From the Tree to the Labyrinth

13

On the Silence of Kant

Paragraph II.4 of linguist Tullio De Mauro’s Introduzione alla semantica (“Introduction to Semantics”) is entitled “Il silenzio di Kant” (“The Silence of Kant”) and clearly alludes (given the context) to Kant’s silence regarding the problem of language. Since then, much has been written on the subject of Kantian semiotics (we have only to think, in Italian, of the contributions of Emilio Garroni). But did De Mauro’s title really exclude Kant from a history of linguistics, if not semiotics? If Kant was (putatively) silent on the issue, not so De Mauro, who immediately went on to point out two crucial passages in which Kant had posed the problem of meaning, perhaps without being fully aware of what he was doing. One was the section in the Critique of Pure Reason, entitled Analytic of Principles, where the German philosopher speaks of the schema, and the other was paragraph 59 of the Critique of Judgment.¹ We will have occasion to come back to both of them, but let us first consider De Mauro’s comments on the passage concerning the schema:

What can this mysterious technique be if not the ability to connect signs of generic value with single images and concepts? We may ask ourselves whether it is possible for Kant not to have been aware that this is precisely the essential function performed by language in Locke and Berkeley’s system, especially when the expressions and examples he uses coincide with those adopted by Locke and Berkeley with reference to the meaning of words. (De Mauro 1965: 65)

We can only confirm our agreement and attempt to develop a few suggestions of our own.

13.1. Empirical Concepts

In Kant the semiotic problem has the right of citizenship, for him as much as it did for Aristotle, if we consider the purely verbal origins of his categorial apparatus (based, in the last analysis, on the structures of their respective languages). In the work he devoted to Kant, Heidegger (1997: 19) remarked: “Finite, intuiting creatures must be able to share in the specific intuition of beings. First of all, however, finite intuition as intuition always remains bound to the specifically intuited particulars. The intuited is only a known being if everyone can make it understandable to oneself and to others and can thereby communicate it.”

To speak of what is signifies making communicable what we know about it. But to know it, and communicate it, implies appealing to the generic, which is already an effect of semiosis, and depends on a segmentation of the content of which Kant’s system of categories, anchored to a venerable philosophical tradition, is itself a cultural product already established, culturally rooted, and linguistically fixed. When the manifold of the intuition is referred to the unity of the concept, the percipienda are by now already perceived just as culture has taught us to speak of them.²

Yet if a semiosic foundation is implied by the general framework of Kantian doctrine, that is one thing; it is entirely another question whether Kant ever developed a theory of how we assign names to the things we perceive, whether they be trees, dogs, stones, or horses. Given the question “How do we assign names to things?,” as Kant had inherited the problem of a theory of knowledge, the responses were essentially two. One came from the tradition that we may call “Scholastic” (but which begins with Plato and Aristotle): things present themselves to the world already ontologically defined in their essence, matter organized by a form. It is not important to decide whether this (universal) form is ante rem or in re: it is offered to us, it shines in the individual substance, it is grasped by the intellect, it is thought and defined (and therefore named) as a quiddity. Our mind has no work to do, or only insofar as the agent intellect does, which (wherever it may work) does so in a flash.

The second response was that of British empiricism. We know nothing of substances, and even if they existed, they would reveal nothing to us. For Locke, what we have are sensations, which propose simple ideas to us, either primary or secondary, but still unconnected: a rhapsody of weights, measures, sizes, and then colors, sounds, flavors, reflections changing with the hours of the day and the conditions of the subject. Here the intellect acts, in the sense that it works: it combines, correlates, and abstracts, in a way that is certainly spontaneous and natural to it, but only thus does it coordinate simple ideas to form those complex ideas to which we give the name of man, horse, tree, and then again, triangle, beauty, cause and effect. To know is to give names to these compositions of simple ideas. For Hume, the work of the intellect, as regards the recognition of things, is even simpler (we work directly on impressions of which ideas are faded images): the problem arises, if anything, in positing relations between ideas of things, as occurs in affirmations of causality. Here we would say that there is work, but performed without effort, by dint of habit and a natural disposition toward belief, even if we are required to consider the contiguity, priority, or constancy in the succession of our impressions.

Kant certainly does not believe that the Scholastic solution can be proposed again. Indeed, if there is truly a Copernican aspect to his revolution, it lies in the fact that he suspends all judgment on form in re and assigns a productive-synthetic, and not merely abstractive, function to the traditional agent intellect. As for the English empiricists, Kant seeks a transcendental foundation for the process they accepted as a reasonable way of moving in the world, whose legality was confirmed by the very fact that, when all was said and done, it worked.

At the same time, however, Kant noticeably shifts the focus of interest for a theory of knowledge. It is rash to say, as Heidegger (1997) did, that the Critique of Pure Reason has nothing to do with a theory of knowledge but is rather a questioning by ontology of its intrinsic possibility. Yet, it is also true, to quote Heidegger again, that it has little to do with a theory of ontic knowledge, in other words, of experience.

Nevertheless, Kant believed in the evidence of phenomena, he believed that our sensible intuitions came from somewhere, and he was concerned to articulate a rebuttal of idealism. But it appears to have been Hume who roused Kant from his dogmatic sleep, problematizing the causal relationship between things, and not Locke, though it was Locke who brought to the table the problem of an activity of the intellect in the naming of things.

A fundamental problem for the empiricists was saying why we decide, upon receiving sensible impressions from something, whether they refer to a tree or a stone. Yet it seems to have become a secondary problem for Kant, who was too preoccupied with guaranteeing our knowledge of heavenly mechanics.

In fact, the first Critique does not construct a gnoseology so much as an epistemology. As Rorty (1979) sums it up, Kant wasn’t interested in knowledge of but in knowledge that: not, then, in the conditions of knowledge (and therefore the naming) of objects. Kant asked himself how pure mathematics and physics are possible, or how it is possible to make mathematics and physics two theoretical fields of knowledge that must determine their objects a priori. The nucleus of the first Critique concerns the search to provide philosophical warrant for a legislation of the intellect regarding those propositions that have their model in Newton’s laws—and that, out of the need for exemplification, are sometimes illustrated by more comprehensible and venerable propositions such as All bodies are heavy. Kant is concerned to guarantee the knowledge of those laws fundamental to nature, understood as the totality of objects of experience. But he appears uninterested (at least until his Critique of Judgment) in clarifying how we know the objects of daily experience, what nowadays we call natural kinds, for example, camel, beech tree, beetle—with which the empiricists, on the other hand, were concerned.

Husserl, a philosopher interested in knowledge of, realized this, with evident disappointment (Investigation VI, ch. 8, para. 66):

In Kant’s thought categorial (logical) functions play a great role, but he fails to achieve our fundamental extension of the concepts of perception and intuition over the categorial realm.… He therefore also fails to distinguish between concepts, as the universal meanings of words, and concepts as species of authentic universal presentation, and between both, and concepts as universal objects, as the intentional correlates of universal presentations. Kant drops from the outset into the channel of a metaphysical epistemology in that he attempts a critical ‘saving’ of mathematics, natural science and metaphysics, before he has subjected knowledge as such, the whole sphere of acts in which pre-logical objectivation and logical thought are performed, to a clarifying critique and analysis of essence, and before he has traced back the primitive logical concepts and laws to their phenomenological sources.³

Husserl’s disappointment is converted into satisfaction for someone who maintains instead that the problem of knowledge can be resolved only in terms internal to language, namely in terms of coherence among propositions. And here Rorty (1979: sect. 3.3) takes issue with the idea that knowledge must be “the Mirror of Nature,” and he even asks how it was possible for Kant to assert that intuition offers us the manifold, when this manifold is known only after it has been unified in the synthesis of the intellect. In this sense, Kant would have taken a step forward with regard to the gnoseological tradition going from Aristotle to Locke, a tradition in which philosophers attempted to model knowledge on perception. Kant would have liquidated the problem of perception, insisting that knowledge concerns propositions and not objects.

Rorty’s satisfaction has evident reasons: although he proposes to challenge the very paradigm of analytical philosophy, it is this paradigm that is his point of departure, and therefore Kant seems to him to have been the first to suggest to the analytical tradition that we should not be asking what a dog is but rather what follows if the proposition dogs are animals is true.

What Rorty seems not to consider is that, if the opposition is between knowing what X is like and knowing what type of thing X is (as he himself quotes Sellars), we would still have to ask how one could respond to this second question without having responded to the first one.⁴ And it is worthwhile asking ourselves to what extent the opposition cited reproposes the old question (treated in Chapter 1 of the present volume) between encyclopedia and dictionary knowledge.

Kant’s position is still more embarrassing. He not only appears uninterested in explaining how we understand what X is like, but also incapable of explaining how we decide what type of thing X is. In other words not only is the problem of how one understands that a dog is a dog and not a cat absent from the first Critique, but even the problem of how we are able to say that a dog is a mammal.

More than of a lack of interest on Kant’s part, we should perhaps speak of a cultural difficulty.⁵ Kant, as an example of rigorous knowledge constructible a priori, had mathematical and physical sciences at his disposal, as established and laid down from Newton onward, and knew very well how to define weight, extension, force, mass, a triangle, and a circle. On the other hand, he did not have at his disposal a science of dogs, beech or linden trees, or beetles. When Kant writes his first Critique, hardly more than twenty years had passed since the definitive edition of Linnaeus’s Systema naturae, the first attempt to establish a classification of natural species. The older editions of the classic Italian dictionary first published in 1612 by the Accademia della Crusca still defined a dog as a “well-known animal,” the attempts at universal classification like those of Dalgarno or Wilkins (seventeenth century) used taxonomies that we would today call approximate (as we have seen, in this volume, in both Chapters 1 and 11. This is why Kant spoke of empirical concepts, and often repeated that we couldn’t know all of the marks of these concepts. To take up our main point again, he was concerned by the fact that encyclopedic knowledge was potentially infinite. Thus the first Critique opens (Introduction, VII) with the declaration that concepts containing empirical elements must not appear in transcendental philosophy. The object of an a prior synthesis cannot be the nature of things, which in itself is “unlimited.”

But even if Kant had been conscious of reducing knowledge to knowledge of propositions (and hence to linguistic knowledge), he still would not have been able to formulate the problem, which Peirce on the other hand will formulate, of the nonexclusively linguistic but semiosic nature of knowledge. To be more precise, if he fails to do so in the first Critique, he will move in this direction in the third. But to be able to set out along this road, he needed to bring the notion of schema into the picture.

According to one of Kant’s examples, you can go from an unrelated succession of phenomena (there is a stone, it is struck by the sun, the stone is hot—and, as we will see, this is an example of perceptual judgment) to the proposition the sun heats up the stone (P, 23). Let us suppose that the sun is A, the stone B, being hot C, and we can say that A is the cause by which B is C.

The tables of categories, transcendental schemata, and principles of the pure intellect instruct us on how to proceed. The axioms of intuition tell us that all intuitions are extensive quantities and, through the schema of number, we apply the category of singularity to A and B. Through the anticipations of perception, applying the schema of Degree, the reality of the phenomenon (in the existential sense of Realität) supplied by our intuition is affirmed. Through the analogies of experience, A and B are seen as substances, permanent in time, to which accidents inhere. We therefore establish that accident C (heat) of B (stone) is caused by A (sun). And thus we finally decide that what is connected to the material conditions of experience is real (reality in the modal sense, Wirklichkeit) and applying the schema of existence in a determined time, we assert that the phenomenon is truly the case. Likewise, if the proposition was by the law of nature, it happens that always and necessarily the light of the sun heats up (all) stones, the category of unity should first be applied, and finally that of necessity. Accepting the transcendental foundation of synthetic judgments a priori (but this isn’t the matter in contention), Kant’s theoretical apparatus has explained to us why one can say with certainty that A necessarily causes the fact that B is C.

But why is A perceived as sun and B as stone? How do the concepts of the pure intellect intervene to make it possible to understand a stone as such, as distinct from the other stones in the heap of stones, from the solar light heating it up, from the rest of the universe? The concepts of the pure intellect that constitute the categories are too vast and too general to allow us to consent to recognize the stone, the sun, and the heat. Kant promises (CPR/B: 94) that once a list of pure primitive concepts has been designated, we will “easily” be able to add those derived from and subordinate to them; however, since at the present time he is concerned not with the completeness of the system but with its principles, he will reserve this supplement for another work. Furthermore, he informs us that in any case all we have to do is to consult the manuals of ontology, thus deftly subordinating the predicates of force, action, or passion to the category of causality, or the predicates of being born, perishing, or changing to the category of modality. But this is not enough, because we are still at such a level of abstraction that we are not able to say this B is a stone.

The table of categories does not allow us to say how we perceive a stone as such. The concepts of the pure intellect are only logical functions, not concepts of objects (P, 39). But, if we are not able to say not only that this A is the sun and this B is a stone, but also that this B is at least a body, all the universal and necessary laws that these concepts guarantee are worth nothing, because they could refer to any datum of experience. One could perhaps say that there is an A that heats up everything, whatever constraints there might be on variable B, but we still wouldn’t know what this entity is that heats things up, because variable A would remain unconstrained. The concepts of the pure intellect not only need sensible intuition, but also the concepts of the objects to which they must be applied.

The empirical concepts of sun, stone, water, and air are not very different from what the empiricists called “ideas” (of genera and species). Sometimes Kant speaks of generic concepts, which are concepts, but not in the sense in which he often calls concepts “categories,” which are indeed concepts, but of the pure intellect. Categories are extremely abstract concepts, such as unity, reality, causality, possibility, and necessity. We cannot determine the concept of horse through the application of pure concepts of the intellect. Horse is instead an empirical concept deriving from sensation, through comparison of the objects of experience.

Empirical concepts are not studied by general logic, which is not supposed to investigate “the source of concepts, or the way in which concepts have an origin, insofar as they are representations” (L I, 55, my emphasis). Nor are empirical concepts studied by critical philosophy, which deals not with “the genesis of experience, but about that which lies in experience”; of the two objects of study, “the former belongs to empirical psychology” (P, 21). We ought to say then that we arrive at the formulation of empirical concepts in ways that have nothing to do with the legislative activity of the intellect, which rescues the matter of the intuition from its own blindness. In which case we should know horses and houses either through their manifest quiddities (as occurred in the Aristotelian-Scholastic line of thought) or through a simple task of combination, correlation, and abstraction, as was the case for Locke.

There is a passage from the Logic that could confirm our interpretation:

In order to make our presentations into concepts, one must thus be able to compare, reflect, and abstract, for these three logical operations of the understanding are the essential and general conditions of generating any concept whatever. For example, I see a fir, a willow and a linden. In firstly comparing these objects, I notice that they are different from one another in respect of trunk, branches, leaves and the like; further, however, I reflect only on what they have in common, the trunk, the branches, the leaves themselves, and abstract from their size, shape, and so forth; thus I gain a concept of tree. (L, 100)

But the passage would be Lockean if a term like “understanding” were to retain what is, after all, its weak meaning of “Human Understanding.” Instead, this could not happen in the case of the mature Kant, who had already published the three Critiques. Whatever process the intellect goes through in order to understand that a willow and a linden are trees, it does not find this “treeness” in the sensible intuition. And in any case Kant has not told us why having a given intuition allows us to understand that it is an intuition of a linden tree.

Even “to abstract” in Kant doesn’t mean take from or make spring from (which would still be the Scholastic prospective), and not even construct by means of (which would be the empirical position): it is purely considering separately, it is a negative condition, a supreme maneuver of the intellect that knows that the opposite of abstraction would be the conceptus omnimode determinatus, the concept of an individual, which in the Kantian system is impossible. Sensible intuition must be worked upon by the intellect and illuminated by general or generic determinations.

The cited passage perhaps responded to necessities of didactic simplification (in a text that gathers and certainly reelaborates notes taken by others in the course of his lectures, and is approved by an already mentally weakened Kant), because it is in clear contrast with what is said two pages before: “the empirical concept derives from the senses by the comparison of objects of experience and only receives the form of universality thanks to the intellect” (L 1, 3). “Only” here appears to be a euphemism.

13.2. Judgments of Perception

When Kant dealt with empirical psychology, in the decade preceding the first Critique (and here, too, we have to rely on lectures given somewhat under constraint and transcribed by others⁶), he already knew that knowledge provided by the senses is not sufficient, because it is necessary for the intellect to reflect on what the senses have offered it. The fact that we believe we know things on the basis of the sole testimony of the senses depends on a vitium subreptionis: from infancy we are so used to grasping things as if they already appeared given in our intuition that we have never made an issue out of the role performed by the intellect in this process. Not being aware that the intellect is in action does not mean that it is not working. Thus, in his Logic Kant alludes to many automatisms of this kind, such as when we speak, demonstrating that we know the rules of language; and yet, if asked, we wouldn’t be able to say what they were, and maybe we wouldn’t be even able to say they exist (L, Intro. I, 13).

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 possibilities, 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 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.

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).

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 Unknown 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 fact 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)

Kant has just told us how one develops an abduction worthy of Robinson Crusoe. And if someone were to observe that in this case art has nonetheless imitated a regular figure, not invented by art, but produced by pure mathematical intuition, we have only to cite an example that occurs shortly before the one just quoted. In that case, as an illustration of empirical finality (as opposed to the pure finality of the circle, which seems to have been invented for the purpose of highlighting all of the demonstrations that can be deduced from it), Kant pictures a beautiful garden, in the French style with its well-ordered flowerbeds and avenues, where art prevails over nature; and he speaks of empirical, certainly, and of real finality, for we are well aware that the garden has been planned with an aim and a function in mind. We may say that seeing the garden or the chair as a organism oriented toward an end calls for a less risky hypothesis, because I already know that artificial objects respond to the intentions of the artificer, while judgment postulates purpose (and indirectly a creative formativity, a sort of natura naturans) as the only way to understand it. But in any case even the artificial object cannot help being invested with reflective judgment.

This teleological version of the schema is not developed with absolute clarity even in the third Critique. See, for instance, the famous paragraph 59 which has always seduced anyone who attempted to find in Kant the elements of a philosophy of language. In the first place, a distinction is made between schemata, specific to the pure concepts of the intellect, and examples (Beispiele), valid for empirical concepts. The idea in itself is not without its appeal: in the schema of the dog or the tree prototypical ideas come into play, as if all dogs could be represented by the ostension of a dog (or by the image of a single dog). It remains to be seen how this image, which is supposed to mediate between the manifold of the intuition and the concept, can avoid being interwoven with concepts—being the image of a dog in general and not of that dog. And, once again, what “example” of a dog could mediate between intuition and concept, since it certainly appears that for empirical concepts the schema ends up coinciding with the possibility of “figuring” a generic concept?

Immediately afterward, Kant says that making something perceptible to the senses (“hypotyposis”) may be schematic when a concept grasped by the intellect is given the corresponding intuition is given (and this is valid for the schema of the circle, indispensable for understanding the concept of “plate”). On the other hand, Kant continues, it is symbolic when, to a concept that only Reason can think of, to which there exists no corresponding intuition, one is provided by analogy, as would be the case, for example, if I chose to represent the monarchical state as a human body. Here certainly Kant is speaking not only of symbols in the logical-formal sense (which for him are mere “characterisms”) but also of phenomena such as metaphor or allegory. But a gap still remains between schemata and symbols (we have only to think of the platypus): there is intuition, but not yet the concept, and I cannot recognize it or define it through a metaphor.

13.6.

Opus Postumum

Kant bridges this gap in his Opus Postumum, in which he again tries even harder to determine the various particular laws of physics that cannot be deduced from the categories alone. In order to ground physics, he must postulate the ether as matter that, distributed throughout cosmic space, is found in and penetrates all bodies.

External perceptions, as material for a possible experience, which lack only the form of their connection, are the effect of the moving (or driving) forces of matter. Now, to mediate the application of these motor forces to the relations that occur in experience calls for identifying empirical laws. These latter are not given a priori, they need concepts constructed by us (selbstgemachte). These are not concepts given by reason or experience but factitious concepts. They are problematic (and we recall that a problematic judgment depends on the Postulate of Empirical Thought in General, so that what is in harmony with the formal conditions of experience is possible).

Concepts of this kind must be thought as the foundation of natural inquiry. We must therefore postulate (in the case of the factitious concept of ether) an absolute whole that subsists in matter. Kant repeats on various occasions that this concept is not a hypothesis but a postulate of reason, but his suspicion of the term hypothesis has Newtonian roots. In fact, a concept (built on nothing, so to speak) that renders possible the totality of experience is an abduction, which, in order to explain certain Results, appeals to a Rule constructed ex novo.¹²

As Mathieu (1984) observes, apropos of Kant’s last writings, “The intellect makes experience by designing the structure according to which the driving forces of the object can act.” The reflective judgment, more than observing (and subsequently producing schemata), produces schemata so as to observe and test. And “such doctrine goes beyond that of the first Critique for the freedom that it assigns to the intellectual designing of the object” (Mathieu 1984: 231, n. 1). It is Mathieu (1984: 21) who again observes that “even keeping unchanged the necessary structure of the categories, one can equally take a further spontaneous activity into consideration, which the intellect performs starting with categories, but without remaining stalled at them … constructing not simply what derives from them, but all that we are able to think, and without falling into contradiction.” Perhaps to arrive at such boldness Kant had needed to pass through the aesthetic reflection of the third Critique; only then “is a new schematism born—the free schematism of the imagination, without concepts—as the primary capacity to organize perceptions” (cf. Garroni 1986: 226).

With this late schematism the intellect does not construct the simple definition of a possible object, but makes the object, constructs it, and in this activity (problematic in itself) it proceeds by trial and error.

At this point the notion of trial and error becomes crucial. If the schema of empirical concepts is a construct that attempts to make the objects of nature thinkable, and if a complete synthesis of empirical concepts can never be given, because new notes of the concept can always be discovered through experience (LI, 103), then the schemata themselves can only be revisable, fallible, destined to evolve over time. If the pure concepts of the intellect were to constitute a sort of intemporal repertoire, empirical concepts can only become “historic,” or cultural, however you choose to say it.¹³

Kant did not, in fact, say this, but it seems hard not to say it if one takes the doctrine of schematism to its logical conclusions. Peirce, for one, saw it this way, firmly putting the entire cognitive process down to hypothetical inference. Sensations appear as interpretations of stimuli; perceptions as interpretations of sensations; judgments of perception as the interpretation of perceptions; particular and general propositions as interpretations of perceptual judgments; and scientific theories as interpretations of a series of propositions (cf. Bonfantini and Grazia 1976: 13).

Given the infinite segmentability of experience, both perceptual schemata and propositions concerning the laws of nature themselves carve out entities or relations that—to a greater or lesser degree—always remain hypothetical and subject to the possibility of fallibilism.

Naturally at this point transcendentalism too will undergo its Copernican revolution. The guarantee that our hypotheses are “right” (or at least acceptable as such until proved otherwise) will no longer be sought in the a priori of the pure intellect (though its most abstract logical forms will be retained) but rather in the consensus, historic, progressive, and temporal of the Community.¹⁴ In the face of the risk of fallibilism, the transcendental too becomes historicized, an accumulation of received interpretations, accepted after a process of discussion, selection, and repudiation.¹⁵ An unstable foundation, if you will, based on the pseudo-transcendental of the Community (an optative idea more than a sociological category); and yet it is the Consensus of the Community that today makes us incline toward the Keplerian abduction rather than that of Tycho Brahe. Naturally the Community has come up with what we call called proofs, but it is not the authority of the proofs in themselves that convinces us, or keeps us from falsifying them. Rather, it is the difficulty of calling into question one proof without overturning the entire system and the paradigm on which it is based.

This detranscendentalization of knowledge comes up again, thanks to the explicit influence of Peirce, in Dewey’s notion of the “warranted assertion” (or, as we prefer to call it today, “warranted assertibility”) and remains present in the various holistic conceptions of knowledge.

—Translated by Jacob D. Blakesley and Anthony Oldcorn

A revised version of “Il silenzio di Kant sull’ornitorinco” (Eco 1998a). The subject is treated at greater length in Eco (1997b: ch. 2).

1. For the works of Kant we will use the following abbreviations: Critique of Pure Reason (CPR/A and CPR/B, according to whether the reference is to the first or second edition), Critique of Judgment (CJ), Prolegomena (P), Logic (L), and Opus Postumum (OP). [Translator’s note: The present translation has greatly benefited from the example of Alastair McEwen’s excellent English version of Eco’s Kant and the Platypus, which, in ch. 2 “Kant, Peirce and the Platypus,” covers much of the same ground.]

2. Semiotic interests are evident in some pre-Critique writings such as paragraph 10 Kant’s inaugural dissertation, De mundi sensibilis atque intelligibilis forma et principiis (“On the Forms and Principles of the Sensible and Intelligible World”), while, in his Anthropology from a Pragmatic Point of View (http://link.springer.com/content/pdf/bfm%3A978-94-010-2018-3%2F1.pdf), we see how, in the courses taught in his later years, Kant outlined (at least as a didactic tool) a summary theory of the sign—not original, but indebted to traditional doctrines, from Sextus Empiricus to Locke and perhaps Lambert, but nevertheless showing a respectful interest in the theme of semiotics. For Kant and semiotics, see Garroni (1972, 1977).

3. Husserl (1970a: 2, 833).

4. Cf. the objections by Marconi and Vattimo (1986: xix) in their introduction to the Italian translation of Rorty (1979).

5. I owe this reflection to Ugo Volli (personal communication).

6. See Kant (1968: 221–301).

7. In P, para. 18 he also speaks of a kind of superordinate genus of empirical judgments (Empirischen Urteile), based on the perception of the senses, to which judgments of experience add the concepts originating in the pure intellect. It is not clear how these empirical judgments differ from perceptual judgments, but here perhaps (without getting into Kantian philology) we can limit the comparison to perceptual judgments and judgments of experience.

8. CPR/B: 107. Therefore, “the question is not at all resolved” (Martinetti 1946: 65) concerning the difference between judgments of perception and judgments of experience. Cassirer (1918) realized this too, although he only alludes to it in note 20 of chapter II, 2: “it must be noted that a similar exposition of empirical knowledge … is not so much the description of a real objective fact, as much as the construction of a borderline case.… For Kant, no ‘singular judgment’ is given that does not already claim some form of ‘universality.’ No ‘empirical’ proposition exists that does not include in itself something asserted ‘a priori’: since the very form of the judgment already contains this claim to ‘universal objective validity.’ ” Why such an important statement only in a footnote? Because Cassirer knows that he is extrapolating according to good sense and systematic coherence what Kant should have said plainly, in order to exclude any other ambiguous formulation.

9. Here we will leave undecided whether he has perceived the stones, but has repressed this perception, so to speak, or whether he perceives only when he responds, interpreting memories of still unconnected visual sensations.

10. See, on this issue, Garroni (1968: 123; 1986, III, 2, 2) and also De Mauro (1965: 2, 4).

11. On the other hand, let us put ourselves in the shoes of a hypothetical Adam who sees a cat for the first time, without ever having seen any other animals. For this Adam, a cat will be schematized as “something that moves,” and for the moment this quality will make the cat similar to water and to clouds. But one imagines that it will not take Adam long to place the cat together with dogs and hens, among moving bodies that react unforeseeably to his solicitation and quite foreseeably to his call. Thus he will distinguish the cat from water and clouds, which appear to move, but are indifferent to his presence.

12. In “Horns, Hooves, Shoes” (in Eco 1990b) I defined the phenomenon we are dealing with as creative abduction, Cf. also Bonfantini and Proni (1983). Even though the postulate of ether was subsequently shown to be erroneous, it worked pretty well for a considerable time. Abductions (one thinks of the theory of epicycles and deferents) are shown to be helpful when they hold up for a long time, until a more suitable, economical, and potent abduction comes onto the scene.

13. Or, as Paci (1957: 185) has it, they are founded not on necessity but on possibility: “a synthesis is impossible without time and therefore without the schema, without an image which is always something more than the simple projection, something new, or as we would say, something projecting, open to the future, open to the possible.”

14. Cf. Apel (1995). The transcendental subject of knowledge becomes the community that almost “evolutionistically” approaches what could become knowable “in the long run,” through processes of trial and error. See also Apel (1975). This induces us to reread the anti-Cartesian polemic and the refusal to admit unknowable data, which could be defined as a cautious and preemptive distancing from the Kantian idea of the thing in itself. The Dynamic Object starts as something in itself but in the process of interpretation becomes ever more—even if only potentially—appropriate.

15. The rehabilitation of Kant by Popper (1969, I, I, v) should be read in this sense. “When Kant said, ‘Our intellect does not draw its laws from nature but imposes its laws upon nature,’ he was right. But in thinking that these laws are necessarily true, or that we necessarily succeed in imposing them upon nature, he was wrong. Nature very often resists quite successfully, forcing us to discard our laws as refuted; but if we live we may try again.” Therefore Popper reformulates Kant’s dictum: “The intellect does not draw its laws from nature but tries (with a variable possibility of success) to impose on it the laws it freely invents” (I, 8).