- Space is a necessary presentation a priori, which underlies all external perceptions; for
we cannot imagine that there should be no space, although we can imagine that there
should be nothing in space. - Space is not a discursive or general concept of the relations of things in general, for there
is only one space, of which what we call "spaces" are parts, not instances. - Space is presented as an infinite given magnitude, which holds within itself all the parts
of space; this relation is different from that of a concept to its instances, and therefore
space is not a concept but an Anschauung.
The transcendental argument concerning space is derived from-713-geometry. Kant holds that Euclidean geometry is known a priori, although it is synthetic, i.e., not
deducible from logic alone. Geometrical proofs, he considers, depend upon the figures; we can
see, for instance, that, given two intersecting straight lines at right angles to each other, only one
straight line at right angles to both can be drawn through their point of intersection. This
knowledge, he thinks, is not derived from experience. But the only way in which my intuition can
anticipate what will be found in the object is if it contains only the form of my sensibility,
antedating in my subjectivity all the actual impressions. The objects of sense must obey geometry,
because geometry is concerned with our ways of perceiving, and therefore we cannot perceive
otherwise. This explains why geometry, though synthetic, is a priori and apodeictic.
The arguments with regard to time are essentially the same, except that arithmetic replaces
geometry with the contention that counting takes time.
Let us now examine these arguments one by one.
The first of the metaphysical arguments concerning space says: "Space is not an empirical concept
abstracted from external experiences. For in order that certain sensations may be referred to
something outside me [i.e., to something in a different position in space from that in which I find
myself], and further in order that I may be able to perceive them as outside and beside each other,
and thus as not merely different, but in different places, the presentation of space must already
give the foundation [zum Grunde liegen]." Therefore external experience is only possible through
the presentation of space.
The phrase "outside me [i.e., in a different place from that in which I find myself]" is a difficult
one. As a thing-in-itself, I am not anywhere, and nothing is spatially outside me; it is only my
body as a phenomenon that can be meant. Thus all that is really involved is what comes in the
second part of the sentence, namely that I perceive different objects as in different places. The
image which arises in one's mind is that of a cloak-room attendant who hangs different coats on
different pegs; the pegs must already exist, but the attendant's subjectivity arranges the coats.
There is here, as throughout Kant's theory of the subjectivity of space and time, a difficulty which
he seems to have never felt. What induces me to arrange objects of perception as I do rather than
other-