Critique of Pure Reason

(Analytic of Principles)

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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 know-
ledge), 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 requir-
ing to take account of the special nature of the knowledge
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 tran-
scendental 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 in-
dicating the nature of our task. 
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 con-
tains, 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 pur-
pose 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 judg-
ment. 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 judg-
ment 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 ter-
minis). Besides, they often weaken that effort which is re-
quired of the understanding to comprehend properly the rules
in their universality, in independence of the particular circum-
stances 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 judg-
ment, 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 stupid-
ity, and for such a failing there is no remedy. An obtuse or narrow-
minded 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,
P 179
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 re-
sources 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 con-
ditions 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 con-
ditions 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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In all subsumptions of an object under a concept the repre-
sentation 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 hetero-
geneous 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 appear-
ance. How, then, is the subsumption of intuitions under pure
concepts, the application of a category to appearances, pos-
sible? 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 appear-
ances. 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 homo-
geneous on the one hand with the category, and on the other
hand with the appearance, and which thus makes the appli-
cation 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 con-
dition 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 con-
stitutes 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 cate-
gories, 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 employ-
ment; 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 alto-
gether 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 appli-
cable 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 under-
standing 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 re-
presented 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 imagina-
tion, as a rule for the determination of our intuition, in accord-
ance 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 repre-
sent 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 whatso-
ever. 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 imagina-
tion, 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
Reality, in the pure concept of understanding, is that
which corresponds to a sensation in general; it is that, there-
fore, 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 sensa-
tion 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 con-
tinuous 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
The schema of community or reciprocity, the reciprocal
causality of substances in respect of their accidents, is the co-
existence, 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
The schema of necessity is existence of an object at all
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 under-
standing 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 ob-
tain 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 ex-
 All our knowledge falls within the bounds of possible ex-
perience, and just in this universal relation to possible experi-
ence consists that transcendental truth which precedes all
empirical truth and makes it possible. 
But it is also evident that although the schemata of sensi-
bility 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, pro-
perly, only the phenomenon, or sensible concept, of an object
in agreement with the category. (Numerus est quantitas phaeno-
menon, sensatio realitas phaenomenon, constans et perdurabile
rerum substantia phaenomenon, aeternitas necessitas phaeno-
menon, 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 cate-
gories 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 determina-
tion 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] mean-
ing they acquire from sensibility, which realises the under-
standing in the very process of restricting it. 
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In the preceding chapter we have considered transcendental
judgment with reference merely to the universal conditions
under which it is alone justified in employing pure concepts
of understanding for synthetic judgments. Our task now is
to exhibit, in systematic connection, the judgments which
understanding, under this critical provision, actually achieves
a priori. There can be no question that in this enquiry our
table of categories is the natural and the safe guide. For since
it is through the relation of the categories to possible experi-
ence that all pure a priori knowledge of understanding has
to be constituted, their relation to sensibility in general will
exhibit completely and systematically all the transcendental
principles of the use of the understanding. 
Principles a priori are so named not merely because they
contain in themselves grounds of other judgements, but also
because they are not themselves grounded in higher and more
universal modes of knowledge. But this characteristic does not
remove them beyond the sphere of proof. This proof cannot,
indeed, be carried out in any objective fashion, since such
principles [do not rest on objective considerations but] lie at
the foundation of all knowledge of objects. This does not,
however, prevent our attempting a proof, from the subjective
sources of the possibility of knowledge of an object in general. 
Such proof is, indeed, indispensable, if the propositions are not
to incur the suspicion of being merely surreptitious assertions. 
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Secondly, we shall limit ourselves merely to those prin-
ciples which stand in relation to the categories. The principles
of the Transcendental Aesthetic, according to which space and
time are the conditions of the possibility of all things as ap-
pearances, and likewise the restriction of these principles,
namely, that they cannot be applied to things in themselves,
are matters which do not come within the range of our present
enquiry. For similar reasons mathematical principles form
no part of this system. They are derived solely from intuition,
not from the pure concept of understanding. Nevertheless,
since they too are synthetic a priori judgments, their possi-
bility must receive recognition in this chapter. For though
their correctness and apodeictic certainty do not indeed re-
quire to be established, their possibility, as cases of evident
a priori knowledge, has to be rendered conceivable, and to be
We shall also have to treat of the principle of analytic
judgments, in so far as it stands in contrast with that of syn-
thetic judgments with which alone strictly we have to deal. 
For by thus contrasting them we free the theory of synthetic
judgments from all misunderstanding, and have them in their
own peculiar nature clear before us. 
Section 1
The universal, though merely negative, condition of all our
judgments in general, whatever be the content of our know-
ledge, and however it may relate to the object, is that they be
not self-contradictory; for if self-contradictory, these judgments
are in themselves, even without reference to the object, null and
void. But even if our judgment contains no contradiction, it may
connect concepts in a manner not borne out by the object, or
else in a manner for which no ground is given, either a priori
or a posteriori, sufficient to justify such judgment, and so may
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still, in spite of being free from all inner contradiction, be
either false or groundless. 
 The proposition that no predicate contradictory of a thing
can belong to it, is entitled the principle of contradiction, and
is a universal, though merely negative, criterion of all truth. 
For this reason it belongs only to logic. It holds of knowledge,
merely as knowledge in general, irrespective of content; and
asserts that the contradiction completely cancels and in-
validates it. 
But it also allows of a positive employment, not merely,
that is, to dispel falsehood and error (so far as they rest on
contradiction), but also for the knowing of truth. For, if
the judgment is analytic, whether negative or affirmative, its
truth can always be adequately known in accordance with the
principle of contradiction. The reverse of that which as con-
cept is contained and is thought in the knowledge of the object,
is always rightly denied. But since the opposite of the concept
would contradict the object, the concept itself must neces-
sarily be affirmed of it. 
The principle of contradiction must therefore be recognised
as being the universal and completely sufficient principle of
all analytic knowledge; but beyond the sphere of analytic
knowledge it has, as a sufficient criterion of truth, no authority
and no field of application. The fact that no knowledge can
be contrary to it without self-nullification, makes this prin-
ciple a conditio sine qua non, but not a determining ground,
of the truth of our [non-analytic] knowledge. Now in our
critical enquiry it is only with the synthetic portion of our
knowledge that we are concerned; and in regard to the truth
of this kind of knowledge we can never look to the above
principle for any positive information, though, of course, since
it is inviolable, we must always be careful to conform to it. 
 Although this famous principle is thus without content and
merely formal, it has sometimes been carelessly formulated in
a manner which involves the quite unnecessary admixture of
a synthetic element. The formula runs: It is impossible that
something should at one and the same time both be and not be. 
Apart from the fact that the apodeictic certainty, expressed
through the word 'impossible', is superfluously added -- since
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it is evident of itself from the [very nature of the] proposition
-- the proposition is modified by the condition of time. It then,
as it were, asserts: A thing = A, which is something = B, can-
not at the same time be not-B, but may very well in succession
be both B and not-B. For instance, a man who is young cannot
at the same time be old, but may very well at one time be young
and at another time not-young, that is, old. The principle of
contradiction, however, as a merely logical principle, must not
in any way limit its assertions to time-relations. The above
formula is therefore completely contrary to the intention of the
principle. The misunderstanding results from our first of all
separating a predicate of a thing from the concept of that
thing, and afterwards connecting this predicate with its op-
posite -- a procedure which never occasions a contradiction with
the subject but only with the predicate which has been syn-
thetically connected with that subject, and even then only
when both predicates are affirmed at one and the same time. 
If I say that a man who is unlearned is not learned, the con-
dition, at one and the same time, must be added; for he who
is at one time unlearned can very well at another be learned. 
But if I say, no unlearned man is learned, the proposition is
analytic, since the property, unlearnedness, now goes to make
up the concept of the subject, and the truth of the negative
judgment then becomes evident as an immediate consequence
of the principle of contradiction, without requiring the supple-
mentary condition, at one and the same time. This, then, is
the reason why I have altered its formulation, namely, in order
that the nature of an analytic proposition be clearly expressed
through it. 
Section 2
The explanation of the possibility of synthetic judgments
is a problem with which general logic has nothing to do. It
need not even so much as know the problem by name. But in
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transcendental logic it is the most important of all questions;
and indeed, if in treating of the possibility of synthetic a priori
judgments we also take account of the conditions and scope of
their validity, it is the only question with which it is concerned. 
For upon completion of this enquiry, transcendental logic is
in a position completely to fulfil its ultimate purpose, that of
determining the scope and limits of pure understanding. 
In the analytic judgment we keep to the given concept,
and seek to extract something from it. If it is to be affirmative,
I ascribe to it only what is already thought in it. If it is to be
negative, I exclude from it only its opposite. But in synthetic
judgments I have to advance beyond the given concept,
viewing as in relation with the concept something altogether
different from what was thought in it. This relation is con-
sequently never a relation either of identity or of contradiction;
and from the judgment, taken in and by itself, the truth or
falsity of the relation can never be discovered. 
Granted, then, that we must advance beyond a given
concept in order to compare it synthetically with another, a
third something is necessary, as that wherein alone the syn-
thesis of two concepts can be achieved. What, now, is this
third something that is to be the medium of all synthetic
judgments? There is only one whole in which all our re-
presentations are contained, namely, inner sense and its
a priori form, time. The synthesis of representations rests on
imagination; and their synthetic unity, which is required for
judgment, on the unity of apperception. In these, therefore,
[in inner sense, imagination, and apperception], we must
look for the possibility of synthetic judgments; and since all
three contain the sources of a priori representations, they
must also account for the possibility of pure synthetic judg-
ments. For these reasons they are, indeed, indispensably
necessary for any knowledge of objects, which rests entirely
on the synthesis of representations. 
If knowledge is to have objective reality, that is, to re-
late to an object, and is to acquire meaning and significance
in respect to it, the object must be capable of being in some
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manner given. Otherwise the concepts are empty; through
them we have indeed thought, but in this thinking we have
really known nothing; we have merely played with repre-
sentations. That an object be given (if this expression be
taken, not as referring to some merely mediate process, but as
signifying immediate presentation in intuition), means simply
that the representation through which the object is thought
relates to actual or possible experience. Even space and time,
however free their concepts are from everything empirical,
and however certain it is that they are represented in the mind
completely a priori, would yet be without objective validity,
senseless and meaningless, if their necessary application to
the objects of experience were not established. Their repre-
sentation is a mere schema which always stands in relation
to the reproductive imagination that calls up and assembles
the objects of experience. Apart from these objects of ex-
perience, they would be devoid of meaning. And so it is with
concepts of every kind. 
The possibility of experience is, then, what gives objective
reality to all our a priori modes of knowledge. Experience,
however, rests on the synthetic unity of appearances, that is,
on a synthesis according to concepts of an object of appear-
ances in general. Apart from such synthesis it would not be
knowledge, but a rhapsody of perceptions that would not fit
into any context according to rules of a completely intercon-
nected (possible) consciousness, and so would not conform to
the transcendental and necessary unity of apperception. Ex-
perience depends, therefore, upon a priori principles of its
form, that is, upon universal rules of unity in the synthesis of
appearances. Their objective reality, as necessary conditions
of experience, and indeed of its very possibility, can always
be shown in experience. Apart from this relation synthetic
a priori principles are completely impossible. For they have
then no third something, that is, no object, in which the
synthetic unity can exhibit the objective reality of its concepts. 
Although we know a priori in synthetic judgments a great
deal regarding space in general and the figures which produc-
P 194
tive imagination describes in it, and can obtain such judg-
ments without actually requiring any experience, yet even this
knowledge would be nothing but a playing with a mere fig-
ment of the brain, were it not that space has to be regarded as
a condition of the appearances which constitute the material
for outer experience. Those pure synthetic judgments there-
fore relate, though only mediately, to possible experience, or
rather to the possibility of experience; and upon that alone is
founded the objective validity of their synthesis. 
Accordingly, since experience, as empirical synthesis, is,
in so far as such experience is possible, the one species of
knowledge which is capable of imparting reality to any non-
empirical synthesis, this latter [type of synthesis], as know-
ledge a priori, can possess truth, that is, agreement with the
object, only in so far as it contains nothing save what is
necessary to synthetic unity of experience in general. 
The highest principle of all synthetic judgments is there-
fore this: every object stands under the necessary conditions of
synthetic unity of the manifold of intuition in a possible ex-
Synthetic a priori judgements are thus possible when we re-
late the formal conditions of a priori intuition, the synthesis of
imagination and the necessary unity of this synthesis in a tran-
scendental apperception, to a possible empirical knowledge in
general. We then assert that the conditions of the possibility
of experience in general are likewise conditions of the possi-
bility of the objects of experience, and that for this reason they
have objective validity in a synthetic a priori judgment. 
Section 3
That there should be principles at all is entirely due to the
pure understanding. Not only is it the faculty of rules in re-
P 195
spect of that which happens, but is itself the source of principles
according to which everything that can be presented to us as
an object must conform to rules. For without such rules ap-
pearances would never yield knowledge of an object corre-
sponding to them. Even natural laws, viewed as principles of
the empirical employment of understanding, carry with them
an expression of necessity, and so contain at least the sugges-
tion of a determination from grounds which are valid a priori
and antecedently to all experience. The laws of nature, in-
deed, one and all, without exception, stand under higher prin-
ciples of understanding. They simply apply the latter to special
cases [in the field] of appearance. These principles alone supply
the concept which contains the condition, and as it were the
exponent, of a rule in general. What experience gives is the
instance which stands under the rule. 
There can be no real danger of our regarding merely em-
pirical principles as principles of pure understanding, or con-
versely. For the necessity according to concepts which distin-
guishes the principles of pure understanding, and the lack
of which is evident in every empirical proposition, however
general its application, suffices to make this confusion easily
preventable. But there are pure a priori principles that we
may not properly ascribe to the pure understanding, which is
the faculty of concepts. For though they are mediated by the
understanding, they are not derived from pure concepts but
from pure intuitions. We find such principles in mathematics. 
The question, however, of their application to experience, that
is, of their objective validity, nay, even the deduction of the
possibility of such synthetic a priori knowledge, must always
carry us back to the pure understanding. 
While, therefore, I leave aside the principles of mathe-
matics, I shall none the less include those [more fundamental]
principles upon which the possibility and a priori objective
validity of mathematics are grounded. These latter must be
regarded as the foundation of all mathematical principles. 
They proceed from concepts to intuition, not from intuition to
In the application of pure concepts of understanding to
P 196
possible experience, the employment of their synthesis is either
mathematical or dynamical; for it is concerned partly with the
mere intuition of an appearance in general, partly with its
existence. The a priori conditions of intuition are absolutely
necessary conditions of any possible experience; those of the
existence of the objects of a possible empirical intuition are in
themselves only accidental. The principles of mathematical
employment will therefore be unconditionally necessary, that
is, apodeictic. Those of dynamical employment will also in-
deed possess the character of a priori necessity, but only under
the condition of empirical thought in some experience, there-
fore only mediately and indirectly. Notwithstanding their un-
doubted certainty throughout experience, they will not con-
tain that immediate evidence which is peculiar to the former. 
But of this we shall be better able to judge at the conclusion of
this system of principles. 
The table of categories is quite naturally our guide in the
construction of the table of principles. For the latter are simply
rules for the objective employment of the former. All principles
of pure understanding are therefore --
of intuition. 
of perception. 
P 196
of experience. 
of empirical thought in general. 
P 196
These titles I have intentionally chosen in order to give
prominence to differences in the evidence and in the applica-
tion of the principles. It will soon become clear that the
principles involved in the a priori determination of appear-
ances according to the categories of quantity and of quality
(only the formal aspect of quantity and quality being con-
sidered) allow of intuitive certainty, alike as regards their
evidential force and as regards their a priori application to
P 197
appearances. They are thereby distinguished from those of
the other two groups, which are capable only of a merely
discursive certainty. This distinction holds even while we
recognise that the certainty is in both cases complete. I shall
therefore entitle the former principles mathematical, and
the latter dynamical. But it should be noted that we are as
little concerned in the one case with the principles of mathe-
matics as in the other with the principles of general physical
dynamics. We treat only of the principles of pure understand-
ing in their relation to inner sense (all differences among the
given representations being ignored). It is through these
principles of pure understanding that the special principles of
mathematics and of dynamics become possible. I have named
them, therefore, on account rather of their application than
of their content. I now proceed to discuss them in the order
in which they are given in the above table. 
Their principle is: All intuitions are extensive magnitudes. 
++ The Axioms of intuition. 
Principle of the pure understanding: All appearances
are, in their intuition, extensive magnitudes. 
++ All combination (conjunctio) is either com-
position (compositio) or connection (nexus). The former is the syn-
thesis of the manifold where its constituents do not necessarily be-
long to one another. For example, the two triangles into which a
square is divided by its diagonal do not necessarily belong to one
another. Such also is the synthesis of the homogeneous in everything
which can be mathematically treated. This synthesis can itself be
divided into that of aggregation and that of coalition, the former
P 198n
applying to extensive and the latter to intensive quantities. 
P 197
Appearances, in their formal aspect, contain an intuition
in space and time, which conditions them, one and all,
P 198
a priori. They cannot be apprehended, that is, taken up into
empirical consciousness, save through that synthesis of the
manifold whereby the representations of a determinate space
or time are generated, that is, through combination of the
homogeneous manifold and consciousness of its synthetic
unity. Consciousness of the synthetic unity of the manifold
[and] homogeneous in intuition in general, in so far as the
representation of an object first becomes possible by means
of it, is, however, the concept of a magnitude (quantum). 
Thus even the perception of an object, as appearance, is only
possible through the same synthetic unity of the manifold of
the given sensible intuition as that whereby the unity of the
combination of the manifold [and] homogeneous is thought
in the concept of a magnitude. In other words, appearances
are all without exception magnitudes, indeed extensive mag-
nitudes. As intuitions in space or time, they must be repre-
sented through the same synthesis whereby space and time
in general are determined. 
I entitle a magnitude extensive when the representation
of the parts makes possible, and therefore necessarily precedes,
the representation of the whole. I cannot represent to myself
a line, however small, without drawing it in thought, that
is, generating from a point all its parts one after another. 
Only in this way can the intuition be obtained. Similarly
with all times, however small. In these I think to myself
only that successive advance from one moment to another,
whereby through the parts of time and their addition a de-
terminate time-magnitude is generated. 
second mode of combination (nexus) is the synthesis of the manifold
so far as its constituents necessarily belong to one another, as, for
example, the accident to some substance, or the effect to the cause. 
It is therefore synthesis of that which, though heterogeneous, is yet
represented as combined a priori. This combination, as not being
arbitrary and as concerning the connection of the existence of the
manifold, I entitle dynamical. Such connection can itself, in turn,
be divided into the physical connection of the appearances with one
another, and their metaphysical connection in the a priori faculty of
P 198
As the [element of]
P 199
pure intuition in all appearances is either space or time, every
appearance is as intuition an extensive magnitude; only
through successive synthesis of part to part in [the process of]
its apprehension can it come to be known. All appearances
are consequently intuited as aggregates, as complexes of
previously given parts. This is not the case with magnitudes
of every kind, but only with those magnitudes which are
represented and apprehended by us in this extensive fashion. 
The mathematics of space (geometry) is based upon this
successive synthesis of the productive imagination in the
generation of figures. This is the basis of the axioms which
formulate the conditions of sensible a priori intuition under
which alone the schema of a pure concept of outer appear-
ance can arise -- for instance, that between two points only
one straight line is possible, or that two straight lines cannot
enclose a space, etc. These are the axioms which, strictly,
relate only to magnitudes (quanta) as such. 
As regards magnitude (quantitas), that is, as regards
the answer to be given to the question, 'What is the magnitude
of a thing? ' there are no axioms in the strict meaning of the
term, although there are a number of propositions which are
synthetic and immediately certain (indemonstrabilia). The
propositions, that if equals be added to equals the wholes
are equal, and if equals be taken from equals the remainders
are equal, are analytic propositions; for I am immediately
conscious of the identity of the production of the one magni-
tude with the production of the other. [Consequently, they
are not] axioms, [for these] have to be a priori synthetic pro-
positions. On the other hand, the evident propositions of
numerical relation are indeed synthetic, but are not general
like those of geometry, and cannot, therefore, be called axioms
but only numerical formulas. The assertion that 7 & 5 is equal
to 12 is not an analytic proposition. For neither in the repre-
sentation of 7, nor in that of 5, nor in the representation of the
combination of both, do I think the number 12. (That I must
do so in the addition of the two numbers is not to the point,
since in the analytic proposition the question is only whether
I actually think the predicate in the representation of the
subject. ) But although the proposition is synthetic, it is also
P 200
only singular. So far as we are here attending merely to the
synthesis of the homogeneous (of units), that synthesis can
take place only in one way, although the employment of
these numbers is general. If I assert that through three
lines, two of which taken together are greater than the
third, a triangle can be described, I have expressed merely
the function of productive imagination whereby the lines
can be drawn greater or smaller, and so can be made to
meet at any and every possible angle. The number 7, on the
other hand, is possible only in one way. So also is the
number 12, as thus generated through the synthesis of 7
with 5. Such propositions must not, therefore, be called
axioms (that would involve recognition of an infinite number
of axioms), but numerical formulas. 
This transcendental principle of the mathematics of ap-
pearances greatly enlarges our a priori knowledge. For it alone
can make pure mathematics, in its complete precision, appli-
cable to objects of experience. Without this principle, such
application would not be thus self-evident; and there has indeed
been much confusion of thought in regard to it. Appear-
ances are not things in themselves. Empirical intuition is
possible only by means of the pure intuition of space and of
time. What geometry asserts of pure intuition is therefore
undeniably valid of empirical intuition. The idle objections,
that objects of the senses may not conform to such rules of
construction in space as that of the infinite divisibility of lines
or angles, must be given up. For if these objections hold good,
we deny the objective validity of space, and consequently of
all mathematics, and no longer know why and how far
mathematics can be applicable to appearances. The synthesis
of spaces and times, being a synthesis of the essential forms
of all intuition, is what makes possible the apprehension of
appearance, and consequently every outer experience and all
knowledge of the objects of such experience. Whatever pure
mathematics establishes in regard to the synthesis of the form
of apprehension is also necessarily valid of the objects appre-
hended. All objections are only the chicanery of a falsely
P 201
instructed reason, which, erroneously professing to isolate the
objects of the senses from the formal condition of our sen-
sibility, represents them, in spite of the fact that they are mere
appearances, as objects in themselves, given to the understand-
ing. Certainly, on that assumption, no synthetic knowledge
of any kind could be obtained of them a priori, and nothing
therefore could be known of them synthetically through pure
concepts of space. Indeed, the science which determines these
concepts, namely geometry, would not itself be possible. 
In all appearances, the real that is an object of sensation
has intensive magnitude, that is, a degree. 
Perception is empirical consciousness, that is, a conscious-
ness in which sensation is to be found. Appearances, as objects
of perception, are not pure, merely formal, intuitions, like space
and time. For in and by themselves these latter cannot be per-
ceived. Appearances contain in addition to intuition the matter
for some object in general (whereby something existing in space
or time is represented); they contain, that is to say, the real
of sensation as merely subjective representation, which gives
us only the consciousness that the subject is affected, and
which we relate to an object in general. Now from empirical
consciousness to pure consciousness a graduated transition
is possible, the real in the former completely vanishing and a
merely formal a priori consciousness of the manifold in space
and time remaining. 
++ The Anticipations of Perception 
The principle which anticipates all perceptions, as such, is
as follows: In all appearances sensation, and the real which
corresponds to it in the object (realitas phaenomenon), has an
intensive magnitude, that is, a degree. 
P 201
Consequently there is also possible a
P 202
synthesis in the process of generating the magnitude of a sen-
sation from its beginning in pure intuition = 0, up to any
required magnitude. Since, however, sensation is not in itself
an objective representation, and since neither the intuition
of space nor that of time is to be met with in it, its mag-
nitude is not extensive but intensive. This magnitude is
generated in the act of apprehension whereby the empirical
consciousness of it can in a certain time increase from nothing
= 0 to the given measure. Corresponding to this intensity
of sensation, an intensive magnitude, that is, a degree of
influence on the sense [i.e. on the special sense involved],
must be ascribed to all objects of perception, in so far as
the perception contains sensation. 
All knowledge by means of which I am enabled to know
and determine a priori what belongs to empirical knowledge
may be entitled an anticipation; and this is undoubtedly the
sense in which Epicurus employed the term prolepsis. But as
there is an element in the appearances (namely, sensation, the
matter of perception) which can never be known a priori, and
which therefore constitutes the distinctive difference between
empirical and a priori knowledge, it follows that sensation is
just that element which cannot be anticipated. On the other
hand, we might very well entitle the pure determinations in
space and time, in respect of shape as well as of magnitude,
anticipations of appearances, since they represent a priori that
which may always be given a posteriori in experience. If,
however, there is in every sensation, as sensation in general
(that is, without a particular sensation having to be given),
something that can be known a priori, this will, in a quite
especial sense, deserve to be named anticipation. For it does
indeed seem surprising that we should forestall experience,
precisely in that which concerns what is only to be obtained
through it, namely, its matter. Yet, none the less, such is
actually the case. 
Apprehension by means merely of sensation occupies only
an instant, if, that is, I do not take into account the succes-
sion of different sensations. As sensation is that element in
P 203
the [field of] appearance the apprehension of which does not
involve a successive synthesis proceeding from parts to the
whole representation, it has no extensive magnitude. The
absence of sensation at that instant would involve the re-
presentation of the instant as empty, therefore as = 0. Now
what corresponds in empirical intuition to sensation is reality
(realitas phaenomenon); what corresponds to its absence is
negation = 0. Every sensation, however, is capable of diminu-
tion, so that it can decrease and gradually vanish. Between
reality in the [field of] appearance and negation there is there-
fore a continuity of many possible intermediate sensations,
the difference between any two of which is always smaller than
the difference between the given sensation and zero or com-
plete negation. In other words, the real in the [field of] ap-
pearance has always a magnitude. But since its apprehension
by means of mere sensation takes place in an instant and not
through successive synthesis of different sensations, and there-
fore does not proceed from the parts to the whole, the mag-
nitude is to be met with only in the apprehension. The real
has therefore magnitude, but not extensive magnitude. 
A magnitude which is apprehended only as unity, and
in which multiplicity can be represented only through ap-
proximation to negation = 0, I entitle an intensive magnitude. 
Every reality in the [field of] appearance has therefore inten-
sive magnitude or degree. If this reality is viewed as cause,
either of sensation or of some other reality in the [field of]
appearance, such as change, the degree of the reality as cause
is then entitled a moment, the moment of gravity. It is so
named for the reason that degree signifies only that magnitude
the apprehension of which is not successive, but instan-
taneous. This, however, I touch on only in passing; for with
causality I am not at present dealing. 
Every sensation, therefore, and likewise every reality in
the [field of] appearance, however small it may be, has a
degree, that is, an intensive magnitude which can always be
diminished. Between reality and negation there is a con-
tinuity of possible realities and of possible smaller perceptions. 
P 204
Every colour, as for instance red, has a degree which, how-
ever small it may be, is never the smallest; and so with heat,
the moment of gravity, etc. 
The property of magnitudes by which no part of them is
the smallest possible, that is, by which no part is simple, is
called their continuity. Space and time are quanta continua,
because no part of them can be given save as enclosed between
limits (points or instants), and therefore only in such fashion
that this part is itself again a space or a time. Space therefore
consists solely of spaces, time solely of times. Points and instants
are only limits, that is, mere positions which limit space and
time. But positions always presuppose the intuitions which
they limit or are intended to limit; and out of mere positions,
viewed as constituents capable of being given prior to space
or time, neither space nor time can be constructed. Such mag-
nitudes may also be called flowing, since the synthesis of
productive imagination involved in their production is a pro-
gression in time, and the continuity of time is ordinarily
designated by the term flowing or flowing away. 
 All appearances, then, are continuous magnitudes, alike in
their intuition, as extensive, and in their mere perception
(sensation, and with it reality) as intensive. If the synthesis of
the manifold of appearance is interrupted, we have an aggre-
gate of different appearances, and not appearance as a genuine
quantum. Such an aggregate is not generated by continuing
without break productive synthesis of a certain kind, but
through repetition of an ever-ceasing synthesis. If I called
thirteen thalers a quantum of money, I should be correct, pro-
vided my intention is to state the value of a mark of fine silver. 
For this is a continuous magnitude in which no part is the
smallest, and in which every part can constitute a piece of coin
that always contains material for still smaller pieces. But if
I understand by the phrase thirteen round thalers, so many
coins, quite apart from the question of what their silver
standard may be, I then use the phrase, quantum of thalers,
inappropriately. It ought to be entitled an aggregate, that is,
a number of pieces of money. But as unity must be presup-
posed in all number, appearance as unity is a quantum, and
as a quantum is always a continum. 
P 205
Since all appearances, alike in their extensive and in their
intensive aspect, are thus continuous magnitudes, it might
seem to be an easy matter to prove with mathematical con-
clusiveness the proposition that all alteration (transition of a
thing from one state to another), is continuous. But the caus-
ality of an alteration in general, presupposing, as it does, em-
pirical principles, lies altogether outside the limits of a tran-
scendental philosophy. For upon the question as to whether
a cause capable of altering the state of a thing, that is, of
determining it to the opposite of a certain given state, may
be possible, the a priori understanding casts no light; and
this not merely because it has no insight into its possibility
(such insight is lacking to us in many other cases of a priori
knowledge), but because alterableness is to be met with
only in certain determinations of appearances, and because,
whereas [in fact] the cause of these determinations lies
in the unalterable, experience alone can teach what they are. 
Since in our present enquiry we have no data of which we
can make use save only the pure fundamental concepts of all
possible experience, in which there must be absolutely nothing
that is empirical, we cannot, without destroying the unity of
our system, anticipate general natural science, which is based
on certain primary experiences. 
At the same time, there is no lack of proofs of the great
value of our principle in enabling us to anticipate perceptions,
and even to some extent to make good their absence, by
placing a check upon all false inferences which might be
drawn from their absence. 
If all reality in perception has a degree, between which
and negation there exists an infinite gradation of ever smaller
degrees, and if every sense must likewise possess some par-
ticular degree of receptivity of sensations, no perception, and
consequently no experience, is possible that could prove,
either immediately or mediately (no matter how far-ranging
the reasoning may be), a complete absence of all reality in the
[field of] appearance. In other words, the proof of an empty
space or of an empty time can never be derived from experi-
ence. For, in the first place, the complete absence of reality
P 206
from a sensible intuition can never be itself perceived; and,
secondly, there is no appearance whatsoever and no difference
in the degree of reality of any appearance from which it can
be inferred. It is not even legitimate to postulate it in order
to explain any difference. For even if the whole intuition of a
certain determinate space or time is real through and through,
that is, though no part of it is empty, none the less, since every
reality has its degree, which can diminish to nothing (the
void) through infinite gradations without in any way altering
the extensive magnitude of the appearance, there must be
infinite different degrees in which space and time may be filled. 
Intensive magnitude can in different appearances be smaller
or greater, although the extensive magnitude of the intuition
remains one and the same. 
 Let us give an example. Almost all natural philosophers,
observing -- partly by means of the moment of gravity or
weight, partly by means of the moment of opposition to other
matter in motion -- a great difference in the quantity of various
kinds of matter in bodies that have the same volume, unani-
mously conclude that this volume, which constitutes the ex-
tensive magnitude of the appearance, must in all material
bodies be empty in varying degrees. Who would ever have
dreamt of believing that these students of nature, most of
whom are occupied with problems in mathematics and
mechanics, would base such an inference solely on a meta-
physical presupposition -- the sort of assumption they so stoutly
profess to avoid? They assume that the real in space (I may
not here name it impenetrability or weight, since these are
empirical concepts) is everywhere uniform and varies only
in extensive magnitude, that is, in amount. Now to this pre-
supposition, for which they could find no support in experi-
ence, and which is therefore purely metaphysical, I oppose a
transcendental proof, which does not indeed explain the
difference in the filling of spaces, but completely destroys the
supposed necessity of the above presupposition, that the
difference is only to be explained on the assumption of empty
space. My proof has the merit at least of freeing the under-
standing, so that it is at liberty to think this difference in
some other manner, should it be found that some other
hypothesis is required for the explanation of the natural
P 207
appearances. For we then recognise that although two equal
spaces can be completely filled with different kinds of matter,
so that there is no point in either where matter is not present,
nevertheless every reality has, while keeping its quality un-
changed, some specific degree (of resistance or weight) which
can, without diminution of its extensive magnitude or amount,
become smaller and smaller in infinitum, before it passes
into the void and [so] vanishes [out of existence]. Thus a
radiation which fills a space, as for instance heat, and
similarly every other reality in the [field of] appearance,
can diminish in its degree in infinitum, without leaving
the smallest part of this space in the least empty. It may
fill the space just as completely with these smaller degrees as
another appearance does with greater degrees. I do not at all
intend to assert that this is what actually occurs when material
bodies differ in specific gravity, but only to establish from a
principle of pure understanding that the nature of our per-
ceptions allows of such a mode of explanation, that we are
not justified in assuming the real in appearances to be uniform
in degree, differing only in aggregation and extensive magni-
tude, and that we are especially in error when we claim that
such interpretation can be based on an a priori principle of
the understanding. 
This anticipation of perception must always, however
appear somewhat strange to anyone trained in transcend-
ental reflection, and to any student of nature who by such
teaching has been trained to circumspection. The assertion
that the understanding anticipates such a synthetic principle,
ascribing a degree to all that is real in the appearances, and
so asserting the possibility of an internal distinction in sensa-
tion itself (abstraction being made of its empirical quality),
awakens doubts and difficulties. It is therefore a question
not unworthy of solution, how the understanding can thus in
a priori fashion pronounce synthetically upon appearances,
and can indeed anticipate in that which in itself is merely
empirical and concerns only sensation. 
The quality of sensation, as for instance in colours, taste,
etc. , is always merely empirical, and cannot be represented
P 208
a priori. But the real, which corresponds to sensations in
general, as opposed to negation = 0, represents only that
something the very concept of which includes being, and
signifies nothing but the synthesis in an empirical conscious-
ness in general. Empirical consciousness can in inner sense
be raised from 0 to any higher degree, so that a certain ex-
tensive magnitude of intuition, as for instance of illuminated
surface, may excite as great a sensation as the combined
aggregate of many such surfaces has illuminated. [Since the
extensive magnitude of the appearance thus varies independ-
ently], we can completely abstract from it, and still represent
in the mere sensation in any one of its moments a synthesis
that advances uniformly from 0 to the given empirical con-
sciousness. Consequently, though all sensations as such are
given only a posteriori, their property of possessing a degree
can be known a priori. It is remarkable that of magnitudes
in general we can know a priori only a single quality, namely,
that of continuity, and that in all quality (the real in appear-
ances) we can know a priori nothing save [in regard to]
their intensive quantity, namely that they have degree. 
Everything else has to be left to experience. 
The principle of the analogies is: Experience is possible
only through the representation of a necessary connection
of perceptions. 
Experience is an empirical knowledge, that is, a know-
ledge which determines an object through perceptions.
++ The Analogies of Experience 
The general principle of the analogies is: All appearances
are, as regards their existence, subject a priori to rules deter-
mining their relation to one another in one time. 
P 209
It is a synthesis of perceptions, not contained in perception but
itself containing in one consciousness the synthetic unity of
the manifold of perceptions. This synthetic unity constitutes
the essential in any knowledge of objects of the senses, that is,
in experience as distinguished from mere intuition or sensa-
tion of the senses. In experience, however, perceptions come
together only in accidental order, so that no necessity deter-
mining their connection is or can be revealed in the perceptions
themselves. For apprehension is only a placing together of the
manifold of empirical intuition; and we can find in it no re-
presentation of any necessity which determines the appearances
thus combined to have connected existence in space and time. 
But since experience is a knowledge of objects through percep-
tions, the relation [involved] in the existence of the manifold has
to be represented in experience, not as it comes to be constructed
in time but as it exists objectively in time. Since time, however,
cannot itself be perceived, the determination of the existence
of objects in time can take place only through their relation in
time in general, and therefore only through concepts that con-
nect them a priori. Since these always carry necessity with
them, it follows that experience is only possible through a re-
presentation of necessary connection of perceptions. 
The three modes of time are duration, succession, and co-
existence. There will, therefore, be three rules of all relations
of appearances in time, and these rules will be prior to all ex-
perience, and indeed make it possible. By means of these rules
the existence of every appearance can be determined in respect
of the unity of all time. 
The general principle of the three analogies rests on the
necessary unity of apperception, in respect of all possible em-
pirical consciousness, that is, of all perception, at every [instant
of] time. And since this unity lies a priori at the foundation
of empirical consciousness, it follows that the above principle
rests on the synthetic unity of all appearances as regards their
relation in time. For the original apperception stands in rela-
tion to inner sense (the sum of all representations), and indeed
a priori to its form, that is, to the time-order of the manifold
empirical consciousness. All this manifold must, as regards
its time-relations, be united in the original apperception. This
P 210
is demanded by the a priori transcendental unity of appercep-
tion, to which everything that is to belong to my knowledge
(that is, to my unified knowledge), and so can be an object for
me, has to conform. This synthetic unity in the time-relations
of all perceptions, as thus determined a priori, is the law, that
all empirical time-determinations must stand under rules of
universal time-determination. The analogies of experience, with
which we are now to deal, must be rules of this description. 
These principles have this peculiarity, that they are not
concerned with appearances and the synthesis of their em-
pirical intuition, but only with the existence of such appearances
and their relation to one another in respect of their existence. 
The manner in which something is apprehended in appear-
ance can be so determined a priori that the rule of its synthesis
can at once give, that is to say, can bring into being, this
[element of] a priori intuition in every example that comes
before us empirically. The existence of appearances cannot,
however, be thus known a priori; and even granting that we
could in any such manner contrive to infer that something
exists, we could not know it determinately, could not, that is,
anticipate the features through which its empirical intuition is
distinguished from other intuitions. 
The two previous principles, which, as justifying the ap-
plication of mathematics to appearances, I entitled the mathe-
matical, referred to the possibility of appearances, and taught
how, alike as regards their intuition and the real in their per-
ception, they can be generated according to rules of a mathe-
matical synthesis. Both principles justify us in employing
numerical magnitudes, and so enable us to determine appear-
ance as magnitude. For instance, I can determine a priori, that
is, can construct, the degree of sensations of sunlight by com-
bining some 20,000 illuminations of the moon. These first
principles may therefore be called constitutive. 
 It stands quite otherwise with those principles which seek
to bring the existence of appearances under rules a priori. 
For since existence cannot be constructed, the principles can
apply only to the relations of existence, and can yield only re-
gulative principles. We cannot, therefore, expect either axioms
P 211
or anticipations. If, however, a perception is given in a time-
relation to some other perception, then even although this
latter is indeterminate, and we consequently cannot decide
what it is, or what its magnitude may be, we may none the
less assert that in its existence it is necessarily connected
with the former in this mode of time. In philosophy analogies
signify something very different from what they represent in
mathematics. In the latter they are formulas which express
the equality of two quantitative relations, and are always con-
stitutive; so that if three members of the proportion are given,
the fourth is likewise given, that is, can be constructed. But
in philosophy the analogy is not the equality of two quantitative
but of two qualitative relations; and from three given mem-
bers we can obtain a priori knowledge only of the relation to a
fourth, not of the fourth member itself. The relation yields, how-
ever, a rule for seeking the fourth member in experience, and
a mark whereby it can be detected. An analogy of experience
is, therefore, only a rule according to which a unity of experi-
ence may arise from perception. It does not tell us how mere
perception or empirical intuition in general itself comes about. 
It is not a principle constitutive of the objects, that is, of the
appearances, but only regulative. The same can be asserted of
the postulates of empirical thought in general, which concern
the synthesis of mere intuition (that is, of the form of appear-
ance), of perception (that is, of the matter of perception), and
of experience (that is, of the relation of these perceptions). 
They are merely regulative principles, and are distinguished
from the mathematical, which are constitutive, not indeed in
certainty -- both have certainty a priori -- but in the nature of
their evidence, that is, as regards the character of the intuitive
(and consequently of the demonstrative) factors peculiar to
the latter. 
In this connection what has been said of all principles that
are synthetic must be specially emphasised, namely, that these
analogies have significance and validity only as principles of
the empirical, not of the transcendental, employment of under-
standing; that only as such can they be established; and that
appearances have therefore to be subsumed, not simply under
P 212
the categories, but under their schemata. For if the objects
to which these principles are to be related were things in them-
selves, it would be altogether impossible to know anything of
them synthetically a priori. They are, however, nothing but
appearances; and complete knowledge of them, in the further-
ance of which the sole function of a priori principles must
ultimately consist, is simply our possible experience of them. 
The principles can therefore have no other purpose save that
of being the conditions of the unity of empirical knowledge in
the synthesis of appearances. But such unity can be thought
only in the schema of the pure concept of understanding. The
category expresses a function which is restricted by no sensible
condition, and contains the unity of this schema, [in so far
only] as [it is the schema] of a synthesis in general. By these
principles, then, we are justified in combining appearances
only according to what is no more than an analogy with the
logical and universal unity of concepts. In the principle itself
we do indeed make use of the category, but in applying it to
appearances we substitute for it its schema as the key to its
employment, or rather set it alongside the category, as its re-
stricting condition, and as being what may be called its formula. 
Principle of Permanence of Substance 
In all change of appearances substance is permanent; its
quantum in nature is neither increased nor diminished. 
++ All appearances contain the permanent (substance) as the
object itself, and the transitory as its mere determination
that is, as a way in which the object exists. 
P 213
All appearances are in time; and in it alone, as substratum
(as permanent form of inner intuition), can either coexistence
or succession be represented. Thus the time in which all
change of appearances has to be thought, remains and does
not change. For it is that in which, and as determinations of
which, succession or coexistence can alone be represented. 
Now time cannot by itself be perceived. Consequently there
must be found in the objects of perception, that is, in the
appearances, the substratum which represents time in general;
and all change or coexistence must, in being apprehended,
be perceived in this substratum, and through relation of the
appearances to it. But the substratum of all that is real, that is,
of all that belongs to the existence of things, is substance;
and all that belongs to existence can be thought only as a
determination of substance. Consequently the permanent, in
relation to which alone all time-relations of appearances can
be determined, is substance in the [field of] appearance, that
is, the real in appearance, and as the substrate of all change
remains ever the same. And as it is thus unchangeable in
its existence, its quantity in nature can be neither increased nor
Our apprehension of the manifold of appearance is always
successive, and is therefore always changing. Through it alone
we can never determine whether this manifold, as object of
experience, is coexistent or successive. For such determination
we require an underlying ground which exists at all times, that
is, something abiding and permanent, of which all change
and coexistence are only so many ways (modes of time) in
which the permanent exists. 
++ Proof of this first Analogy 
All appearances are in time. Time can determine them as
existing in a twofold manner, either as in succession to one
another or as coexisting. Time, in respect of the former, is
viewed as time-series, in respect of the latter as time-volume. 
P 214
And simultaneity and succession being the only relations in time, it follows tha
t only in
the permanent are relations of time possible. In other words,
the permanent is the substratum of the empirical representa-
tion of time itself; in it alone is any determination of time
possible. Permanence, as the abiding correlate of all existence
of appearances, of all change and of all concomitance, ex-
presses time in general. For change does not affect time itself,
but only appearances in time. (Coexistence is not a mode of
time itself; for none of the parts of time coexist; they are all
in succession to one another. ) If we ascribe succession to time
itself, we must think yet another time, in which the sequence
would be possible. Only through the permanent does existence
in different parts of the time-series acquire a magnitude which
can be entitled duration. For in bare succession existence is
always vanishing and recommencing, and never has the least
magnitude. Without the permanent there is therefore no time-
relation. Now time cannot be perceived in itself; the permanent
in the appearances is therefore the substratum of all deter-
mination of time, and, as likewise follows, is also the condition
of the possibility of all synthetic unity of perceptions, that is,
of experience. All existence and all change in time have thus
to be viewed as simply a mode of the existence of that which
remains and persists. In all appearances the permanent is the
object itself, that is, substance as phenomenon; everything, on
the other hand, which changes or can change belongs only to
the way in which substance or substances exist, and therefore
to their determinations. 
I find that in all ages, not only philosophers, but even
the common understanding, has recognised this permanence
as a substratum of all change of appearances, and always
assume it to be indubitable. The only difference in this matter
between the common understanding and the philosopher is
that the latter expresses himself somewhat more definitely,
asserting that throughout all changes in the world substance
remains, and that only the accidents change. But I nowhere
find even the attempt at a proof of this obviously synthetic
proposition. Indeed, it is very seldom placed, where it truly
belongs, at the head of those laws of nature which are pure
and completely a priori. Certainly the proposition, that sub-
stance is permanent, is tautological. For this permanence is
P 215
our sole ground for applying the category of substance to
appearance; and we ought first to have proved that in all
appearances there is something permanent, and that the tran-
sitory is nothing but determination of its existence. But such
a proof cannot be developed dogmatically, that is, from con-
cepts, since it concerns a synthetic a priori proposition. Yet
as it never occurred to anyone that such propositions are
valid only in relation to possible experience, and can therefore
be proved only through a deduction of the possibility of ex-
perience, we need not be surprised that though the above
principle is always postulated as lying at the basis of ex-
perience (for in empirical knowledge the need of it is felt), it
has never itself been proved. 
A philosopher, on being asked how much smoke weighs,
made reply: "Subtract from the weight of the wood burnt
the weight of the ashes which are left over, and you have the
weight of the smoke". He thus presupposed as undeniable
that even in fire the matter (substance) does not vanish, but
only suffers an alteration of form. The proposition, that noth-
ing arises out of nothing, is still another consequence of the
principle of permanence, or rather of the ever-abiding exist-
ence, in the appearances, of the subject proper. For if that in
the [field of] appearance which we name substance is to be
the substratum proper of all time-determination, it must
follow that all existence, whether in past or in future time,
can be determined solely in and by it. We can therefore give
an appearance the title 'substance' just for the reason that we
presuppose its existence throughout all time, and that this is not
adequately expressed by the word permanence, a term which
applies chiefly to future time. But since the inner necessity of
persisting is inseparably bound up with the necessity of always
having existed, the expression [principle of permanence] may
be allowed to stand. Gigni de nihilo nihil, in nihilum nil
posse reverti, were two propositions which the ancients al-
ways connected together, but which are now sometimes mis-
takenly separated owing to the belief that they apply to things
in themselves, and that the first would run counter to the
dependence of the world -- even in respect of its substance --
upon a supreme cause. But such apprehension is unneces-
sary. For we have here to deal only with appearances in the
P 216
field of experience; and the unity of experience would never
be possible if we were willing to allow that new things, that is,
new substances, could come into existence. For we should then
lose that which alone can represent the unity of time, namely,
the identity of the substratum, wherein alone all change has
thoroughgoing unity. This permanence is, however, simply
the mode in which we represent to ourselves the existence of
things in the [field of] appearance. 
The determinations of a substance, which are nothing but
special ways in which it exists, are called accidents. They are
always real, because they concern the existence of substance. 
(Negations are only determinations which assert the non-
existence of something in substance. ) If we ascribe a special
[kind of] existence to this real in substance (for instance, to
motion, as an accident of matter), this existence is entitled
inherence, in distinction from the existence of substance which
is entitled subsistence. But this occasions many misunder-
standings; it is more exact and more correct to describe an
accident as being simply the way in which the existence of
a substance is positively determined. But since it is unavoid-
able, owing to the conditions of the logical employment of our
understanding, to separate off, as it were, that which in the
existence of a substance can change while the substance still
remains, and to view this variable element in relation to the
truly permanent and radical, this category has to be assigned
a place among the categories of relation, but rather as the
condition of relations than as itself containing a relation. 
The correct understanding of the concept of alteration is
also grounded upon [recognition of] this permanence. Coming
to be and ceasing to be are not alterations of that which comes
to be or ceases to be. Alteration is a way of existing which
follows upon another way of existing of the same object. All
that alters persists, and only its state changes. Since this
change thus concerns only the determinations, which can
cease to be or begin to be, we can say, using what may seem
a somewhat paradoxical expression, that only the permanent
P 217
(substance) is altered, and that the transitory suffers no
alteration but only a change, inasmuch as certain determina-
tions cease to be and others begin to be. 
Alteration can therefore be perceived only in substances. A
coming to be or ceasing to be that is not simply a determination
of the permanent but is absolute, can never be a possible per-
ception. For this permanent is what alone makes possible the
representation of the transition from one state to another, and
from not-being to being. These transitions can be empirically
known only as changing determinations of that which is per-
manent. If we assume that something absolutely begins to be,
we must have a point of time in which it was not. But to what
are we to attach this point, if not to that which already exists? 
For a preceding empty time is not an object of perception. 
But if we connect the coming to be with things which pre-
viously existed, and which persist in existence up to the
moment of this coming to be, this latter must be simply a de-
termination of what is permanent in that which precedes it. 
Similarly also with ceasing to be; it presupposes the empirical
representation of a time in which an appearance no longer
Substances, in the [field of] appearance, are the substrata
of all determinations of time. If some of these substances could
come into being and others cease to be, the one condition of
the empirical unity of time would be removed. The appear-
ances would then relate to two different times, and existence
would flow in two parallel streams -- which is absurd. There
is only one time in which all different times must be located
not as coexistent but as in succession to one another. 
Permanence is thus a necessary condition under which
alone appearances are determinable as things or objects in a
possible experience. We shall have occasion in what follows
to make such observations as may seem necessary in regard
to the empirical criterion of this necessary permanence -- the
criterion, consequently, of the substantiality of appearances. 
P 218
Principle of Succession in Time, in accordance with the
Law of Causality 
All alterations take place in conformity with the law of the
connection of cause and effect. 
(The preceeding principle has shown that all appearances
of succession in time are one and all only alterations, that is
a successive being and not-being of the determinations of
substance which abides; and therefore that the being of
substance as following on its not-being, or its not-being as
following upon its being cannot be admitted -- in other words,
that there is no coming into being or passing away of sub-
stance itself. Still otherwise expressed the principle is, that
all change (succession) of appearances is merely alteration. 
Coming into being and passing away of substance are not
alterations of it, since the concept of alteration presupposes
one and the same subject as existing with two opposite deter-
minations, and therefore as abiding. With this preliminary
reminder, we pass to the proof. )
I perceive that appearances follow one another, that is, that
there is a state of things at one time the opposite of which was
in the preceding time. Thus I am really connecting two percep-
tions in time. Now connection is not the work of mere sense
and intuition, but is here the product of a synthetic faculty
of imagination, which determines inner sense in respect of the
++ Principle of Production 
Everything that happens, that is, begins to be, presupposes
something upon which it follows according to a rule. 
P 218
But imagination can connect these two states
P 219
in two ways, so that either the one or the other precedes in
time. For time cannot be perceived in itself, and what precedes
and what follows cannot, therefore, by relation to it, be em-
pirically determined in the object. I am conscious only that
my imagination sets the one state before and the other after,
not that the one state precedes the other in the object. In other
words, the objective relation of appearances that follow upon
one another is not to be determined through mere perception. 
In order that this relation be known as determined, the rela-
tion between the two states must be so thought that it is there-
by determined as necessary which of them must be placed
before, and which of them after, and that they cannot be
placed in the reverse relation. But the concept which carries
with it a necessity of synthetic unity can only be a pure
concept that lies in the understanding, not in perception;
and in this case it is the concept of the relation of cause
and effect, the former of which determines the latter in time,
as its consequence -- not as in a sequence that may occur
solely in the imagination (or that may not be perceived at
all). Experience itself -- in other words, empirical knowledge
of appearances -- is thus possible only in so far as we subject
the succession of appearances, and therefore all alteration,
to the law of causality; and, as likewise follows, the appear-
ances, as objects of experience, are themselves possible only
in conformity with the law. 
The apprehension of the manifold of appearance is always
successive. The representations of the parts follow upon one
another. Whether they also follow one another in the object
is a point which calls for further reflection, and which is not
decided by the above statement. Everything, every repre-
sentation even, in so far as we are conscious of it, may be
entitled object. But it is a question for deeper enquiry what
the word 'object' ought to signify in respect of appearances
when these are viewed not in so far as they are (as representa-
tions) objects, but only in so far as they stand for an object. The
appearances, in so far as they are objects of consciousness
simply in virtue of being representations, are not in any way
distinct from their apprehension, that is, from their recep-
tion in the synthesis of imagination; and we must therefore
P 220
agree that the manifold of appearances is always generated in
the mind successively. Now if appearances were things in them-
selves, then since we have to deal solely with our representations,
we could never determine from the succession of the representa-
tions how their manifold may be connected in the object. How
things may be in themselves, apart from the representations
through which they affect us, is entirely outside our sphere of
knowledge. In spite, however, of the fact that the appearances
are not things in themselves, and yet are what alone can be
given to us to know, in spite also of the fact that their repre-
sentation in apprehension is always successive, I have to show
what sort of a connection in time belongs to the manifold
in the appearances themselves. For instance, the apprehen-
sion of the manifold in the appearance of a house which
stands before me is successive. The question then arises,
whether the manifold of the house is also in itself suc-
cessive. This, however, is what no one will grant. Now im-
mediately I unfold the transcendental meaning of my concepts
of an object, I realise that the house is not a thing in itself,
but only an appearance, that is, a representation, the tran-
scendental object of which is unknown. What, then, am I to
understand by the question: how the manifold may be con-
nected in the appearance itself, which yet is nothing in itself? 
That which lies in the successive apprehension is here viewed
as representation, while the appearance which is given to
me, notwithstanding that it is nothing but the sum of these
representations, is viewed as their object; and my concept,
which I derive from the representations of apprehension, has
to agree with it. Since truth consists in the agreement of
knowledge with the object, it will at once be seen that we can
here enquire only regarding the formal conditions of empirical
truth, and that appearance, in contradistinction to the repre-
sentations of apprehension, can be represented as an object
distinct from them only if it stands under a rule which dis-
tinguishes it from every other apprehension and necessitates
some one particular mode of connection of the manifold. The
object is that in the appearance which contains the condition
of this necessary rule of apprehension. 
Let us now proceed to our problem. That something
happens, i.e. that something, or some state which did not pre-
P 221
viously exist, comes to be, cannot be perceived unless it is
preceded by an appearance which does not contain in itself this
state. For an event which should follow upon an empty time,
that is, a coming to be preceded by no state of things, is as
little capable of being apprehended as empty time itself. Every
apprehension of an event is therefore a perception that fol-
lows upon another perception. But since, as I have above
illustrated by reference to the appearance of a house, this like-
wise happens in all synthesis of apprehension, the apprehen-
sion of an event is not yet thereby distinguished from other
apprehensions. But, as I also note, in an appearance which
contains a happening (the preceding state of the percep-
tion we may entitle A, and the succeeding B) B can be
apprehended only as following upon A; the perception A
cannot follow upon B but only precede it. For instance, I
see a ship move down stream. My perception of its lower
position follows upon the perception of its position higher
up in the stream, and it is impossible that in the appre-
hension of this appearance the ship should first be per-
ceived lower down in the stream and afterwards higher up. 
The order in which the perceptions succeed one another in
apprehension is in this instance determined, and to this order
apprehension is bound down. In the previous example of a
house my perceptions could begin with the apprehension of
the roof and end with the basement, or could begin from below
and end above; and I could similarly apprehend the manifold
of the empirical intuition either from right to left or from left
to right. In the series of these perceptions there was thus no
determinate order specifying at what point I must begin in
order to connect the manifold empirically. But in the percep-
tion of an event there is always a rule that makes the order in
which the perceptions (in the apprehension of this appearance)
follow upon one another a necessary order. 
In this case, therefore, we must derive the subjective suc-
cession of apprehension from the objective succession of ap-
pearances. Otherwise the order of apprehension is entirely
undetermined, and does not distinguish one appearance from
another. Since the subjective succession by itself is altogether
P 222
arbitrary, it does not prove anything as to the manner in
which the manifold is connected in the object. The objective
succession will therefore consist in that order of the manifold
of appearance according to which, in conformity with a
rule, the apprehension of that which happens follows upon
the apprehension of that which precedes. Thus only can I be
justified in asserting, not merely of my apprehension, but of
appearance itself, that a succession is to be met with in it. 
This is only another way of saying that I cannot arrange the
apprehension otherwise than in this very succession. 
In conformity with such a rule there must lie in that which
precedes an event the condition of a rule according to which
this event invariably and necessarily follows. I cannot reverse
this order, proceeding back from the event to determine
through apprehension that which precedes. For appearance
never goes back from the succeeding to the preceding point
of time, though it does indeed stand in relation to some pre-
ceding point of time. The advance, on the other hand, from
a given time to the determinate time that follows is a neces-
sary advance. Therefore, since there certainly is something
that follows [i.e. that is apprehended as following], I must refer
it necessarily to something else which precedes it and upon
which it follows in conformity with a rule, that is, of necessity. 
The event, as the conditioned, thus affords reliable evidence of
some condition, and this condition is what determines the event. 
Let us suppose that there is nothing antecedent to an event,
upon which it must follow according to rule. All succession of
perception would then be only in the apprehension, that is,
would be merely subjective, and would never enable us to de-
termine objectively which perceptions are those that really
precede and which are those that follow. We should then
have only a play of representations, relating to no object;
that is to say, it would not be possible through our percep-
tion to distinguish one appearance from another as regards
relations of time. For the succession in our apprehension
would always be one and the same, and there would be nothing
in the appearance which so determines it that a certain se-
quence is rendered objectively necessary. I could not then
assert that two states follow upon one another in the [field of]
P 223
appearance, but only that one apprehension follows upon the
other. That is something merely subjective, determining no
object; and may not, therefore, be regarded as knowledge of
any object, not even of an object in the [field of] appearance. 
If, then, we experience that something happens, we in
so doing always presuppose that something precedes it, on
which it follows according to a rule. Otherwise I should not
say of the object that it follows. For mere succession in my
apprehension, if there be no rule determining the succession
in relation to something that precedes, does not justify me
in assuming any succession in the object. I render my sub-
jective synthesis of apprehension objective only by reference
to a rule in accordance with which the appearances in their
succession, that is, as they happen, are determined by the pre-
ceding state. The experience of an event [i.e. of anything as
happening] is itself possible only on this assumption. 
This may seem to contradict all that has hitherto been
taught in regard to the procedure of our understanding. The
accepted view is that only through the perception and compari-
son of events repeatedly following in a uniform manner upon
preceding appearances are we enabled to discover a rule
according to which certain events always follow upon certain
appearances, and that this is the way in which we are first led
to construct for ourselves the concept of cause. Now the con-
cept, if thus formed, would be merely empirical, and the rule
which it supplies, that everything which happens has a cause,
would be as contingent as the experience upon which it is
based. Since the universality and necessity of the rule would
not be grounded a priori, but only on induction, they would
be merely fictitious and without genuinely universal validity. 
It is with these, as with other pure a priori representations --
for instance, space and time. We can extract clear concepts
of them from experience, only because we have put them into
experience, and because experience is thus itself brought
about only by their means. Certainly, the logical clearness of
this representation of a rule determining the series of events is
possible only after we have employed it in experience. Never-
P 224
theless, recognition of the rule, as a condition of the synthetic
unity of appearances in time, has been the ground of ex-
perience itself, and has therefore preceded it a priori. 
We have, then, to show, in the case under consideration,
that we never, even in experience, ascribe succession (that is,
the happening of some event which previously did not exist)
to the object, and so distinguish it from subjective sequence
in our apprehension, except when there is an underlying rule
which compels us to observe this order of perceptions rather
than any other; nay, that this compulsion is really what first
makes possible the representation of a succession in the object. 
We have representations in us, and can become conscious
of them. But however far this consciousness may extend, and
however careful and accurate it may be, they still remain mere
representations, that is, inner determinations of our mind in
this or that relation of time. How, then, does it come about
that we posit an object for these representations, and so, in
addition to their subjective reality, as modifications, ascribe
to them some mysterious kind of objective reality. Objective
meaning cannot consist in the relation to another representa-
tion (of that which we desire to entitle object), for in that case
the question again arises, how this latter representation goes
out beyond itself, acquiring objective meaning in addition to
the subjective meaning which belongs to it as determination
of the mental state. If we enquire what new character relation
to an object confers upon our representations, what dignity they
thereby acquire, we find that it results only in subjecting the
representations to a rule, and so in necessitating us to connect
them in some one specific manner; and conversely, that only
in so far as our representations are necessitated in a certain
order as regards their time-relations do they acquire objective
 In the synthesis of appearances the manifold of representa-
tions is always successive. Now no object is hereby represented,
since through this succession, which is common to all appre-
hensions, nothing is distinguished from anything else. But
immediately I perceive or assume that in this succession there
is a relation to the preceding state, from which the representa-
P 225
tion follows in conformity with a rule, I represent something
as an event, as something that happens; that is to say, I appre-
hend an object to which I must ascribe a certain determinate
position in time -- a position which, in view of the preceding
state, cannot be otherwise assigned. When, therefore, I per-
ceive that something happens, this representation first of all
contains [the consciousness] that there is something preceding,
because only by reference to what precedes does the appear-
ance acquire its time-relation, namely, that of existing after a
preceding time in which it itself was not. But it can acquire
this determinate position in this relation of time only in so far
as something is presupposed in the preceding state upon which
it follows invariably, that is, in accordance with a rule. From
this there results a twofold consequence. In the first place, I
cannot reverse the series, placing that which happens prior to
that upon which it follows. And secondly, if the state which
precedes is posited, this determinate event follows inevitably
and necessarily. The situation, then, is this: there is an order
in our representations in which the present, so far as it has
come to be, refers us to some preceding state as a correlate of
the event which is given; and though this correlate is, indeed,
indeterminate, it none the less stands in a determining relation
to the event as its consequence, connecting the event in neces-
sary relation with itself in the time-series. 
If, then, it is a necessary law of our sensibility, and there-
fore a formal condition of all perceptions, that the preceding
time necessarily determines the succeeding (since I cannot ad-
vance to the succeeding time save through the preceding), it is
also an indispensable law of empirical representation of the
time-series that the appearances of past time determine all
existences in the succeeding time, and that these latter, as
events, can take place only in so far as the appearances of past
time determine their existence in time, that is, determine them
according to a rule. For only in appearances can we empirically
apprehend this continuity in the connection of times. 
Understanding is required for all experience and for its
possibility. Its primary contribution does not consist in making
the representation of objects distinct, but in making the repre-
P 226
sentation of an object possible at all. This it does by carrying
the time-order over into the appearances and their existence. 
For to each of them, [viewed] as [a] consequent, it assigns,
through relation to the preceding appearances, a position de-
termined a priori in time. Otherwise, they would not accord
with time itself, which [in] a priori [fashion] determines the
position of all its parts. Now since absolute time is not an ob-
ject of perception, this determination of position cannot be de-
rived from the relation of appearances to it. On the contrary,
the appearances must determine for one another their position
in time, and make their time-order a necessary order. In other
words, that which follows or happens must follow in con-
formity with a universal rule upon that which was contained in
the preceding state. A series of appearances thus arises which,
with the aid of the understanding, produces and makes neces-
sary the same order and continuous connection in the series
of possible perceptions as is met with a priori in time -- the
form of inner intuition wherein all perceptions must have a
That something happens is, therefore, a perception which
belongs to a possible experience. This experience becomes
actual when I regard the appearance as determined in its posi-
tion in time, and therefore as an object that can always be
found in the connection of perceptions in accordance with a
rule. This rule, by which we determine something according to
succession of time, is, that the condition under which an event
invariably and necessarily follows is to be found in what pre-
cedes the event. The principle of sufficient reason is thus the
ground of possible experience, that is, of objective knowledge
of appearances in respect of their relation in the succession of
The proof of this principle rests on the following considera-
tions. All empirical knowledge involves the synthesis of the
manifold by the imagination. This synthesis is always succes-
sive, that is, the representations in it are always sequent upon
one another. In the imagination this sequence is not in any
way determined in its order, as to what must precede and
what must follow, and the series of sequent representations
P 227
can indifferently be taken either in backward or in forward
order. But if this synthesis is a synthesis of apprehension of
the manifold of a given appearance, the order is determined
in the object, or, to speak more correctly, is an order of suc-
cessive synthesis that determines an object. In accordance
with this order something must necessarily precede, and when
this antecedent is posited, something else must necessarily
follow. If, then, my perception is to contain knowledge of an
event, of something as actually happening, it must be an
empirical judgment in which we think the sequence as deter-
mined; that is, it presupposes another appearance in time,
upon which it follows necessarily, according to a rule. Were
it not so, were I to posit the antecedent and the event were
not to follow necessarily thereupon, I should have to regard
the succession as a merely subjective play of my fancy; and if
I still represented it to myself as something objective, I should
have to call it a mere dream. Thus the relation of appearances
(as possible perceptions) according to which the subsequent
event, that which happens, is, as to its existence, necessarily
determined in time by something preceding in conformity
with a rule -- in other words, the relation of cause to effect -- is
the condition of the objective validity of our empirical judg-
ments, in respect of the series of perceptions, and so of their
empirical truth; that is to say, it is the condition of experience. 
The principle of the causal relation in the sequence of appear-
ances is therefore also valid of all objects of experience ([in
so far as they are] under the conditions of succession), as
being itself the ground of the possibility of such experience. 
At this point a difficulty arises with which we must at
once deal. The principle of the causal connection among ap-
pearances is limited in our formula to their serial succession,
whereas it applies also to their coexistence, when cause and
effect are simultaneous. For instance, a room is warm while
the outer air is cool. I look around for the cause, and find a
heated stove. Now the stove, as cause, is simultaneous with its
effect, the heat of the room. Here there is no serial succession
in time between cause and effect. They are simultaneous, and
P 228
yet the law is valid. The great majority of efficient natural
causes are simultaneous with their effects, and the sequence
in time of the latter is due only to the fact that the cause
cannot achieve its complete effect in one moment. But in
the moment in which the effect first comes to be, it is in-
variably simultaneous with the causality of its cause. If the
 cause should have ceased to exist a moment before, the effect
would never have come to be. Now we must not fail to note
that it is the order of time, not the lapse of time, with which
we have to reckon; the relation remains even if no time has
elapsed. The time between the causality of the cause and its
immediate effect may be [a] vanishing [quantity], and they
may thus be simultaneous; but the relation of the one to the
other will always still remain determinable in time. If I view
as a cause a ball which impresses a hollow as it lies on a
stuffed cushion, the cause is simultaneous with the effect. But
I still distinguish the two through the time-relation of their
dynamical connection. For if I lay the ball on the cushion,
a hollow follows upon the previous flat smooth shape; but
if (for any reason) there previously exists a
cushion, a leaden ball does not follow upon it. 
The sequence in time is thus the sole empirical criterion
of an effect in its relation to the causality of the cause which
precedes it. A glass [filled with water] is the cause of the rising
of the water above its horizontal surface, although both appearances
are simultaneous. For immediately I draw off
water from a larger vessel into the glass, something follows,
namely the alteration from the horizontal position which the
water then had to the concave form which it assumes in the
Causality leads to the concept of action, this in turn to the
concept of force, and thereby to the concept of substance. 
As my critical scheme, which is concerned solely with the
sources of synthetic a priori knowledge, must not be compli-
cated through the introduction of analyses which aim only
at the clarification, not at the extension, of concepts, I leave
detailed exposition of my concepts to a future
system of pure reason. Such an analysis has already, indeed, been developed
in considerable detail in the text-books. But I must
not leave unconsidered the empirical criterion of a substance,
P 229
in so far as substance appears to manifest itself not through
permanence of appearance, but more adequately and easily
through action. 
Wherever there is action -- and therefore activity and force
 -- there is also substance, and it is in substance alone that the
seat of this fruitful source of appearances must be sought. 
This is, so far, well said; but when we seek to explain what
is to be understood by substance, and in so doing are careful
to avoid the fallacy of reasoning in a circle, the discovery of
an answer is no easy task. How are we to conclude directly
from the action to the permanence of that which acts? For
that is an essential and quite peculiar characteristic of sub-
stance (as phenomenon). But while according to the usual pro-
cedure, which deals with concepts in purely analytic fashion, this
question would be completely insoluble, it presents no such
difficulty from the standpoint which we have been formulating. 
Action signifies the relation of the subject of causality to its
effect. Since, now, every effect consists in that which happens,
and so in the transitory, which signifies time in its character
of succession, its ultimate subject, as the substratum of
everything that changes, is the permanent, that is, substance. 
For according to the principle of causality actions are always
the first ground of all change of appearances, and cannot
therefore be found in a subject which itself changes, because
in that case other actions and another subject would be re-
quired to determine this change. For this reason action is a
sufficient empirical criterion to establish the substantiality
of a subject, without my requiring first to go in quest of its
permanence through the comparison of perceptions. Besides,
by such method (of comparison) we could not achieve the
completeness required for the magnitude and strict univer-
sality of the concept. That the first subject of the causality
of all coming to be and ceasing to be cannot itself, in the field
of appearances, come to be and cease to be, is an assured
conclusion which leads to [the concept of] empirical necessity
and permanence in existence, and so to the concept of a sub-
stance as appearance. 
When something happens, the mere coming to be, apart
from all question of what it is that has come to be, is already in
P 230
itself a matter for enquiry. The transition from the not-being
of a state to this state, even supposing that this state [as it
occurs] in the [field of] appearance exhibited no quality, of
itself demands investigation. This coming to be, as was shown
above in the First Analogy, does not concern substance, which
does not come to be out of nothing. For if coming to be out of
nothing is regarded as effect of a foreign cause, it has to be
entitled creation, and that cannot be admitted as an event
among appearances since its mere possibility would destroy
the unity of experience. On the other hand, when I view all
things not as phenomena but as things in themselves, and
as objects of the mere understanding, then despite their
being substances they can be regarded, in respect of their
existence, as depending upon a foreign cause. But our
terms would then carry with them quite other meanings,
and would not apply to appearances as possible objects of
How anything can be altered, and how it should be possible
that upon one state in a given moment an opposite state may
follow in the next moment -- of this we have not, a priori, the
least conception. For that we require knowledge of actual
forces, which can only be given empirically, as, for instance,
of the moving forces, or what amounts to the same thing, of
certain successive appearances, as motions, which indicate [the
presence of] such forces. But apart from all question of what
the content of the alteration, that is, what the state which
is altered, may be, the form of every alteration, the condition
under which, as a coming to be of another state, it can alone
take place, and so the succession of the states themselves (the
happening), can still be considered a priori according to the
law of causality and the conditions of time. 
 If a substance passes from one state, a, to another, b, the
point of time of the second is distinct from that of the first, and follows upon
++ It should be carefully noted that I speak not of the alteration
of certain relations in general, but of alteration of state. Thus, when
a body moves uniformly, it does not in any way alter its state (of
motion); that occurs only when its motion increases or diminishes. 
P 231
Similarly, the second state as reality in the
[field of] appearance differs from the first wherein it did not
exist, as b from zero. That is to say, even if the state b
differed from the state a only in magnitude, the alteration
would be a coming to be of b - a, which did not exist in the
previous state, and in respect of which it = 0. 
The question therefore arises how a thing passes from one
state = a to another = b. Between two instants there is al-
ways a time, and between any two states in the two instants
there is always a difference which has magnitude. For all parts
of appearances are always themselves magnitudes. All transi-
tion from one state to another therefore occurs in a time which
is contained between two instants, of which the first deter-
mines the state from which the thing arises, and the second
that into which it passes. Both instants, then, are limits of the
time of a change, and so of the intermediate state between the
two states, and therefore as such form part of the total alteration. 
Now every alteration has a cause which evinces its causality in
the whole time in which the alteration takes place. This cause,
therefore, does not engender the alteration suddenly, that is, at
once or in one instant, but in a time; so that, as the time in-
creases from the initial instant a to its completion in b, the
magnitude of the reality (b - a) is in like manner generated
through all smaller degrees which are contained between the
first and the last. All alteration is thus only possible through a
continuous action of the causality which, so far as it is uniform,
is entitled a moment. The alteration does not consist of these
moments, but is generated by them as their effect. 
That is the law of the continuity of all alteration. Its ground
is this: that neither time nor appearance in time consists of parts
which are the smallest [possible], and that, nevertheless, the
state of a thing passes in its alteration through all these parts,
as elements, to its second state. In the [field of] appearance
there is no difference of the real that is the smallest, just as in
the magnitude of times there is no time that is the smallest;
and the new state of reality accordingly proceeds from the
first wherein this reality was not, through all the infinite de-
grees, the differences of which from one another are all smaller
than that between 0 and a. 
P 232
While we are not concerned to enquire what utility this
principle may have in the investigation of nature, what does
imperatively call for investigation is the question how such a
principle, which seems to extend our knowledge of nature, can
be possible completely a priori. Such an enquiry cannot be dis-
pensed with, even though direct inspection may show the prin-
ciple to be true and [empirically] real, and though the question,
how it should be possible, may therefore be considered super-
fluous. For there are so many ungrounded claims to the
extension of our knowledge through pure reason, that we must
take it as a universal principle that any such pretension is of
itself a ground for being always mistrustful, and that, in the
absence of evidence afforded by a thoroughgoing deduction,
we may not believe and assume the justice of such claims, no
matter how clear the dogmatic proof of them may appear to be. 
All increase in empirical knowledge, and every advance of
perception, no matter what the objects may be, whether ap-
pearances or pure intuitions, is nothing but an extension of the
determination of inner sense, that is, an advance in time. This
advance in time determines everything, and is not in itself deter-
mined through anything further. That is to say, its parts are
given only in time, and only through the synthesis of time; they
are not given antecedently to the synthesis. For this reason
every transition in perception to something which follows in
time is a determination of time through the generation of this
perception, and since time is always and in all its parts a mag-
nitude, is likewise the generation of a perception as a magnitude
through all degrees of which no one is the smallest, from zero
up to its determinate degree. This reveals the possibility of
knowing a priori a law of alterations, in respect of their form. 
We are merely anticipating our own apprehension, the formal
condition of which, since it dwells in us prior to all appearance
that is given, must certainly be capable of being known a priori. 
In the same manner, therefore, in which time contains the
sensible a priori condition of the possibility of a continuous
advance of the existing to what follows, the understanding,
by virtue of the unity of apperception, is the a priori condi-
tion of the possibility of a continuous determination of all posi-
tions for the appearances in this time, through the series of
P 233
causes and effects, the former of which inevitably lead to the
existence of the latter, and so render the empirical knowledge
of the time-relations valid universally for all time, and there-
fore objectively valid. 
Principle of Coexistence, in accordance with the Law of
Reciprocity or Community 
All substances, in so far as they can be perceived to coexist in
space, are in thoroughgoing reciprocity. 
 Things are coexistent when in empirical intuition the
perceptions of them can follow upon one another recipro-
cally, which, as has been shown in the proof of the second
principle, cannot occur in the succession of appearances. 
Thus I can direct my perception first to the moon and then
to the earth, or, conversely, first to the earth and then to the
moon; and because the perceptions of these objects can follow
each other reciprocally, I say that they are coexistent. Now
coexistence is the existence of the manifold in one and the
same time. But time itself cannot be perceived, and we are
not, therefore, in a position to gather, simply from things
being set in the same time, that their perceptions can follow
each other reciprocally. The synthesis of imagination in
apprehension would only reveal that the one perception is
in the subject when the other is not there, and vice versa,
but not that the objects are coexistent, that is, that if the one
exists the other exists at the same time, and that it is only
because they thus coexist that the perceptions are able to follow one another re
++ Principle of Community 
All substances, so far as they coexist, stand in thorough-
going community, that is, in mutual interaction. 
P 234
Consequently, in the case of
things which coexist externally to one another, a pure concept
of the reciprocal sequence of their determinations is required,
if we are to be able to say that the reciprocal sequence of the
perceptions is grounded in the object, and so to represent the
coexistence as objective. But the relation of substances in
which the one contains determinations the ground of which
is contained in the other is the relation of influence; and
when each substance reciprocally contains the ground of the
determinations in the other, the relation is that of community
or reciprocity. Thus the coexistence of substances in space
cannot be known in experience save on the assumption of
their reciprocal interaction. This is therefore the condition
of the possibility of the things themselves as objects of
Things are coexistent so far as they exist in one and the
same time. But how do we know that they are in one and the
same time? We do so when the order in the synthesis of ap-
prehension of the manifold is a matter of indifference, that is,
whether it be from A through B, C, D to E, or reversewise
from E to A. For if they were in succession to one another
in time, in the order, say, which begins with A and ends in
E, it is impossible that we should begin the apprehension in
the perception of E and proceed backwards to A, since A
belongs to past time and can no longer be an object of appre-
 Now assuming that in a manifold of substances as appear-
ances each of them is completely isolated, that is, that no one
acts on any other and receives reciprocal influences in return,
I maintain that their coexistence would not be an object of a
possible perception and that the existence of one could not
lead by any path of empirical synthesis to the existence of
another. For if we bear in mind that they would be separated
by a completely empty space, the perception which advances
from one to another in time would indeed, by means of a
succeeding perception, determine the existence of the latter,
but would not be able to distinguish whether it follows object-
P 235
ively upon the first or whether it is not rather coexistent
with it. 
There must, therefore, besides the mere existence of A and
B, be something through which A determines for B, and also
reversewise B determines for A, its position in time, because
only on this condition can these substances be empirically
represented as coexisting. Now only that which is the cause of
another, or of its determinations, determines the position of the
other in time. Each substance (inasmuch as only in respect of
its determinations can it be an effect) must therefore contain
in itself the causality of certain determinations in the other
substance, and at the same time the effects of the causality of
that other; that is, the substances must stand, immediately or
mediately, in dynamical community, if their coexistence is to
be known in any possible experience. Now, in respect to the
objects of experience, everything without which the experi-
ence of these objects would not itself be possible is necessary. 
It is therefore necessary that all substances in the [field of]
appearance, so far as they coexist, should stand in thorough-
going community of mutual interaction. 
The word community is in the German language ambigu-
ous. It may mean either communio or commercium. We here
employ it in the latter sense, as signifying a dynamical com-
munity, without which even local community (communio spatii)
could never be empirically known. We may easily recognise
from our experiences that only the continuous influences in all
parts of space can lead our senses from one object to another. 
The light, which plays between our eye and the celestial bodies,
produces a mediate community between us and them, and
thereby shows us that they coexist. We cannot empirically
change our position, and perceive the change, unless matter
in all parts of space makes perception of our position possible
to us. For only thus by means of their reciprocal influence can
the parts of matter establish their simultaneous existence, and
thereby, though only mediately, their coexistence, even to
the most remote objects. Without community each percep-
tion of an appearance in space is broken off from every other,
and the chain of empirical representations, that is, experience,
P 236
would have to begin entirely anew with each new object,
without the least connection with the preceding representation,
and without standing to it in any relation of time. I do not by
this argument at all profess to disprove void space, for it may
exist where perceptions cannot reach, and where there is,
therefore, no empirical knowledge of coexistence. But such a
space is not for us an object of any possible experience. 
The following remarks may be helpful in [further] elucida-
tion [of my argument]. In our mind, all appearances, since
they are contained in a possible experience, must stand in
community (communio) of apperception, and in so far as the
objects are to be represented as coexisting in connection with
each other, they must mutually determine their position in
one time, and thereby constitute a whole. If this subjective
community is to rest on an objective ground, or is to hold of
appearances as substances, the perception of the one must
as ground make possible the perception of the other, and
reversewise -- in order that the succession which is always
found in the perceptions, as apprehensions, may not be as-
cribed to the objects, and in order that, on the contrary, these
objects may be represented as coexisting. But this is a re-
ciprocal influence, that is, a real community (commercium) of
substances; without it the empirical relation of coexistence
could not be met with in experience. Through this com-
mercium the appearances, so far as they stand outside one
another and yet in connection, constitute a composite (com-
positum reale), and such composites are possible in many
different ways. The three dynamical relations, from which
all others spring, are therefore inherence, consequence, and
These, then, are the three analogies of experience. They are
simply principles of the determination of the existence of ap-
pearances in time, according to all its three modes, viz. the rela-
tion to time itself as a magnitude (the magnitude of existence,
that is, duration), the relation in time as a successive series, and
finally the relation in time as a sum of all simultaneous exist-
ence. This unity of time-determination is altogether dynamical. 
P 237
For time is not viewed as that wherein experience immedi-
ately determines position for every existence. Such deter-
mination is impossible, inasmuch as absolute time is not an
object of perception with which appearances could be con-
fronted. What determines for each appearance its position in
time is the rule of the understanding through which alone the
existence of appearances can acquire synthetic unity as regards
relations of time; and that rule consequently determines the
position [in a manner that is] a priori and valid for each and
every time. 
By nature, in the empirical sense, we understand the con-
nection of appearances as regards their existence according
to necessary rules, that is, according to laws. There are certain
laws which first make a nature possible, and these laws are
a priori. Empirical laws can exist and be discovered only
through experience, and indeed in consequence of those original
laws through which experience itself first becomes possible. 
Our analogies therefore really portray the unity of nature in
the connection of all appearances under certain exponents
which express nothing save the relation of time (in so far as
time comprehends all existence) to the unity of apperception
-- such unity being possible only in synthesis according to
rules. Taken together, the analogies thus declare that all
appearances lie, and must lie, in one nature, because without
this a priori unity no unity of experience, and therefore no
determination of objects in it, would be possible. 
As to the mode of proof of which we have made use in
these transcendental laws of nature, and as to their peculiar
character, an observation has to be made which must likewise
be of very great importance as supplying a rule to be followed
in every other attempt to prove a priori propositions that are
intellectual and at the same time synthetic. Had we attempted
to prove these analogies dogmatically; had we, that is to say,
attempted to show from concepts that everything which exists
is to be met with only in that which is permanent, that every
event presupposes something in the preceding state upon
which it follows in conformity with a rule; and finally, that
in the manifold which is coexistent the states coexist in rela-
tion to one another in conformity with a rule and so stand in
P 238
community, all our labour would have been wasted. For through
mere concepts of these things, analyse them as we may, we can
never advance from one object and its existence to the exist-
ence of another or to its mode of existence. But there is an
alternative method, namely, to investigate the possibility of
experience as a knowledge wherein all objects -- if their repre-
sentation is to have objective reality for us -- must finally be
capable of being given to us. In this third [medium], the
essential form of which consists in the synthetic unity of the
apperception of all appearances, we have found a priori con-
ditions of complete and necessary determination of time for
all existence in the [field of] appearance, without which even
empirical determination of time would be impossible. In it we
have also found rules of synthetic unity a priori, by means of
which we can anticipate experience. For lack of this method,
and owing to the erroneous assumption that synthetic proposi-
tions, which the empirical employment of the understanding
recommends as being its principles, may be proved dogmatic-
ally, the attempt has, time and again, been made, though
always vainly, to obtain a proof of the principle of sufficient
reason. And since the guiding-thread of the categories, which
alone can reveal and make noticeable every gap in the under-
standing, alike in regard to concepts and to principles, has
hitherto been lacking, no one has so much as thought of the
other two analogies, although use has always tacitly been
made of them. 
++ The unity of the world-whole, in which all appearances have
to be connected, is evidently a mere consequence of the tacitly
assumed principle of the community of all substances which are
coexistent. For if they were isolated, they would not as parts con-
stitute a whole. And if their connection (the reciprocal action of the
manifold) were not already necessary because of their coexistence,
we could not argue from this latter, which is a merely ideal relation
to the former, which is a real relation. We have, however, in the
proper context, shown that community is really the ground of the
possibility of an empirical knowledge of coexistence, and that the
inference, rightly regarded, is simply from this empirical knowledge
to community as its condition. 
P 239
1. That which agrees with the formal conditions of ex-
perience, that is, with the conditions of intuition and of con-
cepts, is possible. 
2. That which is bound up with the material conditions
of experience, that is, with sensation, is actual. 
3. That which in its connection with the actual is deter-
mined in accordance with universal conditions of experience,
is (that is, exists as) necessary. 
The categories of modality have the peculiarity that, in
determining an object, they do not in the least enlarge the
concept to which they are attached as predicates. They only
express the relation of the concept to the faculty of knowledge. 
Even when the concept of a thing is quite complete, I can still
enquire whether this object is merely possible or is also actual,
or if actual, whether it is not also necessary. No additional
determinations are thereby thought in the object itself; the
question is only how the object, together with all its deter-
minations, is related to understanding and its empirical em-
ployment, to empirical judgment, and to reason in its appli-
cation to experience. 
Just on this account also the principles of modality are
nothing but explanations of the concepts of possibility, actual-
ity, and necessity, in their empirical employment; at the same
time they restrict all categories to their merely empirical em-
ployment, and do not approve or allow their transcendental
employment. For if they are not to have a purely logical sig-
nificance, analytically expressing the form of thought, but are
to refer to the possibility, actuality, or necessity of things, they
must concern possible experience and its synthetic unity, in
which alone objects of knowledge can be given. 
The postulate of the possibility of things requires that
the concept of the things should agree with the formal con-
ditions of an experience in general. But this, the objective
form of experience in general, contains all synthesis that is
P 240
required for knowledge of objects. A concept which contains
a synthesis is to be regarded as empty and as not related to
any object, if this synthesis does not belong to experience
either as being derived from it, in which case it is an empirical
concept, or as being an a priori condition upon which experi-
ence in general in its formal aspect rests, in which case it is
a pure concept. In the latter case it still belongs to experience,
inasmuch as its object is to be met with only in experience. 
For whence shall we derive the character of the possibility of
an object which is thought through a synthetic a priori con-
cept, if not from the synthesis which constitutes the form of
the empirical knowledge of objects? It is, indeed, a necessary
logical condition that a concept of the possible must not con-
tain any contradiction; but this is not by any means sufficient
to determine the objective reality of the concept, that is, the pos-
sibility of such an object as is thought through the concept. 
Thus there is no contradiction in the concept of a figure which
is enclosed within two straight lines, since the concepts of two
straight lines and of their coming together contain no negation
of a figure. The impossibility arises not from the concept in
itself, but in connection with its construction in space, that is,
from the conditions of space and of its determination. And
since these contain a priori in themselves the form of experi-
ence in general, they have objective reality, that is, they apply
to possible things. 
We shall now proceed to show the far-reaching utility and
influence of this postulate of possibility. If I represent to my-
self a thing which is permanent, so that everything in it which
changes belongs only to its state, I can never know from such
a concept that a thing of this kind is possible. Or if I represent
to myself something which is so constituted that if it is posited
something else invariably and inevitably follows from it, this
may certainly be so thought without contradiction; but this
thought affords no means of judging whether this property
(causality) is to be met with in any possible thing. Lastly,
I can represent to myself diverse things (substances), which
are so constituted that the state of the one carries with it some
consequence in the state of the other, and this reciprocally;
but I can never determine from these concepts, which contain
a merely arbitrary synthesis, whether a relation of this kind
P 241
can belong to any [possible] things. Only through the fact that
these concepts express a priori the relations of perceptions in
every experience, do we know their objective reality, that is
their transcendental truth, and this, indeed, independently of
experience, though not independently of all relation to the
form of an experience in general, and to the synthetic unity
in which alone objects can be empirically known. 
But if we should seek to frame quite new concepts of sub-
stances, forces, reciprocal actions, from the material which
perception presents to us, without experience itself yielding
the example of their connection, we should be occupying our-
selves with mere fancies, of whose possibility there is absolutely
no criterion since we have neither borrowed these concepts
[directly] from experience, nor have taken experience as our
instructress in their formation. Such fictitious concepts, un-
like the categories, can acquire the character of possibility not
in a priori fashion, as conditions upon which all experience
depends, but only a posteriori as being concepts which are
given through experience itself. And, consequently, their pos-
sibility must either be known a posteriori and empirically, or
it cannot be known at all. A substance which would be per-
manently present in space, but without filling it (like that
mode of existence intermediate between matter and thinking
being which some would seek to introduce), or a special ulti-
mate mental power of intuitively anticipating the future (and
not merely inferring it), or lastly a power of standing in com-
munity of thought with other men, however distant they may
be -- are concepts the possibility of which is altogether ground-
less, as they cannot be based on experience and its known laws;
and without such confirmation they are arbitrary combinations
of thoughts, which, although indeed free from contradiction,
can make no claim to objective reality, and none, therefore, as
to the possibility of an object such as we here profess to think. 
As regards reality, we obviously cannot think it in concreto,
without calling experience to our aid. For reality is bound up
with sensation, the matter of experience, not with that form
of relation in regard to which we can, if we so choose, resort
to a playful inventiveness. 
But I leave aside everything the possibility of which can
P 242
be derived only from its actuality in experience, and have here
in view only the possibility of things through a priori concepts;
and I maintain the thesis that their possibility can never be
established from such concepts taken in and by themselves,
but only when the concepts are viewed as formal and objective
conditions of experience in general. 
It does, indeed, seem as if the possibility of a triangle could
be known from its concept in and by itself (the concept is cer-
tainly independent of experience), for we can, as a matter of
fact, give it an object completely a priori, that is, can construct
it. But since this is only the form of an object, it would remain
a mere product of imagination, and the possibility of its object
would still be doubtful. To determine its possibility, something
more is required, namely, that such a figure be thought under
no conditions save those upon which all objects of experience
rest. That space is a formal a priori condition of outer experi-
ences, that the formative synthesis through which we con-
struct a triangle in imagination is precisely the same as that
which we exercise in the apprehension of an appearance, in
making for ourselves an empirical concept of it -- these are the
considerations that alone enable us to connect the representa-
tion of the possibility of such a thing with the concept of it. 
Similarly, since the concepts of continuous magnitudes, indeed
of magnitudes in general, are one and all synthetic, the possi-
bility of such magnitudes is never clear from the concepts them-
selves, but only when they are viewed as formal conditions
of the determination of objects in experience in general. And
where, indeed, should we seek for objects corresponding to
these concepts if not in experience, through which alone ob-
jects are given to us? We can, indeed, prior to experience
itself, know and characterise the possibility of things, merely
by reference to the formal conditions under which in experi-
ence anything whatsoever is determined as object, and
therefore can do so completely a priori. But, even so, this is
possible only in relation to experience and within its limits. 
 The postulate bearing on the knowledge of things as
actual does not, indeed, demand immediate perception (and,
therefore, sensation of which we are conscious) of the object
whose existence is to be known. What we do, however,
P 243
require is the connection of the object with some actual
perception, in accordance with the analogies of experi-
ence, which define all real connection in an experience in
In the mere concept of a thing no mark of its existence is
to be found. For though it may be so complete that nothing
which is required for thinking the thing with all its inner deter-
minations is lacking to it, yet existence has nothing to do with
all this, but only with the question whether such a thing be so
given us that the perception of it can, if need be, precede the
concept. For that the concept precedes the perception signi-
fies the concept's mere possibility; the perception which sup-
plies the content to the concept is the sole mark of actuality. 
We can also, however, know the existence of the thing prior to
its perception and, consequently, comparatively speaking, in
an a priori manner, if only it be bound up with certain percep-
tions, in accordance with the principles of their empirical con-
nection (the analogies). For the existence of the thing being
thus bound up with our perceptions in a possible experience,
we are able in the series of possible perceptions and under the
guidance of the analogies to make the transition from our
actual perception to the thing in question. Thus from the per-
ception of the attracted iron filings we know of the existence
of a magnetic matter pervading all bodies, although the con-
stitution of our organs cuts us off from all immediate percep-
tion of this medium. For in accordance with the laws of sensi-
bility and the context of our perceptions, we should, were our
senses more refined, come also in an experience upon the im-
mediate empirical intuition of it. The grossness of our senses
does not in any way decide the form of possible experience in
general. Our knowledge of the existence of things reaches,
then, only so far as perception and its advance according
to empirical laws can extend. If we do not start from ex-
perience, or do not proceed accordance with laws of the em-
P 244
pirical connection of appearances, our guessing or enquiring
into the existence of anything will only be an idle pretence. 
Idealism raises, however, what is a serious objection to these
rules for proving existence mediately; and this is the proper
place for its refutation. 
Refutation of Idealism 
Idealism -- meaning thereby material idealism -- is the
theory which declares the existence of objects in space out-
side us either to be merely doubtful and indemonstrable or to
be false and impossible. The former is the problematic ideal-
ism of Descartes, which holds that there is only one empirical
assertion that is indubitably certain, namely, that 'I am'. The
latter is the dogmatic idealism of Berkeley. He maintains that
space, with all the things of which it is the inseparable condi-
tion, is something which is in itself impossible; and he there-
fore regards the things in space as merely imaginary entities. 
Dogmatic idealism is unavoidable, if space be interpreted as a
property that must belong to things in themselves. For in that
case space, and everything to which it serves as condition, is a
non-entity. The ground on which this idealism rests has al-
ready been undermined by us in the Transcendental Aesthetic. 
Problematic idealism, which makes no such assertion, but
merely pleads incapacity to prove, through immediate experi-
ence, any existence except our own, is, in so far as it allows
of no decisive judgment until sufficient proof has been found,
reasonable and in accordance with a thorough and philo-
sophical mode of thought. The required proof must, therefore,
show that we have experience, and not merely imagination of
outer things; and this, it would seem, cannot be achieved save
by proof that even our inner experience, which for Descartes
is indubitable, is possible only on the assumption of outer ex-
P 245
The mere, but empirically determined, consciousness of my
own existence proves the existence of objects in space
outside me. 
I am conscious of my own existence as determined in
time. All determination of time presupposes something per-
manent in perception. This permanent cannot, however,
be something in me, since it is only through this per-
manent that my existence in time can itself be deter-
mined. Thus perception of this permanent is possible only
through a thing outside me and not through the mere re-
presentation of a thing outside me; and consequently the
determination of my existence in time is possible only through
the existence of actual things which I perceive outside me. 
Now consciousness [of my existence] in time is necessarily
bound up with consciousness of the [condition of the] possi-
bility of this time-determination; and it is therefore necessarily
bound up with the existence of things outside me, as the
condition of the time-determination. In other words, the con-
sciousness of my existence is at the same time an immediate
consciousness of the existence of other things outside me. 
Note 1. It will be observed that in the foregoing proof
the game played by idealism has been turned against itself,
and with greater justice. Idealism assumed that the only
immediate experience is inner experience, and that from it
we can only infer outer things -- and this, moreover, only in an
untrustworthy manner, as in all cases where we are inferring
from given effects to determinate causes. In this particular case,
the cause of the representations, which we ascribe, perhaps
falsely, to outer things, may lie in ourselves. But in the above
proof it has been shown that outer experience is really
P 246
immediate, and that only by means of it is inner experience
-- not indeed the consciousness of my own existence, but the
determination of it in time -- possible. Certainly, the repre-
sentation 'I am', which expresses the consciousness that can
accompany all thought, immediately includes in itself the
existence of a subject; but it does not so include any knowledge
of that subject, and therefore also no empirical knowledge,
that is, no experience of it. For this we require, in addition to
the thought of something existing, also intuition, and in this
case inner intuition, in respect of which, that is, of time, the
subject must be determined. But in order so to determine it,
outer objects are quite indispensable; and it therefore follows
that inner experience is itself possible only mediately, and
only through outer experience. 
Note 2. With this thesis all employment of our cognitive
faculty in experience, in the determination of time, entirely
agrees. Not only are we unable to perceive any deter-
mination of time save through change in outer relations
(motion) relatively to the permanent in space (for instance,
the motion of the sun relatively to objects on the earth), we
have nothing permanent on which, as intuition, we can base
the concept of a substance, save only matter; and even this
permanence is not obtained from outer experience, but is
presupposed a priori as a necessary condition of determina-
tion of time, and therefore also as a determination of inner
sense in respect of [the determination of] our own existence
through the existence of outer things. 
++ The immediate consciousness of the existence of outer things
is, in the preceding thesis, not presupposed, but proved, be the
possibility of this consciousness understood by us or not. The ques-
tion as to its possibility would be this: whether we have an inner
sense only, and no outer sense, but merely an outer imagination. It
is clear, however, that in order even only to imagine something as
outer, that is, to present it to sense in intuition, we must already
have an outer sense, and must thereby immediately distinguish the
mere receptivity of an outer intuition from the spontaneity which
characterises every act of imagination. For should we merely be
imagining an outer sense, the faculty of intuition, which is to be
determined by the faculty of imagination, would itself be annulled. 
P 246
The consciousness of
myself in the representation 'I' is not an intuition, but a
P 247
merely intellectual representation of the spontaneity of a
thinking subject. This 'I' has not, therefore, the least pre-
dicate of intuition, which, as permanent, might serve as cor-
relate for the determination of time in inner sense -- in the
manner in which, for instance, impenetrability serves in our
empirical intuition of matter. 
Note 3. From the fact that the existence of outer things
is required for the possibility of a determinate consciousness
of the self, it does not follow that every intuitive representa-
tion of outer things involves the existence of these things,
for their representation can very well be the product merely
of the imagination (as in dreams and delusions). Such re-
presentation is merely the reproduction of previous outer
perceptions, which, as has been shown, are possible only
through the reality of outer objects. All that we have here
sought to prove is that inner experience in general is possible
only through outer experience in general. Whether this or that
supposed experience be not purely imaginary, must be ascer-
tained from its special determinations, and through its con-
gruence with the criteria of all real experience. 
Lastly, as regards the third postulate, it concerns material
necessity in existence, and not merely formal and logical
necessity in the connection of concepts. Since the existence of
any object of the senses cannot be known completely a priori,
but only comparatively a priori, relatively to some other pre-
viously given existence; and since, even so, we can then
arrive only at such an existence as must somewhere be
contained in the context of the experience, of which the
given perception is a part, the necessity of existence can
never be known from concepts, but always only from con-
nection with that which is perceived, in accordance with
universal laws of experience. Now there is no existence that
can be known as necessary under the condition of other given
appearances, save the existence of effects from given causes,
P 248
in accordance with laws of causality. It is not, therefore, the
existence of things (substances) that we can know to be neces-
sary, but only the existence of their state; and this necessity
of the existence of their state we can know only from other
states, which are given in perception, in accordance with
empirical laws of causality. It therefore follows that the cri-
terion of necessity lies solely in the law of possible experience,
the law that everything which happens is determined a priori
through its cause in the [field of] appearance. We thus know
the necessity only of those effects in nature the causes of which
are given to us, and the character of necessity in existence
extends no further than the field of possible experience, and
even in this field is not applicable to the existence of things as
substances, since substances can never be viewed as empirical
effects -- that is, as happening and coming to be. Necessity con-
cerns only the relations of appearances in conformity with the
dynamical law of causality and the possibility grounded upon
it of inferring a priori from a given existence (a cause) to
another existence (the effect). That everything which happens
is hypothetically necessary is a principle which subordinates
alteration in the world to a law, that is, to a rule of necessary
existence, without which there would be nothing that could be
entitled nature. The proposition that nothing happens through
blind chance (in mundo non datur casus) is therefore an a -
priori law of nature. So also is the proposition that no neces-
sity in nature is blind, but always a conditioned and therefore
intelligible necessity (non datur fatum). Both are laws through
which the play of alterations is rendered subject to a nature of
things (that is, of things as appearances), or what amounts to
the same thing, to the unity of understanding, in which
alone they can belong to one experience, that is, to the syn-
thetic unity of appearances. Both belong to the class of
dynamical principles. The first is really a consequence of the
principle of causality, and so belongs to the analogies of
experience. The second is a principle of modality; but this
modality, while adding the concept of necessity to causal
determination, itself stands under a rule of understanding. 
The principle of continuity forbids any leap in the series of
appearances, that is, of alterations (in mundo non datur saltus);
P 249
it also forbids, in respect of the sum of all empirical intuitions
in space, any gaps or cleft between two appearances (non
datur hiatus); for so we may express the proposition, that
nothing which proves a vacuum, or which even admits it as a
part of empirical synthesis, can enter into experience. As regards
a void which may be conceived to lie beyond the field of possible
experience, that is, outside the world, such a question does not
come within the jurisdiction of the mere understanding -- which
decides only upon questions that concern the use to be made
of given appearances for the obtaining of empirical know-
ledge. It is a problem for that ideal reason which goes out
beyond the sphere of a possible experience and seeks to judge
of that which surrounds and limits it; and is a problem which
will therefore have to be considered in the Transcendental
Dialectic. These four propositions (in mundo non datur
hiatus, non datur saltus, non datur casus, non datur fatum),
like all principles of transcendental origin, we can easily ex-
hibit in their order, that is, in accordance with the order of
the categories, and so assign to each its proper place. But the
reader has now had sufficient practice to allow of his doing
this for himself, or of easily discovering the guiding principle
for so doing. They are all entirely at one in this, that they
allow of nothing in the empirical synthesis which may do
violence or detriment to the understanding and to the con-
tinuous connection of all appearances -- that is, to the unity of
the concepts of the understanding. For in the understanding
alone is possible the unity of experience, in which all percep-
tions must have their place. 
To enquire whether the field of possibility is larger than the
field which contains all actuality, and this latter, again, larger
than the sum of that which is necessary, is to raise somewhat
subtle questions which demand a synthetic solution and yet
come under the jurisdiction of reason alone. For they are
tantamount to the enquiry whether things as appearances one
and all belong to the sum and context of a single experience,
of which every given perception is a part, a part which there-
fore cannot be connected with any other [series of] appearances,
or whether my perceptions can belong, in their general con-
nection, to more than one possible experience. The under-
P 250
standing, in accordance with the subjective and formal con-
ditions of sensibility as well as of apperception, prescribes
a priori to experience in general the rules which alone make
experience possible. Other forms of intuition than space and
time, other forms of understanding than the discursive forms
of thought, or of knowledge through concepts, even if they
should be possible, we cannot render in any way conceivable
and comprehensible to ourselves; and even assuming that we
could do so, they still would not belong to experience -- the
only kind of knowledge in which objects are given to us. 
Whether other perceptions than those belonging to our whole
possible experience, and therefore a quite different field of
matter, may exist, the understanding is not in a position to
decide. It can deal only with the synthesis of that which is
given. Moreover, the poverty of the customary inferences
through which we throw open a great realm of possibility, of
which all that is actual (the objects of experience) is only a small
part, is patently obvious. Everything actual is possible; from
this proposition there naturally follows, in accordance with the
logical rules of conversion, the merely particular proposition,
that some possible is actual; and this would seem to mean
that much is possible which is not actual. It does indeed
seem as if we were justified in extending the number of
possible things beyond that of the actual, on the ground
that something must be added to the possible to constitute
the actual. But this [alleged] process of adding to the pos-
sible I refuse to allow. For that which would have to be
added to the possible, over and above the possible, would
be impossible. What can be added is only a relation to my
understanding, namely that in addition to agreement with
the formal conditions of experience there should be connect-
tion with some perception. But whatever is connected with
perception in accordance with empirical laws is actual, even
although it is not immediately perceived. That yet another
series of appearances in thoroughgoing connection with that
which is given in perception, and consequently that more
than one all-embracing experience is possible, cannot be in-
ferred from what is given; and still less can any such infer-
ence be drawn independently of anything being given -- since
P 251
without material nothing whatsoever can be thought. What
is possible only under conditions which themselves are merely
possible is not in all respects possible. But such [absolute]
possibility is in question when it is asked whether the possi-
bility of things extends further than experience can reach. 
I have made mention of these questions only in order to
omit nothing which is ordinarily reckoned among the concepts
of understanding. But as a matter of fact absolute possibility,
that which is in all respects valid, is no mere concept of
understanding, and can never be employed empirically. It
belongs exclusively to reason, which transcends all possible
empirical employment of the understanding. We have there-
fore had to content ourselves with some merely critical re-
marks; the matter must otherwise be left in obscurity until we
come to the proper occasion for its further treatment. 
Before concluding this fourth section, and therewith the
system of all principles of pure understanding, I must explain
why I have entitled the principles of modality postulates. I
interpret this expression not in the sense which some recent
philosophical writers, wresting it from its proper mathematical
significance, have given to it, namely, that to postulate should
mean to treat a proposition as immediately certain, with-
out justification or proof. For if, in dealing with synthetic
propositions, we are to recognise them as possessing un-
conditioned validity, independently of deduction, on the evi-
dence [merely] of their own claims, then no matter how evident
they may be, all critique of understanding is given up. And
since there is no lack of audacious pretensions, and these are
supported by common belief (though that is no credential of
their truth), the understanding lies open to every fancy, and is
in no position to withhold approval of those assertions which,
though illegitimate, yet press upon us, in the same confident
tone, their claims to be accepted as actual axioms. Whenever,
therefore, an a priori determination is synthetically added to
the concept of a thing, it is indispensable that, if not a proof,
at least a deduction of the legitimacy of such an assertion
should be supplied. 
The principles of modality are not, however, objectively
synthetic. For the predicates of possibility, actuality, and
P 252
necessity do not in the least enlarge the concept of which they
are affirmed, adding something to the representation of the
object. But since they are none the less synthetic, they are so
subjectively only, that is, they add to the concept of a thing (of
something real), of which otherwise they say nothing, the cog-
nitive faculty from which it springs and in which it has its seat. 
Thus if it is in connection only with the formal conditions of
experience, and so merely in the understanding, its object is
called possible. If it stands in connection with perception, that is,
with sensation as material supplied by the senses, and through
perception is determined by means of the understanding, the
object is actual. If it is determined through the connection of per-
ceptions according to concepts, the object is entitled necessary. 
The principles of modality thus predicate of a concept nothing
but the action of the faculty of knowledge through which it
is generated. Now in mathematics a postulate means the prac-
tical proposition which contains nothing save the synthesis
through which we first give ourselves an object and generate
its concept -- for instance, with a given line, to describe a circle
on a plane from a given point. Such a proposition cannot be
proved, since the procedure which it demands is exactly that
through which we first generate the concept of such a figure. 
With exactly the same right we may postulate the principles of
modality, since they do not increase our concept of things,
but only show the manner in which it is connected with the
faculty of knowledge. 
 General Note on the System of the Principles 
That the possibility of a thing cannot be determined from
the category alone, and that in order to exhibit the objective
reality of the pure concept of understanding we must always
have an intuition, is a very noteworthy fact. 
++ Through the actuality of a thing I certainly posit more than
the possibility of it, but not in the thing. For it can never contain
more in its actuality than is contained in its complete possibility. 
But while possibility is merely a positing of the thing in relation to
the understanding (in its empirical employment), actuality is at the
same time a connection of it with perception. 
P 253
Take, for instance,
the categories of relation. We cannot determine from mere
concepts how (1) something can exist as subject only, and not
as a mere determination of other things, that is, how a thing
can be substance, or (2) how, because something is, something
else must be, and how, therefore, a thing can be a cause, or (3)
when several things exist, how because one of them is there,
something follows in regard to the others and vice versa, and
how in this way there can be a community of substances. 
This likewise applies to the other categories; for example,
how a thing can be equal to a number of things taken together,
that is, can be a quantity. So long as intuition is lacking, we do
not know whether through the categories we are thinking an
object, and whether indeed there can anywhere be an object
suited to them. In all these ways, then, we obtain confirmation
that the categories are not in themselves knowledge, but are
merely forms of thought for the making of knowledge from
given intuitions. 
For the same reason it follows that no synthetic proposi-
tion can be made from mere categories. For instance, we are
not in a position to say that in all existence there is substance,
that is, something which can exist only as subject and not as
mere predicate; or that everything is a quantum, etc. For if
intuition be lacking, there is nothing which can enable us to
go out beyond a given concept, and to connect another with it. 
No one, therefore, has ever yet succeeded in proving a syn-
thetic proposition merely from pure concepts of the under-
standing -- as, for instance, that everything which exists con-
tingently has a cause. We can never get further than proving,
that without this relation we are unable to comprehend the
existence of the contingent, that is, are unable a priori through
the understanding to know the existence of such a thing --
from which it does not, however, follow that this is also a con-
dition of the possibility of the things themselves. If the reader
will go back to our proof of the principle of causality -- that
everything which happens, that is, every event, presupposes a
cause -- he will observe that we were able to prove it only of
objects of possible experience; and even so, not from pure con-
cepts, but only as a principle of the possibility of experience,
and therefore of the knowledge of an object given in empirical
P 254
intuition. We cannot, indeed, deny that the proposition, that
everything contingent must have a cause, is patent to every-
one from mere concepts. But the concept of the contingent
is then being apprehended as containing, not the category
of modality (as something the not-being of which can be
thought), but that of relation (as something which can exist
only as consequence of something else); and it is then, of
course, an identical proposition -- that which can exist only
as consequence has a cause. As a matter of fact, when we are
required to cite examples of contingent existence, we invari-
ably have recourse to alterations, and not merely to the possi-
bility of entertaining the opposite in thought. Now alteration
is an event which, as such, is possible only through a cause, and
the not-being of which is therefore in itself possible. In other
words, we recognise contingency in and through the fact that
something can exist only as the effect of a cause; and if, there-
fore, a thing is assumed to be contingent, it is an analytic pro-
position to say that it has a cause. 
But it is an even more noteworthy fact, that in order to
understand the possibility of things in conformity with the
categories, and so to demonstrate the objective reality of the
latter, we need, not merely intuitions, but intuitions that are in
all cases outer intuitions. When, for instance, we take the pure
concepts of relation, we find, firstly, that in order to obtain
something permanent in intuition corresponding to the con-
cept of substance, and so to demonstrate the objective reality
of this concept, we require an intuition in space (of matter). 
++ We can easily think the non-existence of matter. From this
the ancients did not, however, infer its contingency. Even the
change from being to not-being of a given state of a thing, in which
all alteration consists, does not prove the contingency of this
state, on the ground of the reality of its opposite. For instance, that
a body should come to rest after having been in motion does not
prove the contingency of the motion as being the opposite of the
state of rest. For this opposite is opposed to the other only logically,
not realiter. To prove the contingency of its motion, we should have
to prove that instead of the motion at the preceding moment, it was
possible for the body to have been then at rest, not that it is after-
wards at rest; for in the latter case the opposites are quite consistent
with each other. 
P 255
For space alone is determined as permanent, while time, and
therefore everything that is in inner sense, is in constant flux. 
Secondly, in order to exhibit alteration as the intuition corre-
sponding to the concept of causality, we must take as our
example motion, that is, alteration in space. Only in this way
can we obtain the intuition of alterations, the possibility of
which can never be comprehended through any pure under-
standing. For alteration is combination of contradictorily
opposed determinations in the existence of one and the same
thing. Now how it is possible that from a given state of a thing
an opposite state should follow, not only cannot be conceived
by reason without an example, but is actually incomprehensible
to reason without intuition. The intuition required is the in-
tuition of the movement of a point in space. The presence of
the point in different locations (as a sequence of opposite de-
terminations) is what alone first yields to us an intuition of
alteration. For in order that we may afterwards make inner
alterations likewise thinkable, we must represent time (the
form of inner sense) figuratively as a line, and the inner
alteration through the drawing of this line (motion), and so
in this manner by means of outer intuition make compre-
hensible the successive existence of ourselves in different
states. The reason of this is that all alteration, if it is to be
perceived as alteration, presupposes something permanent in
intuition, and that in inner sense no permanent intuition is
to be met with. Lastly, the possibility of the category of
community cannot be comprehended through mere reason
alone; and consequently its objective reality is only to be de-
termined through intuition, and indeed through outer intuition
in space. For how are we to think it to be possible, when several
substances exist, that, from the existence of one, something (as
effect) can follow in regard to the existence of the others, and
vice versa; in other words, that because there is something
in the one there must also in the others be something which
is not to be understood solely from the existence of these
others? For this is what is required in order that there be com-
munity; community is not conceivable as holding between
things each of which, through its subsistence, stands in com-
plete isolation. Leibniz, in attributing to the substances of the
P 256
world, as thought through the understanding alone, a com-
munity, had therefore to resort to the mediating intervention
of a Deity. For, as he justly recognised, a community of sub-
stances is utterly inconceivable as arising simply from their
existence. We can, however, render the possibility of com-
munity -- of substances as appearances -- perfectly compre-
hensible, if we represent them to ourselves in space, that is,
in outer intuition. For this already contains in itself a priori
formal outer relations as conditions of the possibility of the
real relations of action and reaction, and therefore of the
possibility of community. 
Similarly, it can easily be shown that the possibility of
things as quantities, and therefore the objective reality of
quantity, can be exhibited only in outer intuition, and that
only through the mediation of outer intuition can it be applied
also to inner sense. But, to avoid prolixity, I must leave the
reader to supply his own examples of this. 
These remarks are of great importance, not only in con-
firmation of our previous refutation of idealism, but even
more, when we come to treat of self-knowledge by mere inner
consciousness, that is, by determination of our nature without
the aid of outer empirical intuitions -- as showing us the limits
of the possibility of this kind of knowledge. 
The final outcome of this whole section is therefore this:
all principles of the pure understanding are nothing more than
principles a priori of the possibility of experience, and to
experience alone do all a priori synthetic propositions relate --
indeed, their possibility itself rests entirely on this relation. 
P 257
WE have now not merely explored the territory of pure under-
standing, and carefully surveyed every part of it, but have
also measured its extent, and assigned to everything in it its
rightful place. This domain is an island, enclosed by nature
itself within unalterable limits. It is the land of truth -- en-
chanting name! -- surrounded by a wide and stormy ocean,
the native home of illusion, where many a fog bank and many
a swiftly melting iceberg give the deceptive appearance of
farther shores, deluding the adventurous seafarer ever anew
with empty hopes, and engaging him in enterprises which
he can never abandon and yet is unable to carry to com-
pletion. Before we venture on this sea, to explore it in
all directions and to obtain assurance whether there be any
ground for such hopes, it will be well to begin by casting
a glance upon the map of the land which we are about
to leave, and to enquire, first, whether we cannot in any
case be satisfied with what it contains -- are not, indeed,
under compulsion to be satisfied, inasmuch as there may be
no other territory upon which we can settle; and, secondly,
by what title we possess even this domain, and can consider
ourselves as secured against all opposing claims. Although
we have already given a sufficient answer to these questions
in the course of the Analytic, a summary statement of its
solutions may nevertheless help to strengthen our conviction,
by focussing the various considerations in their bearing on
the questions now before us. 
P 258
We have seen that everything which the understanding
derives from itself is, though not borrowed from experience,
at the disposal of the understanding solely for use in experi-
ence. The principles of pure understanding, whether con-
stitutive a priori, like the mathematical principles, or merely
regulative, like the dynamical, contain nothing but what
may be called the pure schema of possible experience. For
experience obtains its unity only from the synthetic unity
which the understanding originally and of itself confers
upon the synthesis of imagination in its relation to apper-
ception; and the appearances, as data for a possible know-
ledge, must already stand a priori in relation to, and in agree-
ment with, that synthetic unity. But although these rules of
understanding are not only true a priori, but are indeed
the source of all truth (that is, of the agreement of our know-
ledge with objects), inasmuch as they contain in themselves
the ground of the possibility of experience viewed as the sum
of all knowledge wherein objects can be given to us, we are
not satisfied with the exposition merely of that which is true,
but likewise demand that account be taken of that which we
desire to know. If, therefore, from this critical enquiry we
learn nothing more than what, in the merely empirical em-
ployment of understanding, we should in any case have
practised without any such subtle enquiry, it would seem
as if the advantage derived from it by no means repays
the labour expended. The reply may certainly be made that
in the endeavour to extend our knowledge a meddlesome
curiosity is far less injurious than the habit of always insisting,
before entering on any enquiries, upon antecedent proof of
the utility of the enquiries -- an absurd demand, since prior
to completion of the enquiries we are not in a position to form
the least conception of this utility, even if it were placed before
our eyes. There is, however, one advantage which may be
made comprehensible and of interest even to the most re-
fractory and reluctant learner, the advantage, that while the
understanding, occupied merely with its empirical employ-
ment, and not reflecting upon the sources of its own know-
ledge, may indeed get along quite satisfactorily, there is yet
one task to which it is not equal, that, namely, of determining
the limits of its employment, and of knowing what it is that
P 259
may lie within and what it is that lies without its own proper
sphere. This demands just those deep enquiries which we have
instituted. If the understanding in its empirical employment
cannot distinguish whether certain questions lie within its
horizon or not, it can never be assured of its claims or of its
possessions, but must be prepared for many a humiliating
disillusionment, whenever, as must unavoidably and con-
stantly happen, it oversteps the limits of its own domain,
and loses itself in opinions that are baseless and mis-
If the assertion, that the understanding can employ its
various principles and its various concepts solely in an em-
pirical and never in a transcendental manner, is a proposition
which can be known with certainty, it will yield important
consequences. The transcendental employment of a concept
in any principle is its application to things in general and in
themselves; the empirical employment is its application merely
to appearances; that is, to objects of a possible experience. That
the latter application of concepts is alone feasible is evident
from the following considerations. We demand in every con-
cept, first, the logical form of a concept (of thought) in general,
and secondly, the possibility of giving it an object to which
it may be applied. In the absence of such object, it has no
meaning and is completely lacking in content, though it may
still contain the logical function which is required for making
a concept out of any data that may be presented. Now the
object cannot be given to a concept otherwise than in intui-
tion; for though a pure intuition can indeed precede the object
a priori, even this intuition can acquire its object, and there-
fore objective validity, only through the empirical intuition
of which it is the mere form. Therefore all concepts, and
with them all principles, even such as are possible a priori,
relate to empirical intuitions, that is, to the data for a
possible experience. Apart from this relation they have no
objective validity, and in respect of their representations are
a mere play of imagination or of understanding. Take, for
instance, the concepts of mathematics, considering them first
of all in their pure intuitions. Space has three dimensions;
between two points there can be only one straight line, etc. 
Although all these principles, and the representation of the
P 260
object with which this science occupies itself, are generated
in the mind completely a priori, they would mean nothing,
were we not always able to present their meaning in appear-
ances, that is, in empirical objects. We therefore demand
that a bare concept be made sensible, that is, that an object
corresponding to it be presented in intuition. Otherwise the
concept would, as we say, be without sense, that is, without
meaning. The mathematician meets this demand by the con-
struction of a figure, which, although produced a priori, is an
appearance present to the senses. In the same science the
concept of magnitude seeks its support and sensible meaning
in number, and this in turn in the fingers, in the beads of the
abacus, or in strokes and points which can be placed before
the eyes. The concept itself is always a priori in origin, and
so likewise are the synthetic principles or formulas derived
from such concepts; but their employment and their relation
to their professed objects can in the end be sought nowhere
but in experience, of whose possibility they contain the formal
 That this is also the case with all categories and the prin-
ciples derived from them, appears from the following con-
sideration. We cannot define any one of them in any real
fashion, that is, make the possibility of their object under-
standable, without at once descending to the conditions of
sensibility, and so to the form of appearances -- to which, as
their sole objects, they must consequently be limited. For if
this condition be removed, all meaning, that is, relation to the
object, falls away; and we cannot through any example make
comprehensible to ourselves what sort of a thing is to be meant
by such a concept. 
++ In the above statement of the table of categories, we relieved
ourselves of the task of defining each of them, as our purpose,
which concerned only their synthetic employment, did not
require such definition, and we are not called upon to incur
any responsibility through unnecessary undertakings from
which we can be relieved. 
P 261
The concept of magnitude in general can never be explained
except by saying that it is that determination of a thing
whereby we are enabled to think how many times a unit is posited
in it. But this how-many-times is based on successive repetition,
and therefore on time and the synthesis of the homogeneous
in time. Reality, in contradistinction to negation, can be ex-
plained only if we think time (as containing all being) as either
filled with being or as empty. If I leave out permanence (which
is existence in all time), nothing remains in the concept of sub-
stance save only the logical representation of a subject -- a re-
presentation which I endeavour to realise by representing to
myself something which can exist only as subject and never as predicate. 
++ It was no evasion but an important
prudential maxim, not to embark upon the task of definition,
attempting or professing to attain completeness and precision
in the determination of a concept, so long as we can achieve our
end with one or other of its properties, without requiring a
complete enumeration of all those that constitute the com-
plete concept. But we now perceive that the ground of this
precaution lies still deeper. We realise that we are unable to
define them even if we wished. For if we remove all those
conditions of sensibility which mark them out as concepts of
possible empirical employment, and view them as concepts of
things in general and therefore of transcendental employment,
all that we can then do with them is to regard the logical
function in judgments [to which they give expression] as the
condition of the possibility of the things themselves, without
in the least being able to show how they can have application
to an object, that is, how in pure understanding, apart from
sensibility, they can have meaning and objective validity. 
++ I here mean real definition -- which does not merely substitute
for the name of a thing other more intelligible words, but contains
a clear property by which the defined object can always be known
with certainty, and which makes the explained concept serviceable
in application. Real explanation would be that which makes clear
not only the concept but also its objective reality. Mathematical
explanations which present the object in intuition, in conformity
with the concept, are of this latter kind. 
P 262
But not only am I ignorant of any conditions under
which this logical pre-eminence may belong to anything; I
can neither put such a concept to any use, nor draw the least
inference from it. For no object is thereby determined for
its employment, and consequently we do not know whether
it signifies anything whatsoever. If I omit from the concept
of cause the time in which something follows upon some-
thing else in conformity with a rule, I should find in the pure
category nothing further than that there is something from
which we can conclude to the existence of something else. In
that case not only would we be unable to distinguish cause and
effect from one another, but since the power to draw such in-
ferences requires conditions of which I know nothing, the con-
cept would yield no indication how it applies to any object. 
The so-called principle, that everything accidental has a cause,
presents itself indeed somewhat pompously, as self-sufficing
in its own high dignity. But if I ask what is understood by
accidental, and you reply, "That the not-being of which is
possible," I would gladly know how you can determine this
possibility of its not-being, if you do not represent a succession
in the series of appearances and in it a being which follows
upon not-being (or reversewise), that is, a change. For to say
that the not-being of a thing does not contradict itself, is a lame
appeal to a logical condition, which, though necessary to the
concept, is very far from being sufficient for real possibility. 
I can remove in thought every existing substance without
contradicting myself, but I cannot infer from this their objec-
tive contingency in existence, that is, that their non-existence
is possible. As regards the concept of community, it is easily
seen that inasmuch as the pure categories of substance
and causality admit of no explanation determinant of the
object, neither is any such explanation possible of reciprocal
causality in the relation of substances to one another (com-
mercium). So long as the definition of possibility, existence,
and necessity is sought solely in pure understanding, they can-
not be explained save through an obvious tautology. For to
substitute the logical possibility of the concept (namely, that
the concept does not contradict itself) for the transcendental
possibility of things (namely, that an object corresponds to
P 263
the concept) can deceive and leave satisfied only the simple-
++ There is something strange and even absurd in the asser-
tion that there should be a concept which possesses a meaning
and yet is not capable of any explanation. But the categories
have this peculiar feature, that only in virtue of the general
condition of sensibility can they possess a determinate mean-
ing and relation to any object. Now when this condition has
been omitted from the pure category, it can contain nothing but
the logical function for bringing the manifold under a concept. 
By means of this function or form of the concept, thus taken
by itself, we cannot in any way know and distinguish what
object comes under it, since we have abstracted from the sens-
ible condition through which alone objects can come under it. 
Consequently, the categories require, in addition to the pure
concept of understanding, determinations of their application to
sensibility in general (schemata). Apart from such application
they are not concepts through which an object is known and
distinguished from others, but only so many modes of think-
ing an object for possible intuitions, and of giving it meaning,
under the requisite further conditions, in conformity with some
function of the understanding, that is, of defining it. But they
cannot themselves be defined. The logical functions of judg-
ments in general, unity and plurality, assertion and denial,
subject and predicate, cannot be defined without perpetrat-
ing a circle, since the definition must itself be a judgment, and
so must already contain these functions. The pure categories
are nothing but representations of things in general, so far as
the manifold of their intuition must be thought through one or
other of these logical functions. 
++ In a word, if all sensible intuition, the only kind of intuition
which we possess, is removed, not one of these concepts can in any
fashion verify itself, so as to show its real possibility. Only logical
possibility then remains, that is, that the concept or thought is pos-
sible. That, however, is not what we are discussing, but whether
the concept relates to an object and so signifies something. 
P 264
 From all this it undeniably follows that the pure concepts of
understanding can never admit of transcendental but always
only of empirical employment, and that the principles of pure
understanding can apply only to objects of the senses under
the universal conditions of a possible experience, never to
things in general without regard to the mode in which we are
able to intuit them. 
Accordingly the Transcendental Analytic leads to this
important conclusion, that the most the understanding can
achieve a priori is to anticipate the form of a possible experi-
ence in general. And since that which is not appearance can-
not be an object of experience, the understanding can never
transcend those limits of sensibility within which alone objects
can be given to us. Its principles are merely rules for the ex-
position of appearances; and the proud name of an Ontology
that presumptuously claims to supply, in systematic doctrinal
form, synthetic a priori knowledge of things in general (for
instance, the principle of causality) must, therefore, give place
to the modest title of a mere Analytic of pure understanding. 
 Thought is the act which relates given intuition to an
object. If the mode of this intuition is not in any way
given, the object is merely transcendental, and the concept of
understanding has only transcendental employment, namely,
as the unity of the thought of a manifold in general. Thus no
object is determined through a pure category in which ab-
straction is made of every condition of sensible intuition -- the
only kind of intuition possible to us. 
P 263
Magnitude is the determination
P 264
which can be thought only through a judgment which has
quantity (judicium commune); reality is that determination
which can be thought only through an affirmative judgment;
substance is that which, in relation to intuition, must be the
last subject of all other determinations. But what sort of a
thing it is that demands one of these functions rather than
another, remains altogether undetermined. Thus the cate-
gories, apart from the condition of sensible intuition, of
which they contain the synthesis, have no relation to any
determinate object, cannot therefore define any object, and
so do not in themselves have the validity of objective concepts. 
P 264
It then expresses only the
P 265
thought of an object in general, according to different modes. 
Now the employment of a concept involves a function of judg-
ment whereby an object is subsumed under the concept, and
so involves at least the formal condition under which some-
thing can be given in intuition. If this condition of judgment
(the schema) is lacking, all subsumption becomes impossible. 
For in that case nothing is given that could be subsumed under
the concept. The merely transcendental employment of the cate-
gories is, therefore, really no employment at all, and has no
determinate object, not even one that is determinable in its
mere form. It therefore follows that the pure category does not
suffice for a synthetic a priori principle, that the principles
of pure understanding are only of empirical, never of tran-
scendental employment, and that outside the field of possible
experience there can be no synthetic a priori principles. 
It may be advisable, therefore, to express the situation as
follows. The pure categories, apart from formal conditions of
sensibility, have only transcendental meaning; nevertheless
they may not be employed transcendentally, such employment
being in itself impossible, inasmuch as all conditions of any
employment in judgments are lacking to them, namely, the
formal conditions of the subsumption of any ostensible object
under these concepts. Since, then, as pure categories merely,
they are not to be employed empirically, and cannot be em-
ployed transcendentally, they cannot, when separated from all
sensibility, be employed in any manner whatsoever, that is,
they cannot be applied to any ostensible object. They are the
pure form of the employment of understanding in respect of
objects in general, that is, of thought; but since they are
merely its form, through them alone no object can be thought
or determined. 
++ Appearances, so far as they are thought as objects accord-
ing to the unity of the categories, are called phaenomena. But
if I postulate things which are mere objects of understanding,
and which, nevertheless, can be given as such to an intuition,
P 266
although not to one that is sensible -- given therefore coram
intuitu intellectuali -- such things would be entitled noumena
P 266
But we are here subject to an illusion from which it is
difficult to escape. The categories are not, as regards their
origin, grounded in sensibility, like the forms of intuition,
space and time; and they seem, therefore, to allow of an
application extending beyond all objects of the senses. As a
matter of fact they are nothing but forms of thought, which
contain the merely logical faculty of uniting a priori in one con-
sciousness the manifold given in intuition; and apart, therefore,
from the only intuition that is possible to us, they have even
less meaning than the pure sensible forms. Through these
forms an object is at least given, whereas a mode of com-
bining the manifold -- a mode peculiar to our understanding --
by itself, in the absence of that intuition wherein the mani-
fold can alone be given, signifies nothing at all. At the
same time, if we entitle certain objects, as appearances,
sensible entities (phenomena), then since we thus distin-
guish the mode in which we intuit them from the nature that
belongs to them in themselves, 
++ Now we must bear in mind that the concept of appear-
ances, as limited by the Transcendental Aesthetic, already of
itself establishes the objective reality of noumena and justifies
the division of objects into phaenomena and noumena, and so
of the world into a world of the senses and a world of the under-
standing (mundus sensibilis et intelligibilis), and indeed in
such manner that the distinction does not refer merely to the
logical form of our knowledge of one and the same thing, ac-
cording as it is indistinct or distinct, but to the difference in
the manner in which the two worlds can be first given to our
knowledge, and in conformity with this difference, to the
manner in which they are in themselves generically distinct
from one another. For if the senses represent to us something
merely as it appears, this something must also in itself be a
P 267
thing, and an object of a non-sensible intuition, that is, of the
P 267
it is implied in this distinction
that we place the latter, considered in their own nature,
although we do not so intuit them, or that we place other
possible things, which are not objects of our senses but are
thought as objects merely through the understanding, in
opposition to the former, and that in so doing we entitle them
intelligible entities (noumena). The question then arises,
whether our pure concepts of understanding have meaning
in respect of these latter, and so can be a way of knowing
At the very outset, however, we come upon an ambiguity
which may occasion serious misapprehension. The under-
standing, when it entitles an object in a [certain] relation
mere phenomenon, at the same time forms, apart from
that relation, a representation of an object in itself, and so
comes to represent itself as also being able to form con-
cepts of such objects. 
In other words, a [kind of] knowledge must be
possible, in which there is no sensibility, and which alone has
reality that is absolutely objective. Through it objects will be
represented as they are, whereas in the empirical employment
of our understanding things will be known only as they appear. 
If this be so, it would seem to follow that we cannot assert,
what we have hitherto maintained, that the pure modes of
knowledge yielded by our understanding are never anything
more than principles of the exposition of appearance, and that
even in their a priori application they relate only to the formal
possibility of experience. On the contrary, we should have to
recognise that in addition to the empirical employment of the
categories, which is limited to sensible conditions, there is like-
wise a pure and yet objectively valid employment. For a field
quite different from that of the senses would here lie open to
us, a world which is thought as it were in the spirit (or even
perhaps intuited), and which would therefore be for the under-
standing a far nobler, not a less noble, object of contemplation. 
P 267
And since the understanding yields no
concepts additional to the categories, it also supposes that
the object in itself must at least be thought through these
P 268
pure concepts, and so is misled into treating the entirely
indeterminate concept of an intelligible entity, namely, of a
something in general outside our sensibility, as being a de-
terminate concept of an entity that allows of being known in
a certain [purely intelligible] manner by means of the under-
If by 'noumenon' we mean a thing so far as it is not an
object of our sensible intuition, and so abstract from our mode
of intuiting it, this is a noumenon in the negative sense of the
term. But if we understand by it an object of a non-sensible
intuition, we thereby presuppose a special mode of intuition,
namely, the intellectual, which is not that which we possess,
and of which we cannot comprehend even the possibility. 
This would be 'noumenon' in the positive sense of the term. 
The doctrine of sensibility is likewise the doctrine of the
noumenon in the negative sense, that is, of things which the
understanding must think without this reference to our mode
of intuition, therefore not merely as appearances but as
things in themselves. 
++ All our representations are, it is true, referred by the under-
standing to some object; and since appearances are nothing
but representations, the understanding refers them to a some-
thing, as the object of sensible intuition. But this something,
thus conceived, is only the transcendental object; and by that
is meant a something = X, of which we know, and with the
present constitution of our understanding can know, nothing
whatsoever, but which, as a correlate of the unity of apper-
ception, can serve only for the unity of the manifold in sensible
intuition. By means of this unity the understanding combines
the manifold into the concept of an object. This transcendental
object cannot be separated from the sense data, for nothing is
then left through which it might be thought. Consequently it
is not in itself an object of knowledge, but only the representa-
tion of appearances under the concept of an object in general
-- a concept which is determinable through the manifold of
these appearances. 
P 268
At the same time the understanding is
P 269
well aware that in viewing things in this manner, as thus
apart from our mode of intuition, it cannot make any use of
the categories. For the categories have meaning only in rela-
tion to the unity of intuition in space and time; and even this
unity they can determine, by means of general a priori con-
necting concepts, only because of the mere ideality of space
and time. In cases where this unity of time is not to be found,
and therefore in the case of the noumenon, all employment,
and indeed the whole meaning of the categories, entirely
vanishes; for we have then no means of determining whether
things in harmony with the categories are even possible. On
this point I need only refer the reader to what I have said in
the opening sentences of the General Note appended to the
preceding chapter. The possibility of a thing can never be
proved merely from the fact that its concept is not self-con-
tradictory, but only through its being supported by some
corresponding intuition. 
P 268a
Just for this reason the categories represent no special ob-
ject, given to the understanding alone, but only serve to determine
P 269a
the transcendental object, which is the concept of some-
thing in general, through that which is given in sensibility, in
order thereby to know appearances empirically under concepts
of objects. 
The cause of our not being satisfied with the substrate of
sensibility, and of our therefore adding to the phenomena nou-
mena which only the pure understanding can think, is simply
as follows. The sensibility (and its field, that of the appear-
ances) is itself limited by the understanding in such fashion that
it does not have to do with things in themselves but only with
the mode in which, owing to our subjective constitution, they
appear. The Transcendental Aesthetic, in all its teaching, has
led to this conclusion; and the same conclusion also, of course,
follows from the concept of an appearance in general; namely,
that something which is not in itself appearance must cor-
respond to it. For appearance can be nothing by itself, outside
our mode of representation. Unless, therefore, we are to move
constantly in a circle, the word appearance must be recognised
as already indicating a relation to something, the immediate
P 270a
representation of which is, indeed, sensible, but which, even
apart from the constitution of our sensibility (upon which the
form of our intuition is grounded), must be something in itself,
that is, an object independent of sensibility. 
P 269
If, therefore, we should attempt to
apply the categories to objects which are not viewed as being
appearances, we should have to postulate an intuition other
P 270
than the sensible, and the object would thus be a noumenon
in the positive sense. Since, however, such a type of intuition,
intellectual intuition, forms no part whatsoever of our
faculty of knowledge, it follows that the employment of
the categories can never extend further than to the objects
of experience. Doubtless, indeed, there are intelligible entities
corresponding to the sensible entities; there may also be in-
telligible entities to which our sensible faculty of intuition
has no relation whatsoever; but our concepts of understand-
ing, being mere forms of thought for our sensible intuition,
could not in the least apply to them. That, therefore, which
we entitle 'noumenon' must be understood as being such
only in a negative sense. 
If I remove from empirical knowledge all thought (through
categories), no knowledge of any object remains. For through
mere intuition nothing at all is thought, and the fact that this
affection of sensibility is in me does not [by itself] amount to
a relation of such representation to any object. But if, on the
other hand, I leave aside all intuition, the form of thought still remains 
++ There thus results the concept of a noumenon. It is not
of anything, but signifies only the thought of something in
general, in which I abstract from everything that belongs to
the form of sensible intuition. But in order that a noumenon
may signify a true object, distinguishable from all phenomena,
it is not enough that I free my thought from all conditions of
sensible intuition; I must likewise have ground for assuming
another kind of intuition, different from the sensible, in which
such an object may be given. For otherwise my thought, while
indeed without contradictions, is none the less empty. We have
not, indeed, been able to prove that sensible intuition is the only
possible intuition, but only that it is so for us. But neither have
we been able to prove that another kind of intuition is possible. 
P 271
 -- that is, the mode of determining an object for
the manifold of a possible intuition. The categories accord-
ingly extend further than sensible intuition, since they think
objects in general, without regard to the special mode (the
sensibility) in which they may be given. But they do not
thereby determine a greater sphere of objects. For we cannot
assume that such objects can be given, without presupposing
the possibility of another kind of intuition than the sensible;
and we are by no means justified in so doing. 
If the objective reality of a concept cannot be in any way
known, while yet the concept contains no contradiction and also
at the same time is connected with other modes of knowledge
that involve given concepts which it serves to limit, I entitle
that concept problematic. The concept of a noumenon -- that is,
of a thing which is not to be thought as object of the senses
but as a thing in itself, solely through a pure understanding --
is not in any way contradictory. For we cannot assert of sensi-
bility that it is the sole possible kind of intuition. 
P 270a
Consequently, although our thought can abstract from all
P 271a
++ sensibility, it is still an open question whether the notion of
a noumenon be not a mere form of a concept, and whether,
when this separation has been made, any object whatsoever
is left. 
The object to which I relate appearance in general is
the transcendental object, that is, the completely indeter-
minate thought of something in general. This cannot be
entitled the noumenon; for I know nothing of what it is in
itself, and have no concept of it save as merely the object of
a sensible intuition in general, and so as being one and the
same for all appearances. I cannot think it through any cate-
gory; for a category is valid [only] for empirical intuition, as
bringing it under a concept of object in general. A pure use of
the category is indeed possible [logically], that is, without con-
tradiction; but it has no objective validity, since the category
is not then being applied to any intuition so as to impart to it
the unity of an object. For the category is a mere function
of thought, through which no object is given to me, and by
which I merely think that which may be given in intuition. 
P 272
Further, the concept of a noumenon is necessary, to prevent sensible intuition
from being extended to things in themselves, and thus to limit
the objective validity of sensible knowledge. The remaining
things, to which it does not apply, are entitled noumena, in
order to show that this knowledge cannot extend its domain
over everything which the understanding thinks. But none the
less we are unable to comprehend how such noumena can be
possible, and the domain that lies out beyond the sphere of
appearances is for us empty. That is to say, we have an
understanding which problematically extends further, but
we have no intuition, indeed not even the concept of a
possible intuition, through which objects outside the field
of sensibility can be given, and through which the under-
standing can be employed assertorically beyond that
field. The concept of a noumenon is thus a merely limiting
concept, the function of which is to curb the pretensions of
sensibility; and it is therefore only of negative employment. 
At the same time it is no arbitrary invention; it is bound up
with the limitation of sensibility, though it cannot affirm any-
thing positive beyond the field of sensibility. 
The division of objects into phenomena and noumena, and
the world into a world of the senses and a world of the under-
standing, is therefore quite inadmissible in the positive sense
although the distinction of concepts as sensible and intellectual
is certainly legitimate. For no object can be determined for the
latter concepts, and consequently they cannot be asserted to be
objectively valid. If we abandon the senses, how shall we make
it conceivable that our categories, which would be the sole re-
maining concepts for noumena, should still continue to signify
something, since for their relation to any object more must be
given than merely the unity of thought -- namely, in addition,
a possible intuition, to which they may be applied. None the
less, if the concept of a noumenon be taken in a merely prob-
lematic sense, it is not only admissible, but as setting limits
to sensibility is likewise indispensable. But in that case a nou-
menon is not for our understanding a special [kind of] object,
namely, an intelligible object; the [sort of] understanding to
which it might belong is itself a problem. For we cannot in
P 273
the least represent to ourselves the possibility of an under-
standing which should know its object, not discursively
through categories, but intuitively in a non-sensible intuition. 
What our understanding acquires through this concept of a
noumenon, is a negative extension; that is to say, under-
standing is not limited through sensibility; on the contrary,
it itself limits sensibility by applying the term noumena to
things in themselves (things not regarded as appearances). 
But in so doing it at the same time sets limits to itself, recog-
nising that it cannot know these noumena through any of the
categories, and that it must therefore think them only under
the title of an unknown something. 
In the writings of modern philosophers I find the expres-
sions mundus sensibilis and intelligibilis used with a mean-
ing altogether different from that of the ancients -- a meaning
which is easily understood, but which results merely in an
empty play upon words. According to this usage, some have
thought good to entitle the sum of appearances, in so far as
they are intuited, the world of the senses, and in so far as their
connection is thought in conformity with laws of understand-
ing, the world of the understanding. Observational astronomy,
which teaches merely the observation of the starry heavens,
would give an account of the former; theoretical astronomy,
on the other hand, as taught according to the Copernican
system, or according to Newton's laws of gravitation, would
give an account of the second, namely, of an intelligible
world. But such a twisting of words is a merely sophistical
subterfuge; it seeks to avoid a troublesome question by
changing its meaning to suit our own convenience. Under-
standing and reason are, indeed, employed in dealing with
++ We must not, in place of the expression mundus intelligibilis,
use the expression 'an intellectual world', as is commonly done
in German exposition. For only modes of knowledge are either
intellectual or sensuous. What can only be an object of the one
or the other kind of intuition must be entitled (however harsh-
sounding) intelligible or sensible. 
P 273
but the question to be answered is whether they
have also yet another employment, when the object is not a
P 274
phenomenon (that is, is a noumenon); and it is in this latter
sense that the object is taken, when it is thought as merely
intelligible, that is to say, as being given to the understanding
alone, and not to the senses. The question, therefore, is whether
in addition to the empirical employment of the understanding
-- to its employment even in the Newtonian account of the
structure of the universe -- there is likewise possible a tran-
scendental employment, which has to do with the noumenon
as an object. This question we have answered in the negative. 
 When, therefore, we say that the senses represent objects
as they appear, and the understanding objects as they are, the
latter statement is to be taken, not in the transcendental, but
in the merely empirical meaning of the terms, namely as
meaning that the objects must be represented as objects of
experience, that is, as appearances in thoroughgoing inter-
connection with one another, and not as they may be apart
from their relation to possible experience (and consequently
to any senses), as objects of the pure understanding. Such
objects of pure understanding will always remain unknown
to us; we can never even know whether such a transcen-
dental or exceptional knowledge is possible under any con-
ditions -- at least not if it is to be the same kind of know-
ledge as that which stands under our ordinary categories. 
Understanding and sensibility, with us, can determine objects
only when they are employed in conjunction. When we separ-
ate them, we have intuitions without concepts, or concepts
without intuitions -- in both cases, representations which we
are not in a position to apply to any determinate object. 
If, after all these explanations, any one still hesitates to
abandon the merely transcendental employment of the cate-
gories, let him attempt to obtain from them a synthetic pro-
position. An analytic proposition carries the understanding no
further; for since it is concerned only with what is already
thought in the concept, it leaves undecided whether this con-
cept has in itself any relation to objects, or merely signifies
the unity of thought in general -- complete abstraction being
made from the mode in which an object may be given. The
understanding [in its analytic employment] is concerned only
to know what lies in the concept; it is indifferent as to the
P 275
object to which the concept may apply. The attempt must
therefore be made with a synthetic and professedly tran-
scendental principle, as, for instance, 'Everything that exists,
exists as substance, or as a determination inherent in it', or
'Everything contingent exists as an effect of some other thing,
namely, of its cause'. Now whence, I ask, can the understand-
ing obtain these synthetic propositions, when the concepts are
to be applied, not in their relation to possible experience, but
to things in themselves (noumena)? Where is here that third
something, which is always required for a synthetic proposi-
tion, in order that, by its mediation, the concepts which have
no logical (analytic) affinity may be brought into connection
with one another? The proposition can never be established,
nay, more, even the possibility of any such pure assertion can-
not be shown, without appealing to the empirical employment
of the understanding, and thereby departing completely from
the pure and non-sensible judgment. Thus the concept of pure
and merely intelligible objects is completely lacking in all
principles that might make possible its application. For we
cannot think of any way in which such intelligible objects
might be given. The problematic thought which leaves open
a place for them serves only, like an empty space, for the
limitation of empirical principles, without itself containing or
revealing any other object of knowledge beyond the sphere of
those principles. 
P 276
Reflection (reflexio) does not concern itself with objects them-
selves with a view to deriving concepts from them directly,
but is that state of mind in which we first set ourselves
to discover the subjective conditions under which [alone] we
are able to arrive at concepts. It is the consciousness of the re-
lation of given representations to our different sources of know-
ledge; and only by way of such consciousness can the relation
of the sources of knowledge to one another be rightly deter-
mined. Prior to all further treatment of our representations,
this question must first be asked: In which of our cognitive
faculties are our representations connected together? Is it the
understanding, or is it the senses, by which they are combined
or compared? Many a judgment is accepted owing to custom
or is grounded in inclination; but since no reflection precedes
it, or at least none follows critically upon it, it is taken as
having originated in the understanding. An examination
(i.e. the direction of our attention to the grounds of the truth
of a judgment) is not indeed required in every case; for if the
judgment is immediately certain (for instance, the judgment
that between two points there can only be one straight line),
there can be no better evidence of its truth than the judgment
itself. All judgments, however, and indeed all comparisons,
require reflection, i.e. distinction of the cognitive faculty to
which the given concepts belong. The act by which I confront
P 277
the comparison of representations with the cognitive faculty
to which it belongs, and by means of which I distinguish
whether it is as belonging to the pure understanding or to
sensible intuition that they are to be compared with each
other, I call transcendental reflection. Now the relations in
which concepts in a state of mind can stand to one another are
those of identity and difference, of agreement and opposition,
of the inner and the outer, and finally of the determinable and
the determination (matter and form). The right determining
of the relation depends on the answer to the question, in which
faculty of knowledge they belong together subjectively -- in the
sensibility or in the understanding. For the difference between
the faculties makes a great difference to the mode in which we
have to think the relations. 
Before constructing any objective judgment we compare
the concepts to find in them identity (of many representa-
tions under one concept) with a view to universal judgments,
difference with a view to particular judgments, agreement
with a view to affirmative judgments, opposition with a view
to negative judgments, etc. For this reason we ought, it seems,
to call the above-mentioned concepts, concepts of comparison
(conceptus comparationis). If, however, the question is not
about the logical form, but about the content of the concepts,
i.e. whether things are themselves identical or different, in
agreement or in opposition, etc. , then since the things can have
a twofold relation to our faculty of knowledge, namely, to sensi-
bility and to understanding, it is the place to which they belong
in this regard that determines the mode in which they belong
to one another. For this reason the interrelations of given re-
presentations can be determined only through transcendental
reflection, that is, through [consciousness of] their relation to
one or other of the two kinds of knowledge. Whether things are
identical or different, in agreement or in opposition, etc. , can-
not be established at once from the concepts themselves by
mere comparison (comparatio), but solely by means of tran-
scendental consideration (reflexio), through distinction of the
cognitive faculty to which they belong. We may therefore say
P 278
that logical reflection is a mere act of comparison; for since
we take no account whatsoever of the faculty of knowledge to
which the given representations belong, the representations
must be treated as being, so far as their place in the mind is
concerned, all of the same order. Transcendental reflection, on
the other hand, since it bears on the objects themselves, con-
tains the ground of the possibility of the objective comparison
of representations with each other, and is therefore altogether
different from the former type of reflection. Indeed they do
not even belong to the same faculty of knowledge. This trans-
cendental consideration is a duty from which nobody who
wishes to make any a priori judgments about things can claim
exemption. We shall now take it in hand, and in so doing shall
obtain no little light for the determining of the real business
of the understanding. 
1. Identity and Difference. -- If an object is presented to us
on several occasions but always with the same inner determina-
tions (qualitas et quantitas), then if it be taken as object of
pure understanding, it is always one and the same, only one
thing (numerica identitas), not many. But if it is appearance,
we are not concerned to compare concepts; even if there is
no difference whatever as regards the concepts, difference of
spatial position at one and the same time is still an adequate
ground for the numerical difference of the object, that is, of the
object of the senses. Thus in the case of two drops of water
we can abstract altogether from all internal difference (of
quality and quantity), and the mere fact that they have been
intuited simultaneously in different spatial positions is suffi-
cient justification for holding them to be numerically different. 
Leibniz took the appearances for things-in-themselves, and so
for intelligibilia, i.e. objects of the pure understanding (al-
though, on account of the confused character of our represen-
tations of them, he still gave them the name of phenomena),
and on that assumption his principle of the identity of indis-
cernibles (principium identitatis indiscernibilium) certainly
could not be disputed. But since they are objects of sensibility,
in relation to which the employment of the understanding is
not pure but only empirical, plurality and numerical difference
are already given us by space itself, the condition of outer
P 279
appearances. For one part of space, although completely simi-
lar and equal to another part, is still outside the other, and for
this very reason is a different part, which when added to it
constitutes with it a greater space. The same must be true of
all things which exist simultaneously in the different spatial
positions, however similar and equal they may otherwise be. 
2. Agreement and Opposition. -- If reality is represented
only by the pure understanding (realitas noumenon), no oppo-
sition can be conceived between the realities, i.e. no relation
of such a kind that, when combined in the same subject, they
cancel each other's consequences and take a form like 3 - 3 = 0. 
On the other hand, the real in appearance (realitas phaeno-
menon) may certainly allow of opposition. When such realities
are combined in the same subject, one may wholly or partially
destroy the consequences of another, as in the case of two
moving forces in the same straight line, in so far as they either
attract or impel a point in opposite directions, or again in the
case of a pleasure counterbalancing pain. 
3. The Inner and the Outer. -- In an object of the pure
understanding that only is inward which has no relation what-
soever (so far as its existence is concerned) to anything different
from itself. It is quite otherwise with a substantia phaenomenon
in space; its inner determinations are nothing but relations, and
it itself is entirely made up of mere relations. We are acquainted
with substance in space only through forces which are active
in this and that space, either bringing other objects to it (at-
traction), or preventing them penetrating into it (repulsion
and impenetrability). We are not acquainted with any other
properties constituting the concept of the substance which
appears in space and which we call matter. As object of pure
understanding, on the other hand, every substance must have
inner determinations and powers which pertain to its inner
reality. But what inner accidents can I entertain in thought,
save only those which my inner sense presents to me? They
must be something which is either itself a thinking or ana-
logous to thinking. For this reason Leibniz, regarding sub-
stances as noumena, took away from them, by the manner in
which he conceived them, whatever might signify outer re-
lation, including also, therefore, composition, and so made
P 280
them all, even the constituents of matter, simple subjects with
powers of representation -- in a word, MONADS. 
4. Matter and Form. -- These two concepts underlie all
other reflection, so inseparably are they bound up with all
employment of the understanding. The one [matter] signifies
the determinable in general, the other [form] its determina-
tion -- both in the transcendental sense, abstraction being
made from all differences in that which is given and from the
mode in which it is determined Logicians formerly gave the
name 'matter' to the universal, and the name 'form' to the
specific difference. In any judgment we can call the given
concepts logical matter (i.e. matter for the judgment), and
their relation (by means of the copula) the form of the judg-
ment. In every being the constituent elements of it (essentialia)
are the matter, the mode in which they are combined in one
thing the essential form. Also as regards things in general
unlimited reality was viewed as the matter of all possibility,
and its limitation (negation) as being the form by which one
thing is distinguished from others according to transcendental
concepts. The understanding, in order that it may be in a posi-
tion to determine anything in definite fashion, demands that
something be first given, at least in concept. Consequently in
the concept of the pure understanding matter is prior to form;
and for this reason Leibniz first assumed things (monads),
and within them a power of representation, in order after-
wards to found on this their outer relation and the community
of their states (i.e. of the representations). Space and time
-- the former through the relation of substances, the latter
through the connection of their determinations among them-
selves -- were thus, on this view, possible as grounds and con-
sequents. This, in fact, is how it would necessarily be, if the
pure understanding could be directed immediately to objects,
and if space and time were determinations of things-in-them-
selves. But if they are only sensible intuitions, in which we
determine all objects merely as appearances, then the form of
intuition (as a subjective property of sensibility) is prior to all
matter (sensations); space and time come before all appear-
ances and before all data of experience, and are indeed what
make the latter at all possible. The intellectualist philo-
sopher could not endure to think of the form as preceding
P 281
the things themselves and determining their possibility -- a
perfectly just criticism on the assumption that we intuit things
as they really are, although in confused representation. But
since sensible intuition is a quite specific subjective condition,
which lies a priori at the foundation of all perception, as its
original form, it follows that the form is given by itself, and that
so far is the matter (or the things themselves which appear)
from serving as the foundation (as we should have to judge
if we followed mere concepts) that on the contrary its own
possibility presupposes a formal intuition (time and space)
as antecedently given. 
Let me call the place which we assign to a concept, either
in sensibility or in pure understanding, its transcendental
location. Thus the decision as to the place which belongs to
every concept according to difference in the use to which it
is put, and the directions for determining this place for all
concepts according to rules, is a transcendental topic. This
doctrine, in distinguishing the cognitive faculty to which in
each case the concepts properly belong, will provide a sure
safeguard against the surreptitious employment of pure under-
standing and the delusions which arise therefrom. We may
call every concept, every heading, under which many items of
knowledge fall, a logical location. On this is based the logical
topic of Aristotle, of which teachers and orators could make
use in order under given headings of thought to find what
would best suit the matter in hand, and then, with some
appearance of thoroughness, to argue or be eloquent about it. 
The transcendental topic, on the other hand, contains no
more than the above-mentioned four headings of all com-
parison and distinction. They are distinguished from cate-
gories by the fact that they do not present the object accord-
ing to what constitutes its concept (quantity, reality), but
only serve to describe in all its manifoldness the comparison
of the representations which is prior to the concept of things. 
But this comparison requires in the first place a reflection,
that is, a determination of the location to which the repre-
P 282
sentations of the things that are being compared belong,
namely, whether they are thought by the pure understanding
or given in appearance by sensibility. 
Concepts can be compared logically without our troubling
to which faculty their objects belong, that is, as to whether
their objects are noumena for the understanding, or are
phenomena for the sensibility. But if we wish to advance
to the objects with these concepts, we must first resort to tran-
scendental reflection, in order to determine for which cognitive
faculty they are to be objects, whether for pure understanding
or for sensibility. In the absence of such reflection, the use of
these concepts is very unsafe, giving birth to alleged synthetic
principles, which the critical reason cannot recognise, and
which are based on nothing better than a transcendental
amphiboly, that is, a confounding of an object of pure under-
standing with appearance. 
Having no such transcendental topic, and being therefore
deceived by the amphiboly of the concepts of reflection, the
celebrated Leibniz erected an intellectual system of the world,
or rather believed that he could obtain knowledge of the
inner nature of things by comparing all objects merely with
the understanding and with the separated, formal concepts
of its thought. Our table of concepts of reflection gives us the
unexpected advantage of putting before our eyes the distinct-
ive features of his system in all its parts, and at the same time
the chief ground of this peculiar way of thinking, which indeed
rested on nothing but a misunderstanding. He compared all
things with each other by means of concepts alone, and natur-
ally found no other differences save those through which
the understanding distinguishes its pure concepts from one
another. The conditions of sensible intuition, which carry
with them their own differences, he did not regard as original,
sensibility being for him only a confused mode of representa-
tion, and not a separate source of representations. Appear-
ance was, on his view, the representation of the thing in
itself. Such representation is indeed, as he recognised,
different in logical form from knowledge through the under-
standing, since, owing to its usual lack of analysis, it intro-
duces a certain admixture of accompanying representations
P 283
into the concept of the thing, an admixture which the under-
standing knows how to separate from it. In a word, Leibniz
intellectualised appearances, just as Locke, according to his
system of noogony (if I may be allowed the use of such ex-
pressions), sensualised all concepts of the understanding, i.e.
interpreted them as nothing more than empirical or abstracted
concepts of reflection. Instead of seeking in understanding
and sensibility two sources of representations which, while
quite different, can supply objectively valid judgments of
things only in conjunction with each other, each of these great
men holds to one only of the two, viewing it as in immediate
relation to things in themselves. The other faculty is then
regarded as serving only to confuse or to order the represen-
tations which this selected faculty yields. 
Leibniz therefore compared the objects of the senses
with each other merely in regard to understanding, taking
them as things in general. First, he compared them in so far
as they are to be judged by understanding to be identical or
to be different. And since he had before him only their con-
cepts and not their position in intuition (wherein alone the
objects can be given), and left entirely out of account the
transcendental place of these concepts (whether the object is
to be reckoned among appearances or things in themselves),
it inevitably followed that he should extend his principle of
the identity of indiscernibles, which is valid only of concepts
of things in general, to cover also the objects of the senses
(mundus phaenomenon), and that he should believe that in
so doing he had advanced our knowledge of nature in no
small degree. Certainly, if I know a drop of water in all its
internal determinations as a thing in itself, and if the whole
concept of any one drop is identical with that of every other,
I cannot allow that any drop is different from any other. But
if the drop is an appearance in space, it has its location not
only in understanding (under concepts) but in sensible outer
intuition (in space), and the physical locations are there quite
indifferent to the inner determinations of the things. A loca-
tion b can contain a thing which is completely similar and
equal to another in a location a, just as easily as if the things
were inwardly ever so different. Difference of locations, with-
out any further conditions, makes the plurality and distinction
P 284
of objects, as appearances, not only possible but also neces-
sary. Consequently, the above so-called law is no law of
nature. It is only an analytic rule for the comparison of
things through mere concepts. 
Secondly, the principle that realities (as pure assertions)
never logically conflict with each other is an entirely true
proposition as regards the relation of concepts, but has not
the least meaning in regard either to nature or to anything
in itself. For real conflict certainly does take place; there are
cases where A - B = 0, that is, where two realities combined
in one subject cancel one another's effects. This is brought
before our eyes incessantly by all the hindering and counter-
acting processes in nature, which, as depending on forces,
must be called realitates phaenomena. General mechanics can
indeed give the empirical condition of this conflict in an a -
priori rule, since it takes account of the opposition in the
direction of forces, a condition totally ignored by the tran-
scendental concept of reality. Although Herr von Leibniz did
not indeed announce the above proposition with all the pomp
of a new principle, he yet made use of it for new assertions,
and his successors expressly incorporated it into their Leib-
nizian - Wolffian system. Thus, according to this principle all
evils are merely consequences of the limitations of created
beings, that is, negations, since negations alone conflict
with reality. (This is indeed the case as regards the mere
concept of a thing in general, but not as regards things as
appearances. ) Similarly his disciples consider it not only pos-
sible, but even natural, to combine all reality in one being,
without fear of any conflict. For the only conflict which they
recognise is that of contradiction, whereby the concept of a
thing is itself removed. They do not admit the conflict of re-
ciprocal injury, in which each of two real grounds destroys the
effect of the other -- a conflict which we can represent to our-
selves only in terms of conditions presented to us in sensibility. 
Thirdly, Leibniz's monadology has no basis whatsoever
save his mode of representing the distinction of inner and
outer merely in relation to the understanding. Substances in
general must have some internal nature, which is therefore
free from all outer relations, and consequently also from com-
P 285
position. The simple is therefore the basis of that which is
inner in things-in-themselves. But that which is inner in the
state of a substance cannot consist in place, shape, contact,
or motion (these determinations being all outer relations), and
we can therefore assign to substances no inner state save that
through which we ourselves inwardly determine our sense,
namely, the state of the representations. This, therefore, com-
pleted the conception of the monads, which, though they have
to serve as the basic material of the whole universe, have no
other active power save only that which consists in representa-
tions, the efficacy of which is confined, strictly speaking, to
For this very reason his principle of the possible reciprocal
community of substances had to be a pre-established harmony,
and could not be a physical influence. For since everything is
merely inward, i.e. concerned with its own representations, the
state of the representations of one substance could not stand
in any effective connection whatever with that of another. 
There had to be some third cause, determining all substances
whatsoever, and so making their states correspond to each
other, not indeed by an occasional special intervention in each
particular case (systema assistentiae), but by the unity of the
idea of a cause valid for all substances, and in which they
must one and all obtain their existence and permanence, and
consequently also their reciprocal correspondence, according
to universal laws. 
Fourthly, Leibniz's famous doctrine of time and space, in
which he intellectualised these forms of sensibility, owed its
origin entirely to this same fallacy of transcendental reflec-
tion. If I attempt, by the mere understanding, to represent to
myself outer relations of things, this can only be done by means
of a concept of their reciprocal action; and if I seek to connect
two states of one and the same thing, this can only be in the
order of grounds and consequences. Accordingly, Leibniz
conceived space as a certain order in the community of sub-
stances, and time as the dynamical sequence of their states. 
That which space and time seem to possess as proper to them-
selves, in independence of things, he ascribed to the confusion
in their concepts, which has led us to regard what is a mere
P 286
form of dynamical relations as being a special intuition, self-
subsistent and antecedent to the things themselves. Thus space
and time were for him the intelligible form of the connection
of things (substances and their states) in themselves; and the
things were intelligible substances (substantiae noumena). 
And since he allowed sensibility no mode of intuition peculiar
to itself but sought for all representation of objects, even the
empirical, in the understanding, and left to the senses nothing
but the despicable task of confusing and distorting the repre-
sentations of the former, he had no option save to treat the
[intellectualised] concepts as being likewise valid of appear-
But even if we could by pure understanding say anything
synthetically in regard to things-in-themselves (which, how-
ever, is impossible), it still could not be applied to appear-
ances, which do not represent things-in-themselves. In dealing
with appearances I shall always be obliged to compare my
concepts, in transcendental reflection, solely under the con-
ditions of sensibility; and accordingly space and time will not
be determinations of things-in-themselves but of appearances. 
What the things-in-themselves may be I do not know, nor do
I need to know, since a thing can never come before me except
in appearance. 
The remaining concepts of reflection have to be dealt with
in the same manner. Matter is substantia phaenomenon. That
which inwardly belongs to it I seek in all parts of the space
which it occupies, and in all effects which it exercises, though
admittedly these can only be appearances of outer sense. I
have therefore nothing that is absolutely, but only what is
comparatively inward and is itself again composed of outer
relations. The absolutely inward [nature] of matter, as it would
have to be conceived by pure understanding, is nothing but
a phantom; for matter is not among the objects of pure
understanding, and the transcendental object which may be
the ground of this appearance that we call matter is a mere
something of which we should not understand what it is, even
if someone were in a position to tell us. For we can understand
only that which brings with it, in intuition, something corre-
sponding to our words. If by the complaints -- that we have no
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insight whatsoever into the inner [nature] of things -- it be
meant that we cannot conceive by pure understanding what
the things which appear to us may be in themselves, they are
entirely illegitimate and unreasonable. For what is demanded
is that we should be able to know things, and therefore to
intuit them, without senses, and therefore that we should have
a faculty of knowledge altogether different from the human,
and this not only in degree but as regards intuition likewise
in kind -- in other words, that we should be not men but
beings of whom we are unable to say whether they are even
possible, much less how they are constituted. Through ob-
servation and analysis of appearances we penetrate to nature's
inner recesses, and no one can say how far this knowledge
may in time extend. But with all this knowledge, and even if
the whole of nature were revealed to us, we should still never
be able to answer those transcendental questions which go
beyond nature. The reason of this is that it is not given to us
to observe our own mind with any other intuition than that
of inner sense; and that it is yet precisely in the mind that
the secret of the source of our sensibility is located. The rela-
tion of sensibility to an object and what the transcendental
ground of this [objective] unity may be, are matters undoubtedly
so deeply concealed that we, who after all know even ourselves
only through inner sense and therefore as appearance, can
never be justified in treating sensibility as being a suitable
instrument of investigation for discovering anything save
always still other appearances -- eager as we yet are to explore
their non-sensible cause. 
What makes this critique of conclusions based merely on
acts of reflection so exceedingly useful is that it renders mani-
fest the nullity of all conclusions about objects which are
compared with each other solely in the understanding, and at
the same time confirms our principal contention, namely, that
although appearances are not included as things-in-them-
selves among the objects of pure understanding, they are yet
the only objects in regard to which our knowledge can possess
objective reality, that is, in respect of which there is an in-
tuition corresponding to the concepts. 
If we reflect in a merely logical fashion, we are only com-
P 288
paring our concepts with each other in the understanding, to
find whether both have the same content, whether they are
contradictory or not, whether something is contained within
the concept or is an addition from outside, which of the two
is given and which should serve only as a mode of thinking
what is given. But if I apply these concepts to an object in
general (in the transcendental sense), without determining
whether it be an object of sensible or of intellectual intuition,
limitations are at once revealed in the very notion of this
object which forbid any non-empirical employment of the
concepts, and by this very fact prove that the representation
of an object as a thing in general is not only insufficient, but,
when taken without sensible determination, and independ-
ently of any empirical condition, self-contradictory. The con-
clusion is that we must either abstract from any and every
object (as in logic), or, if we admit an object, must think it
under the conditions of sensible intuition. For the intelligible
would require a quite peculiar intuition which we do not
possess, and in the absence of this would be for us nothing at
all; and, on the other hand, it is also evident that appearances
could not be objects in themselves. If I think to myself merely
things in general, the difference in their outer relations cannot
constitute a difference in the things themselves; on the con-
trary, it presupposes this difference. And if there is no inward
difference between the concept of the one and the concept of the
other, I am only positing one and the same thing in different
relations. Further, the addition of one sheer affirmation
(reality) to another increases the positive in them; nothing is
withdrawn or inhibited; accordingly the real in things cannot
be in conflict with itself -- and so on. 
As we have shown, the concepts of reflection, owing to a
certain misinterpretation, have exercised so great an influence
upon the employment of the understanding that they have
misled even one of the most acute of all philosophers into a
supposititious system of intellectual knowledge, which under-
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takes to determine its objects without any assistance from the
senses. For this reason the exposition of the cause of what is
deceptive -- occasioning these false principles -- in the amphi-
boly of these concepts, is of great utility as a reliable method of
determining and securing the limits of the understanding. 
It is indeed true that whatever universally agrees with or
contradicts a concept also agrees with or contradicts every
particular which is contained under it (dictum de omni et
nullo); but it would be absurd to alter this logical principle so
as to read: -- what is not contained in a universal concept is also
not included in the particular concepts which stand under it. 
For these are particular concepts just because they include in
themselves more than is thought in the universal. Nevertheless
it is upon this latter principle that the whole intellectual sys-
tem of Leibniz is based; and with this principle it therefore
falls, together with all the ambiguities (in the employment of
the understanding) that have thence arisen. 
The principle of the identity of indiscernibles is really based
on the presupposition, that if a certain distinction is not found
in the concept of a thing in general, it is also not to be found
in the things themselves, and consequently that all things
which are not distinguishable from one another in their con-
cepts (in quality or quantity) are completely identical (numero
eadem). Because in the mere concept of a thing in general we
abstract from the many necessary conditions of its intuition,
the conditions from which we have abstracted are, with strange
presumption, treated as not being there at all, and nothing is
allowed to the thing beyond what is contained in its concept. 
The concept of a cubic foot of space, wherever and how-
ever often I think it, is in itself throughout one and the same. 
But two cubic feet are nevertheless distinguished in space by
the mere difference of their locations (numero diversa); these
locations are conditions of the intuition wherein the object of
this concept is given; they do not, however, belong to the con-
cept but entirely to sensibility. Similarly there is no conflict
in the concept of a thing unless a negative statement is com-
bined with an affirmative; merely affirmative concepts cannot,
when combined, produce any cancellation. But in the sensible
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intuition, wherein reality (e.g. motion) is given, there are
conditions (opposite directions), which have been omitted in
the concept of motion in general, that make possible a conflict
(though not indeed a logical one), namely, as producing from
what is entirely positive a zero (=0). We are not, therefore, in
a position to say that since conflict is not to be met with in
the concepts of reality, all reality is in agreement with itself. 
 According to mere concepts the inner is the substratum of
all relational or outer determinations. If, therefore, I abstract
from all conditions of intuition and confine myself to the con-
cept of a thing in general, I can abstract from all outer rela-
tion, and there must still be left a concept of something which
signifies no relation, but inner determinations only. From this
it seems to follow that in whatever is a thing (substance) there
is something which is absolutely inward and precedes all outer
determinations, inasmuch as it is what first makes them
possible; and consequently, that this substratum, as no longer
containing in itself any outer relations, is simple. (Corporeal
things are never anything save relations only, at least of
their parts external to each other. ) And since we know of no
determinations which are absolutely inner except those [given]
through our inner sense, this substratum is not only simple;
it is likewise (in analogy with our inner sense) determined
through representations; in other words, all things are really
monads, simple beings endowed with representations. These
contentions would be entirely justified, if beyond the con-
cept of a thing in general there were no further conditions
under which alone objects of outer intuition can be given us
-- those from which the pure concept has [as a matter of fact] made abstraction.
++ If we here wished to resort to the usual subterfuge, maintaining
as regards realitates noumena that they at least do not act in opposi-
tion to each other, it would be incumbent on us to produce an ex-
ample of such pure and non-sensuous reality, that it may be dis-
cerned whether such a concept represents something or nothing. 
But no example can be obtained otherwise than from experience,
which never yields more than phenomena. This proposition has
therefore no further meaning than that a concept which only in-
cludes affirmation includes no negation -- a proposition which we
have never doubted. 
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For under these further conditions, as we
find, an abiding appearance in space (impenetrable extension)
can contain only relations and nothing at all that is absolutely
inward, and yet be the primary substratum of all outer per-
ception. Through mere concepts I cannot, indeed, think what
is outer without thinking something that is inner; and this
for the sufficient reason that concepts of relation presuppose
things which are absolutely [i.e. independently] given, and
without these are impossible. But something is contained in
intuition which is not to be met with in the mere concept of a
thing; and this yields the substratum, which could never be
known through mere concepts, namely, a space which with all
that it contains consists solely of relations, formal or, it may be,
also real. Because, without an absolutely inner element, a thing
can never be represented by mere concepts, I may not therefore
claim that there is not also in the things themselves which are
subsumed under these concepts, and in their intuition, some-
thing external that has no basis in anything wholly inward. 
Once we have abstracted from all conditions of intuition, there
is, I admit, nothing left in the mere concept but the inner in
general and its interrelations, through which alone the ex-
ternal is possible. But this necessity, which is founded solely
on abstraction, does not arise in the case of things as given in
intuition with determinations that express mere relations, with-
out having anything inward as their basis; for such are not
things in themselves but merely appearances. All that we
know in matter is merely relations (what we call the inner
determinations of it are inward only in a comparative sense),
but among these relations some are self-subsistent and per-
manent, and through these we are given a determinate object. 
The fact that, if I abstract from these relations, there is no-
thing more left for me to think does not rule out the concept
of a thing as appearance, nor indeed the concept of an object
in abstracto. What it does remove is all possibility of an object
determinable through mere concepts, that is, of a noumenon. 
It is certainly startling to hear that a thing is to be taken as
consisting wholly of relations. Such a thing is, however, mere
appearance, and cannot be thought through pure categories;
P 292
what it itself consists in is the mere relation of something in
general to the senses. Similarly, if we begin with mere con-
cepts, we cannot think the relations of things in abstracto in
any other manner than by regarding one thing as the cause of
determinations in another, for that is how our understanding
conceives of relations. But since we are in that case disregard-
ing all intuition, we have ruled ourselves out from any kind of
recognition of the special mode in which the different elements
of the manifold determine each other's positions, that is, of
the form of sensibility (space), which yet is presupposed in all
empirical causality. 
If by merely intelligible objects we mean those things which
are thought through pure categories, without any schema
of sensibility, such objects are impossible. For the condition of
the objective employment of all our concepts of understanding
is merely the mode of our sensible intuition, by which objects
are given us; if we abstract from these objects, the con-
cepts have no relation to any object. Even if we were willing
to assume a kind of intuition other than this our sensible
kind, the functions of our thought would still be without
meaning in respect to it. If, however, we have in mind only
objects of a non-sensible intuition, in respect of which our
categories are admittedly not valid, and of which therefore
we can never have any knowledge whatsoever (neither in-
tuition nor concept), noumena in this purely negative sense
must indeed be admitted. For this is no more than saying
that our kind of intuition does not extend to all things, but
only to objects of our senses, that consequently its objective
validity is limited, and that a place therefore remains open
for some other kind of intuition, and so for things as its
objects. But in that case the concept of a noumenon is problem-
atic, that is, it is the representation of a thing of which we
can neither say that it is possible nor that it is impossible; for
we are acquainted with no kind of intuition but our own
sensible kind and no kind of concepts but the categories, and
neither of these is appropriate to a non-sensible object. We
cannot, therefore, positively extend the sphere of the objects
of our thought beyond the conditions of our sensibility, and
assume besides appearances objects of pure thought, that is,
P 293
noumena, since such objects have no assignable positive
meaning. For in regard to the categories we must admit that
they are not of themselves adequate to the knowledge of
things in themselves, and that without the data of sensibility
they would be merely subjective forms of the unity of under-
standing, having no object. Thought is in itself, indeed, no
product of the senses, and in so far is also not limited by
them; but it does not therefore at once follow that it has a
pure employment of its own, unaided by sensibility, since it is
then without an object. We cannot call the noumenon such
an object; signifying, as it does, the problematic concept of
an object for a quite different intuition and a quite different
understanding from ours, it is itself a problem. The concept
of the noumenon is, therefore, not the concept of an object,
but is a problem unavoidably bound up with the limitation
of our sensibility -- the problem, namely, as to whether there
may not be objects entirely disengaged from any such kind
of intuition. This is a question which can only be answered
in an indeterminate manner, by saying that as sensible in-
tuition does not extend to all things without distinction, a
place remains open for other and different objects; and con-
sequently that these latter must not be absolutely denied,
though -- since we are without a determinate concept of them
(inasmuch as no category can serve that purpose) -- neither
can they be asserted as objects for our understanding. 
Understanding accordingly limits sensibility, but does
not thereby extend its own sphere. In the process of warning
the latter that it must not presume to claim applicability to
things-in-themselves but only to appearances, it does indeed
think for itself an object in itself, but only as transcendental
object, which is the cause of appearance and therefore not
itself appearance, and which can be thought neither as quan-
tity nor as reality nor as substance etc. (because these concepts
always require sensible forms in which they determine an
object). We are completely ignorant whether it is to be met
with in us or outside us, whether it would be at once removed
with the cessation of sensibility, or whether in the absence of
sensibility it would still remain. If we are pleased to name
this object noumenon for the reason that its representation
is not sensible, we are free to do so. But since we can apply
P 294
to it none of the concepts of our understanding, the repre-
sentation remains for us empty, and is of no service except
to mark the limits of our sensible knowledge and to leave
open a space which we can fill neither through possible ex-
perience nor through pure understanding. 
The critique of this pure understanding, accordingly,
does not permit us to create a new field of objects beyond those
which may be presented to it as appearances, and so to stray
into intelligible worlds; nay, it does not allow of our entertain-
ing even the concept of them. The error, which quite obvi-
ously is the cause of this mistaken venture, and which indeed
excuses though it does not justify it, lies in employing the
understanding, contrary to its vocation, transcendentally, and
in making objects, that is, possible intuitions, conform to con-
cepts, not concepts to possible intuitions, on which alone their
objective validity rests. This error, in turn, is due to the fact
that apperception, and with it thought, precedes all possible
determinate ordering of representations. Consequently what
we do is to think something in general; and while on the one
hand we determine it in sensible fashion, on the other hand we
distinguish from this mode of intuiting it the universal object
represented in abstracto. What we are then left with is a mode
of determining the object by thought alone -- a merely logical
form without content, but which yet seems to us to be a
mode in which the object exists in itself (noumenon) without
regard to intuition, which is limited to our senses. 
 Before we leave the Transcendental Analytic we must
add some remarks which, although in themselves not of
special importance, might nevertheless be regarded as re-
quisite for the completeness of the system. The supreme
concept with which it is customary to begin a transcendental
philosophy is the division into the possible and the impossible. 
But since all division presupposes a concept to be divided, a
still higher one is required, and this is the concept of an object
in general, taken problematically, without its having been
decided whether it is something or nothing. As the categories
are the only concepts which refer to objects in general, the
P 295
distinguishing of an object, whether it is something or
nothing, will proceed according to the order and under the
guidance of the categories. 
I. To the concepts of all, many, and one there is opposed
the concept which cancels everything, that is, none. Thus the
object of a concept to which no assignable intuition whatso-
ever corresponds is = nothing. That is, it is a concept without
an object (ens rationis), like noumena, which cannot be
reckoned among the possibilities, although they must not for
that reason be declared to be also impossible; or like certain
new fundamental forces, which though entertained in thought
without self-contradiction are yet also in our thinking un-
supported by any example from experience, and are therefore
not to be counted as possible. 
2. Reality is something; negation is nothing, namely, a
concept of the absence of an object, such as shadow, cold
(nihil privativum). 
3. The mere form of intuition, without substance, is in
itself no object, but the merely formal condition of an object
(as appearance), as pure space and pure time (ens imagina-
rium). These are indeed something, as forms of intuition,
but are not themselves objects which are intuited. 
4. The object of a concept which contradicts itself is
nothing, because the concept is nothing, is the impossible,
e.g. a two-sided rectilinear figure (nihil negativum). 
The table of this division of the concept of nothing would
therefore have to be drawn up as follows. (The corresponding
division of something follows directly from it): 
Empty concept without object,
ens rationis. 
Empty object of a concept,
nihil privativum. 
P 295
Empty intuition without object,
ens imaginarium. 
Empty object without concept,
nihil negativum. 
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We see that the ens rationis (1) is distinguished from the
nihil negativum (4), in that the former is not to be counted
among possibilities because it is mere fiction (although not
self-contradictory), whereas the latter is opposed to possi-
bility in that the concept cancels itself. Both, however, are
empty concepts. On the other hand, the nihil privativum (2)
and the ens imaginarium (3) are empty data for concepts. If
light were not given to the senses we could not represent dark-
ness, and if extended beings were not perceived we could not
represent space. Negation and the mere form of intuition, in
the absence of a something real, are not objects.