Hans Reichenbach - Geometry Quotes

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We 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

Once a definition of congruence is given, the choice of geometry is no longer in our hands; rather, the geometry is now an empirical fact.

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 Reichenbach

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.

Hans Reichenbach

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry...."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.

Hans Reichenbach