SS 23. Result of this Deduction of the Conceptions of the
Understanding
We cannot think any object except by means of the categories; we cannot
Cognize any thought except by means of intuitions corresponding to these
Conceptions. Now all our intuitions are sensuous, and our cognition
In so far as the object of it is given, is empirical. But empirical
Cognition is experience; consequently no a priori cognition is possible
For us, except of objects of possible experience
But this cognition, which is limited to objects of experience, is not
For that reason derived entirely, from, experience, but--and this
Is a**erted of the pure intuitions and the pure conceptions of the
Understanding--there are, unquestionably, elements of cognition, which
Exist in the mind a priori. Now there are only two ways in which a
Necessary harmony of experience with the conceptions of its objects can
Be cogitated. Either experience makes these conceptions possible, or
The conceptions make experience possible. The former of these statements
Will not bold good with respect to the categories (nor in regard to pure
Sensuous intuition), for they are a priori conceptions, and therefore
Independent of experience. The a**ertion of an empirical origin would
Attribute to them a sort of generatio aequivoca. Consequently, nothing
Remains but to adopt the second alternative (which presents us with a
System, as it were, of the epigenesis of pure reason), namely, that on
The part of the understanding the categories do contain the grounds of
The possibility of all experience. But with respect to the questions
How they make experience possible, and what are the principles of the
Possibility thereof with which they present us in their application to
Phenomena, the following section on the transcendental exercise of the
Faculty of judgement will inform the reader
It is quite possible that someone may propose a species of
Preformation-system of pure reason--a middle way between the two--to
Wit, that the categories are neither innate and first a priori
Principles of cognition, nor derived from experience, but are merely
Subjective aptitudes for thought implanted in us contemporaneously with
Our existence, which were so ordered and disposed by our Creator
That their exercise perfectly harmonizes with the laws of nature which
Regulate experience. Now, not to mention that with such an hypothesis
It is impossible to say at what point we must stop in the employment of
Predetermined aptitudes, the fact that the categories would in this case
Entirely lose that character of necessity which is essentially involved
In the very conception of them, is a conclusive objection to it. The
Conception of cause, for example, which expresses the necessity of an
Effect under a presupposed condition, would be false, if it rested only
Upon such an arbitrary subjective necessity of uniting certain empirical
Representations according to such a rule of relation. I could not then
Say--"The effect is connected with its cause in the object (that is
Necessarily)," but only, "I am so constituted that I can think this
Representation as so connected, and not otherwise." Now this is just
What the sceptic wants. For in this case, all our knowledge, depending
On the supposed objective validity of our judgement, is nothing but
Mere illusion; nor would there be wanting people who would deny any such
Subjective necessity in respect to themselves, though they must feel it
At all events, we could not dispute with any one on that which merely
Depends on the manner in which his subject is organized
Short view of the above Deduction
The foregoing deduction is an exposition of the pure conceptions of the
Understanding (and with them of all theoretical a priori cognition), as
Principles of the possibility of experience, but of experience as
The determination of all phenomena in space and time in general--of
Experience, finally, from the principle of the original synthetical
Unity of apperception, as the form of the understanding in relation to
Time and space as original forms of sensibility
I consider the division by paragraphs to be necessary only up to this
Point, because we had to treat of the elementary conceptions. As we
Now proceed to the exposition of the employment of these, I shall not
Designate the chapters in this manner any further
BOOK II
an*lytic of Principles
General logic is constructed upon a plan which coincides exactly
With the division of the higher faculties of cognition. These are
Understanding, judgement, and reason. This science, accordingly, treats
In its an*lytic of conceptions, judgements, and conclusions in exact
Correspondence with the functions and order of those mental powers which
We include generally under the generic denomination of understanding
As this merely formal logic makes abstraction of all content of
Cognition, whether pure or empirical, and occupies itself with the mere
Form of thought (discursive cognition), it must contain in its an*lytic
A canon for reason. For the form of reason has its law, which, without
Taking into consideration the particular nature of the cognition about
Which it is employed, can be discovered a priori, by the simple an*lysis
Of the action of reason into its momenta
Transcendental logic, limited as it is to a determinate content, that of
Pure a priori cognitions, to wit, cannot imitate general logic in this
Division. For it is evident that the transcendental employment of reason
Is not objectively valid, and therefore does not belong to the logic
Of truth (that is, to an*lytic), but as a logic of illusion, occupies
A particular department in the scholastic system under the name of
Transcendental dialectic
Understanding and judgement accordingly possess in transcendental logic
A canon of objectively valid, and therefore true exercise, and are
Comprehended in the an*lytical department of that logic. But reason
In her endeavours to arrive by a priori means at some true statement
Concerning objects and to extend cognition beyond the bounds of possible
Experience, is altogether dialectic, and her illusory a**ertions cannot
Be constructed into a canon such as an an*lytic ought to contain
Accordingly, the an*lytic of principles will be merely a canon for
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 an*lytically
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 has 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
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, an*lYTIC 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 h*mogeneous 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 h*mogeneous 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 h*mogeneous 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 h*mogeneous 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 h*mogeneous
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 conjoined a
Priori in one conception, conformably to the unity of apperception
Without entering upon a dry and tedious an*lysis of the essential
Requisites of transcendental schemata of the pure conceptions of the
Understanding, we shall rather proceed at once to give an explanation
Of them according to the order of the categories, and in connection
Therewith
For the external sense the pure image of all quantities (quantorum) is
Space; the pure image of all objects of sense in general, is time
But the pure schema of quantity (quantitatis) as a conception of
The understanding, is number, a representation which comprehends the
Successive addition of one to one (h*mogeneous quantities). Thus, number
Is nothing else than the unity of the synthesis of the manifold in
A h*mogeneous intuition, by means of my generating time itself in my
Apprehension of the intuition
Reality, in the pure conception of the understanding, is that which
Corresponds to a sensation in general; that, consequently, the
Conception of which indicates a being (in time). Negation is that the
Conception of which represents a not-being (in time). The opposition of
These two consists therefore in the difference of one and the same
Time, as a time filled or a time empty. Now as time is only the form of
Intuition, consequently of objects as phenomena, that which in objects
Corresponds to sensation is the transcendental matter of all objects
As things in themselves (Sachheit, reality). Now every sensation has
A degree or quantity by which it can fill time, that is to say, the
Internal sense in respect of the representation of an object, more or
Less, until it vanishes into nothing (= 0 = negatio). Thus there is
A relation and connection between reality and negation, or rather a
Transition from the former to the latter, which makes every reality
Representable to us as a quantum; and the schema of a reality as the
Quantity of something in so far as it fills time, is exactly this
Continuous and uniform generation of the reality in time, as we descend
In time from the sensation which has a certain degree, down to the
Vanishing thereof, or gradually ascend from negation to the quantity
Thereof
The schema of substance is the permanence of the real in time; that is
The representation of it as a substratum of the empirical determination
Of time; a substratum which therefore remains, whilst all else changes
(Time pa**es not, but in it pa**es the existence of the changeable. To
Time, therefore, which is itself unchangeable and permanent, corresponds
That which in the phenomenon is unchangeable in existence, that is
Substance, and it is only by it that the succession and coexistence of
Phenomena can be determined in regard to time.)
The schema of cause and of the causality of a thing is the real which
When posited, is always followed by something else. It consists
Therefore, in the succession of the manifold, in so far as that
Succession is subjected to a rule
The schema of community (reciprocity of action and reaction), or the
Reciprocal causality of substances in respect of their accidents, is the
Coexistence of the determinations of the one with those of the other
According to a general rule
The schema of possibility is the accordance of the synthesis of
Different representations with the conditions of time in general (as
For example, opposites cannot exist together at the same time in
The same thing, but only after each other), and is therefore the
Determination of the representation of a thing at any time
The schema of reality is existence in a determined time
The schema of necessity is the existence of an object in all time
It is clear, from all this, that the schema of the category of quantity
Contains and represents the generation (synthesis) of time itself, in
The successive apprehension of an object; the schema of quality the
Synthesis of sensation with the representation of time, or the filling
Up of time; the schema of relation the relation of perceptions to each
Other in all time (that is, according to a rule of the determination
Of time): and finally, the schema of modality and its categories, time
Itself, as the correlative of the determination of an object--whether it
Does belong to time, and how. The schemata, therefore, are nothing but
A priori determinations of time according to rules, and these, in regard
To all possible objects, following the arrangement of the categories
Relate to the series in time, the content in time, the order in time
And finally, to the complex or totality in time
Hence it is apparent that the schematism of the understanding, by means
Of the transcendental synthesis of the imagination, amounts to nothing
Else than the unity of the manifold of intuition in the internal
Sense, and thus indirectly to the unity of apperception, as a function
Corresponding to the internal sense (a receptivity). Thus, the schemata
Of the pure conceptions of the understanding are the true and only
Conditions whereby our understanding receives an application to objects
And consequently significance. Finally, therefore, the categories are
Only capable of empirical use, inasmuch as they serve merely to subject
Phenomena to the universal rules of synthesis, by means of an a priori
Necessary unity (on account of the necessary union of all consciousness
In one original apperception); and so to render them susceptible of a
Complete connection in one experience. But within this whole of possible
Experience lie all our cognitions, and in the universal relation to this
Experience consists transcendental truth, which antecedes all empirical
Truth, and renders the latter possible
It is, however, evident at first sight, that although the schemata of
Sensibility are the sole agents in realizing the categories, they do
Nevertheless, also restrict them, that is, they limit the categories
By conditions which lie beyond the sphere of understanding--namely, in
Sensibility. Hence the schema is properly only the phenomenon, or the
Sensuous conception of an object in harmony with the category. (Numerus
Est quantitas phaenomenon--sensatio realitas phaenomenon; constans
Et perdurabile rerum substantia phaenomenon--aeternitas, necessitas
Phaenomena, etc.) Now, if we remove a restrictive condition, we thereby
Amplify, it appears, the formerly limited conception. In this way, the
Categories in their pure signification, free from all conditions of
Sensibility, ought to be valid of things as they are, and not, as the
Schemata represent them, merely as they appear; and consequently the
Categories must have a significance far more extended, and wholly
Independent of all schemata. In truth, there does always remain to the
Pure conceptions of the understanding, after abstracting every sensuous
Condition, a value and significance, which is, however, merely logical
But in this case, no object is given them, and therefore they have no
Meaning sufficient to afford us a conception of an object. The notion
Of substance, for example, if we leave out the sensuous determination
Of permanence, would mean nothing more than a something which can be
Cogitated as subject, without the possibility of becoming a predicate to
Anything else. Of this representation I can make nothing, inasmuch as
It does not indicate to me what determinations the thing possesses which
Must thus be valid as premier subject. Consequently, the categories
Without schemata are merely functions of the understanding for the
Production of conceptions, but do not represent any object. This
Significance they derive from sensibility, which at the same time
Realizes the understanding and restricts it