...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 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
