the arrangement of the categories； relate to the series in time； the
content in time； the order in time； and finally； to the plex or
totality in time。
Hence it is apparent that the schematism of the understanding； by
means of the transcendental synthesis of the imagination； amounts to
nothing else than the unity of the manifold of intuition in the
internal sense； and thus indirectly to the unity of apperception； as a
function corresponding to the internal sense （a receptivity）。 Thus；
the schemata of the pure conceptions of the understanding are the true
and only conditions whereby our understanding receives an
application to objects； and consequently significance。 Finally；
therefore； the categories are only capable of empirical use；
inasmuch as they serve merely to subject phenomena to the universal
rules of synthesis； by means of an a priori necessary unity （on
account of the necessary union of all consciousness in one original
apperception）； and so to render them susceptible of a plete
connection in one experience。 But within this whole of possible
experience lie all our cognitions； and in the universal relation to
this experience consists transcendental truth； which antecedes all
empirical truth； and renders the latter possible。
It is； however； evident at first sight； that although the schemata
of sensibility are the sole agents in realizing the categories； they
do； nevertheless； also restrict them； that is； they limit the
categories by conditions which lie beyond the sphere of understanding…
namely； in sensibility。 Hence the schema is properly only the
phenomenon； or the sensuous conception of an object in harmony with
the category。 （Numerus est quantitas phaenomenon… sensatio realitas
phaenomenon； constans et perdurabile rerum substantia phaenomenon…
aeternitas； necessitas； phaenomena； etc。） Now； if we remove a
restrictive condition； we thereby amplify； it appears； the formerly
limited conception。 In this way； the categories in their pure
signification； free from all conditions of sensibility； ought to be
valid of things as they are； and not； as the schemata represent
them； merely as they appear； and consequently the categories must have
a significance far more extended； and wholly independent of all
schemata。 In truth； there does always remain to the pure conceptions
of the understanding； after abstracting every sensuous condition； a
value and significance； which is； however； merely logical。 But in this
case； no object is given them； and therefore they have no meaning
sufficient to afford us a conception of an object。 The notion of
substance； for example； if we leave out the sensuous determination
of permanence； would mean nothing more than a something which can be
cogitated as subject； without the possibility of being a
predicate to anything else。 Of this representation I can make nothing；
inasmuch as it does not indicate to me what determinations the thing
possesses which must thus be valid as premier subject。 Consequently；
the categories； without schemata are merely functions of the
understanding for the production of conceptions； but do not
represent any object。 This significance they derive from
sensibility； which at the same time realizes the understanding and
restricts it。
CHAPTER II。 System of all Principles of the Pure Understanding。
In the foregoing chapter we have merely considered the general
conditions under which alone the transcendental faculty of judgement
is justified in using the pure conceptions of the understanding for
synthetical judgements。 Our duty at present is to exhibit in
systematic connection those judgements which the understanding
really produces a priori。 For this purpose； our table of the
categories will certainly afford us the natural and safe guidance。 For
it is precisely the categories whose application to possible
experience must constitute all pure a priori cognition of the
understanding； and the relation of which to sensibility will； on
that very account； present us with a plete and systematic catalogue
of all the transcendental principles of the use of the understanding。
Principles a priori are so called； not merely because they contain
in themselves the grounds of other judgements； but also because they
themselves are not grounded in higher and more general cognitions。
This peculiarity； however； does not raise them altogether above the
need of a proof。 For although there could be found no higher
cognition； and therefore no objective proof； and although such a
principle rather serves as the foundation for all cognition of the
object； this by no means hinders us from drawing a proof from the
subjective sources of the possibility of the cognition of an object。
Such a proof is necessary； moreover； because without it the
principle might be liable to the imputation of being a mere gratuitous
assertion。
In the second place； we shall limit our investigations to those
principles which relate to the categories。 For as to the principles of
transcendental aesthetic； according to which space and time are the
conditions of the possibility of things as phenomena； as also the
restriction of these principles； namely； that they cannot be applied
to objects as things in themselves… these； of course； do not fall
within the scope of our present inquiry。 In like manner； the
principles of mathematical science form no part of this system；
because they are all drawn from intuition； and not from the pure
conception of the understanding。 The possibility of these
principles； however； will necessarily be considered here； inasmuch
as they are synthetical judgements a priori； not indeed for the
purpose of proving their accuracy and apodeictic certainty； which is
unnecessary； but merely to render conceivable and deduce the
possibility of such evident a priori cognitions。
But we shall have also to speak of the principle of analytical
judgements； in opposition to synthetical judgements； which is the
proper subject of our inquiries； because this very opposition will
free the theory of the latter from all ambiguity； and place it clearly
before our eyes in its true nature。
SYSTEM OF THE PRINCIPLES OF THE PURE UNDERSTANDING。
SECTION I。 Of the Supreme Principle of all Analytical Judgements。
Whatever may be the content of our cognition； and in whatever manner
our cognition may be related to its object； the universal； although
only negative conditions of all our judgements is that they do not
contradict themselves； otherwise these judgements are in themselves
（even without respect to the object） nothing。 But although there may
exist no contradiction in our judgement； it may nevertheless connect
conceptions in such a manner that they do not correspond to the
object； or without any grounds either a priori or a posteriori for
arriving at such a judgement； and thus； without being
self…contradictory； a judgement may nevertheless be either false or
groundless。
Now； the proposition： 〃No subject can have a predicate that
contradicts it；〃 is called the principle of contradiction； and is a
universal but purely negative criterion of all truth。 But it belongs
to logic alone； because it is valid of cognitions； merely as
cognitions and without respect to their content； and declares that the
contradiction entirely nullifies them。 We can also； however； make a
positive use of this principle； that is； not merely to banish
falsehood and error （in so far as it rests upon contradiction）； but
also for the cognition of truth。 For if the judgement is analytical；
be it affirmative or negative； its truth must always be recognizable
by means of the principle of contradiction。 For the contrary of that
which lies and is cogitated as conception in the cognition of the
object will be always properly negatived； but the conception itself
must always be affirmed of the object； inasmuch as the contrary
thereof would be in contradiction to the object。
We must therefore hold the principle of contradiction to be the
universal and fully sufficient Principle of all analytical
cognition。 But as a sufficient criterion of truth； it has no further
utility or authority。 For the fact that no cognition can be at
variance with this principle without nullifying itself； constitutes
this principle the sine qua non； but not the determining ground of the
truth of our cognition。 As our business at present is properly with
the synthetical part of our knowledge only； we shall always be on
our guard not to transgress this inviolable principle； but at the same
time not to expect from it any direct assistance in the
establishment of the truth of any synthetical proposition。
There exists； however； a formula of this celebrated principle… a
principle merely formal and entirely without content… which contains a
synthesis that has been inadvertently and quite unnecessarily mixed up
with it。 It is this： 〃It is impossible for a thing to be and not to be
at the same time。〃 Not to mention the superfluousness of the
addition of the word impossible to indicate the apodeictic
certainty； which ought to be self…evident from the proposition itself；
the proposition is affected by the condition of time； and as it were
says： 〃A thing = A； which is something = B； cannot at the same time be
non…B。〃 But both； B as well as non…B； may quite well exist in
succession。 For example； a man who is young cannot at the same time be
old； but the same man can very well be at one time young； and at
another not young； that is； old。 Now the principle of contradiction as
a merely logical proposition must not by any means limit its
application merely to relations of time； and consequently a formula
like the preceding is quite foreign to its true purpose。 The
misunderstanding arises in this way。 We first of all separate a
predicate of a thing from the conception of the thing； and
afterwards connect with this predicate its opposite； and hence do
not establish any contradiction with the subject； but only with its
predicate； which has been conjoined with the subject synthetically…
a contradiction； moreover； which obtains only when the first and
second predicate are affirmed in the same time。 If I say： 〃A man who
is ignorant is not learned；〃