Hans Reichenbach quotes

Hans Reichenbach was a German philosopher and physicist, recognized as a leading figure in the philosophy of science and logical empiricism. His work deeply influenced the analysis of scientific knowledge, probability, and the nature of time. He contributed significantly to the development of the Berlin Circle and the popularization of scientific philosophy in the twentieth century. Here are 35 of his quotes:

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

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

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

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

...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

...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

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 heat were the affecting force, direct indications of its presence could be found which would not make use of geometry as an indirect method. ...direct evidence for the presence of heat is based on the fact that it affects different materials in different ways. ...The forces... which we have introduced... have two properties: (a) They affect all materials in the same way. (b) There are no insulating [or isolating] walls. ...the definition of the insulating wall may be added here: it is a covering made of any kind of material which does not act upon the enclosed object with forces having property a. Let us call the forces which have the properties a and b universal forces; all other forces are called differential forces. Then it can be said that differential forces, but not universal forces, are directly demonstrable.

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

...introduce the auxiliary concept of first-signal...defined as the fastest message carrier between any two points in space. We now send a first-signal from P, calling the event of departure E1... The event of its arrival at P' is called E'. Simultaneously with the arrival of this signal, another first signal is sent from P'. The arrival of this signal at P is the event E2. ...the time interval between E1 and E2 is coordinated to the event E', [E1 is earlier than E' and E2 is later than E'] and every event of this time interval except for the endpoints is inderterminate as to the time order relative to E.

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

If error is corrected whenever it is recognized as such, the path of error is the path of truth.

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

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

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

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

...the relation of betweenness on the torus is undetermined for curves that cannot be contracted to a point [e. g., circles around a doughnut hole], i. e., for three of such curves it is not uniquely determined which of them lies between the other two... This indeterminateness... has the consequence that such a curve [alone] does not divide the surface of the torus into two separate domains; between points to the "right" and to the "left" of the line.

Hans Reichenbach

There is no pure visualization in the sense of a priori philosophies; every visualization is determined by previous sense perceptions, and any separation into perceptual space and space of visualization is not permissible, since the specifically visual elements of the imagination are derived from perceptual space. What led to the mistaken conception of pure visualization was rather an improper interpretation of the normative function... an essential element of all visual representations. Indeed, all arguments which have been introduced for the distinction of perceptual space and space of visualization are base on this normative component of the imagination.

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

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