As I have shown elsewhere (see, for instance, Eco 1975), from the moment one takes the route of the encyclopedia, two theoretically crucial distinctions are lost: (i) in the first place, that between natural language and other semiotic systems, since properties expressed in nonverbal form can also constitute part of the encyclopedic representation of a given term or corresponding concept (in the sense that a potentially infinite number of images of dogs are part of the encyclopedic representation of the notion “dog”); and (ii) in the second place, the distinction between semiotic system as object and theoretical metalanguage. It is impossible in fact to create a metalanguage as a theoretical construct composed of a finite number of universal primitives: such a construct, as we have seen, explodes, and when it explodes it reveals that its own metalinguistic terms are nothing other than terms of the object language—though they may be used provisionally as not susceptible of further definition.
The encyclopedia is dominated by the Peircean principle of interpretation and consequently of unlimited semiosis. Every expression of the semiotic system is interpretable by other expressions, and these by still others, in a self-sustaining semiotic process, even if, from a Peircean point of view, this flight of interpretants generates habits and hence modalities of transformation of the natural world. Every result of this action on the world must, however, be interpreted in its turn, and in this way the circle of semiosis is on the one hand constantly opening up to what lies outside and on the other constantly reproducing itself within.
Furthermore, the encyclopedia generates ever new interpretations that depend on changing contexts and circumstances (and hence semantics incorporates within itself pragmatics). Therefore we can never give it a definitive and closed representation: an encyclopedic representation is never global but invariably local, and it is activated as a function of determined contexts and circumstances. The expression “dog” occurring in a universe of discourse regarding fireplace furniture generates different interpretants from the same expression occurring in a universe of discourse regarding animals; while, within a discourse on animals, the same expression generates different ramifications of interpretants depending on whether the subject is zoology or hunting.
1.5. Labyrinths
D’Alembert spoke of a labyrinth, and he naturally attempted to express the concept through that of a map, without, however, being able to speak of the topological model of a polydimensional network. The Porphyrian tree represented an attempt to reduce the polydimensional labyrinth to a bidimensional schema. But we have observed how, even in this simple classificatory instrument, the tree regenerated the labyrinth (of differences) at every fresh step.
We must first reach a consensus on the concept of labyrinth, because labyrinths come in three varieties (cf. Santarcangeli 1967; Bord 1976; Kern 1981). The classic labyrinth of Cnossos is unicursaclass="underline" there is only one path. Once one enters one cannot help reaching the center (and from the center one cannot help finding the way out). If the unicursal labyrinth were to be “unrolled,” we would find we had a single thread in our hands—the thread of Ariadne which the legend presents as the means (alien to the labyrinth) of extricating oneself from the labyrinth, whereas in fact all it is is the labyrinth itself.31 The unicursal labyrinth, then, does not represent a model for an encyclopedia (Figure 1.15)
The second type is the Mannerist labyrinth or Irrweg. The Irrweg proposes alternative choices, but all the paths lead to a dead point—all but one, that is, which leads to the way out (Figure 1.16). If it were “unrolled,” the Irrweg would assume the form of a tree, of a structure of blind alleys (except for one).32 One can take the wrong path, in which case one is obliged to retrace one’s steps (in a certain sense the Irrweg works like a flowchart).
Figure 1.15
Figure 1.16
The third kind of labyrinth is a network, in which every point may be connected with any other point (Figure 1.17).
Figure 1.17
A network cannot be “unrolled.” One reason for this is because, whereas the first two kinds of labyrinth have an inside and an outside, from which one enters and toward which one exits, the third kind of labyrinth, infinitely extendible, has no inside and no outside.
Since every one of its points can be connected with any other, and since the process of connection is also a continual process of correction of the connections, its structure will always be different from what it was a moment ago, and it can be traversed by taking a different route each time. Those who travel in it, then, must also learn to correct constantly the image they have of it, whether this be a concrete (local) image of one of its sections, or the hypothetical regulatory image concerning its global structure (which cannot be known, for reasons both synchronic and diachronic).
A network is a tree plus an infinite number of corridors that connect its nodes. The tree may become (multidimensionally) a polygon, a system of interconnected polygons, an immense megahedron. But even this comparison is misleading: a polygon has outside limits, whereas the abstract model of the network has none.
In Eco (1984b: ch. 2), as a metaphor for the network model, I chose the rhizome (Deleuze and Guattari 1976). Every point of the rhizome can be connected to any other point; it is said that in the rhizome there are no points or positions, only lines; this characteristic, however, is doubtful, because every intersection of two lines makes it possible to identify a point; the rhizome can be broken and reconnected at any point; the rhizome is anti-genealogical (it is not an hierarchized tree); if the rhizome had an outside, with that outside it could produce another rhizome, therefore it has neither an inside nor an outside; the rhizome can be taken to pieces and inverted; it is susceptible to modification; a multidimensional network of trees, open in all directions, creates rhizomes, which means that every local section of the rhizome can be represented as a tree, as long as we bear in mind that this is a fiction that we indulge in for the sake of our temporary convenience; a global description of the rhizome is not possible, either in time or in space; the rhizome justifies and encourages contradictions; if every one of its nodes can be connected with every other node, from every node we can reach all the other nodes, but loops can also occur; only local descriptions of the rhizome are possible; in a rhizomic structure without an outside, every perspective (every point of view on the rhizome) is always obtained from an internal point, and, as Rosenstiehl (1979) suggests, it is a short-sighted algorithm in the sense that every local description tends to be a mere hypothesis about the network as a whole. Within the rhizome, thinking means feeling one’s way, in other words, by conjecture.
Naturally it is legitimate to inquire whether we are entitled to deduce this idea of an open-ended encyclopedia from a few allusions in Leibniz and an elegant metaphor in the Encyclopédie, or whether instead we are attributing to our ancestors ideas that were only developed considerably later. But the fact that, starting from the medieval dogmatics of the Arbor Porphyriana and by way of the last attempts at classification of the Renaissance, we slowly evolved toward an open-ended conception of knowledge, has its roots in the Copernican revolution. The model of the tree, in the sense of a supposedly closed catalogue, reflected the notion of an ordered and self-contained cosmos with a finite and unalterable number of concentric spheres. With the Copernican revolution the Earth was first moved to the periphery, encouraging changing perspectives on the universe, then the circular orbits of the planets became elliptical, putting yet another criterion of perfect symmetry in crisis, and finally—first at the dawn of the modern world, with Nicholas of Cusa’s idea of a universe with its center everywhere and its circumference nowhere, and then with Giordano Bruno’s vision of an infinity of worlds, the universe of knowledge too strives little by little to imitate the model of the planetary universe.