Immanuel Kant's

trans. by Norman Kemp Smith

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P 188
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 
experience 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.
P 189
Secondly, we shall limit ourselves merely to those principles
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 
appearances, 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 
possibility must receive recognition in this chapter. For though
their correctness and apodeictic certainty do not indeed require
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 
synthetic 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 knowledge,
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
P 190
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 
invalidates 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 concept
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 
necessarily 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 
principle 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, cannot
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 opposite
-- a procedure which never occasions a contradiction with
the subject but only with the predicate which has been 
synthetically 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 
condition, 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 
supplementary 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
P 192
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 consequently
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 
synthesis 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 
representations 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 
judgments. 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 relate
to an object, and is to acquire meaning and significance
in respect to it, the object must be capable of being in some
P 193
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 
representations. 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 
representation 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 
experience, 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 appearances
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 interconnected
(possible) consciousness, and so would not conform to
the transcendental and necessary unity of apperception. 
Experience 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 productive
P 194
imagination describes in it, and can obtain such judgments
without actually requiring any experience, yet even this
knowledge would be nothing but a playing with a mere figment
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 therefore
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 knowledge
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 therefore
this: every object stands under the necessary conditions of
synthetic unity of the manifold of intuition in a possible 
experience. 
Synthetic a priori judgements are thus possible when we relate
the formal conditions of a priori intuition, the synthesis of
imagination and the necessary unity of this synthesis in a 
transcendental 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 possibility
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 respect
P 195
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 
appearances would never yield knowledge of an object 
corresponding 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 suggestion
of a determination from grounds which are valid a priori
and antecedently to all experience. The laws of nature, indeed,
one and all, without exception, stand under higher principles
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 empirical
principles as principles of pure understanding, or conversely.
For the necessity according to concepts which distinguishes
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 mathematics,
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 indeed
possess the character of a priori necessity, but only under
the condition of empirical thought in some experience, therefore
only mediately and indirectly. Notwithstanding their 
undoubted certainty throughout experience, they will not contain
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 application
of the principles. It will soon become clear that the
principles involved in the a priori determination of appearances
according to the categories of quantity and of quality
(only the formal aspect of quantity and quality being 
considered) 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 mathematics
as in the other with the principles of general physical
dynamics. We treat only of the principles of pure understanding
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 composition
(compositio) or connection (nexus). The former is the synthesis
of the manifold where its constituents do not necessarily belong
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 
magnitudes. As intuitions in space or time, they must be 
represented 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 
determinate 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 appearance
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 
magnitude with the production of the other. [Consequently, they
are not] axioms, [for these] have to be a priori synthetic 
propositions. 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 representation
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 appearances
greatly enlarges our a priori knowledge. For it alone
can make pure mathematics, in its complete precision, applicable
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. Appearances
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 
apprehended. 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 sensibility,
represents them, in spite of the fact that they are mere
appearances, as objects in themselves, given to the understanding.
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 consciousness
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 
perceived. 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 
sensation 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 
magnitude 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 succession
of different sensations. As sensation is that element in
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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 
representation 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 diminution,
so that it can decrease and gradually vanish. Between
reality in the [field of] appearance and negation there is 
therefore 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 complete
negation. In other words, the real in the [field of] 
appearance 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 
therefore does not proceed from the parts to the whole, the 
magnitude 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 
approximation to negation = 0, I entitle an intensive magnitude.
Every reality in the [field of] appearance has therefore intensive
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 instantaneous.
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 continuity
of possible realities and of possible smaller perceptions.
P 204
Every colour, as for instance red, has a degree which, however
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 
magnitudes may also be called flowing, since the synthesis of
productive imagination involved in their production is a 
progression 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 aggregate
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, provided
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 presupposed
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 conclusiveness
the proposition that all alteration (transition of a
thing from one state to another), is continuous. But the causality
of an alteration in general, presupposing, as it does, empirical
principles, lies altogether outside the limits of a 
transcendental 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 particular
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 experience.
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, unanimously
conclude that this volume, which constitutes the extensive
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 metaphysical
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 
presupposition, for which they could find no support in 
experience, 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 
understanding, 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 
unchanged, 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 
perceptions 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 magnitude,
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 transcendental
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 
sensation 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 consciousness
in general. Empirical consciousness can in inner sense
be raised from 0 to any higher degree, so that a certain 
extensive 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 independently],
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 
consciousness. 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 
appearances) 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 
knowledge 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 
determining 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 sensation
of the senses. In experience, however, perceptions come
together only in accidental order, so that no necessity determining
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 
representation 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 perceptions,
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 
connect them a priori. Since these always carry necessity with
them, it follows that experience is only possible through a 
representation of necessary connection of perceptions.
The three modes of time are duration, succession, and coexistence.
There will, therefore, be three rules of all relations
of appearances in time, and these rules will be prior to all 
experience, 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 empirical
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 relation
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 apperception,
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 empirical
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 appearance
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 
application of mathematics to appearances, I entitled the 
mathematical, referred to the possibility of appearances, and taught
how, alike as regards their intuition and the real in their 
perception, they can be generated according to rules of a 
mathematical synthesis. Both principles justify us in employing
numerical magnitudes, and so enable us to determine appearance
as magnitude. For instance, I can determine a priori, that
is, can construct, the degree of sensations of sunlight by 
combining 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 
regulative 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 
constitutive; 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 members
we can obtain a priori knowledge only of the relation to a
fourth, not of the fourth member itself. The relation yields, 
however, 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 
experience 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 appearance),
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 
understanding; 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 
themselves, 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 furtherance
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 
restricting 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 representation
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, expresses
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 determination
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 
substance 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 transitory
is nothing but determination of its existence. But such
a proof cannot be developed dogmatically, that is, from concepts,
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 
experience, we need not be surprised that though the above
principle is always postulated as lying at the basis of experience
(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 nothing
arises out of nothing, is still another consequence of the
principle of permanence, or rather of the ever-abiding existence,
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 
always connected together, but which are now sometimes mistakenly
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 unnecessary.
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 misunderstandings;
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 unavoidable,
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 
determinations 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 
perception. 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 
permanent. 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 
previously existed, and which persist in existence up to the
moment of this coming to be, this latter must be simply a 
determination 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 appearances
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 substance
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 
determinations, 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 
perceptions 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 
empirically 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 relation
between the two states must be so thought that it is thereby
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 appearances,
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 representation
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 representations)
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 reception
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 themselves,
then since we have to deal solely with our representations,
we could never determine from the succession of the representations
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 
representation 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 apprehension
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 
successive. This, however, is what no one will grant. Now 
immediately 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 
transcendental object of which is unknown. What, then, am I to
understand by the question: how the manifold may be connected
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 
representations of apprehension, can be represented as an object
distinct from them only if it stands under a rule which 
distinguishes 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 
P 221
previously 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 
follows upon another perception. But since, as I have above
illustrated by reference to the appearance of a house, this 
likewise happens in all synthesis of apprehension, the apprehension
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 perception
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 
apprehension of this appearance the ship should first be 
perceived 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 perception
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 
succession of apprehension from the objective succession of 
appearances. 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 
preceding point of time. The advance, on the other hand, from
a given time to the determinate time that follows is a necessary
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 
determine 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 perception
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 
sequence 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 subjective
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 
preceding 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 comparison
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 
concept, 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. Nevertheless,
P 224
recognition of the rule, as a condition of the synthetic
unity of appearances in time, has been the ground of 
experience 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 representation
(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 representations
is always successive. Now no object is hereby represented,
since through this succession, which is common to all 
apprehensions, 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 representation
P 225
follows in conformity with a rule, I represent something
as an event, as something that happens; that is to say, I 
apprehend 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 perceive
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 appearance
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 
necessary relation with itself in the time-series.
If, then, it is a necessary law of our sensibility, and therefore
a formal condition of all perceptions, that the preceding
time necessarily determines the succeeding (since I cannot 
advance 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 
P 226
representation 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 
determined 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 
object of perception, this determination of position cannot be 
derived 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 conformity
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 necessary
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 
position 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 precedes
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 considerations.
All empirical knowledge involves the synthesis of the
manifold by the imagination. This synthesis is always successive,
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 
successive 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 
determined; 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 judgments,
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 appearances
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 
appearances 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 
invariably 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 
complicated 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 
substance (as phenomenon). But while according to the usual 
procedure, 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 
required 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 universality
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 
substance 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 
always 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 transition
from one state to another therefore occurs in a time which
is contained between two instants, of which the first determines
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 
increases 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 
degrees, 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 
dispensed with, even though direct inspection may show the principle
to be true and [empirically] real, and though the question,
how it should be possible, may therefore be considered 
superfluous. 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 appearances
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 
determined 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 
magnitude, 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 condition
of the possibility of a continuous determination of all positions
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 
therefore 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 reciprocally,
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 
thoroughgoing 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 
apprehension 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 
apprehension. 
 Now assuming that in a manifold of substances as appearances
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 
P 235
objectively 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 experience
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 
thoroughgoing community of mutual interaction.
The word community is in the German language ambiguous.
It may mean either communio or commercium. We here
employ it in the latter sense, as signifying a dynamical 
community, 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 perception
of an appearance in space is broken off from every other,
and the chain of empirical representations, that is, experience,
P 236
would have to begin entirely anew with each new object,
without the least connection with the preceding representation,
and without standing to it in any relation of time. I do not by
this argument at all profess to disprove void space, for it may
exist where perceptions cannot reach, and where there is,
therefore, no empirical knowledge of coexistence. But such a
space is not for us an object of any possible experience.
The following remarks may be helpful in [further] elucidation
[of my argument]. In our mind, all appearances, since
they are contained in a possible experience, must stand in
community (communio) of apperception, and in so far as the
objects are to be represented as coexisting in connection with
each other, they must mutually determine their position in
one time, and thereby constitute a whole. If this subjective
community is to rest on an objective ground, or is to hold of
appearances as substances, the perception of the one must
as ground make possible the perception of the other, and
reversewise -- in order that the succession which is always
found in the perceptions, as apprehensions, may not be ascribed
to the objects, and in order that, on the contrary, these
objects may be represented as coexisting. But this is a 
reciprocal influence, that is, a real community (commercium) of
substances; without it the empirical relation of coexistence
could not be met with in experience. Through this commercium
the appearances, so far as they stand outside one
another and yet in connection, constitute a composite 
(compositum reale), and such composites are possible in many
different ways. The three dynamical relations, from which
all others spring, are therefore inherence, consequence, and
composition.
***
These, then, are the three analogies of experience. They are
simply principles of the determination of the existence of 
appearances in time, according to all its three modes, viz. the 
relation to time itself as a magnitude (the magnitude of existence,
that is, duration), the relation in time as a successive series, and
finally the relation in time as a sum of all simultaneous existence.
This unity of time-determination is altogether dynamical.
P 237
For time is not viewed as that wherein experience immediately
determines position for every existence. Such determination
is impossible, inasmuch as absolute time is not an
object of perception with which appearances could be 
confronted. What determines for each appearance its position in
time is the rule of the understanding through which alone the
existence of appearances can acquire synthetic unity as regards
relations of time; and that rule consequently determines the
position [in a manner that is] a priori and valid for each and
every time.
By nature, in the empirical sense, we understand the 
connection of appearances as regards their existence according
to necessary rules, that is, according to laws. There are certain
laws which first make a nature possible, and these laws are
a priori. Empirical laws can exist and be discovered only
through experience, and indeed in consequence of those original
laws through which experience itself first becomes possible.
Our analogies therefore really portray the unity of nature in
the connection of all appearances under certain exponents
which express nothing save the relation of time (in so far as
time comprehends all existence) to the unity of apperception
-- such unity being possible only in synthesis according to
rules. Taken together, the analogies thus declare that all
appearances lie, and must lie, in one nature, because without
this a priori unity no unity of experience, and therefore no
determination of objects in it, would be possible.
As to the mode of proof of which we have made use in
these transcendental laws of nature, and as to their peculiar
character, an observation has to be made which must likewise
be of very great importance as supplying a rule to be followed
in every other attempt to prove a priori propositions that are
intellectual and at the same time synthetic. Had we attempted
to prove these analogies dogmatically; had we, that is to say,
attempted to show from concepts that everything which exists
is to be met with only in that which is permanent, that every
event presupposes something in the preceding state upon
which it follows in conformity with a rule; and finally, that
in the manifold which is coexistent the states coexist in 
relation to one another in conformity with a rule and so stand in
P 238
community, all our labour would have been wasted. For through
mere concepts of these things, analyse them as we may, we can
never advance from one object and its existence to the existence
of another or to its mode of existence. But there is an
alternative method, namely, to investigate the possibility of
experience as a knowledge wherein all objects -- if their 
representation is to have objective reality for us -- must finally be
capable of being given to us. In this third [medium], the
essential form of which consists in the synthetic unity of the
apperception of all appearances, we have found a priori 
conditions of complete and necessary determination of time for
all existence in the [field of] appearance, without which even
empirical determination of time would be impossible. In it we
have also found rules of synthetic unity a priori, by means of
which we can anticipate experience. For lack of this method,
and owing to the erroneous assumption that synthetic 
propositions, which the empirical employment of the understanding
recommends as being its principles, may be proved dogmatically,
the attempt has, time and again, been made, though
always vainly, to obtain a proof of the principle of sufficient
reason. And since the guiding-thread of the categories, which
alone can reveal and make noticeable every gap in the 
understanding, alike in regard to concepts and to principles, has
hitherto been lacking, no one has so much as thought of the
other two analogies, although use has always tacitly been
made of them.
++ The unity of the world-whole, in which all appearances have
to be connected, is evidently a mere consequence of the tacitly
assumed principle of the community of all substances which are
coexistent. For if they were isolated, they would not as parts constitute
a whole. And if their connection (the reciprocal action of the
manifold) were not already necessary because of their coexistence,
we could not argue from this latter, which is a merely ideal relation
to the former, which is a real relation. We have, however, in the
proper context, shown that community is really the ground of the
possibility of an empirical knowledge of coexistence, and that the
inference, rightly regarded, is simply from this empirical knowledge
to community as its condition.
P 239
4
THE POSTULATES OF EMPIRICAL THOUGHT IN GENERAL
1. That which agrees with the formal conditions of experience,
that is, with the conditions of intuition and of 
concepts, is possible.
2. That which is bound up with the material conditions
of experience, that is, with sensation, is actual.
3. That which in its connection with the actual is determined
in accordance with universal conditions of experience,
is (that is, exists as) necessary.
Explanation
The categories of modality have the peculiarity that, in
determining an object, they do not in the least enlarge the
concept to which they are attached as predicates. They only
express the relation of the concept to the faculty of knowledge.
Even when the concept of a thing is quite complete, I can still
enquire whether this object is merely possible or is also actual,
or if actual, whether it is not also necessary. No additional
determinations are thereby thought in the object itself; the
question is only how the object, together with all its 
determinations, is related to understanding and its empirical 
employment, to empirical judgment, and to reason in its 
application to experience.
Just on this account also the principles of modality are
nothing but explanations of the concepts of possibility, actuality,
and necessity, in their empirical employment; at the same
time they restrict all categories to their merely empirical 
employment, and do not approve or allow their transcendental
employment. For if they are not to have a purely logical 
significance, analytically expressing the form of thought, but are
to refer to the possibility, actuality, or necessity of things, they
must concern possible experience and its synthetic unity, in
which alone objects of knowledge can be given.
The postulate of the possibility of things requires that
the concept of the things should agree with the formal 
conditions of an experience in general. But this, the objective
form of experience in general, contains all synthesis that is
P 240
required for knowledge of objects. A concept which contains
a synthesis is to be regarded as empty and as not related to
any object, if this synthesis does not belong to experience
either as being derived from it, in which case it is an empirical
concept, or as being an a priori condition upon which experience
in general in its formal aspect rests, in which case it is
a pure concept. In the latter case it still belongs to experience,
inasmuch as its object is to be met with only in experience.
For whence shall we derive the character of the possibility of
an object which is thought through a synthetic a priori concept,
if not from the synthesis which constitutes the form of
the empirical knowledge of objects? It is, indeed, a necessary
logical condition that a concept of the possible must not contain
any contradiction; but this is not by any means sufficient
to determine the objective reality of the concept, that is, the 
possibility of such an object as is thought through the concept.
Thus there is no contradiction in the concept of a figure which
is enclosed within two straight lines, since the concepts of two
straight lines and of their coming together contain no negation
of a figure. The impossibility arises not from the concept in
itself, but in connection with its construction in space, that is,
from the conditions of space and of its determination. And
since these contain a priori in themselves the form of experience
in general, they have objective reality, that is, they apply
to possible things.
We shall now proceed to show the far-reaching utility and
influence of this postulate of possibility. If I represent to 
myself a thing which is permanent, so that everything in it which
changes belongs only to its state, I can never know from such
a concept that a thing of this kind is possible. Or if I represent
to myself something which is so constituted that if it is posited
something else invariably and inevitably follows from it, this
may certainly be so thought without contradiction; but this
thought affords no means of judging whether this property
(causality) is to be met with in any possible thing. Lastly,
I can represent to myself diverse things (substances), which
are so constituted that the state of the one carries with it some
consequence in the state of the other, and this reciprocally;
but I can never determine from these concepts, which contain
a merely arbitrary synthesis, whether a relation of this kind
P 241
can belong to any [possible] things. Only through the fact that
these concepts express a priori the relations of perceptions in
every experience, do we know their objective reality, that is
their transcendental truth, and this, indeed, independently of
experience, though not independently of all relation to the
form of an experience in general, and to the synthetic unity
in which alone objects can be empirically known.
But if we should seek to frame quite new concepts of 
substances, forces, reciprocal actions, from the material which
perception presents to us, without experience itself yielding
the example of their connection, we should be occupying ourselves
with mere fancies, of whose possibility there is absolutely
no criterion since we have neither borrowed these concepts
[directly] from experience, nor have taken experience as our
instructress in their formation. Such fictitious concepts, unlike
the categories, can acquire the character of possibility not
in a priori fashion, as conditions upon which all experience
depends, but only a posteriori as being concepts which are
given through experience itself. And, consequently, their 
possibility must either be known a posteriori and empirically, or
it cannot be known at all. A substance which would be 
permanently present in space, but without filling it (like that
mode of existence intermediate between matter and thinking
being which some would seek to introduce), or a special ultimate
mental power of intuitively anticipating the future (and
not merely inferring it), or lastly a power of standing in 
community of thought with other men, however distant they may
be -- are concepts the possibility of which is altogether groundless,
as they cannot be based on experience and its known laws;
and without such confirmation they are arbitrary combinations
of thoughts, which, although indeed free from contradiction,
can make no claim to objective reality, and none, therefore, as
to the possibility of an object such as we here profess to think.
As regards reality, we obviously cannot think it in concreto,
without calling experience to our aid. For reality is bound up
with sensation, the matter of experience, not with that form
of relation in regard to which we can, if we so choose, resort
to a playful inventiveness.
But I leave aside everything the possibility of which can
P 242
be derived only from its actuality in experience, and have here
in view only the possibility of things through a priori concepts;
and I maintain the thesis that their possibility can never be
established from such concepts taken in and by themselves,
but only when the concepts are viewed as formal and objective
conditions of experience in general.
It does, indeed, seem as if the possibility of a triangle could
be known from its concept in and by itself (the concept is 
certainly independent of experience), for we can, as a matter of
fact, give it an object completely a priori, that is, can construct
it. But since this is only the form of an object, it would remain
a mere product of imagination, and the possibility of its object
would still be doubtful. To determine its possibility, something
more is required, namely, that such a figure be thought under
no conditions save those upon which all objects of experience
rest. That space is a formal a priori condition of outer 
experiences, that the formative synthesis through which we 
construct a triangle in imagination is precisely the same as that
which we exercise in the apprehension of an appearance, in
making for ourselves an empirical concept of it -- these are the
considerations that alone enable us to connect the representation
of the possibility of such a thing with the concept of it.
Similarly, since the concepts of continuous magnitudes, indeed
of magnitudes in general, are one and all synthetic, the possibility
of such magnitudes is never clear from the concepts 
themselves, but only when they are viewed as formal conditions
of the determination of objects in experience in general. And
where, indeed, should we seek for objects corresponding to
these concepts if not in experience, through which alone 
objects are given to us? We can, indeed, prior to experience
itself, know and characterise the possibility of things, merely
by reference to the formal conditions under which in 
experience anything whatsoever is determined as object, and
therefore can do so completely a priori. But, even so, this is
possible only in relation to experience and within its limits.
 The postulate bearing on the knowledge of things as
actual does not, indeed, demand immediate perception (and,
therefore, sensation of which we are conscious) of the object
whose existence is to be known. What we do, however,
P 243
require is the connection of the object with some actual
perception, in accordance with the analogies of experience,
which define all real connection in an experience in
general.
In the mere concept of a thing no mark of its existence is
to be found. For though it may be so complete that nothing
which is required for thinking the thing with all its inner 
determinations is lacking to it, yet existence has nothing to do with
all this, but only with the question whether such a thing be so
given us that the perception of it can, if need be, precede the
concept. For that the concept precedes the perception signifies
the concept's mere possibility; the perception which supplies
the content to the concept is the sole mark of actuality.
We can also, however, know the existence of the thing prior to
its perception and, consequently, comparatively speaking, in
an a priori manner, if only it be bound up with certain perceptions,
in accordance with the principles of their empirical connection
(the analogies). For the existence of the thing being
thus bound up with our perceptions in a possible experience,
we are able in the series of possible perceptions and under the
guidance of the analogies to make the transition from our
actual perception to the thing in question. Thus from the 
perception of the attracted iron filings we know of the existence
of a magnetic matter pervading all bodies, although the 
constitution of our organs cuts us off from all immediate perception
of this medium. For in accordance with the laws of sensibility
and the context of our perceptions, we should, were our
senses more refined, come also in an experience upon the 
immediate empirical intuition of it. The grossness of our senses
does not in any way decide the form of possible experience in
general. Our knowledge of the existence of things reaches,
then, only so far as perception and its advance according
to empirical laws can extend. If we do not start from 
experience, or do not proceed accordance with laws of the 
P 244
empirical connection of appearances, our guessing or enquiring
into the existence of anything will only be an idle pretence.
Idealism raises, however, what is a serious objection to these
rules for proving existence mediately; and this is the proper
place for its refutation.
***
Refutation of Idealism
Idealism -- meaning thereby material idealism -- is the
theory which declares the existence of objects in space outside
us either to be merely doubtful and indemonstrable or to
be false and impossible. The former is the problematic idealism
of Descartes, which holds that there is only one empirical
assertion that is indubitably certain, namely, that 'I am'. The
latter is the dogmatic idealism of Berkeley. He maintains that
space, with all the things of which it is the inseparable condition,
is something which is in itself impossible; and he therefore
regards the things in space as merely imaginary entities.
Dogmatic idealism is unavoidable, if space be interpreted as a
property that must belong to things in themselves. For in that
case space, and everything to which it serves as condition, is a
non-entity. The ground on which this idealism rests has 
already been undermined by us in the Transcendental Aesthetic.
Problematic idealism, which makes no such assertion, but
merely pleads incapacity to prove, through immediate experience,
any existence except our own, is, in so far as it allows
of no decisive judgment until sufficient proof has been found,
reasonable and in accordance with a thorough and philosophical
mode of thought. The required proof must, therefore,
show that we have experience, and not merely imagination of
outer things; and this, it would seem, cannot be achieved save
by proof that even our inner experience, which for Descartes
is indubitable, is possible only on the assumption of outer 
experience. 
P 245
THESIS
The mere, but empirically determined, consciousness of my
own existence proves the existence of objects in space
outside me.
Proof
I am conscious of my own existence as determined in
time. All determination of time presupposes something 
permanent in perception. This permanent cannot, however,
be something in me, since it is only through this 
permanent that my existence in time can itself be determined.
Thus perception of this permanent is possible only
through a thing outside me and not through the mere 
representation of a thing outside me; and consequently the
determination of my existence in time is possible only through
the existence of actual things which I perceive outside me.
Now consciousness [of my existence] in time is necessarily
bound up with consciousness of the [condition of the] possibility
of this time-determination; and it is therefore necessarily
bound up with the existence of things outside me, as the
condition of the time-determination. In other words, the 
consciousness of my existence is at the same time an immediate
consciousness of the existence of other things outside me.
Note 1. It will be observed that in the foregoing proof
the game played by idealism has been turned against itself,
and with greater justice. Idealism assumed that the only
immediate experience is inner experience, and that from it
we can only infer outer things -- and this, moreover, only in an
untrustworthy manner, as in all cases where we are inferring
from given effects to determinate causes. In this particular case,
the cause of the representations, which we ascribe, perhaps
falsely, to outer things, may lie in ourselves. But in the above
proof it has been shown that outer experience is really
P 246
immediate, and that only by means of it is inner experience
-- not indeed the consciousness of my own existence, but the
determination of it in time -- possible. Certainly, the 
representation 'I am', which expresses the consciousness that can
accompany all thought, immediately includes in itself the
existence of a subject; but it does not so include any knowledge
of that subject, and therefore also no empirical knowledge,
that is, no experience of it. For this we require, in addition to
the thought of something existing, also intuition, and in this
case inner intuition, in respect of which, that is, of time, the
subject must be determined. But in order so to determine it,
outer objects are quite indispensable; and it therefore follows
that inner experience is itself possible only mediately, and
only through outer experience.
Note 2. With this thesis all employment of our cognitive
faculty in experience, in the determination of time, entirely
agrees. Not only are we unable to perceive any determination
of time save through change in outer relations
(motion) relatively to the permanent in space (for instance,
the motion of the sun relatively to objects on the earth), we
have nothing permanent on which, as intuition, we can base
the concept of a substance, save only matter; and even this
permanence is not obtained from outer experience, but is
presupposed a priori as a necessary condition of determination
of time, and therefore also as a determination of inner
sense in respect of [the determination of] our own existence
through the existence of outer things.
++ The immediate consciousness of the existence of outer things
is, in the preceding thesis, not presupposed, but proved, be the
possibility of this consciousness understood by us or not. The 
question as to its possibility would be this: whether we have an inner
sense only, and no outer sense, but merely an outer imagination. It
is clear, however, that in order even only to imagine something as
outer, that is, to present it to sense in intuition, we must already
have an outer sense, and must thereby immediately distinguish the
mere receptivity of an outer intuition from the spontaneity which
characterises every act of imagination. For should we merely be
imagining an outer sense, the faculty of intuition, which is to be
determined by the faculty of imagination, would itself be annulled.
P 246
The consciousness of
myself in the representation 'I' is not an intuition, but a
P 247
merely intellectual representation of the spontaneity of a
thinking subject. This 'I' has not, therefore, the least 
predicate of intuition, which, as permanent, might serve as 
correlate for the determination of time in inner sense -- in the
manner in which, for instance, impenetrability serves in our
empirical intuition of matter.
Note 3. From the fact that the existence of outer things
is required for the possibility of a determinate consciousness
of the self, it does not follow that every intuitive representation
of outer things involves the existence of these things,
for their representation can very well be the product merely
of the imagination (as in dreams and delusions). Such 
representation is merely the reproduction of previous outer
perceptions, which, as has been shown, are possible only
through the reality of outer objects. All that we have here
sought to prove is that inner experience in general is possible
only through outer experience in general. Whether this or that
supposed experience be not purely imaginary, must be ascertained
from its special determinations, and through its 
congruence with the criteria of all real experience.
***
Lastly, as regards the third postulate, it concerns material
necessity in existence, and not merely formal and logical
necessity in the connection of concepts. Since the existence of
any object of the senses cannot be known completely a priori,
but only comparatively a priori, relatively to some other 
previously given existence; and since, even so, we can then
arrive only at such an existence as must somewhere be
contained in the context of the experience, of which the
given perception is a part, the necessity of existence can
never be known from concepts, but always only from 
connection with that which is perceived, in accordance with
universal laws of experience. Now there is no existence that
can be known as necessary under the condition of other given
appearances, save the existence of effects from given causes,
P 248
in accordance with laws of causality. It is not, therefore, the
existence of things (substances) that we can know to be necessary,
but only the existence of their state; and this necessity
of the existence of their state we can know only from other
states, which are given in perception, in accordance with
empirical laws of causality. It therefore follows that the criterion
of necessity lies solely in the law of possible experience,
the law that everything which happens is determined a priori
through its cause in the [field of] appearance. We thus know
the necessity only of those effects in nature the causes of which
are given to us, and the character of necessity in existence
extends no further than the field of possible experience, and
even in this field is not applicable to the existence of things as
substances, since substances can never be viewed as empirical
effects -- that is, as happening and coming to be. Necessity 
concerns only the relations of appearances in conformity with the
dynamical law of causality and the possibility grounded upon
it of inferring a priori from a given existence (a cause) to
another existence (the effect). That everything which happens
is hypothetically necessary is a principle which subordinates
alteration in the world to a law, that is, to a rule of necessary
existence, without which there would be nothing that could be
entitled nature. The proposition that nothing happens through
blind chance (in mundo non datur casus) is therefore an a -
priori law of nature. So also is the proposition that no necessity
in nature is blind, but always a conditioned and therefore
intelligible necessity (non datur fatum). Both are laws through
which the play of alterations is rendered subject to a nature of
things (that is, of things as appearances), or what amounts to
the same thing, to the unity of understanding, in which
alone they can belong to one experience, that is, to the 
synthetic unity of appearances. Both belong to the class of
dynamical principles. The first is really a consequence of the
principle of causality, and so belongs to the analogies of
experience. The second is a principle of modality; but this
modality, while adding the concept of necessity to causal
determination, itself stands under a rule of understanding.
The principle of continuity forbids any leap in the series of
appearances, that is, of alterations (in mundo non datur saltus);
P 249
it also forbids, in respect of the sum of all empirical intuitions
in space, any gaps or cleft between two appearances (non
datur hiatus); for so we may express the proposition, that
nothing which proves a vacuum, or which even admits it as a
part of empirical synthesis, can enter into experience. As regards
a void which may be conceived to lie beyond the field of possible
experience, that is, outside the world, such a question does not
come within the jurisdiction of the mere understanding -- which
decides only upon questions that concern the use to be made
of given appearances for the obtaining of empirical knowledge.
It is a problem for that ideal reason which goes out
beyond the sphere of a possible experience and seeks to judge
of that which surrounds and limits it; and is a problem which
will therefore have to be considered in the Transcendental
Dialectic. These four propositions (in mundo non datur
hiatus, non datur saltus, non datur casus, non datur fatum),
like all principles of transcendental origin, we can easily 
exhibit in their order, that is, in accordance with the order of
the categories, and so assign to each its proper place. But the
reader has now had sufficient practice to allow of his doing
this for himself, or of easily discovering the guiding principle
for so doing. They are all entirely at one in this, that they
allow of nothing in the empirical synthesis which may do
violence or detriment to the understanding and to the continuous
connection of all appearances -- that is, to the unity of
the concepts of the understanding. For in the understanding
alone is possible the unity of experience, in which all 
perceptions must have their place.
To enquire whether the field of possibility is larger than the
field which contains all actuality, and this latter, again, larger
than the sum of that which is necessary, is to raise somewhat
subtle questions which demand a synthetic solution and yet
come under the jurisdiction of reason alone. For they are
tantamount to the enquiry whether things as appearances one
and all belong to the sum and context of a single experience,
of which every given perception is a part, a part which therefore
cannot be connected with any other [series of] appearances,
or whether my perceptions can belong, in their general 
connection, to more than one possible experience. The 
P 250
understanding, in accordance with the subjective and formal 
conditions of sensibility as well as of apperception, prescribes
a priori to experience in general the rules which alone make
experience possible. Other forms of intuition than space and
time, other forms of understanding than the discursive forms
of thought, or of knowledge through concepts, even if they
should be possible, we cannot render in any way conceivable
and comprehensible to ourselves; and even assuming that we
could do so, they still would not belong to experience -- the
only kind of knowledge in which objects are given to us.
Whether other perceptions than those belonging to our whole
possible experience, and therefore a quite different field of
matter, may exist, the understanding is not in a position to
decide. It can deal only with the synthesis of that which is
given. Moreover, the poverty of the customary inferences
through which we throw open a great realm of possibility, of
which all that is actual (the objects of experience) is only a small
part, is patently obvious. Everything actual is possible; from
this proposition there naturally follows, in accordance with the
logical rules of conversion, the merely particular proposition,
that some possible is actual; and this would seem to mean
that much is possible which is not actual. It does indeed
seem as if we were justified in extending the number of
possible things beyond that of the actual, on the ground
that something must be added to the possible to constitute
the actual. But this [alleged] process of adding to the 
possible I refuse to allow. For that which would have to be
added to the possible, over and above the possible, would
be impossible. What can be added is only a relation to my
understanding, namely that in addition to agreement with
the formal conditions of experience there should be connecttion
with some perception. But whatever is connected with
perception in accordance with empirical laws is actual, even
although it is not immediately perceived. That yet another
series of appearances in thoroughgoing connection with that
which is given in perception, and consequently that more
than one all-embracing experience is possible, cannot be 
inferred from what is given; and still less can any such 
inference be drawn independently of anything being given -- since
P 251
without material nothing whatsoever can be thought. What
is possible only under conditions which themselves are merely
possible is not in all respects possible. But such [absolute]
possibility is in question when it is asked whether the 
possibility of things extends further than experience can reach.
I have made mention of these questions only in order to
omit nothing which is ordinarily reckoned among the concepts
of understanding. But as a matter of fact absolute possibility,
that which is in all respects valid, is no mere concept of
understanding, and can never be employed empirically. It
belongs exclusively to reason, which transcends all possible
empirical employment of the understanding. We have therefore
had to content ourselves with some merely critical remarks;
the matter must otherwise be left in obscurity until we
come to the proper occasion for its further treatment.
Before concluding this fourth section, and therewith the
system of all principles of pure understanding, I must explain
why I have entitled the principles of modality postulates. I
interpret this expression not in the sense which some recent
philosophical writers, wresting it from its proper mathematical
significance, have given to it, namely, that to postulate should
mean to treat a proposition as immediately certain, without
justification or proof. For if, in dealing with synthetic
propositions, we are to recognise them as possessing 
unconditioned validity, independently of deduction, on the 
evidence [merely] of their own claims, then no matter how evident
they may be, all critique of understanding is given up. And
since there is no lack of audacious pretensions, and these are
supported by common belief (though that is no credential of
their truth), the understanding lies open to every fancy, and is
in no position to withhold approval of those assertions which,
though illegitimate, yet press upon us, in the same confident
tone, their claims to be accepted as actual axioms. Whenever,
therefore, an a priori determination is synthetically added to
the concept of a thing, it is indispensable that, if not a proof,
at least a deduction of the legitimacy of such an assertion
should be supplied.
The principles of modality are not, however, objectively
synthetic. For the predicates of possibility, actuality, and
P 252
necessity do not in the least enlarge the concept of which they
are affirmed, adding something to the representation of the
object. But since they are none the less synthetic, they are so
subjectively only, that is, they add to the concept of a thing (of
something real), of which otherwise they say nothing, the cognitive
faculty from which it springs and in which it has its seat.
Thus if it is in connection only with the formal conditions of
experience, and so merely in the understanding, its object is
called possible. If it stands in connection with perception, that is,
with sensation as material supplied by the senses, and through
perception is determined by means of the understanding, the
object is actual. If it is determined through the connection of 
perceptions according to concepts, the object is entitled necessary.
The principles of modality thus predicate of a concept nothing
but the action of the faculty of knowledge through which it
is generated. Now in mathematics a postulate means the 
practical proposition which contains nothing save the synthesis
through which we first give ourselves an object and generate
its concept -- for instance, with a given line, to describe a circle
on a plane from a given point. Such a proposition cannot be
proved, since the procedure which it demands is exactly that
through which we first generate the concept of such a figure.
With exactly the same right we may postulate the principles of
modality, since they do not increase our concept of things,
but only show the manner in which it is connected with the
faculty of knowledge.
 General Note on the System of the Principles
That the possibility of a thing cannot be determined from
the category alone, and that in order to exhibit the objective
reality of the pure concept of understanding we must always
have an intuition, is a very noteworthy fact.
++ Through the actuality of a thing I certainly posit more than
the possibility of it, but not in the thing. For it can never contain
more in its actuality than is contained in its complete possibility.
But while possibility is merely a positing of the thing in relation to
the understanding (in its empirical employment), actuality is at the
same time a connection of it with perception.
P 253
Take, for instance,
the categories of relation. We cannot determine from mere
concepts how (1) something can exist as subject only, and not
as a mere determination of other things, that is, how a thing
can be substance, or (2) how, because something is, something
else must be, and how, therefore, a thing can be a cause, or (3)
when several things exist, how because one of them is there,
something follows in regard to the others and vice versa, and
how in this way there can be a community of substances.
This likewise applies to the other categories; for example,
how a thing can be equal to a number of things taken together,
that is, can be a quantity. So long as intuition is lacking, we do
not know whether through the categories we are thinking an
object, and whether indeed there can anywhere be an object
suited to them. In all these ways, then, we obtain confirmation
that the categories are not in themselves knowledge, but are
merely forms of thought for the making of knowledge from
given intuitions.
For the same reason it follows that no synthetic proposition
can be made from mere categories. For instance, we are
not in a position to say that in all existence there is substance,
that is, something which can exist only as subject and not as
mere predicate; or that everything is a quantum, etc. For if
intuition be lacking, there is nothing which can enable us to
go out beyond a given concept, and to connect another with it.
No one, therefore, has ever yet succeeded in proving a 
synthetic proposition merely from pure concepts of the understanding
-- as, for instance, that everything which exists contingently
has a cause. We can never get further than proving,
that without this relation we are unable to comprehend the
existence of the contingent, that is, are unable a priori through
the understanding to know the existence of such a thing --
from which it does not, however, follow that this is also a 
condition of the possibility of the things themselves. If the reader
will go back to our proof of the principle of causality -- that
everything which happens, that is, every event, presupposes a
cause -- he will observe that we were able to prove it only of
objects of possible experience; and even so, not from pure 
concepts, but only as a principle of the possibility of experience,
and therefore of the knowledge of an object given in empirical
P 254
intuition. We cannot, indeed, deny that the proposition, that
everything contingent must have a cause, is patent to everyone
from mere concepts. But the concept of the contingent
is then being apprehended as containing, not the category
of modality (as something the not-being of which can be
thought), but that of relation (as something which can exist
only as consequence of something else); and it is then, of
course, an identical proposition -- that which can exist only
as consequence has a cause. As a matter of fact, when we are
required to cite examples of contingent existence, we invariably
have recourse to alterations, and not merely to the possibility
of entertaining the opposite in thought. Now alteration
is an event which, as such, is possible only through a cause, and
the not-being of which is therefore in itself possible. In other
words, we recognise contingency in and through the fact that
something can exist only as the effect of a cause; and if, therefore,
a thing is assumed to be contingent, it is an analytic 
proposition to say that it has a cause.
But it is an even more noteworthy fact, that in order to
understand the possibility of things in conformity with the
categories, and so to demonstrate the objective reality of the
latter, we need, not merely intuitions, but intuitions that are in
all cases outer intuitions. When, for instance, we take the pure
concepts of relation, we find, firstly, that in order to obtain
something permanent in intuition corresponding to the concept
of substance, and so to demonstrate the objective reality
of this concept, we require an intuition in space (of matter).
++ We can easily think the non-existence of matter. From this
the ancients did not, however, infer its contingency. Even the
change from being to not-being of a given state of a thing, in which
all alteration consists, does not prove the contingency of this
state, on the ground of the reality of its opposite. For instance, that
a body should come to rest after having been in motion does not
prove the contingency of the motion as being the opposite of the
state of rest. For this opposite is opposed to the other only logically,
not realiter. To prove the contingency of its motion, we should have
to prove that instead of the motion at the preceding moment, it was
possible for the body to have been then at rest, not that it is afterwards
at rest; for in the latter case the opposites are quite consistent
with each other.
P 255
For space alone is determined as permanent, while time, and
therefore everything that is in inner sense, is in constant flux.
Secondly, in order to exhibit alteration as the intuition 
corresponding to the concept of causality, we must take as our
example motion, that is, alteration in space. Only in this way
can we obtain the intuition of alterations, the possibility of
which can never be comprehended through any pure understanding.
For alteration is combination of contradictorily
opposed determinations in the existence of one and the same
thing. Now how it is possible that from a given state of a thing
an opposite state should follow, not only cannot be conceived
by reason without an example, but is actually incomprehensible
to reason without intuition. The intuition required is the 
intuition of the movement of a point in space. The presence of
the point in different locations (as a sequence of opposite 
determinations) is what alone first yields to us an intuition of
alteration. For in order that we may afterwards make inner
alterations likewise thinkable, we must represent time (the
form of inner sense) figuratively as a line, and the inner
alteration through the drawing of this line (motion), and so
in this manner by means of outer intuition make comprehensible
the successive existence of ourselves in different
states. The reason of this is that all alteration, if it is to be
perceived as alteration, presupposes something permanent in
intuition, and that in inner sense no permanent intuition is
to be met with. Lastly, the possibility of the category of
community cannot be comprehended through mere reason
alone; and consequently its objective reality is only to be 
determined through intuition, and indeed through outer intuition
in space. For how are we to think it to be possible, when several
substances exist, that, from the existence of one, something (as
effect) can follow in regard to the existence of the others, and
vice versa; in other words, that because there is something
in the one there must also in the others be something which
is not to be understood solely from the existence of these
others? For this is what is required in order that there be 
community; community is not conceivable as holding between
things each of which, through its subsistence, stands in complete
isolation. Leibniz, in attributing to the substances of the
P 256
world, as thought through the understanding alone, a community,
had therefore to resort to the mediating intervention
of a Deity. For, as he justly recognised, a community of 
substances is utterly inconceivable as arising simply from their
existence. We can, however, render the possibility of 
community -- of substances as appearances -- perfectly 
comprehensible, if we represent them to ourselves in space, that is,
in outer intuition. For this already contains in itself a priori
formal outer relations as conditions of the possibility of the
real relations of action and reaction, and therefore of the
possibility of community.
Similarly, it can easily be shown that the possibility of
things as quantities, and therefore the objective reality of
quantity, can be exhibited only in outer intuition, and that
only through the mediation of outer intuition can it be applied
also to inner sense. But, to avoid prolixity, I must leave the
reader to supply his own examples of this.
These remarks are of great importance, not only in 
confirmation of our previous refutation of idealism, but even
more, when we come to treat of self-knowledge by mere inner
consciousness, that is, by determination of our nature without
the aid of outer empirical intuitions -- as showing us the limits
of the possibility of this kind of knowledge.
The final outcome of this whole section is therefore this:
all principles of the pure understanding are nothing more than
principles a priori of the possibility of experience, and to
experience alone do all a priori synthetic propositions relate --
indeed, their possibility itself rests entirely on this relation.

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