5 It has hardly struck any psychologist that this imagination is a necessary ingredient of perception. This was partly owing to their confining this faculty to reproduction, partly to our belief that the senses do not only give us impressions, but compound them also for us, thus producing pictures of objects. This, however, beyond our receptivity of impressions, requires something more, namely, a function for their synthesis.
6 Of may be omitted, if we read aller empirischer Gebrauch.
understanding to our sensibility, and through it to all objects of experience, that is the objective validity of the pure concepts a priori of the understanding, conceivable, and thus to establish their origin and their truth.
7 That is, out of one, or out of the unity of apperception.
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Transcendental Analytic
Book II
Analytic of Principles
General logic is built up on a plan that coincides accurately with the division of the higher faculties of knowledge. These are, Understanding, Judgment, and Reason. Logic therefore treats in its analytical portion of concepts, judgments, and syllogisms corresponding with the functions and the order of the above-named faculties of the mind, which are generally comprehended under the vague name of the understanding.
As formal logic takes no account of the contents of our knowledge (pure or empirical), but treats of the form of thought only (discursive knowledge), it may well contain in its analytical portion the canon of reason also, reason being, according to its form, subject to definite rules which, without reference to the particular nature of the knowledge to which they are applied, can be found out a priori by a mere analysis of the acts of reasoning into their component parts.
Transcendental logic, being limited to a certain content, namely, to pure knowledge a priori, cannot follow general logic in this division; for it is clear that the transcendental use of reason cannot be objectively valid, and cannot therefore belong to the logic of truth, that is, to Analytic, but must be allowed to form a separate part of our scholastic system, as a logic of illusion, under the name of transcendental Dialectic.
Understanding and judgment have therefore a canon of their objectively valid, and therefore true use in transcendental logic, and belong to its analytical portion. But reason, in its attempts to determine anything a priori with reference to objects, and to extend knowledge beyond the limits of possible experience, is altogether dialectical, and its illusory assertions have no place in a canon such as Analytic demands.
Our Analytic of principles therefore will be merely a canon of the faculty of judgment, teaching it how to apply to phenomena the concepts of the understanding, which contain the condition of rules a priori. For this reason, and in order to indicate my purpose more clearly, I shall use the name of doctrine of the faculty of judgment, while treating of the real principles of the understanding.
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Introduction
Of the Transcendental Faculty of Judgment in General
If the understanding is explained as the faculty of rules, the faculty of judgment consists in performing the subsumption under these rules, that is, in determining whether anything falls under a given rule (casus datæ legis) or not. General logic contains no precepts for the faculty of judgment and cannot contain them. For as it takes no account of the contents of our knowledge, it has only to explain analytically the mere form of knowledge in concepts, judgments, and syllogisms, and thus to establish formal rules for the proper employment of the understanding. If it were to attempt to show in general how anything should be arranged under these rules, and how we should determine whether something falls under them or not, this could only take place by means of a new rule. This, because it is a new rule, requires a new precept for the faculty of judgment, and we thus learn that, though the understanding is capable of being improved and instructed by means of rules, the faculty of judgment is a special talent which cannot be taught, but must be practised. This is what constitutes our so-called motherwit, the absence of which cannot be remedied by any schooling. For although the teacher may offer, and as it were graft into a narrow understanding, plenty of rules borrowed from the experience of others, the faculty of using them rightly must belong to the pupil himself, and without that talent no precept that may be given is safe from abuse.1 A physician, therefore, a judge, or a politician, may carry in his head many beautiful pathological, juridical, or political rules, nay, he may even become an accurate teacher of them, and he may yet in the application of these rules commit many a blunder, either because he is deficient in judgment, though not in understanding, knowing the general in the abstract, but unable to determine whether a concrete case falls under it; or, it may be, because his judgment has not been sufficiently trained by examples and practical experience. It is the one great advantage of examples that they sharpen the faculty of judgment, but they are apt to impair the accuracy and precision of the understanding, because they fulfil but rarely the conditions of the rule quite adequately (as casus in terminis). Nay, they often weaken the effort of the understanding in comprehending rules according to their general adequacy, and independent of the special circumstances of experience, and accustom us to use those rules in the end as formulas rather than as principles. Examples may thus be called the go-cart of the judgment, which those who are deficient in that natural talent2 can never do without.
But although general logic can give no precepts to the faculty of judgment, the case is quite different with transcendental logic, so that it even seems as if it were the proper business of the latter to correct and to establish by definite rules the faculty of the judgment in the use of the pure understanding. For as a doctrine and a means of enlarging the field of pure knowledge a priori for the benefit of the understanding, philosophy does not seem necessary, but rather hurtful, because, in spite of all attempts that have been hitherto made, hardly a single inch of ground has been gained by it. For critical purposes, however, and in order to guard the faculty of judgment against mistakes (lapsus judicii) in its use of the few pure concepts of the understanding which we possess, philosophy (though its benefits may be negative only) has to employ all the acuteness and penetration at its command.
What distinguishes transcendental philosophy is, that besides giving the rules (or rather the general condition of rules) which are contained in the pure concept of the understanding, it can at the same time indicate a priori the case to which each rule may be applied. The superiority which it enjoys in this respect over all other sciences, except mathematics, is due to this, that it treats of concepts which are meant to refer to their objects a priori, so that their objective validity cannot be proved a posteriori, because this would not affect their own peculiar dignity. It must show, on the contrary, by means of general but sufficient marks, the conditions under which objects can be given corresponding to those concepts; otherwise these would be without any contents, mere logical forms, and not pure concepts of the understanding.
Our transcendental doctrine of the faculty of judgment will consist of two chapters. The first will treat of the sensuous condition under which alone pure concepts of the understanding can be used. This is what I call the schematism of the pure understanding. The second will treat of the synthetical judgments, which can be derived a priori under these conditions from pure concepts of the understanding, and on which all knowledge a priori depends. It will treat, therefore, of the principles of the pure understanding.
1 Deficiency in the faculty of judgment is really what we call stupidity, and there is no remedy for that. An obtuse and narrow mind, deficient in nothing but a proper degree of understanding and correct concepts, may be improved by study, so far as to become even learned. But as even then there is often a deficiency of judgment (secunda Petri) we often meet with very learned men, who in handling their learning betray that original deficiency which can never be mended.
2 Desselben has been changed into derselben in later editions. Desselben,
however, may be meant to refer to Urtheil, as contained in Urtheilskraft. The second edition has desselben.
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The Transcendental Doctrine of the Faculty of Judgment or Analytic of Principles
Chapter I
Of the Schematism of the Pure Concepts of the Understanding
IN comprehending any object under a concept, the representation of the former must be homogeneous with the latter,1 that is, the concept must contain that which is represented in the object to be comprehended under it, for this is the only meaning of the expression that an object is comprehended under a concept. Thus, for instance, the empirical concept of a plate is homogeneous with the pure geometrical concept of a circle, the roundness which is conceived in the first forming an object of intuition in the latter.
Now it is clear that pure concepts of the understanding, as compared with empirical or sensuous impressions in general, are entirely heterogeneous, and can never be met with in any intuition. How then can the latter be comprehended under the former, or how can the categories be applied to phenomena, as no one is likely to say that causality, for instance, could be seen through the senses, and was contained in the phenomenon? It is really this very natural and important question which renders a transcendental doctrine of the faculty of judgment necessary, in order to show how it is possible that any of the pure concepts of the understanding can be applied to phenomena. In all other sciences in which the concepts by which the object is thought in general are not so heterogeneous or different from those which represent it in concreto, and as it is given, there is no necessity to enter into any discussions as to the applicability of the former to the latter.
In our case there must be some third thing homogeneous on the one side with the category, and on the other with the phenomenon, to render the application of the former to the latter possible. This intermediate representation must be pure (free from all that is empirical) and yet intelligible on the one side, and sensuous on the other. Such a representation is the transcendental schema.
The concept of the understanding contains pure synthetical unity of the manifold in general. Time, as the formal condition of the manifold in the internal sense, consequently of the conjunction of all representations, contains a manifold a priori in pure intuition. A transcendental determination of time is so far homogeneous with the category (which constitutes its unity) that it is general and founded on a rule a priori, and it is on the other hand so far homogeneous with the phenomenon, that time must be contained in every empirical representation of the manifold. The application of the category to phenomena becomes possible therefore by means of the transcendental determination of time, which, as a schema of the concepts of the understanding, allows the phenomena to be comprehended under the category.
After what has been said in the deduction of the categories, we hope that nobody will hesitate in answering the question whether these pure concepts of the understanding allow only of an empirical or also of a transcendental application, that is, whether, as conditions of a possible experience, they refer a priori to phenomena only, or whether, as conditions of the possibility of things in general, they may be extended to objects by themselves (without restriction to our sensibility). For there we saw that concepts are quite impossible, and cannot have any meaning unless there be an object given either to them or, at least, to some of the elements of which they consist, and that they can never refer to things by themselves (without regard as to whether and how things may be given to us). We likewise saw that the only way in which objects can be given to us, consists in a modification of our sensibility, and lastly, that pure concepts a priori must contain, besides the function of the understanding in the category itself, formal conditions a priori of sensibility (particularly of the internal sense) which form the general condition under which alone the category may be applied to any object. We shall call this formal and pure condition of sensibility, to which the concept of the understanding is restricted in its application, its schema; and the function of the understanding in these schemata, the schematism of the pure understanding.
The schema by itself is no doubt a product of the imagination only, but as the synthesis of the imagination does not aim at a single intuition, but at some kind of unity alone in the determination of sensibility, the schema ought to be distinguished from the image. Thus, if I place five points, one after the other…., this is an image of the number five. If, on the contrary, I think of a number in general, whether it be five or a hundred, this thinking is rather the representation of a method of representing in one image a certain quantity (for instance a thousand) according to a certain concept, than the image itself, which, in the case of a thousand, I could hardly take in and compare with the concept. This representation of a general procedure of the imagination by which a concept receives its image, I call the schema of such concept.
The fact is that our pure sensuous concepts do not depend on images of objects, but on schemata. No image of a triangle in general could ever be adequate to its concept. It would never attain to that generality of the concept, which makes it applicable to all triangles, whether right-angled, or acute-angled, or anything else, but would always be restricted to one portion only of the sphere of the concept. The schema of the triangle can exist nowhere but in thought, and is in fact a rule for the synthesis of imagination with respect to pure forms in space. Still less does an object of experience or its image ever cover the empirical concept, which always refers directly to the schema of imagination as a rule for the determination of our intuitions, according to a certain general concept. The concept of dog means a rule according to which my imagination can always draw a general outline of the figure of a four-footed animal, without being restricted to any particular figure supplied by experience or to any possible image which I may draw in the concrete. This schematism of our understanding applied to phenomena and their mere form is an art hidden in the depth of the human soul, the true secrets of which we shall hardly ever be able to guess and reveal. So much only we can say, that the image is a product of the empirical faculty of the productive imagination, while the schema of sensuous concepts (such as of figures in space) is a product and so to say a monogram of the pure imagination a priori, through which and according to which images themselves become possible, though they are never fully adequate to the concept, and can be connected with it by means of their schema only. The schema of a pure concept of the understanding, on the contrary, is something which can never be made into an image; for it is nothing but the pure synthesis determined by a rule of unity, according to concepts, a synthesis as expressed by the category, and represents a transcendental product of the imagination, a product which concerns the determination of the internal sense in general, under the conditions of its form (time), with reference to all representations, so far as these are meant to be joined a priori in one concept, according to the unity of apperception.
Without dwelling any longer on a dry and tedious determination of all that is required for the transcendental schemata of the pure concepts of the understanding in general, we shall proceed at once to represent them according to the order of the categories, and in connection with them.
The pure image of all quantities (quanta) before the external sense, is space; that of all objects of the senses in general, time. The pure schema of quantity (quantitas), however, as a concept of the understanding, is number, a representation which comprehends the successive addition of one to one (homogeneous). Number therefore is nothing but the unity of the synthesis of the manifold (repetition) of a homogeneous intuition in general, I myself producing the time in the apprehension of the intuition.
Reality is, in the pure concept of the understanding, that which corresponds to a sensation in general: that, therefore, the concept of which indicates by itself being (in time), while negation is that the concept of which represents not-being (in time). The opposition of the two takes place therefore by a distinction of one and the same time, as either filled
or empty. As time is only the form of intuition, that is, of objects as phenomena, that which in the phenomena corresponds to sensation, constitutes the transcendental matter of all objects, as things by themselves (reality, Sachheit). Every sensation, however, has a degree of quantity by which it can fill the same time (that is, the internal sense, with reference to the same representation of an object), more or less, till it vanishes into nothing (equal to nought or negation). There exists, therefore, a relation and connection, or rather a transition from reality to negation, which makes every reality representable as a quantum; and the schema of a reality, as the quantity of something which fills time, is this very continuous and uniform production of reality in time; while we either descend from the sensation which has a certain degree, to its vanishing in time, or ascend from the negation of sensation to some quantity of it.
The schema of substance is the permanence of the real in time, that is, the representation of it as a substratum for the empirical determination of time in general, which therefore remains while everything else changes. (It is not time that passes, but the existence of the changeable passes in time. What corresponds therefore in the phenomena to time, which in itself is unchangeable and permanent, is the unchangeable in existence, that is, substance; and it is only in it that the succession and the coexistence of phenomena can be determined according to time.)
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