[space] is essentially unique, the manifold in it rests solely on limitations." From this it is
concluded that space is an a priori intuition.
The gist of this argument is the denial of plurality in space itself. What we call "spaces" are
neither instances of a general concept "a space," nor parts of an aggregate. I do not know quite
what, according to Kant, their logical status is, but in any case they are logically subsequent to
space. To those who take, as practically all moderns do, a relational view of space, this argument
becomes incapable of being stated, since neither "space" nor "spaces" can survive as a substantive.
The fourth metaphysical argument is chiefly concerned to prove that space is an intuition, not a
concept. Its premiss is "space is imagined [for presented, vorgestellt] as an infinite given
magnitude." This is the view of a person living in a flat country, like that of Königsberg; I do not
see how an inhabitant of an Alpine valley could adopt it. It is difficult to see how anything infinite
can be "given." I should have thought it obvious that the part of space that is given is that which is
peopled by objects of perception, and that for other parts we have only a feeling of possibility of
motion. And if so vulgar an argument may be intruded, modern astronomers maintain that space is
in fact not infinite, but goes round and round, like the surface of the globe.
The transcendental (or epistemological) argument, which is best stated in the Prolegomena, is
more definite than the metaphysical arguments, and is also more definitely refutable. "Geometry,"
as we now know, is a name covering two different studies. On the one hand, there is pure
geometry, which deduces consequences from axioms, without inquiring whether the axioms are
"true"; this contains nothing that does not follow from logic, and is not "synthetic," and has no
need of figures such as are used in geometrical text-books. On the other hand, there is geometry as
a branch of physics, as it appears, for example, in the general theory of relativity; this is an
empirical science, in which the axioms are inferred from measurements, and are found to differ
from Euclid's. Thus of the two kinds of geometry one is a priori but not synthetic, while the other
is synthetic but not a priori. This disposes of the transcendental argument.
Let us now try to consider the questions raised by Kant as regards space in a more general way. If
we adopt the view, which is taken for granted in physics, that our percepts have external causes
which