Today we would say that to obtain an empirical concept we must be able to produce a judgment of perception or perceptual judgment. But we understand perception as a complex act, an interpretation of sensible data that involves memory and culture and that results in our grasping the nature of the object. Kant, on the other hand, speaks of perceptio or Wahrnehmung only as a “representation with consciousness.” Such perceptions can be distinguished into sensations, which simply modify the state of the subject, and forms of objective knowledge. As such, they can be empirical intuitions, which through sensations refer to the singular object, and are still only appearances, devoid of concept and therefore blind. Or else they are imbued with concept, through a distinctive sign common to many things, a note (CRP/B: 249).
What would a perceptual judgment (Wahrnehmungsurteil) be, then, for Kant and how is it to be distinguished from a judgment based on experience (Erfahrungsurteil)? Perceptual judgments are an inferior logical activity (L, I, 57) that creates the subjective world of personal consciousness; they are judgments such as, When the sun shines on a stone it gets warm. They can also be erroneous and are in any case contingent (P, 20, 22 and footnotes). Judgments of experience, on the other hand, establish a necessary connection (for example, they assert in fact that The sun warms up the stone).7 It would seem, then, that the categorial apparatus is only involved in judgments of experience.
Why, then, are perceptual judgments “judgments”? Judgment is nonimmediate but mediated knowledge of an object: in every judgment there is a concept valid for a plurality of representations (CPR/B: 85). It cannot be denied that having the representation of the stone and its warming already represents a unification effectuated in the manifold of the sensible. To unite representations in a consciousness is already “to think” and “to judge” (P, 22), and judgments are a priori rules (P, 23), “all synthesis, without which even perception would be impossible, is subject to the categories” (CPR/B: 125). It cannot be that (as Kant says in P, 21) “the a priori principles of the possibility of all experience … are nothing other than propositions (Sätze) that subsume all perception … under those pure concepts of the understanding (Verstandesbegriffe)”. A Warnehmungsurteil is already woven, penetrated with Verstandesbegriffe. There can be no argument: recognizing a stone as such is already a perceptual judgment, a perceptual judgment is a judgment, and therefore it too depends on the legislation of the intellect. The manifold is given in the sensible intuition, but the conjunction of a manifold in general can enter into us only through an act of synthesis on the part of the intellect.8
In short, Kant postulates a notion of empirical concepts and perceptual judgment (a crucial problem for the empiricists), but he does not succeed in rescuing both from a quagmire, from the muddy terrain between sensible intuition and the legislatory intervention of the intellect. But for his critical theory this no-man’s-land cannot exist.
The various stages of knowledge, for Kant, could be represented by a series of verbalizations in the following sequence:
1. This stone.
2. This is a stone (or: Here there is a stone).
3a. This stone is white.
3b. This stone is hard.
4. This stone is a mineral and a body.
5. If I throw this stone it will fall back to earth.
6. All stones (being minerals and therefore bodies) are heavy.
The first Critique certainly deals with propositions like (5) and (6). It is doubtful whether it really deals with propositions like (4), and it leaves vague the legitimacy of propositions from (1) through (3b). We are entitled to wonder if (1) and (2) express different locutionary acts. Except in infantile holophrastic language, it is impossible to conceive of someone uttering (1) when confronted with a stone—if anything, this syntagm could only occur in (3a) or (3b). But no one has ever said that there must be a verbalization, or even an act of self-consciousness, that corresponds to every phase of knowledge. Someone can walk along a road, without paying attention to the heaps of stones piled up on either side; but if someone asks the walker what there was by the side of the road, the walker could very well reply that there were only stones.9 Therefore, if the fullness of perception is actually already a perceptual judgment—and if we insist on verbalizing it at all costs, we would have (1) which is not a proposition and therefore does not imply a judgment—by the time we get to verbalizing it we are immediately at (2).
Therefore, if someone who has seen a stone is questioned about what they have seen or are seeing, they would either answer (2) or there would be no guarantee that they had perceived anything. As for (3a) and (3b), the subject can have all possible sensations of whiteness or hardness, but when he predicates whiteness or hardness he has already entered into the categorial, and the quality he predicates is applied to a substance, precisely to determine it at least from a certain point of view. They may start with something expressible, such as this white thing, or this hard thing, but even so he would already have begun the work of hypothesis.
It remains to be decided what happens when our subject says that this stone is a mineral and a body. Peirce would have said that we had already entered into the moment of interpretation, whereas for Kant we have constructed a generic concept (but, as we have seen, he is very vague about this). Kant’s real problem, however, concerns (1–3).
There is a difference between (3a) and (3b). For Locke, while the first expresses a simple secondary idea (color), the second expresses a simple primary idea. Primary and secondary are qualifications of objectivity, not of the certainty of perception. A by no means irrelevant problem is whether someone seeing a red apple or a white stone is also able to understand that the apple is white and juicy inside, and that the stone is hard inside and heavy. We would say that the difference depends on whether the perceived object is already the effect of our segmentation of the continuum or whether it is an unknown object. If we see a stone, “we know” in the very act of recognizing that it is a stone what it is like inside. The person seeing a fossil of coral origin for the first time (a stone in form, but red in color) did not yet know what it was like inside.
But even in the case of a known object, what does it mean that “we know” that the stone, white on the outside, is hard on the inside? If someone were to ask us such an irritating question, we would reply: “I imagined so: that’s how stones usually are.”
It seems curious to put an image at the base of a generic concept. What does “imagine” mean? There is a difference between “to imagine1,” in the sense of evoking an image (here we are in the realm of daydreams, of the delineation of possible worlds, as when we picture to ourselves in our minds a stone we would like to find to split open a nut—and this process does not require the experience of the senses) and “to imagine2,” in the sense that, upon seeing a stone as it is, precisely because of and in concomitance with the sensible impressions that have stimulated our visual organs, we know (but we do not see) that it is hard.
What interests us is “to imagine” in this second meaning. As Kant would say, we can leave the first meaning to empirical psychology; but the second meaning is crucial for a theory of understanding, of the perception of things, or—in Kantian terms—in the construction of empirical concepts. And, in any case, even the first meaning of “imagine” is possible—the desire for a stone to use as a nutcracker—because, when we imagine1 a stone, we imagine2 it to be hard.
Sellars (1978) proposes reserving the term imagining for “imagine1” and using imaging for “imagine2.” I propose to translate imaging with “to figure” (both in the sense of constructing a figure, of delineating a structural framework, and in the sense in which we say, on seeing the stone, “I figure” it is hard inside).
In this act of “figuring” some of the stone’s properties, a choice is made, we “figure” it from a certain point of view. If, when seeing or imagining the stone, we did not intend to crack a nut but rather to chase away a bothersome animal, we would also see the stone in its dynamic possi
bilities, as an object that can be thrown and, due to its heaviness, has the property of falling toward the target rather than rising up in the air.
This “figuring” in order to understand and understanding through “figuring” is crucial to the Kantian system, both for the transcendental grounding of empirical concepts and for permitting perceptual judgments (implicit and nonverbalized) such as (1).
13.3. The Schema
In Kant’s theory, we must explain why categories so astrally abstract can be applied to the concreteness of the sensible intuition. We see the sun and the stone and we must be able to think that star (in a singular judgment) or all stones (in a still more complex, universal judgment, because we have actually seen just one stone, or a few stones, warmed by the sun). Now, “Special laws, therefore, as they refer to phenomena that are empirically determined, cannot be completely derived from the categories.… Experience must be superadded” (CPR/B: 127). But, since the pure concepts of the intellect are heterogeneous with respect to sensible intuitions, “in every subsumption of an object under a concept” (CPR/B: 133; though in fact we should say “in every subsumption of the subject of the intuition under a concept, so that an object may arise”), a third, mediating element is called for that makes it possible, so to speak, for he concept to wrap itself around the intuition and renders the concept applicable to the intuition. This is how the need for a transcendental schema arises.
The transcendental schema is a product of the imagination. Let us set aside for now the discrepancy that exists between the first and the second editions of the Critique of Pure Reason, as a consequence of which in the first edition the Imagination is one of the three faculties of the soul, together with Sense (which empirically represents appearances in perception) and Apperception, while in the second edition, Imagination becomes simply a capacity of the Intellect, an effect that the intellect produces on the sensibility. For many of Kant’s interpreters, like Heidegger, this transformation is immensely relevant, so much so in fact as to oblige us to return to the first edition, overlooking the changes in the second. From our point of view, however, the issue is of minor importance. Let us admit, then, that the Imagination, whatever type of faculty or activity it may be, provides a schema to the intellect, so that it can apply it to the intuition. Imagination is the capacity to represent an object even without its being present in the intuition (but in this sense it is “reproductive,” in the sense we have called “imagining1”), or it is a synthesis speciosa, “productive” imagination, the capacity for “figuring.”
This synthesis speciosa is what allows us to think the empirical concept of a plate, through the pure geometrical concept of a circle, “because rotundity, which is thought in the first, can be intuited in the second” (CPR/B: 134). In spite of this example, the schema is still not an image; and it therefore becomes apparent why we preferred “figure” to “imagine.” For instance, the schema of number is not a quantitative image, as if we were to imagine the number 5 in the form of five dots placed one after the other as in the following example: •••••. It is evident that in such a way we could never imagine the number 1,000, to say nothing of even greater numbers. The schema of number is “rather the representation of a method of representing in one image a certain quantity … according to a certain concept” (CRP/2: 135), so that Peano’s five axioms could be understood as the elements of a schema for representing numbers. Zero is a number; the successor to every number is a number; there are no numbers with the same successor; zero is not the successor of any number; every property belonging to zero, and the successor to every number sharing this property, belongs to all numbers. Thus any series x0, x1, x2, x3 … xn is a series of numbers, under the following assumptions: it is infinite, does not contain repetitions, has a beginning; and, in a finite number of passages, does not contain terms that are unreachable starting from the first.
In the preface to CPR/B Kant cites Thales who, from the figure of one isosceles triangle, in order to discover the properties of all isosceles triangles, does not follow step by step what he sees, but has to produce, to construct the isosceles triangle in general.
The schema is not an image, because the image is a product of the reproductive imagination, while the schema of sensible concepts (and also of figures in space) is a product of the pure a priori capacity to imagine, “a monogram, so to say” (CPR/B: 136). If anything it could be said that the Kantian schema, more than what we usually refer to with the term “mental image” (which evokes the idea of a photograph) is similar to Wittgenstein’s Bild, a proposition that has the same form as the fact that it represents, in the same sense in which we speak of an iconic relation for an algebraic formula, or a model in a technical-scientific sense.
Perhaps, to better grasp the concept of a schema, we could appeal to the idea of the flowchart, used in computer programming. The machine is capable of “thinking” in terms of if … then go to, but a logical system like this is too abstract, since it can be used either to make a calculation or to design a geometrical figure. The flowchart clarifies the steps that the machine must perform and that we must order it to perform: given an operation, a possible alternative is produced at a certain juncture; and, depending on the answer that appears, a choice must be made; depending on the new response, we must go back to a higher node of the flowchart, or proceed further; and so on. The flowchart has something that can be intuited in spatial terms, but at the same time it is substantially based on a temporal progression (the flow), in the same sense in which Kant reminds us that the schemata are fundamentally based on time.
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 digit
ization 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.
13.4. Does the Dog Schema Exist in Kant?
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).