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

8 MATHEMATICAL PHILOSOPHY
profitably? It is natural that you should wish to ask that
question at this point. The question is important and
the answer easy and short: so much mathematical training-so much knowledge of algebra, geometry and trigonometry-as a capable student can acquire in one collegiate year. Compared with the existing science of
mathematics such knowledge is very meagre, a bare beginning; but, taken absolutely, it is much; in respect of
content or mere information as distinguished from insight
and power, it is far more than Thales had, or Pythagoras
or even Plato or even Galileo. It would be very convenient if I might assume more; projective geometry, for
example, and some acquaintance with analytical geometry
-which should remind you of Descartes, and with the
calculus-which should remind you of Leibniz; for 1 shall
be obliged occasionally to employ ideas drawn from these
and other branches of mathematics, and shall have to
interrupt and delay the discussion a little in order to explain the ideas as the necessity arises for using them,
Perhaps I should add that, for understanding the lectures,
a certain intellectual maturity, logical acumen, open-mindedness and philosophical insight are not less essential than
the stated minimum of mathematical knowledge.
I desire to invite you now to a somewhat comprehensive consideration of a much larger question, one of
greater difficulty and far greater importance —a question
of both general and permanent interest. The question
is: How much mathematical training-how much mathematical knowledge, discipline, and habit-may be reasonably regarded as indispensable to the proper equipment of a philosopher? It may well be that you will be
qualified to give a better answer at the end of the course
than that which I am about to submit here at the begin