The purpose of the present paper is to show how we can build up a system of Logic and Mathematics, assuming no other primitive ideas and propositions than those of the Logical Calculus. It is to be remarked that, for foundation of Mathematics, there is hardly any other method to be found. Suppose we assume any system of mathematical axioms: we then must prove, that this system contains no contradiction. To prove anything, we must have some primitive ideas and propositions. These in their turn must contain the primitive ideas and propositions of the Logical Calculus. There is no means of building up a system of Mathematics, without assuming the primitive ideas and propositions of the Logical Calculus, or their equivalents. Therefore any system of Mathematics mus contain the primitive ideas and propositions of the Logical Calculus.