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  A177
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 B219
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 B220
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 A178
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 B221
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 A179
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. B222
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 A180
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 B223
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 A181
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 B224
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 A182
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 B225
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 B226
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, A183
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 B227
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 A184
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, B228
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  A185
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 B229
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 A186
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 B230
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; A187
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 B231
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 A188
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 B232
would flow in two parallel streams -- which is absurd. There
is only one time in which all different times must be located A189
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, B233
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 B234
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 B235
the word 'object' ought to signify in respect of appearances A190
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 B236
of an object, I realise that the house is not a thing in itself,
but only an appearance, that is, a representation, the  A191
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 B237
preceded by an appearance which does not contain in itself this
state. For an event which should follow upon an empty time, A192
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 B238
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 A193
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 B239
this event invariably and necessarily follows. I cannot reverse
this order, proceeding back from the event to determine A194
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  B240
sequence is rendered objectively necessary. I could not then
assert that two states follow upon one another in the [field of] A195
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 B241
appearances, and that this is the way in which we are first led
to construct for ourselves the concept of cause. Now the  A196
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 B242
which compels us to observe this order of perceptions rather
than any other; nay, that this compulsion is really what first A197
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 B243
order as regards their time-relations do they acquire objective
meaning.
 In the synthesis of appearances the manifold of representations A198
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 B244
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 A199
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. B245
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 A200
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 B246
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 A201
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, B247
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 A202
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 B248
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 A203
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 hollow in the  B249
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 A204
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 B250
 -- 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 A205
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 B251
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 A206
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 B252
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 A207
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 B253
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 A208
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  B254
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. A209
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, B255
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, A210
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 B256
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 A211
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, B257
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 B258
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 A212
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 B259
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 A213
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. B260
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, A214
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, B261
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 A215
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  B262
(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  A216 B263
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 B264
event presupposes something in the preceding state upon A217
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 B265
reason. And since the guiding-thread of the categories, which A218
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.