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

44 MATHEMATICAL PHILOSOPHY
In Egypte he tawghte hyt ful wyde,
In dyvers londe on every syde,
Mony erys afterwarde y understonde
Yer that the craft com ynto thys londe.
Thys craft com into England, as y you say,
Yn tyme of good Kyng Adelstone's day."
From which we see that even in the old island home
of our beautiful English tongue the Greek "Craft of
Gemetry" has been known for a thousand years, The
second reason for my selecting Hilbert's system is that
it is the most famous of all existing postulate systems,
save one only-that of Euclid. Hilbert's acquired its
great fame immediately, not entirely by its merits, for
these, as already said, are not superior to the merits of
some other systems, but largely through the fame of its
author, which was world-wide. If you ask why I have
chosen it instead of Euclid's system, which surpasses all
others in fame, the answer is that, though Euclid's system
was good enough to withstand more than two thousand
years of criticism, it is now known, as we shall see later,
to have some grave imperfections —most of them sins
of omission. The postulates of Hilbert's system are
called axioms by him-'axioms of geometry." As,
however, the term axiom as employed by him is exactly
equivalent to the term postulate as I have defined it, I
shall be doing him no injustice in uniformly referring to
his system as a system of postulates, thus avoiding the
term axiom as likely to suggest the unavailable notion (socalled) of "self-evident truth." The postulates of Hilbert fall into six sets: postulates of connection; of order;
of parallels; of congruence; of continuity; of completeness. I give them as found in the authorized English
translation of Hilbert's book by Professor Townsend.