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pure understanding。
TRANSCENDENTAL DOCTRINE OF THE FACULTY OF JUDGEMENT
OR; ANALYTIC OF PRINCIPLES。
CHAPTER I。 Of the Schematism at of the Pure Conceptions
of the Understanding。
In all subsumptions of an object under a conception; the
representation of the object must be homogeneous with the
conception; in other words; the conception must contain that which
is represented in the object to be subsumed under it。 For this is
the meaning of the expression: 〃An object is contained under a
conception。〃 Thus the empirical conception of a plate is homogeneous
with the pure geometrical conception of a circle; inasmuch as the
roundness which is cogitated in the former is intuited in the latter。
But pure conceptions of the understanding; when compared with
empirical intuitions; or even with sensuous intuitions in general; are
quite heterogeneous; and never can be discovered in any intuition。 How
then is the subsumption of the latter under the former; and
consequently the application of the categories to phenomena;
possible?… For it is impossible to say; for example: 〃Causality can be
intuited through the senses and is contained in the phenomenon。〃… This
natural and important question forms the real cause of the necessity
of a transcendental doctrine of the faculty of judgement; with the
purpose; to wit; of showing how pure conceptions of the
understanding can be applied to phenomena。 In all other sciences;
where the conceptions by which the object is thought in the general
are not so different and heterogeneous from those which represent
the object in concreto… as it is given; it is quite unnecessary to
institute any special inquiries concerning the application of the
former to the latter。
Now it is quite clear that there must be some third thing; which
on the one side is homogeneous with the category; and with the
phenomenon on the other; and so makes the application of the former to
the latter possible。 This mediating representation must be pure
(without any empirical content); and yet must on the one side be
intellectual; on the other sensuous。 Such a representation is the
transcendental schema。
The conception of the understanding contains pure synthetical
unity of the manifold in general。 Time; as the formal condition of the
manifold of the internal sense; consequently of the conjunction of all
representations; contains a priori a manifold in the pure intuition。
Now a transcendental determination of time is so far homogeneous
with the category; which constitutes the unity thereof; that it is
universal and rests upon a rule a priori。 On the other hand; it is
so far homogeneous with the phenomenon; inasmuch as time is
contained in every empirical representation of the manifold。 Thus an
application of the category to phenomena becomes possible; by means of
the transcendental determination of time; which; as the schema of
the conceptions of the understanding; mediates the subsumption of
the latter under the former。
After what has been proved in our deduction of the categories; no
one; it is to be hoped; can hesitate as to the proper decision of
the question; whether the employment of these pure conceptions of
the understanding ought to be merely empirical or also transcendental;
in other words; whether the categories; as conditions of a possible
experience; relate a priori solely to phenomena; or whether; as
conditions of the possibility of things in general; their
application can be extended to objects as things in themselves。 For we
have there seen that conceptions are quite impossible; and utterly
without signification; unless either to them; or at least to the
elements of which they consist; an object be given; and that;
consequently; they cannot possibly apply to objects as things in
themselves without regard to the question whether and how these may be
given to us; and; further; that the only manner in which objects can
be given to us is by means of the modification of our sensibility;
and; finally; that pure a priori conceptions; in addition to the
function of the understanding in the category; must contain a priori
formal conditions of sensibility (of the internal sense; namely);
which again contain the general condition under which alone the
category can be applied to any object。 This formal and pure
condition of sensibility; to which the conception of the understanding
is restricted in its employment; we shall name the schema of the
conception of the understanding; and the procedure of the
understanding with these schemata we shall call the schematism of
the pure understanding。
The schema is; in itself; always a mere product of the
imagination。 But; as the synthesis of imagination has for its aim no
single intuition; but merely unity in the determination of
sensibility; the schema is clearly distinguishable from the image。
Thus; if I place five points one after another。。。。 this is an image of
the number five。 On the other hand; if I only think a number in
general; which may be either five or a hundred; this thought is rather
the representation of a method of representing in an image a sum
(e。g。; a thousand) in conformity with a conception; than the image
itself; an image which I should find some little difficulty in
reviewing; and comparing with the conception。 Now this
representation of a general procedure of the imagination to present
its image to a conception; I call the schema of this conception。
In truth; it is not images of objects; but schemata; which lie at
the foundation of our pure sensuous conceptions。 No image could ever
be adequate to our conception of a triangle in general。 For the
generalness of the conception it never could attain to; as this
includes under itself all triangles; whether right…angled;
acute…angled; etc。; whilst the image would always be limited to a
single part of this sphere。 The schema of the triangle can exist
nowhere else than in thought; and it indicates a rule of the synthesis
of the imagination in regard to pure figures in space。 Still less is
an object of experience; or an image of the object; ever to the
empirical conception。 On the contrary; the conception always relates
immediately to the schema of the imagination; as a rule for the
determination of our intuition; in conformity with a certain general
conception。 The conception of a dog indicates a rule; according to
which my imagination can delineate the figure of a four…footed
animal in general; without being limited to any particular
individual form which experience presents to me; or indeed to any
possible image that I can represent to myself in concreto。 This
schematism of our understanding in regard to phenomena and their
mere form; is an art; hidden in the depths of the human soul; whose
true modes of action we shall only with difficulty discover and
unveil。 Thus much only can we say: 〃The image is a product of the
empirical faculty of the