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intuition； and consequently to the subjective constitution of the
mind； without which these predicates of time and space could not be
attached to any object？ In order to bee informed on these points；
we shall first give an exposition of the conception of space。 By
exposition； I mean the clear； though not detailed； representation of
that which belongs to a conception； and an exposition is
metaphysical when it contains that which represents the conception
as given a priori。
1。 Space is not a conception which has been derived from outward
experiences。 For； in order that certain sensations may relate to
something without me （that is； to something which occupies a different
part of space from that in which I am）； in like manner； in order
that I may represent them not merely as without； of； and near to
each other； but also in separate places； the representation of space
must already exist as a foundation。 Consequently； the representation
of space cannot be borrowed from the relations of external phenomena
through experience； but； on the contrary； this external experience
is itself only possible through the said antecedent representation。
2。 Space then is a necessary representation a priori； which serves
for the foundation of all external intuitions。 We never can imagine or
make a representation to ourselves of the non…existence of space；
though we may easily enough think that no objects are found in it。
It must； therefore； be considered as the condition of the
possibility of phenomena； and by no means as a determination dependent
on them； and is a representation a priori； which necessarily
supplies the basis for external phenomena。
3。 Space is no discursive； or as we say； general conception of the
relations of things； but a pure intuition。 For； in the first place； we
can only represent to ourselves one space； and； when we talk of divers
spaces； we mean only parts of one and the same space。 Moreover；
these parts cannot antecede this one all…embracing space； as the
ponent parts from which the aggregate can be made up； but can be
cogitated only as existing in it。 Space is essentially one； and
multiplicity in it； consequently the general notion of spaces； of this
or that space； depends solely upon limitations。 Hence it follows
that an a priori intuition （which is not empirical） lies at the root
of all our conceptions of space。 Thus； moreover； the principles of
geometry… for example； that 〃in a triangle； two sides together are
greater than the third；〃 are never deduced from general conceptions of
line and triangle； but from intuition； and this a priori； with
apodeictic certainty。
4。 Space is represented as an infinite given quantity。 Now every
conception must indeed be considered as a representation which is
contained in an infinite multitude of different possible
representations； which； therefore； prises these under itself； but
no conception； as such； can be so conceived； as if it contained within
itself an infinite multitude of representations。 Nevertheless； space
is so conceived of； for all parts of space are equally capable of
being produced to infinity。 Consequently； the original
representation of space is an intuition a priori； and not a
conception。
SS 3。 Transcendental Exposition of the Conception of Space。
By a transcendental exposition； I mean the explanation of a
conception； as a principle； whence can be discerned the possibility of
other synthetical a priori cognitions。 For this purpose； it is
requisite； firstly； that such cognitions do really flow from the given
conception； and； secondly； that the said cognitions are only
possible under the presupposition of a given mode of explaining this
conception。
Geometry is a science which determines the properties of space
synthetically； and yet a priori。 What； then； must be our
representation of space； in order that such a cognition of it may be
possible？ It must be originally intuition； for from a mere conception；
no propositions can be deduced which go out beyond the conception； and
yet this happens in geometry。 （Introd。 V。） But this intuition must
be found in the mind a priori； that is； before any perception of
objects； consequently must be pure； not empirical； intuition。 For
geometrical principles are always apodeictic； that is； united with the
consciousness of their necessity； as： 〃Space has only three
dimensions。〃 But propositions of this kind cannot be empirical
judgements； nor conclusions from them。 （Introd。 II。） Now； how can an
external intuition anterior to objects themselves； and in which our
conception of objects can be determined a priori； exist in the human
mind？ Obviously not otherwise than in so far as it has its seat in the
subject only； as the formal capacity of the subject's being affected
by objects； and thereby of obtaining immediate representation； that
is； intuition； consequently； only as the form of the external sense in
general。
Thus it is only by means of our explanation that the possibility
of geometry； as a synthetical science a priori； bees
prehensible。 Every mode of explanation which does not show us
this possibility； although in appearance it may be similar to ours；
can with the utmost certainty be distinguished from it by these marks。
SS 4。 Conclusions from the foregoing Conceptions。
（a） Space does Space does not represent any property of objects as
things in themselves； nor does it represent them in their relations to
each other； in other words； space does not represent to us any
determination of objects such as attaches to the objects themselves；
and would remain； even though all subjective conditions of the
intuition were abstracted。 For neither absolute nor relative
determinations of objects can be intuited prior to the existence of
the things to which they belong； and therefore not a priori。
（b） Space is nothing else than the form of all phenomena of the
external sense； that is； the subjective condition of the
sensibility； under which alone external intuition is possible。 Now；
because the receptivity or capacity of the subject to be affected by
objects necessarily antecedes all intuitions of these objects； it is
easily understood how the form of all phenomena can be given in the
mind previous to all actual perceptions； therefore a priori； and how
it； as a pure intuition； in which all objects must be determined；
can contain principles of the relations of these objects prior to
all experience。
It is therefore from the human point of view only that we can
speak of space； extended objects； etc。 If we depart from the
subjective condition； under which alone we can obtain external
intuition； or； in other words； by means of which we are affected by
objects； the representation of space has no meaning whatsoever。 This
predicate is only applicable to things in so far as they appear to us；
that is； are objects of sensibility。 The constant form of this
receptivity； which we call sensibility； is a necessary condition of
all relations in which objects can be intuited as existing without us；
and when abstraction of these objects is made； is a pure intuition； to
which we give the name of space。 It is clear that we cannot ma