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

POSTULATES 43
-constraining men by relentless logical criticism to a
choice of one or the other of two alternatives: coherency
and clarity of speech or-silence. Today, the mind of
the world is a weltering sea of wild passions and wilder
opinions. It can not be calmed by municipal law, but it
can be by disciplining men to a decent respect for the
eternal laws of thought. And that is the supreme obligation of philosophy as the guardian of Reason.
A few moments ago I said that, in the beginning of
the study of postulate systems, we must be content to
define the notion concretely-by means, that is, of examples. Accordingly, I am going to spread before you
presently a definite system of postulates and invite you to
examine it as a geologist might examine a specific rock
formation; or as a student of poetry might examine a
specific poem; or a student of law, the constitution of the
Soviet republic or that of the United States. From the
large variety of postulate systems recently invented for
various mathematical branches, I have selected, as a
specimen for our initial study, the system devised by the
late Professor Hilbert and found in his famous Foundations of Geometry. It is one of several systems invented
in our time to serve as logical bases of Euclidean Geometry. Though it is not intrinsically superior to its
rivals, whether in geometry or in other branches, I have
selected it in preference to them for two reasons. One
of them is that, practical arithmetic not being a science,
Euclidean Geometry is the oldest and most familiar
branch of mathematics, as well as being historically the
most interesting and even romantic.
"The clerk Euclide on this wyse hit fonde
Thys craft of gemetry yn Egypte londe