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 which gives objective
reality to all our a priori cognitions。 Now experience depends upon
the synthetical unity of phenomena； that is； upon a synthesis
according to conceptions of the object of phenomena in general； a
synthesis without which experience never could bee knowledge； but
would be merely a rhapsody of perceptions； never fitting together into
any connected text； according to rules of a thoroughly united
（possible） consciousness； and therefore never subjected to the
transcendental and necessary unity of apperception。 Experience has
therefore for a foundation； a priori principles of its form； that is
to say； general rules of unity in the synthesis of phenomena； the
objective reality of which rules； as necessary conditions even of
the possibility of experience can which rules； as necessary
conditions… even of the possibility of experience… can always be shown
in experience。 But apart from this relation； a priori synthetical
propositions are absolutely impossible； because they have no third
term； that is； no pure object； in which the synthetical unity can
exhibit the objective reality of its conceptions。
Although； then； respecting space； or the forms which productive
imagination describes therein； we do cognize much a priori in
synthetical judgements； and are really in no need of experience for
this purpose； such knowledge would nevertheless amount to nothing
but a busy trifling with a mere chimera； were not space to be
considered as the condition of the phenomena which constitute the
material of external experience。 Hence those pure synthetical
judgements do relate； though but mediately； to possible experience； or
rather to the possibility of experience； and upon that alone is
founded the objective validity of their synthesis。
While then； on the one hand； experience； as empirical synthesis；
is the only possible mode of cognition which gives reality to all
other synthesis； on the other hand； this latter synthesis； as
cognition a priori； possesses truth； that is； accordance with its
object； only in so far as it contains nothing more than what is
necessary to the synthetical unity of experience。
Accordingly； the supreme principle of all synthetical judgements is：
〃Every object is subject to the necessary conditions of the
synthetical unity of the manifold of intuition in a possible
experience。〃
A priori synthetical judgements are possible when we apply the
formal conditions of the a priori intuition； the synthesis of the
imagination； and the necessary unity of that synthesis in a
transcendental apperception； to a possible cognition of experience；
and say： 〃The conditions of the possibility of experience in general
are at the same time conditions of the possibility of the objects of
experience； and have； for that reason； objective validity in an a
priori synthetical judgement。〃
SECTION III。 Systematic Representation of all Synthetical
Principles of the Pure Understanding。
That principles exist at all is to be ascribed solely to the pure
understanding； which is not only the faculty of rules in regard to
that which happens； but is even the source of principles according
to which everything that can be presented to us as an object is
necessarily subject to rules； because without such rules we never
could attain to cognition of an object。 Even the laws of nature； if
they are contemplated as principles of the empirical use of the
understanding； possess also a characteristic of necessity； and we
may therefore at least expect them to be determined upon grounds which
are valid a priori and antecedent to all experience。 But all laws of
nature； without distinction； are subject to higher principles of the
understanding； inasmuch as the former are merely applications of the
latter to particular cases of experience。 These higher principles
alone therefore give the conception； which contains the necessary
condition； and； as it were； the exponent of a rule； experience； on the
other hand； gives the case which es under the rule。
There is no danger of our mistaking merely empirical principles
for principles of the pure understanding； or conversely； for the
character of necessity； according to conceptions which distinguish the
latter； and the absence of this in every empirical proposition； how
extensively valid soever it may be； is a perfect safeguard against
confounding them。 There are； however； pure principles a priori；
which nevertheless I should not ascribe to the pure understanding… for
this reason； that they are not derived from pure conceptions； but
（although by the mediation of the understanding） from pure intuitions。
But understanding is the faculty of conceptions。 Such principles
mathematical science possesses； but their application to experience；
consequently their objective validity； nay the possibility of such a
priori synthetical cognitions （the deduction thereof） rests entirely
upon the pure understanding。
On this account； I shall not reckon among my principles those of
mathematics； though I shall include those upon the possibility and
objective validity a priori； of principles of the mathematical
science； which； consequently； are to be looked upon as the principle
of these； and which proceed from conceptions to intuition； and not
from intuition to conceptions。
In the application of the pure conceptions of the understanding to
possible experience； the employment of their synthesis is either
mathematical or dynamical； for it is directed partly on the
intuition alone； partly on the existence of a phenomenon。 But the a
priori conditions of intuition are in relation to a possible
experience absolutely necessary； those of the existence of objects
of a possible empirical intuition are in themselves contingent。
Hence the principles of the mathematical use of the categories will
possess a character of absolute necessity； that is； will be
apodeictic； those； on the other hand； of the dynamical use； the
character of an a priori necessity indeed； but only under the
condition of empirical thought in an expe