of content all
the more strongly.

(2) If two magnitudes are equal to a third they are equal to one
another; this statement is, as Hegel has shown, a conclusion, upon
the correctness of which all logic depends, and which is demonstrated
therefore outside of pure mathematics. The remaining axioms with
regard to equality and inequality are merely logical extensions of
this conclusion. Such barren statements are not enticing either in
mathematics or anywhere else. To proceed we must have realities,
conditions and forms taken from real material things; representations
of lines, planes, angles, polygons, spheres, etc., are all borrowed
from reality, and it is just naive ideology to believe the
mathematicians, who assert that the first line was made by causing a
point to progress through space, the first plane by means of the
movement of a line, and the first solid by revolving a plane, etc.
Even speech rebels against this idea. A mathematical figure of three
dimensions is called a solid--corpus solidum--and hence, according to
the Latin, a body capable of being handled. It has a name derived,
therefore, by no means from the independent play of imagination but
from solid reality.

But to what purpose is all this prolixity? After Herr Duehring has
enthusiastically proclaimed the independence of pure mathematics of
the world of experience, their apriorism, their connection with free
creation and imagination, he says "it will be readily seen that these
mathematical elements (number, magnitude, time, space, geometric
progression), are therefore ideal forms with relation to absolute
magnitudes and therefore something quite empiric, no matter to what
species they belong." But "mathematical general notions are, apart
from experience, nevertheless capable of sufficient characterization,"
which latter proceeds, more or less, from each abstraction, but does
not by any means prove that it is not deprived from the actual. In the
scheme of the universe of our author pure mathematics originated in
pure thought, in his philosophy of nature it is derived from the
external world and then set apart from it. What are we then to
believe?

_The Scheme of the Universe._

"All-comprehending existence is sole. It is sufficient to itself and
has nothing above or below it. To associate a second existence with it
would be to make it just what it is not, a part of a constituent or
all-embracing whole. When we conceive of our idea of soleness as