philosophy, a schema
) is the procedural rule by which a category or pure
, non-empirical concept
is associated with a mental image of an object. It is supposedly produced by the imagination
through the pure form of time
Kant's architectonic system
Kant created an architectonic system in which there is a progression of phases from the most formal to the most empirical. "Kant develops his system of corporeal nature in the following way. He starts in the Critique
with the most formal act of human cognition, called by him the transcendental unity of apperception, and its various aspects, called the logical functions of judgment. He then proceeds to the pure categories of the understanding, and then to the schematized categories, and finally to the transcendental principles of nature in general. It is within this system that the transcendental schemata serve a crucial purpose.
Purpose of the Schematism chapter
Kant wrote the chapter on Schematism in his Critique of Pure Reason
to solve the problem of "...how we can ensure that categories have 'sense and significance.'
A posteriori concepts have sense when they are derived from a mental image that is based on experienced sense impressions. Kant's a priori concepts are alleged to have sense when they are derived from a non–experienced mental schema, trace, outline, sketch, or minimal image.
Whenever two things are totally different from each other, yet must interact, there must be some common characteristic that they share in order to somehow relate to one another. Categories, or a priori concepts, have, according to Kant, a basic and necessary importance for human knowledge, even though they are totally different from sensations. However, they must be connected in some way with sensed experience because
"… an a priori concept which cannot, as it were, establish any empirical connections is a fraud … the purpose of the Schematism chapter was to show that the categories at least do have satisfactory empirical connections.
Obscurity of the concept "Schema"
Kant introduced the concept of the transcendental schema in his chapter entitled "Of the Schematism of the Pure Concepts of the Understanding. It is considered to be one of Kant's more difficult chapters. Even though he knew that he was not writing for a popular readership, Kant twice tried to apologize for this chapter by calling it "very dry and "dry and tedious. Professor W.H. Walsh, of the University of Edinburgh
, wrote: "The chapter on Schematism probably presents more difficulties to the uncommitted but sympathetic reader than any other part of the Critique of Pure Reason
. Not only are the details of the argument hightly obscure (that, after all, is a common enough experience in reading Kant, though one is not often so baffled as one is here): it is hard to say in plain terms what general point or points Kant is seeking to establish. Kant's "… own disciple Jakob Sigismund Beck
could not understand it. Schopenhauer
referred to it as "…the strange 'Chapter on the Schematism of the Pure Concepts of the Understanding,' which is well known for its great obscurity, since no one has ever been able to make anything out of it. In Schopenhauer's criticism of Kant's schemata
, he attempted to clear up the obscurity by attributing Kant's concept of schemata simply to a psychological need for architectonic symmetry in his writings. Empirical concepts are based on empirical perceptions. Kant, however, tried to claim that, analogously, pure concepts (Categories) also have a basis. But this contradicts his previous assertion that pure concepts simply exist in the human mind and are not based on pure, schematic perceptions. Schopenhauer also alleged that schemata were introduced merely to give plausibility to Kant's description of the categories or pure concepts of the understanding. The article on Kant in the Encyclopedia of Philosophy
calls Kant's schematism a "baffling doctrine " with "cryptic sentences. The Scottish philosopher Robert Adamson
wrote: "Kant's manner of explaining the functions of schematism is extremely apt to be misunderstood, and to mislead.
Explication of the Kantian account of schemata
Three types of concepts and their schemata
An empirical concept is the abstract thought of what is common to several perceptions. When an empirical concept is said to contain an object, whatever is thought in the concept must be intuited in the mental representation of the object. Examples of intuitive perceptions that are the content of empirical concepts
are vague images that are imagined in order to connect a concept
with the perceptions
from which it was derived as their common feature. "Intuitions," Kant wrote, "are always required to verify or demonstrate the reality of our concepts. These examples ensure that "our abstract thinking has not strayed far from the safe ground of perception, and has possibly become somewhat high–flown or even a mere idle display of words.. This is due to the fact that "concepts are quite impossible, and are utterly without meaning or signification, unless an object is given for the concepts themselves, or at least for the elements of which they consist. For example, "The concept of a dog signifies a rule according to which my imagination can trace, delineate, or draw a general outline, figure, or shape of a four-footed animal without being restricted to any single and particular shape supplied by experience. In order to prevent the emptiness of "thoughts without contents, it is "necessary to make our concepts sensible, i.e., to add an object of intuition to them. In order to test whether a concept is sensible, we sometimes " … go back to perception only tentatively and for the moment, by calling up in imagination a perception corresponding to the concept that occupies us at the moment, a perception that can never be quite adequate to the (general) concept, but is a mere representative
of it for the time being. … Kant calls a fleeting phantasm of this kind a schema
Pure sensuous concepts
A pure, sensuous concept is the construction or mental drawing of what is common to several geometrical figures. These mathematical concepts are not based on objective visual images. They are based on schemata that exist only in thought. Any particular image could not be as general as the concept. The schemata are rules that allow the imagination to mentally construct or draw or trace a pure, general geometrical form that gives the pure, sensuous concept significance. "… [T]o possess the schema corresponding to the concept triangle is to be able to envisage the variety of things to which the word "triangle" applies. "[T]he schema of sensuous concepts (such as of figures in space) is a product and, as it were, a monogram of the pure imagination a priori
. Images become possible only through the schema. But the images must always be connected with the concept only by means of the designated schema. Otherwise, the images can never be fully congruent to the general concept.
Pure concepts of the understanding
A pure concept of the understanding, or category, is a characteristic, predicate, attribute, quality, or property of any possible object in general
. These concepts are not abstractions of what is common to several perceived, particular, individual objects, as are empirical concepts. "Since the categories are a priori
and are therefore not abstractions from sense perceptions, they owe their origin to the very nature of the mind itself." They are not derived from perceptions of external objects, as are empirical concepts. Instead, they are the result of the way that the mind is constituted or formed. They come from within, not without.
Kant claimed that the schemata of pure, non-empirical concepts, or categories, provide a reference to intuition in a way similar to the manner of empirical concepts. "If the concepts are empirical, the intuitions are called examples: if they are pure concepts of the understanding, the intuitions are called schemata. In the same way that examples provide signification for empirical concepts, schemata help to answer the question of "whether operating with the categories is anything other than playing with words.
Since the pure concepts of the understanding, or categories, are characteristics of all objects in general, they can never be associated with the image of any specific, particular, individual object. "Since they are pure, they cannot be pictures... "Yet there must be some connection between the abstract idea and the experienced world to which the idea is expected to apply... "In order for the pure categories to have objective validity (and not merely subjective validity) they must be related to sensibility.
Applying pure concepts to sense impressions
The categories, or pure concepts of the understanding, are a priori logical innate
forms that are conditions of the possibility of things in general, or of things as such. A thing can become a known object of thought when an a posteriori
sense impression is comprehended through the forms of the categories. Categories and sense impressions are totally different from each other. Categories are utterly heterogeneous with the perceptions that are experienced through the sense organs. In order for specific phenomena of Nature
to be thought from the combination of categories (pure concepts) and sense perceptions, there must be a third, mediating procedure that connects them. This mediator is a transcendental schema. Transcendental schemata meaningfully join the empty "thoughts without content" and the blind "intuitions without concepts.
Transcendental schema are not related to empirical concepts or to mathematical concepts. These schemata connect pure concepts of the understanding, or categories, to the phenomenal appearance of objects in general, objects as such, or all objects.
Transcendental Schematism results from the ability to make judgments. " … the judgment … schematizes
these concepts a priori and applies these schemata, without which no experiential judgment would be possible, to each empirical synthesis. … the transcendental schematism of judgment provides it [judgment] with a rule under which given empirical intuitions are to be subsumed. Kant defined the Greek word hypotyposis
as a " … rendering perceptible to the senses, making sensual (Versinnlichung). The usual definition is "example, pattern, outline, or sketch." If a hypotyposis is schematic, according to Kant, "...to a concept, which is comprehended by the understanding, the corresponding intuition is given a priori
... This is in opposition to a symbolic hypotyposis, like God, in which the concept can only be thought by Reason and to which no sensible intuition can be adequate. Schemata contain direct presentations of the concept. They make this presentation demonstratively, not by the use of analogies. Judgment, according to Kant, works mechanically with given appearances and brings them under concepts. It does this as a tool that is utilized and controlled by both the understanding and the senses.
Categories, or pure concepts of the understanding, are forms of objects in general. However, they can become forms of specific internal and external objects of thought if they are related to time.
Everything is experienced in time. This applies to our internal selves as well as to all external objects. Since categories are the forms through which every specific thing can be thought as being in time, categories are related to time. Thus, pure concepts, or categories, and phenomenal objects share time as a common feature. Therefore, time is the means by which an intuited phenomenon is subsumed under a pure concept. Schemata are transcendental time determinations. "Hence it will be possible for the category to be applied to appearances by means of the transcendental time determination, which, as the schema of the concepts of the understanding, mediates the subsumption of appearances under the category.
Schemata are procedural rules, not images
Because schemata are determinations of objects in general, not specific, individual objects, they are not particular images. Kant asserted that "… a schema must be distinguished from an image. A schema is a procedural rule. The rule prescribes the way to relate a pure concept to an object in general. Schemata are ways of applying pure concepts (categories) to sense impressions. They are prescriptions for graphically illustrating a pure concept. A schema is a method for representing a non-empirical concept in any image as such or any image in general. "… [T]his representation of a general procedure of the imagination for providing a concept with its image, I call the schema of such a concept. " … [F]or Kant a schema is not an image, but a capacity to form images or (perhaps) to construct models. "The schema of a pure concept of the understanding is something which can never be made into an image...
Illustrations of Different categories and their schemata
Each category has one schema. Some schemas are shared by other categories in their class.
- The categories of quantity all share the schema of number. Quantity is related to a numerical time series. William H.S. Monck claimed that Kant can be understood as saying "In apprehending an object I always successively add part to part, and thus generate a series of determinate magnitude. Unity is one moment in time. Plurality is several moments. Totality is expressed as all moments. But Monck noted that "Kant does not trace out specially the Schemata of the Categories of Unity, Plurality, and Totality. Monck supposed: "In the Category of Unity I presume we should stop at the first term of the Time–series: for the Category of Plurality we should represent the addition of unit to unit without laying down any determinate limit; and for the Category of Totality we should limit the number of units and complete the addition up to this number.
- The categories of quality all have degrees of reality as their schema. Quality is related to the content of real being in time. Kant metaphorically explained the schema of quality as the filling up of time with a sensation. Monck paraphrased Kant as saying, "We may speak of time as being more completely filled when the sensation is more vivid, and less completely filled when the sensation is weaker. If the sensation is sufficiently vivid the present moment is so filled with it that it seems impossible to attend to, or even be conscious of any other sensation simultaneously; but when it becomes weaker we have leisure to perceive other sensations also. This occurs by degrees. "We can represent this filling as taking place by a gradual increase from zero (empty time) to any given degree of vividness, or by a similar descent from the sensation of the moment to zero. Reality is the experience of sensation in time. Negation is the absence of sensation in time. Limitation is the range of degrees, between the transition from full to empty, by which things are sensed in time. But Monck stated that "Again Kant does not here give in detail the Schemata of the Categories of Reality, Negation, and Limitation." He qualifiedly suggested that "In the first case [Reality], we should, perhaps, represent the sensation as occupying the present moment to the exclusion of everything else; in the second [Negation] the sensation as entirely absent from the present moment; in the third [Limitation] the sensation as occupying the present moment along with others.
- "The Schema of the Category of Relation is the Order of Time. In the class of relation, each category has its own schema. Substance's schema is the permanence of the unchanging substance (subject) to which accidents (predicates) belong, or the permanence of the object in time. Causality's schema is the necessary succession of a consequent to an antecedent. That is, "… the Schema of the Category of Cause is its regular Antecedence in Time (i.e. Succession in Time determined by fixed law)." The category of community has the schema of the necessary coexistence of the accidents of one substance with the accidents of another substance. This communal interaction consists of the changing accidents of one substance having their cause in the changing accidents of another substance, and vice versa. This can be understood as "… the Simultaneity of objects in Time.
- "The Schema of the Category of Modality according to Kant is Time itself as related to the Existence of the object." In the class of modality, the category of possibility has the schema of possibility at any time. The schema of actual existence at a certain time belongs to the category of existence. Finally, the category of necessity has the schema of being an object at all times.
Even though Kant provided these illustrations and examples of schemata, author John Mahaffy claimed that the topic remained obscure. He wrote, "I may add, that these illustrations of the various schemata are developed and explained by the succeeding chapters on the Principles which embody them, and that it is impossible to make them clear to the reader until he has studied the theory of the Principles.
Schematized and unschematized categories
The schemata give the categories a "cash value", as though the category is like paper money and sense experience is analogous to precious metal. A schema is the agreement or harmony of a category with sensual phenomena. For example, "Number is the quantity of the phenomenon; sensation is the reality of the phenomenon; the permanence and endurance of things is the substance of the phenomenon, eternity is the necessity of the phenomenon, etc. In this way, the schemata restrict the categories to conditions of sensibility. "Schematism and the schemas thus have the property of 'realizing' the categories at the same time as restricting their scope to appearances. Categories cannot be realized in objects that are not detectable by the senses, that is, are not phenomenal objects or objects that appear to an observer.
"The schemata of the pure concepts of the understanding are, therefore, the true and sole conditions for providing these concepts with a reference to objects and hence with signification. And therefore the categories have, in the end, no other use than a possible empirical one. In order for categories to refer to perceived, experienced objects, they must be schematized. If a category is not schematized, then it has no reference to perception. An unschematized category can be thought, but can not be known. If something can never be perceived, it can never be known. Schemata represent things in general as they appear, not as they might otherwise exist. "Categories, therefore, without schemata are only functions of the understanding necessary for concepts, but do not themselves represent any object. With the transcendental determination of time as the transcendental schema, " … use of the categories is clearly restricted to the range of things that fall within time — meaning, for Kant, restricted to phenomena. Metaphysical entities that are not related to time, such as spontaneous or uncaused movements, immortal souls, and eternal gods, are products of unschematized categories. They can be thought, but not known.
According to Professor W. H. Walsh, there is an apparent discrepancy in Kant's central arguments about schematism. Kant, according to Professor Walsh, first claimed that empirical concepts do not require schemata. Only pure concepts need schemata in order to be realized. This is because pure concepts are totally different from intuitions, whereas, empirical concepts contain intuitions and are therefore homogeneous with them. But in another part of his chapter, Kant states that mathematical concepts have schemata. "In fact," he wrote, "it is schemata, not images of objects, that lie at the basis of our pure sensible (i.e., geometrical) concepts. In discussing schematism as the method of representing in one image a certain mathematical quantity according to a certain concept, he wrote: "This representation of a general procedure of the imagination by which a concept receives its image, I call the schema of such concept." With regard to pure concepts, Kant then declares, "The schema of a pure concept of the understanding, on the contrary, is something which can never be made into an image … ."
Kant, according to Professor Walsh, has two distinct ways of describing schemata. "Sometimes, as at the beginning of his discussion, he speaks as if a schema were a feature of things which could be pointed to … . In another place, Kant " … speaks as if schematism were a procedure … .
Kant said that the schema of a concept is the representation of a general procedure of the imagination by which an image can be supplied for a concept. Kant claimed that time is the only proper and appropriate transcendental schema because it shares the a priori
category's generality and purity as well as any a posteriori
phenomenon's manner of appearance. However, it may be true that time is not the only possible schema.
"Even more remarkable, however, is the fact that in order to understand the possibility of things as consequent upon the categories, and hence in order to establish the categories' objective reality
, we need not merely intuitions but indeed always outer intuitions
. Since space is the form of all appearances of the outer senses, it may seem that space could serve as a schema. Indeed, any phenomenon that requires space, as well as time, as a form would also need a spatial schema. "This suggests that he may have thought at one point of recasting the Schematism argument in a fundamental way, by substituting space for time; but if he had this idea, he did not carry it out.
In order to show how time may not be the only schema, Professor Walsh suggested that there is "… the possibility of making sense of the categories in organic as opposed to mechanical terms. He hypothesized that "Elements in an organic complex would here take the place of elements in a temporal situation. Substance might be interpreted in terms of growth and form as opposed to what underlies mechanical change, and causality be thought of in terms of purpose and function. However, Professor Walsh concluded that Kant's choice of time as schema was more precise than any alternative choices. In spite of the general difficulty in understanding Schematism, he asserted that "… Kant's doctrine of schematism, if not altogether satisfactory at the theoretical level, will continue to stand on the strong empirical ground that the schemata offered do enable us to give real meaning to the categories and find for them a genuine use."
Schemata of systematic unity
In his discussion of the Architectonic of Pure Reason, Kant utilized the concept of schema in a way that was similar to his discussion of the schemata of the Categories. A science's whole systematic organization consists of parts. The parts are various cognitions or units of knowledge. The parts are united under one idea which determines the relation of the parts to each other and also the purpose of the whole system. A schema is needed to execute, carry out, or realize this unifying idea and put it into effect. This schema is a sketch or outline of the way that the parts of knowledge are organized into a whole system of science. A schema which is sketched, designed, or drafted in accordance with accidental, empirical purposes results in mere technical unity. But a schema that is drawn up from an a priori
rational idea is the foundational outline of architectonic unity. Science must have architectonic unity. "For the schema of what we call science must contain the whole's outline (monogramma
) and the whole's division into parts in conformity with the idea — i.e., it must contain these a priori
— and must distinguish this whole from all others with certainty and according to principles. This use of the concept of schema is similar to Kant's previous use. It is a minimal outline, monogram, or diagram that realizes or executes an abstract, general concept or idea (Idee) as actual, perceptual experience.
Scottish philosopher Robert Adamson
wrote from a Hegelian standpoint. He believed that Kant's analysis of knowledge into the separate topics of intuition, schema, and concept was mechanical and artificial. Adamson claimed that "Thought and Intuition are organically united in the schema. "We are not to suppose that the subsumption [of the intuition under the pure notion] is mechanical; that the particular is something distinct from the universal. The union is organic; the particular is only the universal under a special form. The same function of synthesis, which in pure abstraction we call category, is, in realization, the schema, and the intuition is not apart from the schema. Kant's abstract analysis of perceptual knowledge was, according to Adamson, the misleading separation of an organic unity into individual components. He asserted that "… we must on no account regard Notion, Schema, and Intuition, as three parts of perception which would exist in isolation.
Elaborations of Kant's notion of schema in cognitive science
The philosopher Mark Johnson discusses Kant's conception of a schema with respect to developing a theory of the imagination within cognitive science. Johnson's theory makes use of Kant's insights that analogy is the cognitive mechanism which links sensible percepts to their conceptual categories, and that creative analogy--or what Johnson calls conceptual metaphor--is the cognitive mechanism by which we come to have our understanding of those abstract concepts and categories of which we have less direct sensible experience. He proposes that we use imaginative schemata to structure abstract concepts largely in terms a set of spatial analogies he calls image schemata. In Johnson's view, we acquire image schemata primarily from recurrent patterns of experiences in infancy and early childhood, and then reuse these image schemata in a metaphoric fashion both to reason abstractly and as we speak our language.
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