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the faculty of judgement, for the instruction of this faculty in its

application to phenomena of the pure conceptions of the understanding,

which contain the necessary condition for the establishment of a

priori laws. On this account, although the subject of the following

chapters is the especial principles of understanding, I shall make use

of the term Doctrine of the faculty of judgement, in order to define

more particularly my present purpose.

INTRODUCTION. Of the Transcendental Faculty of judgement in General.

If understanding in general be defined as the faculty of laws or

rules, the faculty of judgement may be termed the faculty of

subsumption under these rules; that is, of distinguishing whether this

or that does or does not stand under a given rule (casus datae legis).

General logic contains no directions or precepts for the faculty of

judgement, nor can it contain any such. For as it makes abstraction of

all content of cognition, no duty is left for it, except that of

exposing analytically the mere form of cognition in conceptions,

judgements, and conclusions, and of thereby establishing formal

rules for all exercise of the understanding. Now if this logic

wished to give some general direction how we should subsume under

these rules, that is, how we should distinguish whether this or that

did or did not stand under them, this again could not be done

otherwise than by means of a rule. But this rule, precisely because it

is a rule, requires for itself direction from the faculty of

judgement. Thus, it is evident that the understanding is capable of

being instructed by rules, but that the judgement is a peculiar

talent, which does not, and cannot require tuition, but only exercise.

This faculty is therefore the specific quality of the so-called mother

wit, the want of which no scholastic discipline can compensate.

For although education may furnish, and, as it were, engraft upon

a limited understanding rules borrowed from other minds, yet the power

of employing these rules correctly must belong to the pupil himself;

and no rule which we can prescribe to him with this purpose is, in the

absence or deficiency of this gift of nature, secure from misuse.* A

physician therefore, a judge or a statesman, may have in his head many

admirable pathological, juridical, or political rules, in a degree

that may enable him to be a profound teacher in his particular

science, and yet in the application of these rules he may very

possibly blunder- either because he is wanting in natural judgement

(though not in understanding) and, whilst he can comprehend the

general in abstracto, cannot distinguish whether a particular case

in concreto ought to rank under the former; or because his faculty

of judgement bas not been sufficiently exercised by examples and

real practice. Indeed, the grand and only use of examples, is to

sharpen the judgement. For as regards the correctness and precision of

the insight of the understanding, examples are commonly injurious

rather than otherwise, because, as casus in terminis they seldom

adequately fulfil the conditions of the rule. Besides, they often

weaken the power of our understanding to apprehend rules or laws in

their universality, independently of particular circumstances of

experience; and hence, accustom us to employ them more as formulae

than as principles. Examples are thus the go-cart of the judgement,

which he who is naturally deficient in that faculty cannot afford to

dispense with.

*Deficiency in judgement is properly that which is called stupidity;

and for such a failing we know no remedy. A dull or narrow-minded

person, to whom nothing is wanting but a proper degree of

understanding, may be improved by tuition, even so far as to deserve

the epithet of learned. But as such persons frequently labour under

a deficiency in the faculty of judgement, it is not uncommon to find

men extremely learned who in the application of their science betray a

lamentable degree this irremediable want.

But although general logic cannot give directions to the faculty

of judgement, the case is very different as regards transcendental

logic, insomuch that it appears to be the especial duty of the

latter to secure and direct, by means of determinate rules, the

faculty of judgement in the employment of the pure understanding. For,

as a doctrine, that is, as an endeavour to enlarge the sphere of the

understanding in regard to pure a priori cognitions, philosophy is

worse than useless, since from all the attempts hitherto made,

little or no ground has been gained. But, as a critique, in order to

guard against the mistakes of the faculty of judgement (lapsus

judicii) in the employment of the few pure conceptions of the

understanding which we possess, although its use is in this case

purely negative, philosophy is called upon to apply all its

acuteness and penetration.

But transcendental philosophy has this peculiarity, that besides

indicating the rule, or rather the general condition for rules,

which is given in the pure conception of the understanding, it can, at

the same time, indicate a priori the case to which the rule must be

applied. The cause of the superiority which, in this respect,

transcendental philosophy possesses above all other sciences except

mathematics, lies in this: it treats of conceptions which must

relate a priori to their objects, whose objective validity

consequently cannot be demonstrated a posteriori, and is, at the

same time, under the obligation of presenting in general but

sufficient tests, the conditions under which objects can be given in

harmony with those conceptions; otherwise they would be mere logical

forms, without content, and not pure conceptions of the understanding.

Our transcendental doctrine of the faculty of judgement will contain

two chapters. The first will treat of the sensuous condition under

which alone pure conceptions of the understanding can be employed-

that is, of the schematism of the pure understanding. The second

will treat of those synthetical judgements which are derived a

priori from pure conceptions of the understanding under those

conditions, and which lie a priori at the foundation of all other

cognitions, that is to say, it will treat of the principles of the

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 productive imagination- the schema of

sensuous conceptions (of figures in space, for example) is a

product, and, as it were, a monogram of the pure imagination a priori,

whereby and according to which images first become possible, which,

however, can be connected with the conception only mediately by

means of the schema which they indicate, and are in themselves never

fully adequate to it." On the other hand, the schema of a pure

conception of the understanding is something that cannot be reduced

into any image- it is nothing else than the pure synthesis expressed

by the category, conformably, to a rule of unity according to

conceptions. It is a transcendental product of the imagination, a

product which concerns the determination of the internal sense,

according to conditions of its form (time) in respect to all

representations, in so far as these representations must be