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

INTRODUCTION 95
ago in the following words: "As an enterprise, mathematics is characterized by its aim, and its aim is to think
rigorously whatever is rigorously thinkable or whatever
may become rigorously thinkable in course of the upward
striving and refining evolution of ideas." l The same
feature has been recently indicated, even more clearly
perhaps and somewhat poignantly, in a striking utterance
by Mr. Bertrand Russell. "Pure logic, and pure mathematics (which is the same thing), aims at being true, in
Leibnizian phraseology, in all possible worlds and not
merely in this higgledy-piggledy job-lot of a world in
which chance has imprisoned us." 2
You know, at least in a general way, that in pursuit
of that enterprise and aim through the centuries, the
mathematical spirit has achieved immense result and that
today the science of mathematics, as a body of permanent
knowledge regarding things eternal, is a veritable continent of expanding doctrine. And so it is pertinent to ask:
How can one aspiring to be a philosopher, unless he explores that growing continent of knowledge respecting
what is "true of all possible worlds," be in any proper
sense "a spectator of all time and all existence"? You
may wish to reply that, owing to his other obligations, the
philosopher cannot make the exploration fully; that indeed, owing to the nature of the continent, he cannot,
without exploring it step by step, gain even so much as a
clear knowledge of its contour and relief; that, however,
notwithstanding the endless diversity of the things that
are there, they have a certain essential character in common; that for the philosopher's vocation, knowledge of
1Human Worth of Rigorous Thinking, p. 3. Columbia University
Press.
2Introduction to Mathematical Philosophy. The Macmnillan Company,
New York.