Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

DOCTRINAL INTERPRETATIONS 67
latter figure the truth of the proposition is perfectly and
immediately evident to intuition, while in the former the
truth of the proposition is very far from being thus evident. Why? The question, you observe, is one for
psychologists, like hundreds of similar questions that
arise here and elsewhere in mathematics, if only psychologists would learn enough mathematics even to ask the
questions.
FIG. 6.
Let us now turn to postulate (I3)-the postulate of
parallels. Fig. 6 shows clearly that this famous Euclidean
postulate is satisfied by our new interpretation. Here a
is the given pathopencil; A is any given line not belonging
to a; b is a pathopencil containing A but having no line
in common with a, and there is plainly no other such
pathopencil; in other words, b is parallel to a and there
is no other such pathopencil containing A.
If, now, you attempt to show (and I advise you to
make the attempt) by a figure that postulate (20), or