nconceivable to the metaphysician, because a contradiction. And as he
affirms the inconceivability of motion he admits the existence of this
contradiction against his will and therefore admits that it
constitutes an objective contradiction in actual facts and events, and
is moreover an actual fact.

But if simple mechanical motion contains a contradiction in itself
still more so do the higher forms of motion of matter and to a high
degree organic life and its development. We saw above that life
consists chiefly in this that a being is at one and the same time
itself and something different. Life itself then is likewise a
contradiction contained in things and events, always establishing and
dissolving itself, and as soon as the contradiction ceases life also
ceases, death comes on the scene. Thus we saw also that we cannot put
an end to the Contradictions in the realm of thought, and how for
example the contradiction between the intrinsically unlimited
possibilities of human knowledge and its actual existence in the
persons of human beings with limited faculties and powers of
knowledge, is dissolved in the, for us at least, practically endless
progression of the race, in unending progress.

We stated just now that higher mathematics holds as one of its basic
principles that straight and crooked may be identical under certain
circumstances. It shows another contradiction, that lines which
apparently intersect yet are parallel from five to six centimeters
from the point of intersection, should be such as should never
intersect although indefinitely produced, and yet, notwithstanding
these and even greater contradictions, it produces not only correct
results but results which are unattainable by lower mathematics.

But even in the latter there is a host of contradictions. It is a
contradiction, for example, that a root of A should be and actually is
a power of A. A to the power of one-half equals the square root of A.
It is contradiction that a negative magnitude should be the square of
anything, since every negative magnitude multiplied by itself gives a
positive square. The square root of minus one is therefore not only a
contradiction but an absurd contradiction, a veritable absurdity. And
yet the square root of minus one is in many instances the necessary
result of correct mathematical operations, nay further, where would
mathematics higher or lower be if one were forbidden to operate with
the square root of minus on