The essence of knowledge is generalization. That fire can be produced by rubbing wood in a certain way is a knowledge derived by generalization from ….

...the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condit….

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

...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a cur….

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….

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 geometric….

You see, there is no more purpose or meaning in the world than you put into it..

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry….

Occasionally one speaks... of signals or signal chains. It should be noted that the word signal means the transmission of signs and hence concerns th….

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in thes….

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 ….

The statement that although the past can be recorded, the future cannot, is translatable into the statistical statement: Isolated states of order are….

The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of t….

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians….

Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lin….

Philosophy is regarded by many as inseparable from speculation. ... Philosophy has proceeded from speculation to science..