Page:Landmarks of Scientific Socialism-Anti-Duehring-Engels-Lewis-1907.djvu/154

 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, not withstanding 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