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

by Umberto Eco

  Right after this example, a few lines further on, Kant writes the famous sentence stating that this schematism of our intellect, which also concerns the simple form of appearances, is an art hidden in the depths of the human soul. Schematism is an art, a procedure, a task, a construction, but we know very little about how it works. Because it is clear that our analogy of the flowchart, which was useful in understanding how the schematic construction of the triangle takes place, doesn’t work as well for the dog.

  What is certain is that a computer is able to construct the image of a dog, if it is provided with the appropriate algorithms. But if someone who had never seen a dog were to study the flowchart to see how it was constructed, they would have trouble forming a mental image of it (whatever a mental image may be). We would find ourselves once more faced with a lack of homogeneity between categories and intuition, and the fact that the schema of the dog can be verbalized as a four-legged animal only brings us back to the extreme abstractness of every predication by genus and specific differentia, without helping us distinguish a dog from a horse.

  Deleuze (1963:73) reminds us that “the schema does not consist in an image, but in spatiotemporal relations that incarnate or realize some purely conceptual relations” (my emphasis), and this seems right as far as the schemata of the concepts of the pure intellect go. But it doesn’t seem sufficient when it comes to empirical concepts, since Kant was the first to tell us that to think of a plate we must resort to the image of the circle. While the schema of the circle is not an image but a rule to follow in constructing the image, nevertheless in the empirical concept of plate the constructability of its form should find a place somehow, and precisely in a visual sense.

  We can only conclude that when Kant thinks of the schema of the dog he is thinking of something very close to what Marr and Nishishara (1978), in the field of modern cognitive sciences, called a “3D Model,” which is nothing but a three-dimensional schematization (through the composition and articulation of more elementary forms) of various objects that we are able to recognize. To put it plainly, the 3D model of a human being—thinking of it only in the form of cylindrical elements—is composed of a smaller cylinder attached to a longer cylinder, from which cylindrical joints branch off, corresponding to the upper and lower limbs, including the elbows and knees.

  In the perceptual judgment the 3D model is applied to the manifold of experience, and an x is distinguished as a man and not as a dog. This should demonstrate how a perceptual judgment is not necessarily resolved into a verbal statement. In point of fact, it is based on the application of a structural diagram to the manifold of sensation. The fact that further judgments are required to determine the concept of man with all his possible characteristics is something else entirely (and, as is the case for all empirical concepts, the task appears to be infinite, and never fully realized). With a 3D model, we could even mistake a man for a primate and vice versa—which is exactly what sometimes happens, although it is unlikely that a man would be confused with a snake. The fact is that we somehow start out with this type of schema, even before knowing or asserting that man has a soul, speaks, or even has an opposable thumb.

  We might go so far as to say, then, that the schema of the empirical concept turns out to coincide with the concept of the object and that therefore schema, concept, and meaning are being identified with one another. Producing the schema of the dog implies having at least an initial essential concept of it. A 3D model of a man does not correspond to the concept of man in the classic categorial definition (“mortal rational animal”). But it works as far as recognizing a human being goes, and subsequently adding the characteristics that derive from this first identification. Which explains why Kant (L II, 103) pointed out that a synthesis of empirical concepts can never be complete, because over the course of experience it will always be possible to identify further notes of the object dog or man. Except that, with an overstatement, Kant declared that empirical concepts therefore “cannot even be defined.” We would say instead that they cannot be defined once and for all, like mathematical concepts, but that they do allow a first nucleus to be formed, around which successive categorial definitions will gel (or arrange themselves harmoniously).

  Can we say that this first conceptual nucleus is also the meaning that corresponds to the term with which we express it? Kant doesn’t often use the word meaning (Bedeutung), but he does use it precisely when he is speaking of the schema.10 Concepts are completely impossible, nor can they have any meaning, unless an object is given either to the concepts themselves or at least to the elements of which they consist (CPR/B: 135). Kant is suggesting in a less explicit way that coincidence of linguistic meaning and perceptual meaning, which will later be energetically asserted by Husserl: it is in a “unity of act” that the red object becomes recognized as red and named as red. “To ‘call something red’—in the fully actual sense of ‘calling’ which presupposes an underlying intuition of the so called—and to ‘recognize something as red,’ are in reality synonymous expressions” (Husserl 1970a: II, 691).

  But, that being the case, not only the notion of empirical concept, but also that of the meaning of terms referring back to perceivable objects (for example, the names of natural genera) opens up a new problem. This first nucleus of meaning, the one identified with the conceptual schema, cannot be reduced to mere categorial information: the dog is not understood and identified (and recognized) because it is a mammiferous animal, but because it has a certain physical form. The form of circularity must of necessity correspond to the concept of plate, and Kant has told us that the fact that the dog has paws (four of them altogether) is part of the schema of the dog. A man (in the sense of a member of the human race) is nonetheless something that moves fin accordance with the articulations provided for by the 3D model.

  Now, while a reflection on the pure intuition of space was sufficient in the case of the schemata of geometrical figures, and therefore the schema could be drawn from the very constitution of our intellect, this is certainly not the case for the schema (and therefore the concept) of dog. Otherwise we would have a repertoire, if not of innate ideas, of innate schemata, including the schema of doghood, horsehood, and so on, until the whole furniture of the universe had been exhausted.

  If that were the case, we would also have innate schemata of things we didn’t yet know, and Kant would certainly not subscribe to this type of Platonism—and it is debatable whether Plato himself subscribed to it.

  The empiricists would have said that the schema is drawn from experience, and the schema of the dog would be nothing but the Lockean idea of the dog. But this is unacceptable to Kant, seeing that we have experience precisely by applying the schemata. We cannot abstract the schema of the dog from the data of intuition, because that data becomes thinkable precisely as a result of applying the schema. And therefore we are in a vicious circle of reasoning from which, it would seem, the first Critique does nothing to help us escape.

  There is one other solution left: that by reflecting on the data from the sensible intuition, by comparing it and evaluating it, by activating an arcane and inborn art hidden in the depths of the human soul (and therefore existing within our own transcendental apparatus), we do not abstract but rather we construct the schemata. The schema of the dog comes to us from our education, and we don’t even realize that we are applying it since, by a vitium subreptionis, we are led to believe that we are seeing a dog because we are receiving sensations.

  That Kantian schematism implies—in the sense that it cannot help leading us to think of it—a kind of constructivism is not an original idea, especially given the sort of return to Kant discernible in many contemporary cognitive sciences. But to what degree the schema can and must be a construction ought not to emerge from the fact that preconstructed schemata (such as that of the dog) are applied; the real problem is What happens when we have to construct the schema of an object we do not yet know?

  13.5. How to Construct the Schema of an Unk
nown Object

  In Eco 1997, we discussed at length the history of the platypus, which was discovered in Australia at the end of the eighteenth century. When a stuffed platypus was brought to England, the naturalists believed that it was a taxidermist’s joke. Not surprisingly, the debate became even more heated when this animal with a bill and webbed feet, but at the same time covered in fur and with a beaver’s tail, was found to nurse its young and lay eggs. The platypus appears in the Western world when Kant had already written his works—and indeed had already fallen into a period of mental obnubilation—and when it was finally decided that the platypus is a mammal that lays eggs, Kant had already been dead for some eighty years. To ask ourselves how Kant would have reacted when confronted with a platypus is no more than a mental experiment, but the experiment is useful precisely because it provides an occasion for reflection on how the theory of schematism might explain the experience of an unknown object.

  Kant would have had to figure out the platypus schema, starting from sense impressions, but these sensible impressions would not have fit into any previous schema (how could Kant have conceived of a quadruped bird, or a quadruped with a beak?). Kant, the confuter of idealism, would have been well aware that if the platypus was offered to him by sensible intuition, it existed, and therefore must be thinkable. And, wherever the form he would give it might come from, it had to be possible to construct it. So what problem would he have found himself faced with?

  By introducing schematism into the first version of his system, as Peirce suggested, Kant finds himself holding an explosive concept that compels him to go further: in the direction of the Critique of Judgment. Judgment is the faculty of thinking of the particular as contained in the general, and if the general (the rule, the law) is already given, the judgment is determinant. But if only the particular is given and the general must be sought, the judgment is then reflecting or reflective. Once one arrives at reflective judgment from the schema, the very nature of determinant or determining judgments becomes problematic. Because the capacity of determinant judgment (as we learn in the chapter in the Critique of Judgment on the dialectic of the capacity of teleological judgment) “does not have in itself principles that found concepts of objects.” Determinant judgment limits itself to subsuming objects under given laws or concepts such as principles. “Thus the capacity of transcendental judgment, which contained the conditions for subsumption under categories, was not in itself nomothetic, but simply indicated the conditions of the sensible intuition under which a given concept may be given reality.” Therefore, for any concept of an object to be well-founded, it must be fixed by the reflective judgment, which “is supposed to subsume under a law that is yet to be given” (CJ, para. 69, 257).

  His fundamental realistic assumption prevents Kant from thinking that natural objects somehow do not exist independently from us. They are there in front of us, they function in a certain manner, and they develop by themselves. One tree produces another tree—of the same species—and at the same time it grows and therefore also produces itself as an individual. The bud of one tree leaf grafted onto the branch of another tree produces one more plant of the same species. The tree lives as a whole on which the parts converge, since the leaves are produced by the tree, but defoliation would affect the growth of the trunk. The tree therefore lives and grows by following its own internal organic law (CJ, para. 64).

  But one cannot learn from the tree what this law is, since phenomena do not tell us anything about the noumenal. Nor do the a priori forms of the pure intellect have anything to tell us about it, because natural beings respond to multiple and particular laws. And yet, they should be considered necessary according to the principle of the unity of the manifold, which in any case is beyond our ken.

  These natural objects (over and above the extremely general laws that render the phenomena of physics thinkable) are dogs, stones, horses—and platypuses. We must be able to say how these objects are organized into genera and species, but (and this is important), genera and species do not depend on a classificatory judgment of ours: “There is in nature a subordination of genera and species that we can grasp; that the latter in turn converge in accordance with a common principle, so that a transition from one to the other, thereby to a higher genus is possible” (CJ, Intro., v).

  And so we try to construct the concept of the tree (we assume it) as if trees were the way we can think of them. Something is thought of as possible according to the concept (we try to harmonize the form with the possibility of the thing itself, even if we do not have any concept of it) and we think of it as an organism that obeys certain ends.

  To interpret something as if it was in a certain way means to advance an hypothesis, because the reflective judgment must subsume under a law that is not yet given “and which is in fact it only a principle for reflection on objects for which we are objectively entirely lacking a law or a concept of the object that would be adequate for the cases that come before us” (CJ, para. 69). Moreover, it must be a very risky type of hypothesis, because we must infer an as yet unknown Rule from the particular (from a Result); and to come up with the Rule we must hypothesize that that Result is a Case of the Rule to be constructed. Kant certainly never put it that way, though the Kantian Peirce did. It is clear however that reflective judgment is nothing more or less than an abduction.

  In this abductive process, as we said, genera and species are not merely arbitrary classifications—and if they were, they could only become established once the abduction had taken place, at an advanced stage of conceptual elaboration. In the light of the third Critique it must be admitted that the reflective judgment, insofar as it is teleological, already assigns a character of “animality” (or of “living being”) in the construction of schemata. Let us reflect for a moment on what would have happened if Kant had ever seen a platypus. He would have had the intuition of a multiplicity of traits, compelling him to construct the schema of an autonomous being, not moved by external forces, which exhibited coordination in its own movements, an organic and functional relationship between bill (which allows it to take nourishment), paws (that allow it to swim), head, trunk, and tail. The animality of the object would have seemed to him a fundamental element of the schema of perception, not as a successive abstract attribution (which would have merely served to ratify conceptually what the schema already contained).11

  It appears that one must therefore speak of a form of pre-categorial perception that precedes conceptual categorization, whereby the animality that one perceives on seeing a dog or a cat has nothing to do with the genus ANIMAL on which semantics has insisted at least since the time of the Porphyrian tree. If Kant had been able to observe the platypus (morphology, customs, and behavior), as has been done in the two centuries since Kant, he would have probably have come to the same conclusion as Gould (1991: 277): that this animal is not just a clumsy experiment of nature but a masterpiece of design, a perfect example of environmental adaptation. Indeed, its fur protects it from cold water, it can regulate its own body temperature, its morphology makes it adapted for diving into water and finding food with its eyes and ears closed, its anterior limbs allow it to swim, its posterior limbs and tail act as a rudder, its ankle spurs enable it to compete with other males in mating season. But Gould would probably not have been able to give this “teleological” reading of the platypus if Kant hadn’t suggested to us that “an organized product of nature is that in which everything is an end and reciprocally a means as well” (CJ, para. 66), as well as suggesting that the products of nature appear (unlike machines, which are moved by mere driving force, a bewegende Kraft) as organisms moved from within by a bildende Kraft, a capacity, a formative force.

  And yet Gould, in attempting to define this bildende Kraft, couldn’t come up with anything better than the outdated metaphor of design, which is a way of forming nonnatural beings. I don’t think Kant could have said he was wrong, even if in so doing he would have gotten himself into a happy contradiction. The fac
t is that the Capacity of Judgment, once it comes on the scene as reflective and teleological, overwhelms and dominates the entire universe of the knowable, and invests every thinkable object, even a chair. It is true that a chair, as an object of art, could be judged only as beautiful, as a pure example of finality without a goal and universality without a concept, a source of disinterested pleasure, the result of the free play of the imagination and the intellect. But at this point you do not need much to add a rule and an purpose where we have already tried to abstract them, and the chair will be seen, as was the intention of whomever conceived it, as a functional object oriented toward its own goal, organically structured so that each of its parts supports the whole.

  It is Kant who moves quite nonchalantly on from teleological judgments concerning natural entities to teleological judgments concerning products of artifice:

  If someone were to perceive a geometrical figure, for instance a regular hexagon, drawn in the sand in an apparently uninhabited land, his reflection, working with a concept of it, would become aware of the unity of the principle of its generation by means of reason, even if only obscurely, and thus, in accordance with this, would not be able to judge as a ground of the possibility of such a shape the sand, the nearby sea, the wind, the footprints of any known animals, or any other nonrational cause, because the contingency of coinciding with such a concept, which is possible only in reason, would seem to him so infinitely great that it would be just as good as if there were no natural law of nature, consequently no cause in nature acting merely mechanically, and as if the concept of such an object could be regarded as a concept that can be given only by reason and only by reason compared with the object, thus as if only reason can contain the causality for such an effect, consequently that this object must be thoroughly regarded as an end, but not a natural end, i.e., as a product of art (vestigium hominis video). (CJ, para. 64, emphasis in text)