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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 plete； certitude。 I shall therefore call the former
mathematical； and the latter dynamical principles。* It must be
observed； however； that by these terms I mean just as little in the
one case the principles of mathematics as those of general
（physical） dynamics in the other。 I have here in view merely the
principles of the pure understanding； in their application to the
internal sense （without distinction of the representations given
therein）； by means of which the sciences of mathematics and dynamics
bee possible。 Accordingly； I have named these principles rather
with reference to their application than their content； and I shall
now proceed to consider them in the order in which they stand in the
table。
*All bination （conjunctio） is either position （positio）
or connection （nexus）。 The former is the synthesis of a manifold；
the parts of which do not necessarily belong to each other。 For
example； the two triangles into which a square is divided by a
diagonal； do not necessarily belong to each other； and of this kind is
the synthesis of the homogeneous in everything that can be
mathematically considered。 This synthesis can be divided into those of
aggregation and coalition； the former of which is applied to
extensive； the latter to intensive quantities。 The second sort of
bination （nexus） is the synthesis of a manifold； in so far as its
parts do belong necessarily to each other； for example； the accident
to a substance； or the effect to the cause。 Consequently it is a
synthesis of that which though heterogeneous； is represented as
connected a priori。 This bination… not an arbitrary one… I
entitle dynamical because it concerns the connection of the
existence of the manifold。 This； again； may be divided into the
physical synthesis； of the phenomena divided among each other； and the
metaphysical synthesis； or the connection of phenomena a priori in the
faculty of cognition。
1。 AXIOMS OF INTUITION。
The principle of these is： All Intuitions are Extensive
Quantities。
PROOF。
All phenomena contain； as regards their form； an intuition in
space and time； which lies a priori at the foundation of all without
exception。 Phenomena； therefore； cannot be apprehended； that is；
received into empirical consciousness otherwise than through the
synthesis of a manifold； through which the representations of a
determinate space or time are generated； that is to say； through the
position of the homogeneous and the consciousness of the
synthetical unity of this manifold （homogeneous）。 Now the
consciousness of a homogeneous manifold in intuition； in so far as
thereby the representation of an object is rendered possible； is the
conception of a quantity （quanti）。 Consequently； even the perception
of an object as phenomenon is possible only through the same
synthetical unity of the manifold of the given sensuous intuition；
through which the unity of the position of the homogeneous manifold
in the conception of a quantity is cogitated； that is to say； all
phenomena are quantities； and extensive quantities； because as
intuitions in space or time they must be represented by means of the
same synthesis through which space and time themselves are determined。
An extensive quantity I call that wherein the representation of
the parts renders possible （and therefore necessarily antecedes） the
representation of the whole。 I cannot represent to myself any line；
however small； without drawing it in thought； that is； without
generating from a point all its parts one after another； and in this
way alone producing this intuition。 Precisely the same is the case
with every； even the smallest； portion of time。 I cogitate therein
only the successive progress from one moment to another； and hence； by
means of the different portions of time and the addition of them； a
determinate quantity of time is produced。 As the pure intuition in all
phenomena is either time or space； so is every phenomenon in its
character of intuition an extensive quantity； inasmuch as it can
only be cognized in our apprehension by successive synthesis （from
part to part）。 All phenomena are； accordingly； to be considered as
aggregates； that is； as a collection of previously given parts；
which is not the case with every sort of quantities； but only with
those which are represented and apprehended by us as extensive。
On this succ