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 Copy Share Image
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 Copy Share Image
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… — Hans Reichenbach Copy Share Image
Occasionally one speaks... of signals or signal chains. It should be noted that the word signal means the transmission of signs and hence concerns… — Hans Reichenbach Copy Share Image
The essence of knowledge is generalization. That fire can be produced by rubbing wood in a certain way is a knowledge derived by generalization… — Hans Reichenbach Copy Share Image
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth… — Hans Reichenbach Copy Share Image
...the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can… — Hans Reichenbach Copy Share Image
We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be… — Hans Reichenbach Copy Share Image
Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense… — Hans Reichenbach Copy Share Image
The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of… — Hans Reichenbach Copy Share Image
Philosophy is regarded by many as inseparable from speculation. ... Philosophy has proceeded from speculation to science. — Hans Reichenbach Copy Share Image
The statement that although the past can be recorded, the future cannot, is translatable into the statistical statement: Isolated states of order are always… — Hans Reichenbach Copy Share Image
...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… — Hans Reichenbach Copy Share Image
It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians… — Hans Reichenbach Copy Share Image
