 General Theory is notable for a key innovation in its treatment of concepts, for they are defined in terms of mathematical equations rather than reducing them to complexes of intuitive images (Schlick 2009, Sec. 5). In order to articulate his ideas about the nature of concepts and how they are formed, Schlick borrowed the idea of definition by axioms from recent work in the foundations of geometry by Moritz Pasch, David Hilbert, and Henri Poincaré. In their work on alternative geometries, these mathematicians came to regard the effects of altering the axioms of geometry as changing the meaning of their constituent terms, thus re-defining the primitive geometric concepts. The idea is ingenious in its simplicity, for it treats the geometric primitives as defined by the relations they bear to one another according to the axioms, so the meanings of the terms ‘point’, ‘lies between’, and ‘lies upon’ are fixed by the geometric axioms. The reason mathematicians adopted this method is to insure the certainty of geometry by insuring that it was invulnerable to the criticism that its primitive elements were defined by intuition.