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Frases de Hans Reichenbach

Hans Reichenbach foi um filósofo da ciência alemão.

✵ 26. Setembro 1891 – 9. Abril 1953
Hans Reichenbach photo
Hans Reichenbach: 41   citações 0   Curtidas

Hans Reichenbach: Frases em inglês

“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.”

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Hans Reichenbach

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

“…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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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…”

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Hans Reichenbach

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

“…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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“… the principle of the limiting character of the velocity of light. This statement… is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light.”

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Hans Reichenbach

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

“We are frequently faced with the necessity of looking for the picture required for the visualization of an object, not in the perception of this particular object, but in a different perceptual image. …we can assert the discrepancy between the perceived picture and the objective state. This discrepancy… proves absolutely nothing against the fact that all visualizations are merely sense qualities of the perceptual space. …If the parallelism is …to be visualized, we must supplement our assertion by the description of certain qualities with which we are familiar from perceptual space.”

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Hans Reichenbach

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

“The main objection to the theory of pure visualization is our thesis that the non-Euclidean axioms can be visualized just as rigorously if we adjust the concept of congruence. This thesis is based on the discovery that the normative function of visualization is not of visual but of logical origin and that the intuitive acceptance of certain axioms is based on conditions from which they follow logically, and which have previously been smuggled into the images. The axiom that the straight line is the shortest distance is highly intuitive only because we have adapted the concept of straightness to the system of Eucidean concepts. It is therefore necessary merely to change these conditions to gain a correspondingly intuitive and clear insight into different sets of axioms; this recognition strikes at the root of the intuitive priority of Euclidean geometry. Our solution of the problem is a denial of pure visualization, inasmuch as it denies to visualization a special extralogical compulsion and points out the purely logical and nonintuitive origin of the normative function. Since it asserts, however, the possibility of a visual representation of all geometries, it could be understood as an extension of pure visualization to all geometries. In that case the predicate "pure" is but an empty addition, since it denotes only the difference between experienced and imagined pictures, and we shall therefore discard the term "pure visualization."”

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Hans Reichenbach

Instead we shall speak of the normative function of the thinking process, which can guide the pictorial elements of thinking into any logically permissible structure.
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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

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

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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

“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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“…the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i. e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. …such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.”

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Hans Reichenbach

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.”

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Hans Reichenbach

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

“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

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Hans Reichenbach

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

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