Kantian architectonics

In Kantian philosophy, a transcendental schema (plural: ''schemata''; from grc-gre, σχῆμα, "form, shape, figure") is the procedural rule by which a category or pure, non-empirical concept is associated with a sense impression. A private, subjective intuition is thereby discursively thought to be a representation of an external object. Transcendental schemata are supposedly produced by the imagination in relation to time.

Role in 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 are supposed to serve a crucial purpose. Many interpreters of Kant have emphasized the importance of the schematism.

Purpose of the schematism chapter

If pure concepts of the understanding (Kantian Categories) and sense perceptions are radically different from each other, what common quality allows them to relate? 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, on the other hand, are alleged to have sense when they are derived from a non–experienced mental schema, trace, outline, sketch, monogram, or minimal image. This is similar to a Euclidean geometrical diagram.

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. Kantian 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."
Kant was preoccupied "with bridging the otherwise heterogeneous poles of 'thought' and 'sensation' in the Schematism of the Pure Concepts of the Understanding (A 138/B 177)."

Explication of the Kantian account of schemata

Three types of concept and their schemata

There are three types of concept that require a schema in order to connect them to phenomenal sense perceptions so that they have sense innand meaning edeutung These three types are (1) empirical concepts, (2) pure (mathematical) sensuous concepts, and (3) pure concepts of the understanding, or antianCategories. The first two employ schemata. The third employs transcendental schemata.

Empirical concepts

An empirical concept is the abstract thought of that which 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.''Critique of Pure Reason'', A 137 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."''Critique of Judgment'', § 59 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 because "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."''Critique of Pure Reason'', A 140 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."''Critique of Pure Reason'', A 141 In order to prevent the emptiness of "thoughts without contents,"''Critique of Pure Reason'', A 51 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 (mathematical) concepts

These are concepts that relate, prior to experience, to the external sense of space and the internal sense of time. As such, they are mathematical in that they refer to geometry and arithmetic. 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. "… possess the schema corresponding to the concept triangle is to be able to envisage the variety of things to which the word "triangle" applies."''The Encyclopedia of Philosophy'', Volume 3, "Kant, Immanuel" " e 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."''Critique of Pure Reason'', A 142

Pure concepts of the understanding (Categories)

A pure concept of the understanding, or category, is a characteristic, predicate, attribute, quality, or property of any possible object, that is, an object ''in general'' or ''as such''. 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."Ellington, James W., "The Unity of Kant's Thought in His Philosophy of Corporeal Nature," Part 3 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 the mind, not from outside of the mind.

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

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The categories, or pure concepts of the understanding, are ''a priori'' logical innate