Critique of Pure Reason

(Analytic of Principles)

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TRANSCENDENTAL ANALYTIC
BOOK II
THE ANALYTIC OF PRINCIPLES 
GENERAL logic is constructed upon a ground plan which
exactly coincides with the division of the higher faculties of
knowledge. These are: understanding,judgment, and reason. 
In accordance with the functions and order of these mental
powers, which in current speech are comprehended under the
general title of understanding, logic in its analytic deals with
concepts, judgments, and inferences. 
 Since this merely formal logic abstracts from all content
of knowledge, whether pure or empirical, and deals solely with
the form of thought in general (that is, of discursive 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
involved. 
As transcendental logic is limited to a certain determinate
content, namely, to the content of those modes of knowledge
which are pure and a priori, it cannot follow general logic in
this division. For the transcendental employment of reason is
not, it would seem, objectively valid, and consequently does
not belong to the logic of truth, i.e. to the Analytic. As a
logic of illusion, it calls for separate location in the scholastic
edifice, under the title of Transcendental Dialectic. 
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Understanding and judgment find, therefore, in 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. 
INTRODUCTION
TRANSCENDENTAL JUDGMENT IN GENERAL 
If understanding in general is to be viewed as the faculty of
rules, judgment will be the faculty of subsuming under rules;
that is, of distinguishing whether something does or does not
stand under a given rule (casus datae legis). General logic 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,
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as an attempt to enlarge the sphere of the understanding in
the field of pure a priori knowledge, philosophy is by no means
necessary, and is indeed ill-suited for any such purpose, since
in all attempts hitherto made, little or no ground has been won. 
On the other hand, if what is designed be a critique to guard
against errors of judgment (lapsus judicii) in the employment
of the few pure concepts of understanding that we possess,
the task, merely negative as its advantages must then be, is
one to which philosophy is called upon to devote all its 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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TRANSCENDENTAL DOCTRINE OF JUDGMENT
(OR ANALYTIC OF PRINCIPLES) 
CHAPTER I
THE SCHEMATISM OF THE PURE CONCEPTS OF
UNDERSTANDING 
In all subsumptions of an object under a concept the 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
intuition. 
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
rule. 
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
time. 
The schema of necessity is existence of an object at all
times. 
We thus find that the schema of each category contains and
makes capable of representation only a determination of time. 
The schema of magnitude is the generation (synthesis) of
time itself in the successive apprehension of an object. The
schema of quality is the synthesis of sensation or perception
with the representation of time; it is the filling of time. The
schema of relation is the connecting of perceptions with one
another at all times according to a rule of time-determination. 
Finally the schema of modality and of its categories is time
itself as the correlate of the determination whether and how
an object belongs to time. The schemata are thus nothing
but a priori determinations of time in accordance with rules. 
These rules relate in the order of the categories to the time-
series, the time-content, the time-order, and lastly to the scope
of time in respect of all possible objects. 
It is evident, therefore, that what the schematism of 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-
perience. 
 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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TRANSCENDENTAL DOCTRINE OF JUDGMENT
(OR ANALYTIC OF PRINCIPLES) 
CHAPTER II
SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING 
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
deduced. 
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. 
THE SYSTEM OF THE PRINCIPLES OF PURE
UNDERSTANDING 
Section 1
THE HIGHEST PRINCIPLE OF ALL ANALYTIC JUDGMENTS 
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. 
THE SYSTEM OF THE PRINCIPLES OF PURE
UNDERSTANDING 
Section 2
THE HIGHEST PRINCIPLE OF ALL SYNTHETIC JUDGMENTS 
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-
perience. 
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. 
THE SYSTEM OF THE PRINCIPLES OF PURE
UNDERSTANDING 
Section 3
SYSTEMATIC REPRESENTATION OF ALL THE SYNTHETIC
PRINCIPLES OF PURE UNDERSTANDING 
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
concepts. 
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 --
1
Axioms
of intuition. 
2
Anticipations
of perception. 
P 196
3
Analogies
of experience. 
4
Postulates
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. 
1
AXIOMS OF INTUITION 
Their principle is: All intuitions are extensive magnitudes. 
Proof 
++ 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. 
++The
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
knowledge. 
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. 
2
ANTICIPATIONS OF PERCEPTION 
In all appearances, the real that is an object of sensation
has intensive magnitude, that is, a degree. 
Proof 
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. 
3
ANALOGIES OF EXPERIENCE 
The principle of the analogies is: Experience is possible
only through the representation of a necessary connection
of perceptions. 
Proof 
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. 
A
FIRST ANALOGY
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
Proof 
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
diminished. 
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
exists. 
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
B
SECOND ANALOGY
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. 
Proof 
(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
time-relation. 
++ 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
meaning. 
 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
position. 
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
time. 
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
glass. 
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
experience. 
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. 
++ 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. 
C
THIRD ANALOGY
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. 
Proof 
 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
ciprocally. 
++ 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
experience. 
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-
hension. 
 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 cann