SECTION I.
OF SPACE.
SS 2. Metaphysical Exposition of this Conception.
BY means of the external sense (a property of the mind), we
represent to ourselves objects as without us, and these all in
space. Herein alone are their shape, dimensions, and relations to each
other determined or determinable. The internal sense, by means of
which the mind contemplates itself or its internal state, gives,
indeed, no intuition of the soul as an object; yet there is
nevertheless a determinate form, under which alone the contemplation
of our internal state is possible, so that all which relates to the
inward determinations of the mind is represented in relations of time.
Of time we cannot have any external intuition, any more than we can
have an internal intuition of space. What then are time and space? Are
they real existences? Or, are they merely relations or
determinations of things, such, however, as would equally belong to
these things in themselves, though they should never become objects of
intuition; or, are they such as belong only to the form of
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 become 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
component 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, comprises 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.
[*]
That is, the analysis of a conception only gives you what is contained in it, and does not
add to your knowledge of the object of which you have a conception, but merely evolves it. — Tr.
Thus it is only by means of our explanation that the possibility
of geometry, as a synthetical science a priori, becomes
comprehensible. 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, &c. 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 make the
special conditions of sensibility into conditions of the possibility
of things, but only of the possibility of their existence as far as
they are phenomena. And so we may correctly say that space contains
all which can appear to us externally, but not all things considered
as things in themselves, be they intuited or not, or by whatsoever
subject one will. As to the intuitions of other thinking beings, we
cannot judge whether they are or are not bound by the same
conditions which limit our own intuition, and which for us are
universally valid. If we join the limitation of a judgement to the
conception of the subject, then the judgement will possess
unconditioned validity. For example, the proposition, "All objects are
beside each other in space," is valid only under the limitation that
these things are taken as objects of our sensuous intuition. But if
I join the condition to the conception and say, "All things, as
external phenomena, are beside each other in space," then the rule
is valid universally, and without any limitation. Our expositions,
consequently, teach the
reality (
i.e., the objective validity) of
space in regard of all which can be presented to us externally as
object, and at the same time also the
ideality of space in regard to
objects when they are considered by means of reason as things in
themselves, that is, without reference to the constitution of our
sensibility. We maintain, therefore, the
empirical reality of space in
regard to all possible external experience, although we must admit its
transcendental ideality; in other words, that it is nothing, so soon
as we withdraw the condition upon which the possibility of all
experience depends and look upon space as something that belongs to
things in themselves.
But, with the exception of space, there is no representation,
subjective and ref erring to something external to us, which could
be called objective a priori. For there are no other subjective
representations from which we can deduce synthetical propositions a
priori, as we can from the intuition of space. (See SS 3.)
Therefore, to speak accurately, no ideality whatever belongs to these,
although they agree in this respect with the representation of
space, that they belong merely to the subjective nature of the mode of
sensuous perception; such a mode, for example, as that of sight, of
hearing, and of feeling, by means of the sensations of colour,
sound, and heat, but which, because they are only sensations and not
intuitions, do not of themselves give us the cognition of any
object, least of all, an a priori cognition. My purpose, in the
above remark, is merely this: to guard any one against illustrating
the asserted ideality of space by examples quite insufficient, for
example, by colour, taste, &c.; for these must be contemplated not as
properties of things, but only as changes in the subject, changes
which may be different in different men. For, in such a case, that
which is originally a mere phenomenon, a rose, for example, is taken
by the empirical understanding for a thing in itself, though to
every different eye, in respect of its colour, it may appear
different. On the contrary, the
transcendental conception of phenomena
in space is a critical admonition, that, in general, nothing which
is intuited in space is a thing in itself, and that space is not a
form which belongs as a property to things; but that objects are quite
unknown to us in themselves, and what we call outward objects, are
nothing else but mere representations of our sensibility, whose form
is space, but whose real correlate, the thing in itself, is not
known by means of these representations, nor ever can be, but
respecting which, in experience, no inquiry is ever made.
