Philosophy is regarded by many as inseparable from speculation. ... Philosophy has proceeded from speculation to science.
Hans Reichenbach...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.
Hans ReichenbachCommon to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.
Hans ReichenbachWe must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.
Hans Reichenbach