In Kantian philosophy, a transcendental schema (plural: schemata; from , '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:For an explanation of the logical structure of this progression, see Stephen Palmquist, "The Architectonic Form of Kant's Copernican Logic", Metaphilosophy 17:4 (October 1986), pp. 266–288; revised and reprinted as Chapter III of Stephen Palmquist, Kant's System of Perspectives: An architectonic interpretation of the Critical philosophy (Lanham: University Press of America, 1993). Also see the third appendix, entitled "Common Objections to Architectonic Reasoning. "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."Ellington, James W., "The Unity of Kant's Thought in His Philosophy of Corporeal Nature", Philosophy of Material Nature 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."…if the schemata had been considered early enough, they would have overgrown his [Kant’s] whole work." (Collected Papers of Charles Sanders Peirce, Vol. I, Book I, Chapter I, Section 4, Paragraph 35)"…if we were to reconsider the problem of Kantian schematism, much of the semantics of this century, from the truth–functional to the structural variety, would find itself in difficulty. And this is what has happened in the area usually referred to as 'cognitive studies.'" (Umberto Eco, Kant and the Platypus, § 3.1)"The problem of the Schematism of the pure concepts of the understanding is the question concerning the innermost essence of ontological knowledge….The Doctrine of the Schematism of the pure concepts of the understanding is the decisive stage of the laying of the ground for Metaphysica Generalis." (Heidegger, Kant and the Problem of Metaphysics , Part 2, § 23)"The Schematism chapter is not 'confusing,' but rather leads with an unheard-of certainty into the core of the whole problematic of the Critique of Pure Reason." (Heidegger, Kant and the Problem of Metaphysics , Part 2, § 23)"…in his insistence upon the central role of time in consciousness, upon its being in fact the basic character of that synthesis of the finite and the infinite which is the self, Schelling rescues Kant’s schematism from its obscure hiding place in the text of the First Critique and gives it its proper prominence." (Michael Vater of Marquette University in his introduction to Schelling’s System of Transcendental Idealism, p. xvi, 1997, University of Virginia Press)"…a study of what may be the most puzzling and yet, at the same time, most significant aspect of Kant’s system: his theory of schemata." (Joseph L. Hunter, "Kant’s Doctrine of Schemata," Thesis submitted to the faculty of Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Arts in Philosophy, August 25, 1999)"The opaqueness and obscurity of the Schematism chapter—the chapter which Kant himself thought to be one of the most important pieces of the Critique, and to which Hegel paid tribute as being among the finest pages of the entire Kantian oeuvre—has often been—stressed with undertones ranging from wonder to irritation. From among the earliest statements we recall F. H. Jacobi’s assessment of schematism as 'the most wonderful and most mysterious of all unfathomable mysteries and wonders'…." (Shaper, E. (1964–65). "Kant’s Schematism Reconsidered," Review of Metaphysics 18: 270)John Mahaffy, editor and translator, A Commentary [by Kuno Fischer] on Kant’s Critick of Pure Reason, Introduction, § 3, London, Longmans, Green, & Co., 1866.
Purpose of the schematism chapter If pure concepts of the understanding (the 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.' "Walsh, W. H., "Schematism," Kant-Studien, Band 49"The formation of the schema [Schemabildung] is the making sensible of concepts." (Martin Heidegger, Kant and the Problem of Metaphysics, Indiana University Press, Bloomington and Indianapolis, 1997)
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,A schema is related to a perceived object as a single letter is related to a whole name. 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 experienceA priori concepts, or Categories, "require, in order to be meaningful and significant, a certain concrete use — that is, an application to some intuition by which an object of them is given to us." Prolegomena to Any Future Metaphysics, § 8. 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."Walsh, W. H., "Schematism," Kant-Studien, vol. 49 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)."The Cambridge Companion to Kant, George di Giovanni, Chapter 14, "The first twenty years of critique: The Spinoza connection," Page 442, Note 6.Between any two disparate but related things, such as a pure concept and a phenomenal, sensual perception, there must be something that unites, relates, and connects the two. The connector must share some properties with each of those two things that it connects. Kant’s "transcendental schema" is a "third thing, which must stand in homogeneity with the category [pure concept] on the one hand and the phenomenal appearance on the other…." This third, connecting thing must be time, because "a transcendental time-determination is homogeneous with the category (which constitutes its unity) insofar as it is universal and rests on a rule a priori," "but it is on the other hand homogeneous with the phenomenal appearance insofar as time is contained in every empirical representation of the manifold." (Critique of Pure Reason, A 138–9/B 177–8).
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 [Sinn] and meaning [Bedeutung]. These three types are (1) empirical concepts, (2) pure (mathematical) sensuous concepts, and (3) pure concepts of the understanding, or [Kantian] Categories. The first two employ schemata. The third employs transcendental schemata.
Empirical concepts An empirical concept"Now if a concept is one drawn from the sensory representation, i.e., an empirical concept, it contains as a characteristic, i.e., as a part-representation, something that was already apprehended in the sensory intuition, and differs from the latter in logical form only, viz., in respect of its generality, e.g., the concept of a four-footed animal in the representation of a horse." (Bold characters added) (Kant, What real progress has metaphysics made in Germany since the time of Leibniz and Wolff?, "First Section of the Scope of the Theoretico-Dogmatic Use of Pure Reason") 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.Schopenhauer, The World as Will and Representation, Vol. I, Appendix, "Critique of the Kantian Philosophy," p. 449 f. "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."Schopenhauer, The World as Will and Representation, Vol. I, Appendix, "Critique of the Kantian Philosophy", p. 449 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."Schopenhauer, The World as Will and Representation, Vol. I., Appendix, Critique of the Kantian Philosophy. p. 449
Pure sensuous (mathematical) concepts