  Next, Weyl points out that what has been provided so far is merely an explication of the concepts metric, length connection and symmetric linear connection. Some  claim which goes beyond conceptual analysis has to be made, according to Weyl, in order to prove that among the various types of possible  metrical structures that can be put on a differentiable manifold  representing physical space, the Pythagorean-Riemannian form is  unique. Weyl suggests the following hypothesis: 