is true or false. Aristotle does not say that statements “signify” what is true or false, only that they “say” (the Greek verb is legein) that something given A “belongs” (the verb is uparkein) to something given B.
Thus, from Aristotle on, we find ourselves faced with three questions that will be amply debated throughout the entire Middle Ages: (i) Do signs mean primarily concepts (and can refer to things only through the mediation of concepts), or do they can signify directly, designate, or denote things? (ii) What is the difference between referring to a class of individuals and referring to a concrete individual? (iii) Wherein lies the difference between the correlation signs-concepts-individual things and the correlation sentences-propositional content-extralinguistic state of affairs?
Not that medieval thinkers had all of these different issues clearly in mind from the word go. The most we can say is that question (i) became the object of debate, in terms of the opposition between significare, nominare, and appellare, very early on (at least from the time of Anselm of Canterbury). Question (ii) was probably framed for the first time by Peter of Spain with his distinction between suppositio naturalis and suppositio accidentalis. Question (iii) was variously addressed from Boethius onward—though while, among the commentators of Aristotle, the debate over the relationship of signification was conducted independently from that over true and false assertions, for a number of grammarians and theoreticians of the suppositio, the two issues were often superimposed, until such time as, with Roger Bacon and William of Ockham, they became completely interchangeable.
The fate of terms like denotatio and designatio is bound up with the history of the opposition significatio–nominatio. It would appear that, for a long time (at least until the fourteenth century), these terms were used sometimes in an intensional and sometimes in an extensional sense. The terms were already present in the traditional Latin lexicon and signified, among their many other meanings,
“to stand as a sign for something”—regardless of whether that something was a concept or a thing. In the case of designatio the etymology speaks for itself, in the case of denotatio, however, we must bear in mind that the term nota indicated a sign, a token, a symbol, something that referred back to something else (see also Lyons 1968: ch. 9). According to Maierù (1972: 394), Aristotle’s term symbolon was in fact generally translated as nota: “nota vero est quae rem quamquam designat. Quo fit ut omne nomen nota sit” (“a sign is that which designates any thing. Hence every name is a sign”)(Boethius 1988: p. 108).3
It is important, then, to establish (i) what happened to the term significatio; and (ii) when denotatio (along with designatio) occurs in connection with significatio, and when, on the contrary, it occurs in opposition to it.
As far as denotatio goes, it is important to record its occurrence in each of the following three usages: (i) in a strong intensional sense (denotation is related to meaning); (ii) in a strong extensional sense (denotation is related to things or states of things); (iii) in a weak sense (denotation is undecided between intension and extension, but with good reason to lean toward intension). We will see that the weak sense is the predominant one at least up until the fourteenth century.
9.3. Boethius
From Augustine to the thirteenth century, the possibility of referring to things is always mediated by meaning. For Augustine, “signum est enim res praeter speciem, quam ingerit sensibus, aliud aliquid ex se faciens in cogitationem venire” (“a sign is something which, offering itself to the senses, conveys something other to the intellect”) (De doctrina christiana II, 1, 1) and signification is the action a sign performs on the mind. Only through this mediation can one refer to things (see Figure 9.2).
Figure 9.2
Boethius had already introduced the term propositio to indicate the complex expressions that assert that something is either true or false. It is difficult to decide whether by “proposition” he meant the expression itself or the corresponding concept, but it is clear that truth or falsehood were connected with propositions and not with isolated terms. Boethius affirms that the isolated terms signify the corresponding concept or the universal idea, and he takes significare—as he does, though more rarely, designare—in the intensional sense. Words are conventional tools that serve to make manifest thoughts, sensa or sententias (De interpretatione I). Words do not designate res subiectae but passiones animae. The most we can say of the thing designated is that it is “implied by its concept” (significationi supposita or suppositum, see De Rijk 1962–1967: 180–181).
In his first commentary on Aristotle’s Peri hermeneias, II, in a discussion as to whether words refer directly to concepts or to things, in both cases Boethius uses the expression designare. He says “vox vero conceptiones animi intellectusque significant” and “voces vero quae intellectus designant,” and, speaking of litterae, voces, intellectus, res, he states that “litterae verba nominaque significant” and that “haec vero (nomina) principaliter quidem intellectus secundo vero loco res quoque designant. Intellectus vero ipsi nihil aliud nisi rerum significativi sunt.” In Categories, col. 159 B4–C8, he says that “prima igitur illa fuit nominum positio per quam vel intellectui subiecta vel sensibus designaret.” It seems to me that in these examples designare and significare are considered as more or less interchangeable.
Figure 9.3
Therefore, for Boethius too, words signify concepts and it is only as a consequence of this that they may refer to things (see Figure 9.3).
9.4. Anselm’s Appellatio
It is thanks to the theory of appellatio, proposed in his De Grammatico by Anselm of Canterbury, that a more clear-cut distinction is posited between signifying and referring.
Building on Aristotle’s theory of paronyms, Anselm says that, when we call a given individual a grammaticus or grammarian, we are using the term paronymically. The word still signifies the quality of being a grammarian, but it is used to refer to a specific person. To indicate reference, then, Anselm uses the term appellatio, while, to indicate meaning, he uses significatio (De Grammatico, 4, 30 et seq.). A distinction of this kind between meaning and appellation (or naming) is also observed by Abelard.
9.5. Abelard
In the case of Abelard it is not possible to identify a logical terminology established once and for all, since he frequently uses the same terms in more than one sense. Nevertheless, he is the first author in whom the distinction between the intensional and extensional aspects is clearly made (if not always consistently from the terminological point of view). While he speaks indifferently of significatio de rebus and significatio de intellectibus, he nevertheless considers the principal meaning of significatio to be (we would say) intensional, in conformity with the anti-Aristotelian tradition, for which significare means to constituere (or “to generate”) a mental concept.
In his Ingredientibus (Geyer 1927: 307), Abelard states unambiguously that the intellectual plane is the necessary intermediary between things and concepts. “Not only is the significatio intellectuum a privileged significatio, it is also the only legitimate semantic function of a noun, the only one a dialectician must bear in mind when examining a discourse” (Beonio-Brocchieri Fumagalli 1969: 37).
But if we consider the various contexts in which terms such as significare, designare, denotare, nominare, appellare are compared and contrasted with one another, we are entitled to conclude that Abelard uses significare to refer to the intellectus generated in the mind of the listener, nominare instead for the referential function, and—at least in certain passages in the Dialectica, but in a way that leaves no room for doubt—designare and denotare for the relationship between a word and its definition or sententia (the sententia being what we would call the “encyclopedic” meaning of the term, whose definition represents a particular “dictionary” selection for the purposes of disambiguating the meaning of the term itself).4
We have already stressed, not only the frequently contradictory nature of Abelard’s terminology, but also how the terms designare and denotare had continued to enjoy a remarkably vague definitional status down to his time. There are passages in which we encounter designare with a strong extensional sense, such as Dialectica (I, III, 2, 1, p. 119), where Abelard argues against those who maintain that syncategorematic words do not produce concepts, but merely indicate a number of res subiectae. In this passage Abelard goes on to speak of the possibility of designating things, and he seems to use designare to indicate the first imposition of names upon things (seen as a kind of baptism in which there is a strict designatory link between the namer and the thing named). See, for instance, Dialectica (I, III, 3, p. 114): “ad res designandas imposite.”
It is also true, however, that in certain passages (see, for instance, I, III, 3, 1, p. 123), designare and denotare do not seem to have the same meaning, while in others (such as I, II, 3, 9, p. 97, and I, III, 3, 1, p. 121) the use of designare suggests an intensional interpretation.
Furthermore, there are two contexts (I, III, 1, 1, pp. 112–113) in which what is designated is the relationship between a name and its corresponding definition, and the denotation is explicitly linked to the meaning (or sententia) of an expression.
Taking issue with those who maintained that the things upon which the vox or name has been imposed are directly signified by the vox itself, Abelard stresses the fact that names signify “ea sola quae in voce denotantur atque in sententia ipsius tenentur.” He then adds that words do not signify everything they can name, but what they designate by a definition. For example, Latin animal signifies a sensitive animal substance, and this is precisely what is denoted by (or in) the word (see Figure 9.4).
Figure 9.4
It is clear then that both designation and denotation continue to maintain a decidedly strong intensional sense and to refer to the relationship between an expression and its corresponding definitional content.
As for signification, it has nothing to do with the naming of things, since
it continues to exist “nominatis rebus destructis” (“if the things named are destroyed”), making it possible to understand the meaning of nulla rosa est (Ingredientibus, Geyer ed., p. 309).
Abelard makes a further distinction between two specific meanings of signification that continue to be a source of perplexity even today. Spade (1982) has stressed the fact that for the Scholastics significatio is not the same as our “meaning”: a term significat what it succeeds in bringing to someone’s mind (and this is undoubtedly the sense intended by Augustine). In this way signification, unlike meaning, is a kind of causal relationship. Meaning (be it mental correlate, semantic content, intension, or any form of noematic, ideal, or cultural entity) is not represented in the Middle Ages—and throughout the entire Aristotelian tradition—by the term significatio but by sententia or definitio.
True, in the medieval tradition we find both significare in the sense of constituere intellectus, as well as the expression significare speciem (which seems more tied to a noncausal notion of signification), but this distinction seems to become clear only with Abelard: a word significat something to the mind causally, while the same word is correlated by way of designation and/or denotation with a meaning, that is, with a sententia or a definition.
Accordingly, we can say that what Abelard’s theory envisaged was not a semiotic triangle, but a sort of square according to which a vox: (i) significat intellectus, (ii) designat vel denotat sententiam vel definitionem, and (iii) nominat vel appellat res.