consists in its general relation to that experience.
But although the schemata of sensibility serve
thus to realise the categories, it must strike every-
body that they at the same time restrict them, that
is, limit them by conditions foreign to the under-
standing and belonging to sensibility. Hence the
schema is really the phenomenon, or the sensuous
concept of an object in agreement with the category
(numerus est quantitas phaenomenon, sensatio realitas
phaenomenon, constans et joerdurabile rerum sub-
stantia phenomenon seternitas necessitas pheno-
menon, etc.). If we omit a restrictive condition, it
would seem that we amplify a formerly limited
concept, and that therefore the categories [p. 147]
VOL. IL K
-
I30 TRANSCENDENTAL ANALYTIC.
in their pure meaning, free from all conditions of
sensibility, should be valid of things in general, as
they are, while their schemata represent them only as
they appear, so that these categories might claim a far
more extended power, independent of all schemata.
And in truth we must allow to these pure concepts
of the understanding, apart from all sensuous con-
ditions, a certain significance, though a logical one
only, with regard to the mere unity of representa-
tions, although these representations have no object
and therefore no meaning that could give us a concept
of an object. Thus substance, if we leave out the
sensuous condition of permanence, would mean no-
thing but a something that may be conceived as
a subject, without being the predicate of anything
else. Of such a representation we can make nothing,
because it does not teach us how that thing is de-
termined which is thus to be considered as the first
subject. Categories therefore without schemata, are
functions only of the understanding necessary for
concepts, but do not themselves represent any object.
This character is given to them by sensibility only,
which realises the understanding by, at the same
time, restricting it.
THE TRANSCENDENTAL DOCTRINE
[p. i 4 8.]
OF THE
FACULTY OF JUDGMENT
OR
ANALYTIC OF PRINCIPLES.
CHAPTER II.
SYSTEM OF ALL PRINCIPLES OF THE PURE
UNDERSTANDING.
We have in the preceding chapter considered the
transcendental faculty of judgment with reference
to those general conditions only under which it is
justified in using the pure concepts of the under-
standing for synthetical judgments. It now becomes
our duty to represent systematically those judg-
ments which, under that critical provision, the under-
standing can really produce a priori. For this
purpose our table of categories will be without doubt
our natural and best guide. For it is the relation of
the categories to all possible experience which must
constitute all pure a priori knowledge of the under-
standing ; and their relation to sensibility in general
will therefore exhibit completely and systematically
all the transcendental principles of the use of the
understanding 1 .
1 The insertion of man, as suggested by Rosenkranz, is im-
possible.
K 2
132 TRANSCENDENTAL ANALYTIC.
Principles a priori are so called, not only because
they contain the grounds for other judgments, but
also because they themselves are not founded, on
higher and more general kinds of knowledge. This
peculiarity, however, does not enable them to dis-
pense with every kind of proof; for although [p. 149]
this could not be given objectively, as all knowledge
of its object really rests on it, this does not prevent
us from attempting to produce a proof drawn from
the subjective sources of the possibility of a know-
ledge of the object in general; nay, it may be ne-
cessary to do so, because, without it, our assertion
might be suspected of being purely gratuitous.
We shall treat, however, of those principles only
which relate to the categories. We shall have no-
thing to do with the principles of transcendental
aesthetic, according to which space and time are the
conditions of the possibility of all things as phe-
nomena, nor of the limitation of those principles,
prohibiting their application to things by themselves.
Mathematical principles also do not belong to this
part of our discussion, because they are derived from
intuition, and not from the pure concept of the un-
derstanding. As they are however synthetical judg-
ments a priori, their possibility will have to be dis-
cussed, not in order to prove their correctness and
apodictic certainty, which would be unnecessary, but
in order to make the possibility of such self-evident
knowledge a priori conceivable and intelligible.
We shall also have to speak of the principle of ana-
lytical as opposed to synthetical judgments, [p. 150]
the latter being the proper subject of our enquiries,
TRANSCENDENTAL ANALYTIC. I 33
because this very opposition frees the theory of the
latter from all misunderstandings, and places them
clearly before us in their own peculiar character.
SYSTEM OF THE PRINCIPLES OF THE PURE
UNDERSTANDING.
Section I.
Of the highest principle of all analytical judgments.
Whatever the object of our knowledge may be,
and whatever the relation between our knowledge
and its object, it must always submit to that
general, though only negative condition of all our
judgments, that they do not contradict themselves ;
otherwise these judgments, without any reference
to their object, are in themselves nothing. But
although there may be no contradiction in our judg-
ment, it may nevertheless connect concepts in a
manner not warranted by the object, or without
there being any ground, whether a priori or a
posteriori, to confirm such a judgment. A judg-
ment may therefore be false or groundless, though
in itself it is free from all contradiction.
The proposition that no subject can have [p.15 1 ]
a predicate which contradicts it, is called the prin-
ciple of contradiction. It is a general though only
negative criterion of all truth, and belongs to logic
only, because it applies to knowledge as knowledge
only, without reference to its object, and simply de-
clares that such contradiction would entirely destroy
and annihilate it.
134 TRANSCENDENTAL ANALYTIC
Nevertheless, a positive use also may be made of
that principle, not only in order to banish falsehood
and error, so far as they arise from contradiction, but
also in order to discover truth. For in an analytical
judgment, whether negative or affirmative, its truth
can always be sufficiently tested by the principle of
contradiction, because the opposite of that which
exists and is thought as a concept in our knowledge
of an object, is always rightly negatived, while the
concept itself is necessarily affirmed of it, for the
simple reason that its opposite would be in contra-
diction with the object.
It must therefore be admitted that the principle of
contradiction is the general and altogether sufficient
principle of all analytical knowledge, though beyond
this its authority and utility, as a sufficient criterion
of truth, must not be allowed to extend. For the fact
that no knowledge can run counter to that principle,
without destroying itself, makes it no doubt [p. 152]
a conditio sine qua non, but never a test of the truth
of our knowledge. Now, as in our present enquiry
we are chiefly concerned with the synthetical part of
our knowledge, we must no doubt take great care
never to offend against that inviolable principle, but
we ought never to expect from it any help with
regard to the truth of this kind of knowledge.
There is, however, a formula of this famous prin-
ciple a principle merely formal and void of all con-
tents which contains a synthesis that has been
mixed up with it from mere carelessness and without
any real necessity. This formula is : It is impossible
that anything should be and at the same time not
TRANSCENDENTAL ANALYTIC 1 35
be. Here, first of all, the apodictic certainty ex-
pressed by the word impossible is added unneces-
sarily, because it is understood by itself from the
nature of the proposition ; secondly, the proposition
is affected by the condition of time, and says, as it
were, something = A, which is something = B, cannot
be at the same time not-B, but it can very well be
both (B and not-B) in succession. For instance, a
man who is young cannot be at the same time old,
but the same man may very well be young at one
time and not young, that is, old, at another. We
see therefore that the principle of contradiction, as
a purely logical principle, must not be limited in its
application by time, and that the before-men- [p. 153]
tioned formula runs counter to its very nature. The
misunderstanding arises from our first separating one
predicate of an object from its concept, and by our
afterwards joining its opposite with that predicate,
which gives us a contradiction, not with the subject,
but with one of its predicates which is synthetically
connected with it, and this again only on condition
that the first and second predicate have both been
applied at the same time. If I want to say that a
man who is unlearned is not learned, I must add
the condition ' at the same time/ for a man who is
unlearned at one time may very well be learned at
another. But if I say no unlearned man is learned,
then the proposition is analytical, because the
characteristic (unlearnedness) forms part now of
the concept of the subject, so that the negative
proposition becomes evident directly from the prin-
ciple of contradiction, and without the necessity of
136 TRANSCENDENTAL ANALYTIC.
adding the condition, ' at the same time ' This is
the reason why I have so altered the wording of that
formula that it displays at once the nature of an
analytical proposition.
SYSTEM OF THE PRINCIPLES OF THE PURE [p. 154]
UNDERSTANDING.
Section II.
Of the highest principle of all synthetical judgments.
The explanation of the possibility of synthetical
judgments is a subject of which general logic knows
nothing, not even its name, while in a transcendental
logic it is the most important task of all, nay, even
the only one, when we have to consider the possi-
bility of synthetical judgments a priori, their con-
ditions, and the extent of their validity. For when
that task is accomplished, the object of transcen-
dental logic, namely, to determine the extent and
limits of the pure understanding, will have been fully
attained.
In forming an analytical judgment I remain within
a given concept, while predicating something of it. If
what I predicate is affirmative, I only predicate of
that concept what is already contained in it ; if it is
negative, I only exclude from it the opposite of it.
In forming synthetical judgments, on the contrary, I
have to go beyond a given concept, in order to bring
something together with it, which is totally different
from what is contained in it. Here we have neither
the relation of identity nor of contradiction, [p. 155]
TRANSCENDENTAL ANALYTIC. 137
and nothing in the judgment itself by which we
can discover its truth or its falsehood.
Granted, therefore, that we must go beyond a given
concept in order to compare it synthetically with
another, something else is necessary in which, as in
a third, the synthesis of two concepts becomes pos-
sible. What, then, is that third % What is the medium
of all synthetical judgments 1 It can only be that in
which all our concepts are contained, namely, the in-
ternal sense and its a priori form, time. The syn-
thesis of representations depends on imagination, but
their synthetical unity, which is necessary for forming
a judgment, depends on the unity of apperception.
It is here therefore that the possibility of syn-
thetical judgments, and (as all the three contain
the sources of representations a priori) the possi-
bility of pure synthetical judgments also, will have
to be discovered ; nay, they will on these grounds
be necessary, if any knowledge of objects is to be
obtained that rests entirely on a synthesis of repre-
sentations.
If knowledge is to have any objective reality, that
is to say, if it is to refer to an object, and find in
it any sense and meaning, the object must neces-
sarily be given in some way or other. Without that
all concepts are empty. We have thought in them, but
we have not, by thus thinking, arrived at any know-
ledge. We have only played with representations.
To give an object, if this is not meant again as [p. 15 6 ]
mediate only, but if it means to represent something
immediately in intuition, is nothing else but to refer
the representation of the object to experience (real
138 TRANSCENDENTAL ANALYTIC.
or possible). Even space and time, however pure
these concepts may be of all that is empirical, and
however certain it is that they are represented in the
mind entirely a priori, would lack nevertheless all
objective validity, all sense and meaning, if we could
not show the necessity of their use with reference to
all objects of experience. Nay, their representation is
a pure schema, always referring to that reproductive
imagination which calls up the objects of experience,
and without which they would be meaningless. The
same applies to all concepts without any distinction.
It is therefore the possibility of experience which
alone gives objective reality to all our knowledge
a priori. Experience, however, depends on the syn-
thetical unity of phenomena, that is, on a synthesis
according to concepts of the object of phenomena in
general. Without it, it would not even be know-
ledge, but only a rhapsody of perceptions, which
would never grow into a connected text according
to the rules of an altogether coherent (possible) con-
sciousness, nor into a transcendental and necessary
unity of apperception. Experience depends there-
fore on a priori principles of its form, that is, on
general rules of unity in the synthesis of phe- [p. 157]
nomena, and the objective reality of these (rules) can
always be shown by their being the necessary con-
ditions in all experience ; nay, even in the possibility
of all experience. Without such a relation synthetical
propositions a priori would be quite impossible, be-
cause they have no third medium, that is, no object
in which the synthetical unity of their concepts could
prove their objective reality.
TRANSCENDENTAL ANALYTIC. 1 39
Although we know therefore a great deal a priori
in synthetical judgments with reference to space in
general, or to the figures which productive imagination
traces in it, without requiring for it any experience,
this our knowledge would nevertheless be nothing
but a playing with the cobwebs of our brain, if space
were not to be considered as the condition of phe-
nomena which supply the material for external ex-
perience. Those pure synthetical judgments therefore
refer always, though mediately only, to possible ex-
perience, or rather to the possibility of experience,
on which alone the objective validity of their syn-
thesis is founded.
As therefore experience, being an empirical syn-
thesis, is in its possibility the only kind of knowledge
that imparts reality to every other synthesis, it
possesses, as knowledge a priori, truth (agreement
with its object) on this condition only, that it con-
tains nothing beyond what is necessary for the
synthetical unity of experience in general. [p. 158]
The highest principle of all synthetical judgments
is therefore this, that every object is subject to the
necessary conditions of a synthetical unity of the
manifold of intuition in a possible experience.
Thus synthetical judgments a priori are possible,
if we apply the formal conditions of intuition a
priori, the synthesis of imagination, and the necessary
unity of it in a transcendental apperception, to a pos-
sible knowledge in general, given in experience, and if
we say that the conditions of the possibility of ex-
perience in general are at the same time conditions
of the possibility of the objects of experience them-
140 TRANSCENDENTAL ANALYTIC.
selves, and thus possess objective validity in a syn-
thetical judgment a priori.
SYSTEM OF THE PRINCIPLES OF THE PURE
UNDERSTANDING.
Section III.
Systematical representation of all synthetical principles
of the understanding.
That there should be principles at all is entirely
due to the pure understanding, which is not only the
faculty of rules in regard to all that happens, but
itself the source of principles, according to [p. 159]
which everything (that can become an object to us)
is necessarily subject to rules, because, without such,
phenomena would never become objects corresponding
to knowledge. Even laws of nature, if they are con-
sidered as principles of the empirical use of the
understanding, carry with them a character of ne-
cessity and thus lead to the supposition that they
rest on grounds which are valid a priori, and before
all experience. Nay, all laws of nature without
distinction are subject to higher principles of the
understanding, which they apply to particular cases
of experience. They alone therefore supply the
concept which contains the condition, and, as it were,
the exponent of a rule in general, while experience
furnishes each case to which the general rule applies.
There can hardly be any danger of our mistaking
purely empirical principles for principles of the pure
understanding or vice versa, for the character of
TRANSCENDENTAL ANALYTIC. 141
necessity which distinguishes the concepts of the
pure understanding, and the absence of which can
easily be perceived in every empirical proposition,
however general it may seem, will always prevent
their confusion. There are, however, pure principles a
priori, which I should not like to ascribe to the pure
understanding, because they are derived, not from
pure concepts, but from pure intuitions, although by
means of the understanding, which is the [p. 160]
faculty of the concepts. We find such principles in
mathematics, but their application to experience,
and therefore their objective validity, nay, even the
possibility of such synthetical knowledge a priori
(the deduction thereof) rests always on the pure
understanding.
Hence my principles will not include the principles
of mathematics, but they will include those on which
the possibility and objective validity a priori of those
mathematical principles are founded, and which con-
sequently are to be looked upon as the source of
those principles, proceeding from concepts to in-
tuitions, and not from intuitions to concepts.
When the pure concepts of the understanding are
applied to every possible experience, their synthesis
is either mathematical or dynamical, for it is directed
partly to the intuition only, partly to the existence
of a phenomenon. The conditions a priori of in-
tuition are absolutely necessary with regard to every
possible experience, while the conditions of the ex-
istence of the object of a possible empirical intuition,
are in themselves accidental only. The principles
of the mathematical use of the categories will there-
142 TRANSCENDENTAL ANALYTIC.
fore be absolutely necessary, that is apodictic, while
those of their dynamical use, though likewise posses-
sing the character of necessity a priori, can possess
such a character subject only to the condition of em-
pirical thought in experience, that is mediately and
indirectly, and cannot therefore claim that immediate
evidence which belongs to the former, although their
certainty with regard to experience in general remains
unaffected by this. Of this we shall be [p. 161]
better qualified to judge at the conclusion of this
system of principles.
Our table of categories gives us naturally the
best instructions for drawing up a table of principles,
because these are nothing but rules for the objective
use of the former. All principles of the pure under-
standing are therefore,
I.
Axioms of Intuition.
II.
III.
Anticipations of
Perception.
IV.
Analogies of
Experience.
Postulates of Empirical
Thought in General.
I have chosen these names not unadvisedly, so that
the difference with regard to the evidence and the
application of those principles should not be over-
looked. We shall soon see that, both with regard
to the evidence and the a priori determination of
phenomena according to the categories of quantity and
quality (if we attend to the form of them only) their
principles differ considerably from those of [p. 162]
the other two classes, inasmuch as the former are
TBANSCENDENTAL ANALYTIC. 1 43
capable of an intuitive, the latter of a merely dis-
cursive, though both of a complete certainty. I shall
therefore call the former mathematical, the latter dy-
namical principles l . It should be observed, however,
that I do not speak here either of the principles of
mathematics, or of those of general physical dynamics,
but only of the principles of the pure understanding in.
relation to the internal sense (without any regard to
the actual representations given in it). It is these
through which the former become possible, and I have
given them their name, not so much in reference to
their application as to their contents. I shall now
proceed to consider them in the same order in which
they stand in the table.
[OF THE AXIOMS OF INTUITION 2 .
Principle of the Pure Understanding :
'All Phenomena are, with reference to their intuition,
extensive quantities.']
I call an extensive quantity that in which the
representation of the whole is rendered possible by
the representation of its parts, and therefore ne-
cessarily preceded by it. I cannot represent to
myself any line, however small it may be, without
drawing it in thought, that is, without producing
all its parts one after the other, starting [p. 163]
from a given point, and thus, first of all, drawing
1 Here follows in the Second Edition, Supplement XV.
2 Here follows in the later Editions, Supplement XVI.
144 TRANSCENDENTAL ANALYTIC.
its intuition. The same applies to every, even the
smallest portion of time. I can only think in it the
successive progress from one moment to another,
thus producing in the end, by all the portions of
time and their addition, a definite quantity of time.
As in all phenomena pure intuition is either space
or time, every phenomenon, as an intuition, must be
an extensive quantity, because it can be known in
apprehension by a successive synthesis only (of part
with part). All phenomena therefore, when per-
ceived in intuition, are aggregates (collections) of
previously given parts, which is not the case with
every kind of quantities, but with those only which
are represented to us and apprehended as exten-
sive.
On this successive synthesis of productive imagi-
nation in elaborating figures are founded the mathe-
matics of extension with their axioms (geometry),
containing the conditions of sensuous intuition a
priori, under which alone the schema of a pure
concept of an external phenomenal appearance can
be produced ; for instance, between two points one
straight line only is possible, or two straight lines
cannot enclose a space, &c. These are the axioms
which properly relate only to quantities (quanta)
as such.
But with regard to quantity (quantitas), that is,
with regard to the answer to the question, how large
something may be, there are no axioms, in the [p. 164]
proper sense of the word, though several of the pro-
positions referring to it possess synthetical and im-
mediate certainty (indemonstrabilia). The propositions
TRANSCENDENTAL ANALYTIC. 1 45
that if equals be added to equals the wholes are equal,
and if equals be taken from equals the remainders
are equal, are really analytical, because I am consci-
ous immediately of the identity of the one quantity
thus produced, with the other ; axioms on the contrary
must be synthetical propositions a priori. The self-
evident propositions on numerical relation again
are no doubt synthetical, but they are not general,
like those of geometry, and therefore cannot be
called axioms, but numerical formulas only. That
7 + 5=12 is not an analytical proposition. For
neither in the representation of 7, nor in that of 5,
nor in that of the combination of both, do I think
the number 12. (That I am meant to think it in
the addition of the two, is not the question here, for
in every analytical proposition all depends on this,
whether the predicate is really thought in the re-
presentation of the subject.) Although the pro-
position is synthetical, it is a singular proposition
only. If in this case we consider only the synthesis
of the homogeneous unities, then the synthesis can