Hans Reichenbach

If along the path of truth, success (which was often near-failure unnoticed) is subjected to the same scrutiny and desire for improvement as failure, we may find ourselves in closer proximity to trees.

— Hans Reichenbach

Although it is admitted that certain differences cannot be verified by experiment, we should not infer from this fact that they do not exist. ...we are accused of having confused subjective inability with objective indeterminacy.

— Hans Reichenbach

...the order of betweenness does not depend on mutual distances... betweenness is purely a relational order.

— 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

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 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

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

Common 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 Reichenbach

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

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

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

— Hans Reichenbach

Occasionally one speaks... of signals or signal chains. It should be noted that the word signal means the transmission of signs and hence concerns the very principle of causal order...

— 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

...absolute time would exist in a causal structure for which the concept indeterminate as to time order lends to a unique simultaneity, i.e., for which there is no finite interval of time between the departure and return of a first-signal...

— Hans Reichenbach

For the Lorentz transformation spatial measurements are also changed, because they are obtained relative to a moving system. In our example only time was transformed, while the distances between points at rest remained the same; the spatial coordinates, therefore, retain their identity.

— Hans Reichenbach

This fact... proves that space measurements are reducible to time measurements. Time is therefore logically prior to space.

— 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

Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms.

— Hans Reichenbach

Clocks are inherently four-dimensional instruments, since the endpoints of their unit distances are events. Measuring rods, on the other hand, are three-dimensional measuring instruments; their end points are space points and they can be changed into four-dimensional measuring instruments only if events are produced at their end points according to a special rule.

— Hans Reichenbach

Why is Einstein's theory better than Lorentz's theory? It would be a mistake to argue that Einstein's theory gives an explanation of Michelson's experiment, since it does not do so. Michelson's experiment is simply taken over as an axiom.

— Hans Reichenbach

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

— Hans Reichenbach