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

2 MATHEMATICAL PHILOSOPHY
and mathematical ignorance of philosophers. No doubt
philosophically unenlightened mathematicians and mathematically unenlightened philosophers will quarrel in the
future as in the past; but in the future as in the past,
the quarreling and the sneering will be the quarreling and
sneering of men and not of the great subjects they represent and misrepresent; for between the spirit of mathematics and the spirit of philosophy there is no discord, no
antagonism, no strife; they are by their natures friendly
rivals in the pursuit of truth and light; they are companions in excellence; they are comrades in the service of
wisdom.
I have said that the "aim" of these lectures is to disclose fundamental connections between mathematics and
philosophy. What I have described as their "aim" is
not so much the aim, or end, as a means. For it will become increasingly evident as we advance that the work
we are to be engaged in is fundamentally the study of
Fate and Freedom-logical fate and intellectual freedom.
I mention the matter here because you ought to have it
consciously in mind from the beginning. You should bear
it in mind at every stage of the discussion, even in connections where so warm an interest may seem remote. A
preliminary word of explanation is therefore desirable.
We are going to deal with ideas-with their characters, with their meanings, with their relations. Now, an
idea is in itself an eternal thing and the relations of an
idea with other ideas are eternal. An idea is jùst what
it is and it is unalterable, a relation among ideas is just
what it is and it is unalterable. We do, indeed, often
speak as if such were not the case; we habitually speak
-as if ideas and their relations were temporal affairs, impermanent, mutable, malleable, capable of growth, of