Hans Reichenbach - Definition 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
If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions.

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
Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations.

Hans Reichenbach
We define: any two events which are indeterminate as to their time order may be called simultaneous.... Simultaneity means the exclusion of causal connection.... Yet we must not commit the mistake of attempting to derive from it the conclusion that this definition coordinates to any given event at a given different place. This would be the case only for a special form of causal structure, a form that does not conform to physical reality.

Hans Reichenbach
If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions.... Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.

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