# Frases de Hans Reichenbach

0   0

## Hans Reichenbach

Data de nascimento: 26. Setembro 1891
Data de falecimento: 9. Abril 1953

Hans Reichenbach foi um filósofo da ciência alemão.

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property.“

The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes. ...but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.
The Philosophy of Space and Time (1928, tr. 1957)

### „…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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „…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…“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „…the order of betweenness does not depend on mutual distances… betweenness is purely a relational order.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

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

The Philosophy of Space and Time (1928, tr. 1957)

#### Help us translate English quotes

Discover interesting quotes and translate them.

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i. e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. …A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. …the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection… analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". …If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels.“

The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.
The Philosophy of Space and Time (1928, tr. 1957)

### „…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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)

### „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...
The Philosophy of Space and Time (1928, tr. 1957)

### „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 rise of scientific philosophy, University of California Press, 1951, 0520010558, 326]

### „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.“

The Philosophy of Space and Time (1928, tr. 1957)