From the Tree to the Labyrinth (85 page)

The idea of the flowchart seems to provide a good explanation what Kant means by the schematic rule that presides over the conceptual construction of geometrical figures. No image of a triangle that we find in experience—the face of a pyramid, for example—can ever be adequate to the concept of the triangle in general, which must be valid for every triangle, whether it be right-angled, isosceles, and scalene (CPR/B: 136). The schema is proposed as a rule for constructing in any situation a figure having the general properties triangles have (without resorting to strict mathematical terminology if we have, say, three toothpicks on the table, one of the steps that the schema would prescribe would be not to go looking for a fourth toothpick, but simply to close up the triangular figure with the three available).

Kant reminds us that we cannot think of a line without tracing it in our mind; we cannot think of a circle without describing it (in order to describe a circle, we must have a rule that tells us that all points of the line describing the circle must be equidistant from the center). We cannot represent the three dimensions of space without placing three lines perpendicular to each other. We cannot even represent time without drawing a straight line (CPR/B: 120, 21 ff.). At this point, what we had initially defined as Kant’s implicit semiotics has been radically modified, because thinking is not just applying pure concepts derived from a preceding verbalization, it is also entertaining diagrammatical representations, for example, flowcharts.

In the construction of these diagrammatical representations, not only is time relevant, but memory too. In the first edition of the first
Critique
(CPR/A: 78–79), Kant says that if, while counting, we forget that the units we presently have in mind have been added gradually, we cannot know the production of plurality through successive addition, and therefore we cannot even know the number. If we were to trace a line with our thought, or if we wished to think of the time between one noon and the next, but in the process of addition we always lost the preceding representations (the first parts of the line, the preceding parts in time) we would never have a complete representation.

Look how schematism works, for example, in the anticipations of perception, a truly fundamental principle because it implies that observable reality is a segmentable continuum. How can we anticipate what we have not yet intuited with our senses? We must work as though degrees could be introduced into experience (as if one could
digitize
the continuous), though without our digitization excluding infinite other intermediate degrees. As Cassirer (1918: 215) points out, “Were we to admit that at instant
a
a body presents itself in state
x
and at instant
b
it presents itself in state
x′
without having travelled through the intermediate values between these two, then we would conclude that it is no longer the ‘same’ body. Rather, we would assert that the body at state
x
disappeared at instant
a,
and that at instant
b
another body in state
x′
appeared. It results that the assumption of the continuity of physical changes is not a single result from observation but a presupposition of the knowledge of nature in general,” and therefore this is one of those principles presiding over the construction of the schemata.

So much for the schemata of the pure concepts of the intellect. But it so happens that it is in the very same chapter on schematism that Kant introduces examples that concern empirical concepts. It is not simply a question of understanding how the schema allows us to homogenize the concepts of unity, reality, inherence, subsistence, possibility, and so on, with the manifold of the intuition. There also exists the
schema of the dog:
“the concept of a dog indicates a rule, according to which my for imaginative capacity can universally trace the figure of a four-legged animal, without being restricted to either a unique particular figure supplied by experience, or to any possible image that I am able to portray
in concrete
” (CPR/B:136).

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?

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?