The horse growls is less daring a metaphor than The theory of relativity growls, because in the play of related properties there is undoubtedly more of a relation between a growl and the ‘animal’ prop-erty of a horse than there is between a growl and the ‘abstract object’ property of the Einsteinian theory. But this useful definition of distance is not capable of deciding which of the two metaphors is better. All the more so, in view of the fact that at the end the author (who knows more about metaphors than the method he chooses in his article allows him) finishes by admitting that «the choice of typical criteria for the similarity function is pragmatically determined on the basis of cultural knowledge and beliefs» (ibid., p. 191).
No greater satisfaction is given by another attempt at formalization, by a logician who takes off right from Aristotle, Guenthner: «If metaphors are to be analyzed within the framework of formal semantics, the first thing will obviously be to provide for a way of implementing information about the meaning structure of predicates which is relevant for their metaphorical behavior» (1975:205). But immediately he says that it will not be necessary, however, to construct this semantic information in the form of an encylopedia, and a few sortal specifications will be enough. Which is exactly the way to preclude an understanding of a trope. Such is the case that, when he analyzes some examples borrowed from Groupe μ, Guenthner rediscovers the same old relation of girl-birch. And as we shall see, the fact that a girl and a birch tree are both flexible is properly an item of encyclopedic information.
At any rate, Guenth-ner’s model (useless for understanding how a metaphor functions) seems more useful than the others for expanding a formal semantics of natural languages. Its author starts, in fact, from a distinction between natural kinds (fish, lion, and so on), opposing these against nonnatural kinds (such as president), and plays on the fact that the properties of a natural kind must be contextually selected (obviously on the basis of the con-text) in order to make the metaphor acceptable and comprehensible. A sortal model is a 4-tuple M = , such that D is a nonempty domain of objects, or a universe of discourse, / a function of interpreta-tion, k a function that assigns to every object in D the kinds to which the object belongs in the model, and s is a function drawn from the group of those predicates not assigned as natural kinds by k. A sortal model de-termines which statements are true, false, or meaningless (that is, liter-ally nonsignificant).
If we now add a function p which assigns to each predicate P in L a set of ‘prominent’ properties, a sortal model accounts for the metaphorical mean-ing of an expression in roughly the following way. If a sentence ф is neither true nor false in M and if ф translates for example the English sentence: John is a mule (ф = E x(x = j & Mx) or Mj) then ф can be interpreted metaphorically if there is a ‘prominent’ property assigned to M such that that property holds true of John. (Note that in our culture such properties are usually rather well delimited, but never related to the basic meaning of the expression —this can be easily tested in translating metaphorical sentences from one natural language into another.) (Ibid., p. 217)
Because entities such as the prominent properties, and every other possible insertion into the sortal apparatus, cannot be accounted for by a formal semantics, the present inspection of this universe of discourse must stop here. And we have to go back, as I said above, to a compo-nential semantics.
3.11. Componential representation and pragmatics of the text
3.11.1. A model by ‘cases’
We can venture at this point an explanation of the metaphorical mecha-nism that (a) is founded on a componential semantics in the format of an encyclopedia and that (b) takes into account, at the same time, rules for contextual insertion. An encyclopedic semantics is undoubtedly more in-teresting than a dictionary. The format of a dictionary, we have seen permits us to understand the mechanism of the synecdoche, but not that of the metaphor. We only have to look at the efforts made by transfor-mational grammar and interpretive semantics approaches. (For a syn-thetic account, see Levin 1977.) Establishing that a ‘transference’ or transfer of properties occurs in the sentence She is a birch, whereby a girl would acquire the seme ‘vegetal’ or birch the seme ‘human’, tells us very little about what happens in the interpretation and production of that trope. In fact, if we try to paraphrase the result («This girl is human but also has a vegetal property») we see that it is not very far from being a parody of itself. The issue here is obviously one of flexibility (but, again: a birch tree is not flexible in the same way that a young girl is . . .), and it cannot be considered within a semantics in the format of a dictionary.
A componential representation in the format of an encyclopedia, how-ever, is potentially infinite and assumes the form of Model Q (Eco 1976), that is to say, of a polydimensional network of properties, in which some properties are the interpretants of others. In the absence of such a network, none of these properties can attain the rank of being a metalinguistic construction or a unit belonging to a privileged set of semantic universals. In a model dominated by the concept of unlimited semiosis, every sign (linguistic and non-) is defined by other signs (lin-guistic and non-), which in turn become terms to be defined by other terms assumed as interpretants. With the advantage that an encyclopedic representation (even if ideal), based on the principle of unlimited in-terpretation, is capable of explaining in purely semiotic terms the con-cept of ‘similarity’ between properties.
By similarity between two semes or semantic properties we mean the fact that in a given system of content those properties are named by the same interpretant, whether it be verbal or not, and independently of the fact that the objects or things for the designation of which that interpre-tant is customarily used may manifest perceptual ‘similarities’. In other words, the teeth of the maiden in the Song of Solomon are like the sheep if, and only if, in that given culture the interpretant white is used to designate both the color of teeth and that of sheep’s fleece.
But metaphors set up not only similarities but also oppositions. A cup and a shield are alike in their/am (round and concave), but opposite in their function (peace vs. war), just as Ares and Dionysus are alike insofar as they are gods, but opposite with regard to the ends they pursue and to the instruments they use. To account for these phenomena, an encyclopedic representation has to assume the form of a case grammar, which should recognize therefore the Subject Agent, the Object on whom the agent executes his action, the Counter Agent who may possibly opposed himself to that action, the Instrument used by the agent, the Goal of the action, and so on. A semantics of this type has been elaborated by various authors (cf. Greimas’ and Tesnière’s actants Fillmore’s grammatical cases, Bierwisch’s semantics, irrespective of their substantial differences; see also Nef 1979).
As a first approach, let us say that the properties that a case-like repre-sentation associates with a given action display a metonymic character: goal, instrument or agent seem to be metonymically linked to the repre-sented action. We shall see later in which sense this kind of metonymic relationship also accounts for synecdochic relationships and ought to be considered as the basis for every metaphoric substitution.
3.11.2. Metonymy
From this perspective a metonymy becomes the substitution of a sememe with one of its semes (for example, /Drink a bottle/ for «drink wine», because a bottle will be registered among the final destinations of wine) or of a seme with the sememe to which it belongs (for example, /Weep thou, О Jerusalem/ for «May the tribe of Israel weep», because among the encyclopedic properties of Jerusalem must be included that of its being the holy city of the Jews).
This type of metonymic substitution is no different from the process Freud called «displacement.» And just as condensation is involved with the process of displacement, so is metaphor involved (as we shall see) with these metonymic exchanges. On the basis of a representation by cases, I attempted to show (1976) the mechanism of displacement from seme to sememe (and vice versa) by analyzing a line from Virgil: Vulnera dirigere et calamos armare veneno (Aeneides 10.1.140).
The verse, which can be translated either as «to distribute wounds with poisoned arrows» or as «to smear with poison the arrows and hurl them,» plays on the fact that /vulnera dirigere/ stands for «dirigere tela» (or dirigere ictus, dirigere plagas, vulnerare). Let us suppose that vulnerare is the right interpretation and imagine a semantic representation in case-grammer form like the following:
/Vulnerare/ (Entailments)
Action Human Human Weapon Wound (Vulnus) Strike
Wound With aim
Here is where the expression /aim the wounds/
