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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 comes 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 experience； therefore only
mediately and indirectly。 Consequently they will not possess that
immediate evidence which is peculiar to the former； although their
application to experience does not； for that reason； lose its truth
and certitude。 But of this point we shall be better able to judge at
the conclusion of this system of principles。
The table of the categories is naturally our guide to the table of
principles； because these are nothing else than rules for the
objective employment of the former。 Accordingly； all principles of the
pure understanding are：
1
Axioms
of Intuition
2 3
Anticipations Analogies
of Perception of Experience
4
Postulates of
Empirical Thought
in general
These appellations I have chosen advisedly； in order that we might
not lose sight of the distinctions in respect of the evidence and
the employment of these principles。 It will； however； soon appear
that… a fact which concerns both the evidence of these principles； and
the a priori determination of phenomena… according to the categories
of quantity and quality （if we attend merely to the form of these）；
the principles of these categories are distinguishable from those of
the two others； in as much as the former are possessed of an
intuitive； but the latter of a merely discursive； though in both
instances a complete； certitude。 I shall therefore call the former
mathematical； and the latter dynamical principles。* It must be
observed；