From the Tree to the Labyrinth: Historical Studies on the Sign and Interpretation

by Umberto Eco

  1.3.6. Leibniz

  Still, we cannot credit Wilkins with an idea he never formulated. The figure who did in some sense express it was Leibniz, perhaps because the opposition between dictionary and encyclopedia characterized his entire research. In fact, starting with his 1666 Dissertatio de arte combinatoria, explicitly inspired by Llull, he will pursue throughout his life the ideal of a characteristica universalis, a rational language, based on a limited number of primitives and logical rules, that would permit wise men to sit around a table and arrive at the truth by way of a calculemus (“let us calculate”). But he quickly becomes convinced that there is no assurance that the primitive terms one arrives at cannot be further broken down into components, and he admits that at best they may be postulated as such for the convenience of the calculus. In such a context, he is more concerned with the form of the propositions that the calculus is able to generate than he is with the meaning of the terms—and he compares in fact his characteristica to an algebra that can be applied, with quantitative rigor, to qualitative notions. And, like algebra, it is a form of cogitatio caeca (or “blind reasoning”) that allows us to perform calculations, and to arrive at exact results, using symbols of whose significance we are not able to have a clear and distinct idea. In so doing Leibniz certainly launched the development of a formal logic in which the symbols do not refer back to a precise idea but stand in its stead.

  But when on the other hand he thinks in terms of a review of universal knowledge, Leibniz assumes an entirely different stance, and in various writings he compares an encyclopedia to a library as a general inventory of all knowledge. In his 1679 Consilium de Encyclopaedia nova conscribendi methodo inventoria, he proposes an encyclopedia that would take in rational grammar, logic, the arts of memory, universal mathematics and its technical applications (geodetics, architecture, optics), mechanics, the science of the physical and chemical properties of bodies, mineralogy, botany and agronomy, animal biology and medicine, ethics, geopolitics, and natural theology. As was the case for Bacon, this encyclopedia must remain open: its order will be discovered little by little as science progresses, and it must also include the unwritten knowledge that is dispersed among people of different professions.

  In his Nouveaux essais sur l’entendement humain, written in 1703–1705, he reminds us that the encyclopedia must have “many cross-references from one place to another, given the fact that most things can be seen from several different points of view, and a truth can be collocated in different places according to the different relationships it has: the people who organize a library often do not know where to classify certain books and remain undecided among two or three equally appropriate placements” (VI, 31). What Leibniz has in mind is what we would call a polydimensional encyclopedia, in which allowance has been made for multiple transversal connections (Gensini 1990: 19).

  1.3.7. The Encyclopédie

  In fact Leibniz anticipates the project later theorized by D’Alembert in the opening pages of the Encyclopédie, and it is on the basis of Leibniz’s suggestions that, with the advent of the Enlightenment, the premises for a critique of any attempt to found an a priori system of ideas begin to take shape. The Enlightenment encyclopedia is determined to be critical and scientific: it refuses to censor any belief, even those considered erroneous, but it exposes them for what they are (see, for instance, the entry on the unicorn, which appears to describe the animal according to tradition, but at the same time underscores its legendary nature). Following the model of the ancient encyclopedia, it aspires to give an account of the entirety of human knowledge, even the “mechanical” knowledge associated with arts and crafts.

  True, the model of the Enlightenment encyclopedia is based on a kind of tree-like pattern (Figure 1.14).

  Figure 1.14

  But D’Alembert, in his “Preliminary Discourse” to the Encyclopédie, while providing information concerning the criteria according to which the work was organized—not immediately obvious given its alphabetical rearrangement—develops on the one hand the metaphor of the tree while simultaneously calling it into question, speaking instead of a “terrestrial globe” and of a labyrinth:

  The general system of the sciences and the arts is a sort of labyrinth, a tortuous road which the intellect enters without quite knowing what direction to take.… However philosophic this disorder may be on the part of the soul, an encyclopedic tree which attempted to portray it would be disfigured, indeed utterly destroyed.…

  Finally, the system of our knowledge is composed of different branches, several of which have a common point of union. Since it is not possible, starting out from this point, to begin following all the routes simultaneously, it is the nature of the different minds that determines which route is chosen.…

  It is not the same with the encyclopedic arrangement of our knowledge. This consists of collecting knowledge into the smallest area possible and of placing the philosopher at a vantage point, so to speak, high above this vast labyrinth, whence he can perceive the principal sciences and the arts simultaneously. From there he can see at a glance the objects of their speculations and the operations which can be made on these objects; he can discern the general branches of human knowledge, the points that separate or unite them; and sometimes he can even glimpse the secrets that relate them to one another. It is a kind of world map which is to show the principal countries, their position and their mutual dependence, the road that leads directly from one to the other. This road is often cut by a thousand obstacles, which are known in each country only to the inhabitants or to travelers, and which cannot be represented except in individual, highly detailed maps. These individual maps will be the different articles of the Encyclopedia and the Tree or Systematic Chart will be its world map.

  But as, in the case of the general maps of the globe we inhabit, objects will be near or far and will have different appearances according to the vantage point at which the eye is placed by the geographer constructing the map, likewise the form of the encyclopedic tree will depend on the vantage point one assumes in viewing the universe of letters. Thus one can create as many different systems of human knowledge as there are world maps having different projections.…

  … But often such an object, which because of one or several of its properties has been placed in one class, belongs to another class by virtue of other properties and might have been placed accordingly. Thus, the general division remains of necessity somewhat arbitrary.29

  D’Alembert’s discourse still suffers from an unresolved tension between the model of the tree and the model of the map. It becomes clear that the sum of our knowledge (present, but also, as it was for Leibniz, future) extends like a geographical map without borders, within which infinite itineraries are possible. But, given that the Encyclopédie, in its printed form, is in alphabetical order, one knows one will need to resort to a number of reductive strategies.

  What we already have, however, is a first hint at the ideal model of an encyclopedia, that is, a hypothetical compendium of all of the knowledge available to a given culture.

  1.4. The Maximal Encyclopedia as Regulatory Idea

  The encyclopedia is potentially infinite because it is forever in fieri, and the discourses we construct on its basis constantly call it into question (in the same way in which the latest article by a nuclear scientist presupposes a series of encyclopedic notions concerning the structure of the atom, but at the same time introduces new ones that render the old ones moot).

  The Maximal Encyclopedia is not content with merely recording what “is true” (whatever meaning we may choose to give to this expression). It records instead everything that has been claimed in a social context, not only what has been accepted as true, but also what has been accepted as imaginary.

  It exists as a regulating principle: yet this regulating idea, which cannot constitute the starting point for a publishable project because it has no organizable form, serves to identify portions of encyclopedias that can be activated, insofar as they
serve to construct provisional hierarchies or manageable networks, with a view to interpreting and explaining the interpretability of certain segments of discourse.

  This encyclopedia is not available for consultation in toto because it is the sum total of everything ever said by humankind, and yet it has a material existence, because what has been said has been deposited in the form of all the books ever written and all the images ever made and all the evidential items that act as reciprocal interpretants in the chain of semiosis.

  Having become transformed over the centuries from an (attainable) utopia of global knowledge into an awareness of the impossibility of global knowledge, but with the certainty of the local availability of the elements of this knowledge, no longer the project for a book, but a method of investigation addressing the general and omnivorous library of culture in its entirety, the Maximal Encyclopedia was envisaged in poetic terms by Dante, when, in Canto 33 of his Paradiso, as he finally attains the vision of God, he is unable to describe what he saw except, precisely, in terms of an encyclopedia:

  In its profundity I saw—ingathered

  and bound by love into one single volume—

  what, in the universe, seems separate, scattered:

  substances, accidents, and dispositions

  as if conjoined—in such a way that what

  I tell is only rudimentary.

  I think I saw the universal shape

  which that knot takes; for, speaking this, I feel

  a joy that is more ample. That one moment

  brings more forgetfulness to me than twenty-

  five centuries have brought to the endeavor

  that startled Neptune with the Argo’s shadow!30

  The encyclopedia is the only means we have of giving an account, not only of the workings of any semiotic system, but also of the life of a given culture as a system of interlocking semiotic systems.

  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 unicursal: 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 no
de, 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.