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

INTRODUCTION S
modification, of decay, of destruction, as when we say,
for example, that we have "changed" our ideas or that
such-and-such an idea has "grown" in importance or has
"become" sterile or is "dead." It is, I fancy, hardly
necessary to say that all such ways of speaking are figurative,-convenient no doubt, often pleasing, sometimes
very effective, yet thoroughly figurative,-and that, if
taken literally, they quickly and inevitably lead to scieintific and philosophic disaster. You or I may abandon an
idea that we have held and we may adopt an idea that is
new to us; the "old" one and the "new" one may closely
resemble each other; they may indeed be identical in some
respect and may even be called by the same name; but
neither of them has been transmuted into the other; each
of them remains and will remain just what it was. Let
me illustrate the eternality of ideas and of their relations
by means of a simple example. You know that in discourse ideas are represented by symbols-by words or
other signs. Consider the symbols 2, 7, 9, +, and-;
each of them stands for an idea familiar to all of us.
The symbols are man-made; but the things they stand
for, though they were discovered by man, are not manmade; they are increate, as Milton would say, and indestructible, and the like ig true of their relations; one of
these is expressed by the statement (a) 2+7=9; the
statement expressing the relation is a creature of man, but
the relation itself is not-man discovered it, but he did
not make it-it is a thing increate and indestructible, the
same yesterday, today and forever. The truth of what
I have just now said is very evident, but the illustration
is arithmetical. Is the eternality equally evident in the
case of all other ideas and their relations? No, it is not
equally evident, but it is none the less true, Shall we take