Note 21 — THE MONIST. (continued 3)

Hermann Grassmann, one of the founders of modern mathematics, has called attention to the fact that Euclid had a clearer conception of the fundamental concepts of mathematics than his ill-informed translators and interpreters. Grassmann says in his Ausdehnungslehre: “From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free, Euclid incorporated the former among his postulates (αἰτήματα) while he separated the latter as common concepts (κοιναὶ ἐννοιαι)—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all.”—Quoted from The Open Court, Vol. II. No. 77, A Flaw in the Foundation of Geometry, by Hermann Grassmann, translated from his Ausdehnungslehre by μκρκ.