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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 with