 A second series of developments that raised questions for logical empiricism to address were developments in the sciences themselves, especially the rise of non-Euclidean geometries in mathematics and the establishment of relativity theory in physics. These posed a serious challenge to what would otherwise be an attractive scientific philosophy, namely some version of Kantianism. Kant had recognized that the best of modern science was often mathematical in character and had labored to integrate both geometry and arithmetic into our empirical picture of the world. He had held that we could not represent the world except as a Euclidean structure and hence Euclidean geometry was, a priori, a permanent feature of any future physics. The demonstration that non-Euclidean pure geometrical structures were as consistent as Euclidean ones and that spaces can indeed be represented as a non-Euclidean manifolds was one half of the problem. The other half came when Einstein argued convincingly that physical space was best described as a non-Euclidean manifold of non-constant curvature. Plainly Euclidean geometry could not be guaranteed a future physics. Modern mathematical logic also posed a problem for other Kantian claims, but not in the same wrenching way.