Hans Reichenbach - Congruence Quotes

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... the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can replace the definition of congruence.

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

Perceptual space is not a special space in addition to physical space, but physical space which we endow with a special subjective metric.... apart from the definition of congruence in physics and that based on perception, there is no third one derived from pure visualization. Any such third definition is nothing but the definition of physical congruence to which our normative function has adjusted the subjective experience of congruence.

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