Critique of Pure Reason (Analytic of Principles

Immanuel Kant's
Critique
trans. by Norman Kemp Smith
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TRANSCENDENTAL ANALYTIC
BOOK II
THE ANALYTIC OF PRINCIPLES
GENERAL logic is constructed upon a ground plan which
exactly coincides with the division of the higher faculties of
knowledge. These are: understanding,judgment, and reason.
In accordance with the functions and order of these mental
powers, which in current speech are comprehended under the
general title of understanding, logic in its analytic deals with
concepts, judgments, and inferences.
 Since this merely formal logic abstracts from all content
of knowledge, whether pure or empirical, and deals solely with
the form of thought in general (that is, of discursive 
knowledge), it can comprehend the canon of reason in its analytic
portion. For the form of reason possesses its established rules,
which can be discovered a priori, simply by analysing the
actions of reason into their components, without our requiring
to take account of the special nature of the knowledge
involved.
As transcendental logic is limited to a certain determinate
content, namely, to the content of those modes of knowledge
which are pure and a priori, it cannot follow general logic in
this division. For the transcendental employment of reason is
not, it would seem, objectively valid, and consequently does
not belong to the logic of truth, i.e. to the Analytic. As a
logic of illusion, it calls for separate location in the scholastic
edifice, under the title of Transcendental Dialectic.
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Understanding and judgment find, therefore, in transcendental
logic their canon of objectively valid and correct
employment; they belong to its analytic portion. Reason, on
the other hand, in its endeavours to determine something a -
priori in regard to objects and so to extend knowledge beyond
the limits of possible experience, is altogether dialectical. Its
illusory assertions cannot find place in a canon such as the
analytic is intended to contain.
The Analytic of Principles will therefore be a canon solely
for judgment, instructing it how to apply to appearances the
concepts of understanding, which contain the condition for
a priori rules. For this reason, while adopting as my theme
the principles of the understanding, strictly so called, I shall
employ the title doctrine of judgment as more accurately 
indicating the nature of our task.
INTRODUCTION
TRANSCENDENTAL JUDGMENT IN GENERAL
If understanding in general is to be viewed as the faculty of
rules, judgment will be the faculty of subsuming under rules;
that is, of distinguishing whether something does or does not
stand under a given rule (casus datae legis). General logic 
contains, and can contain, no rules for judgment. For since general
logic abstracts from all content of knowledge, the sole task that
remains to it is to give an analytical exposition of the form of
knowledge [as expressed] in concepts, in judgments, and in
inferences, and so to obtain formal rules for all employment of
understanding. If it sought to give general instructions how we
are to subsume under these rules, that is, to distinguish whether
something does or does not come under them, that could only
be by means of another rule. This in turn, for the very reason
that it is a rule, again demands guidance from judgment.
And thus it appears that, though understanding is capable of
being instructed, and of being equipped with rules, judgment
is a peculiar talent which can be practised only, and cannot
be taught. It is the specific quality of so-called mother-wit;
and its lack no school can make good. For although an
abundance of rules borrowed from the insight of others may
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indeed be proffered to, and as it were grafted upon, a limited
understanding, the power of rightly employing them must
belong to the learner himself; and in the absence of such a
natural gift no rule that may be prescribed to him for this 
purpose can ensure against misuse. A physician, a judge, or a
ruler may have at command many excellent pathological,
legal, or political rules, even to the degree that he may become
a profound teacher of them, and yet, none the less, may easily
stumble in their application. For, although admirable in
understanding, he may be wanting in natural power of judgment.
He may comprehend the universal in abstracto, and yet
not be able to distinguish whether a case in concreto comes
under it. Or the error may be due to his not having received,
through examples and actual practice, adequate training for
this particular act of judgment. Such sharpening of the judgment
is indeed the one great benefit of examples. Correctness
and precision of intellectual insight, on the other hand, they
more usually somewhat impair. For only very seldom do they
adequately fulfil the requirements of the rule (as casus in 
terminis). Besides, they often weaken that effort which is 
required of the understanding to comprehend properly the rules
in their universality, in independence of the particular 
circumstances of experience, and so accustom us to use rules rather
as formulas than as principles. Examples are thus the go-cart
of judgment; and those who are lacking in the natural talent
can never dispense with them.
 But although general logic can supply no rules for judgment,
the situation is entirely different in transcendental logic.
The latter would seem to have as its peculiar task the correcting
and securing of judgment, by means of determinate rules, in
the use of the pure understanding.
++ Deficiency in judgment is just what is ordinarily called stupidity,
and for such a failing there is no remedy. An obtuse or narrowminded
person to whom nothing is wanting save a proper degree of
understanding and the concepts appropriate thereto, may indeed be
trained through study, even to the extent of becoming learned. But
as such people are commonly still lacking in judgment (secunda
Petri), it is not unusual to meet learned men who in the application
of their scientific knowledge betray that original want, which can
never be made good.
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For as a doctrine, that is,
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as an attempt to enlarge the sphere of the understanding in
the field of pure a priori knowledge, philosophy is by no means
necessary, and is indeed ill-suited for any such purpose, since
in all attempts hitherto made, little or no ground has been won.
On the other hand, if what is designed be a critique to guard
against errors of judgment (lapsus judicii) in the employment
of the few pure concepts of understanding that we possess,
the task, merely negative as its advantages must then be, is
one to which philosophy is called upon to devote all its 
resources of acuteness and penetration.
Transcendental philosophy has the peculiarity that besides
the rule (or rather the universal condition of rules), which is
given in the pure concept of understanding, it can also specify
a priori the instance to which the rule is to be applied. The
advantage which in this respect it possesses over all other
didactical sciences, with the exception of mathematics, is due
to the fact that it deals with concepts which have to relate to
objects a priori, and the objective validity of which cannot
therefore be demonstrated a posteriori, since that would mean
the complete ignoring of their peculiar dignity. It must
formulate by means of universal but sufficient marks the 
conditions under which objects can be given in harmony with
these concepts. Otherwise the concepts would be void of all
content, and therefore mere logical forms, not pure concepts
of the understanding.
This transcendental doctrine of judgment will consist of
two chapters. The first will treat of the sensible condition under
which alone pure concepts of understanding can be employed,
that is, of the schematism of pure understanding. The second
will deal with the synthetic judgments which under these 
conditions follow a priori from pure concepts of understanding,
and which lie a priori at the foundation of all other modes of
knowledge -- that is, with the principles of pure understanding.
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TRANSCENDENTAL DOCTRINE OF JUDGMENT
(OR ANALYTIC OF PRINCIPLES)
CHAPTER I
THE SCHEMATISM OF THE PURE CONCEPTS OF
UNDERSTANDING
In all subsumptions of an object under a concept the 
representation of the object must be homogeneous with the concept;
in other words, the concept must contain something which is
represented in the object that is to be subsumed under it.
This, in fact, is what is meant by the expression, 'an object is
contained under a concept'. Thus the empirical concept of a
plate is homogeneous with the pure geometrical concept of a
circle. The roundness which is thought in the latter can be
intuited in the former.
But pure concepts of understanding being quite heterogeneous
from empirical intuitions, and indeed from all
sensible intuitions, can never be met with in any intuition.
For no one will say that a category, such as that of causality,
can be intuited through sense and is itself contained in 
appearance. How, then, is the subsumption of intuitions under pure
concepts, the application of a category to appearances, possible?
A transcendental doctrine of judgment is necessary just
because of this natural and important question. We must be
able to show how pure concepts can be applicable to appearances.
In none of the other sciences is this necessary. For since
in these sciences the concepts through which the object is
thought in [its] general [aspects] are not so utterly distinct
and heterogeneous from those which represent it in concreto,
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as given, no special discussion of the applicability of the
former to the latter is required.
Obviously there must be some third thing, which is homogeneous
on the one hand with the category, and on the other
hand with the appearance, and which thus makes the application
of the former to the latter possible. This mediating
representation must be pure, that is, void of all empirical
content, and yet at the same time, while it must in one
respect be intellectual, it must in another be sensible. Such a
representation is the transcendental schema.
The concept of understanding contains pure synthetic
unity of the manifold in general. Time, as the formal 
condition of the manifold of inner sense, and therefore of the
connection of all representations, contains an a priori manifold
in pure intuition. Now a transcendental determination of
time is so far homogeneous with the category, which constitutes
its unity, in that it is universal and rests upon an
a priori rule. But, on the other hand, it is so far homogeneous
with appearance, in that time is contained in every empirical
representation of the manifold. Thus an application of the
category to appearances becomes possible by means of the
transcendental determination of time, which, as the schema
of the concepts of understanding, mediates the subsumption
of the appearances under the category.
After what has been proved in the deduction of the categories,
no one, I trust, will remain undecided in regard to
the question whether these pure concepts of understanding
are of merely empirical or also of transcendental employment;
that is, whether as conditions of a possible experience
they relate a priori solely to appearances, or whether, as
conditions of the possibility of things in general, they can be
extended to objects in themselves, without any restriction
to our sensibility. For we have seen that concepts are 
altogether impossible, and can have no meaning, if no object
is given for them, or at least for the elements of which they
are composed. They cannot, therefore, be viewed as applicable
to things in themselves, independent of all question
as to whether and how these may be given to us. We
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have also proved that the only manner in which objects
can be given to us is by modification of our sensibility; and
finally, that pure a priori concepts, in addition to the function
of understanding expressed in the category, must contain
a priori certain formal conditions of sensibility, namely, those
of inner sense. These conditions of sensibility constitute the
universal condition under which alone the category can be
applied to any object. This formal and pure condition of
sensibility to which the employment of the concept of 
understanding is restricted, we shall entitle the schema of the
concept. The procedure of understanding in these schemata
we shall entitle the schematism of pure understanding.
The schema is in itself always a product of imagination.
Since, however, the synthesis of imagination aims at no
special intuition, but only at unity in the determination of
sensibility, the schema has to be distinguished from the image.
If five points be set alongside one another, thus, . . . . . , I
have an image of the number five. But if, on the other hand,
I think only a number in general, whether it be five or a
hundred, this thought is rather the representation of a method
whereby a multiplicity, for instance a thousand, may be 
represented in an image in conformity with a certain concept,
than the image itself. For with such a number as a thousand
the image can hardly be surveyed and compared with the
concept. This representation of a universal procedure of
imagination in providing an image for a concept, I entitle the
schema of this concept.
Indeed it is schemata, not images of objects, which underlie
our pure sensible concepts. No image could ever be adequate
to the concept of a triangle in general. It would never attain
that universality of the concept which renders it valid of all
triangles, whether right-angled, obtuse-angled, or acute-
angled; it would always be limited to a part only of this
sphere. The schema of the triangle can exist nowhere but in
thought. It is a rule of synthesis of the imagination, in respect
to pure figures in space. Still less is an object of experience or
its image ever adequate to the empirical concept; for this latter
always stands in immediate relation to the schema of imagination,
as a rule for the determination of our intuition, in accordance
with some specific universal concept. The concept 'dog'
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signifies a rule according to which my imagination can
delineate the figure of a four-footed animal in a general
manner, without limitation to any single determinate figure
such as experience, or any possible image that I can represent
in concreto, actually presents. This schematism of our
understanding, in its application to appearances and their
mere form, is an art concealed in the depths of the human
soul, whose real modes of activity nature is hardly likely ever
to allow us to discover, and to have open to our gaze. This
much only we can assert: the image is a product of the
empirical faculty of reproductive imagination; the schema of
sensible concepts, such as of figures in space, is a product and,
as it were, a monogram, of pure a priori imagination, through
which, and in accordance with which, images themselves first
become possible. These images can be connected with the
concept only by means of the schema to which they belong.
In themselves they are never completely congruent with the
concept. On the other hand, the schema of a pure concept of
understanding can never be brought into any image whatsoever.
It is simply the pure synthesis, determined by a rule of
that unity, in accordance with concepts, to which the category
gives expression. It is a transcendental product of imagination,
a product which concerns the determination of inner
sense in general according to conditions of its form (time), in
respect of all representations, so far as these representations
are to be connected a priori in one concept in conformity with
the unity of apperception.
That we may not be further delayed by a dry and tedious
analysis of the conditions demanded by transcendental
schemata of the pure concepts of understanding in general,
we shall now expound them according to the order of the
categories and in connection with them.
The pure image of all magnitudes (quantorum) for outer
sense is space; that of all objects of the senses in general is
time. But the pure schema of magnitude (quantitatis), as a
concept of the understanding, is number, a representation
which comprises the successive addition of homogeneous
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units. Number is therefore simply the unity of the synthesis
of the manifold of a homogeneous intuition in general, a unity
due to my generating time itself in the apprehension of the
intuition.
Reality, in the pure concept of understanding, is that
which corresponds to a sensation in general; it is that, therefore,
the concept of which in itself points to being (in time).
Negation is that the concept of which represents not-being
(in time). The opposition of these two thus rests upon the
distinction of one and the same time as filled and as empty.
Since time is merely the form of intuition, and so of objects
as appearances, that in the objects which corresponds to
sensation is not the transcendental matter of all objects as
things in themselves (thinghood, reality). Now every sensation
has a degree or magnitude whereby, in respect of its
representation of an object otherwise remaining the same,
it can fill out one and the same time, that is, occupy inner
sense more or less completely, down to its cessation in
nothingness (= 0 = 1negatio). There therefore exists a relation
and connection between reality and negation, or rather a
transition from the one to the other, which makes every reality
representable as a quantum. The schema of a reality, as the
quantity of something in so far as it fills time, is just this 
continuous and uniform production of that reality in time as we
successively descend from a sensation which has a certain
degree to its vanishing point, or progressively ascend from
its negation to some magnitude of it.
The schema of substance is permanence of the real in time,
that is, the representation of the real as a substrate of empirical
determination of time in general, and so as abiding while all
else changes. (The existence of what is transitory passes away
in time but not time itself. To time, itself non-transitory and
abiding, there corresponds in the [field of] appearance what
is non-transitory in its existence, that is, substance. Only in
[relation to] substance can the succession and coexistence of
appearances be determined in time. )
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The schema of cause, and of the causality of a thing in
general, is the real upon which, whenever posited, something
else always follows. It consists, therefore, in the succession
of the manifold, in so far as that succession is subject to a
rule.
The schema of community or reciprocity, the reciprocal
causality of substances in respect of their accidents, is the 
coexistence, according to a universal rule, of the determinations
of the one substance with those of the other.
The schema of possibility is the agreement of the synthesis
of different representations with the conditions of time in
general. Opposites, for instance, cannot exist in the same thing
at the same time, but only the one after the other. The schema
is therefore the determination of the representation of a thing
at some time or other.
The schema of actuality is existence in some determinate
time.
The schema of necessity is existence of an object at all
times.
We thus find that the schema of each category contains and
makes capable of representation only a determination of time.
The schema of magnitude is the generation (synthesis) of
time itself in the successive apprehension of an object. The
schema of quality is the synthesis of sensation or perception
with the representation of time; it is the filling of time. The
schema of relation is the connecting of perceptions with one
another at all times according to a rule of time-determination.
Finally the schema of modality and of its categories is time
itself as the correlate of the determination whether and how
an object belongs to time. The schemata are thus nothing
but a priori determinations of time in accordance with rules.
These rules relate in the order of the categories to the time-
series, the time-content, the time-order, and lastly to the scope
of time in respect of all possible objects.
It is evident, therefore, that what the schematism of 
understanding effects by means of the transcendental synthesis of
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imagination is simply the unity of all the manifold of intuition
in inner sense, and so indirectly the unity of apperception which
as a function corresponds to the receptivity of inner sense.
The schemata of the pure concepts of understanding are thus
the true and sole conditions under which these concepts obtain
relation to objects and so possess significance. In the end,
therefore, the categories have no other possible employment
than the empirical. As the grounds of an a priori necessary
unity that has its source in the necessary combination of all
consciousness in one original apperception, they serve only to
subordinate appearances to universal rules of synthesis, and
thus to fit them for thoroughgoing connection in one 
experience. 
 All our knowledge falls within the bounds of possible experience,
and just in this universal relation to possible experience
consists that transcendental truth which precedes all
empirical truth and makes it possible.
But it is also evident that although the schemata of sensibility
first realise the categories, they at the same time restrict
them, that is, limit them to conditions which lie outside the
understanding, and are due to sensibility. The schema is, 
properly, only the phenomenon, or sensible concept, of an object
in agreement with the category. (Numerus est quantitas phaenomenon,
sensatio realitas phaenomenon, constans et perdurabile
rerum substantia phaenomenon, aeternitas necessitas phaenomenon,
etc. ) If we omit a restricting condition, we would seem
to extend the scope of the concept that was previously limited.
Arguing from this assumed fact, we conclude that the categories
in their pure significance, apart from all conditions of
sensibility, ought to apply to things in general, as they are,
and not, like the schemata, represent them only as they appear.
They ought, we conclude, to possess a meaning independent
of all schemata, and of much wider application. Now there
certainly does remain in the pure concepts of understanding,
even after elimination of every sensible condition, a meaning;
but it is purely logical, signifying only the bare unity of the
representations. The pure concepts can find no object, and so
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can acquire no meaning which might yield a concept of some
object. Substance, for instance, when the sensible determination
of permanence is omitted, would mean simply a something
which can be thought only as subject, never as a predicate of
something else. Such a representation I can put to no use, for
it tells me nothing as to the nature of that which is thus to
be viewed as a primary subject. The categories, therefore,
without schemata, are merely functions of the understanding
for concepts; and represent no object. This [objective] meaning
they acquire from sensibility, which realises the 
understanding in the very process of restricting it.