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

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.

...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 statement that although the past can be recorded, the future cannot, is translatable into the statistical statement: Isolated states of order are always postinteraction states, never preinteraction states.

...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.

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 philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification.