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；〃 the condition 〃at the same time〃 must
be added； for he who is at one time ignorant； may at another be
learned。 But if I say： 〃No ignorant man is a learned man；〃 the
proposition is analytical； because the characteristic ignorance is now
a constituent part of the conception of the subject； and in this
case the negative proposition is evident immediately from the
proposition of contradiction； without the necessity of adding the
condition 〃the same time。〃 This is the reason why I have altered the
formula of this principle… an alteration which shows very clearly
the nature of an analytical proposition。
SECTION II。 Of the Supreme Principle of all Synthetical Judgements。
The explanation of the possibility of synthetical judgements is a
task with which general logic has nothing to do； indeed she needs
not even be acquainted with its name。 But in transcendental logic it
is the most important matter to be dealt with… indeed the only one； if
the question is of the possibility of synthetical judgements a priori；
the conditions and extent of their validity。 For when this question is
fully decided； it can reach its aim with perfect ease； the
determination； to wit； of the extent and limits of the pure
understanding。
In an analytical judgement I do not go beyond the given
conception； in order to arrive at some decision respecting it。 If
the judgement is affirmative； I predicate of the conception only
that which was already cogitated in it； if negative； I merely
exclude from the conception its contrary。 But in synthetical
judgements； I must go beyond the given conception； in order to
cogitate； in relation with it； something quite different from that
which was cogitated in it； a relation which is consequently never
one either of identity or contradiction； and by means of which the
truth or error of the judgement cannot be discerned merely from the
judgement itself。
Granted； then； that we must go out beyond a given conception； in
order to pare it synthetically with another； a third thing is
necessary； in which alone the synthesis of two conceptions can
originate。 Now what is this tertium quid that is to be the medium of
all synthetical judgements？ It is only a plex in which all our
representations are contained； the internal sense to wit； and its form
a priori； time。
The synthesis of our representations rests upon the imagination；
their synthetical unity （which is requisite to a judgement）； upon
the unity of apperception。 In this； therefore； is to be sought the
possibility of synthetical judgements； and as all three contain the
sources of a priori representations； the possibility of pure
synthetical judgements also； nay； they are necessary upon these
grounds； if we are to possess a knowledge of objects； which rests
solely upon the synthesis of representations。
If a cognition is to have objective reality； that is； to relate to
an object； and possess sense and meaning in respect to it； it is
necessary that the object be given in some way or another。 Without
this； our conceptions are empty； and we may indeed have thought by
means of them； but by such thinking we have not； in fact； cognized
anything； we have merely played with representation。 To give an
object； if this expression be understood in the sense of 〃to
present〃 the object； not mediately but immediately in intuition； means
nothing else than to apply the representation of it to experience；
be that experience real or only possible。 Space and time themselves；
pure as these conceptions are from all that is empirical； and
certain as it is that they are represented fully a priori in the mind；
would be pletely without objective validity； and without sense
and significance； if their necessary use in the objects of
experience were not shown。 Nay； the representation of them is a mere
schema； that always relates to the reproductive imagination； which
calls up the objects of experience； without which they have no
meaning。 And so it is with all conceptions without distinction。
The possibility of experience is； then； that whi