f study, I found them unsupported by solid proof,
subversive of the interest of Man, and fatal to the progress of
his knowledge. To examine the notions in which we have been
educated, and to turn aside from those which will not bear the
test, is a task so painful, that they who shrink from the
sufferings should pause before they reproach those by whom the
suffering is undergone.... Conclusions arrived at in this way are
not to be overturned by stating that they endanger some other
conclusions; nor can they be even affected by allegation against
their supposed tendency. The principles which I advocate are based
upon distinct arguments supported by well ascertained facts. The
only points, therefore, to be ascertained, are, whether the
arguments are fair, and whether the facts are certain. If these
two conditions have been obeyed, the principles follow by an
inevitable inference."

And why have I sought throughout to follow the spirit of mathematics?
Because I have been dealing with ideas and have desired, above all things
else, to be right and clear. Ideas have a character of their own--they are
right or wrong independently of our hopes and passions and will. In the
connection of ideas there is an unbreakable thread of destiny. That is why
in his _Mathematical Philosophy_ Professor Keyser has truly said:

"Mathematics is the study of Fate--not fate in a physical sense,
but in the sense of the binding thread that connects thought with
thought and conclusions with their premises. Where, then, is our
freedom? What do you love? Painting? Poetry? Music? The muses are
_their_ fates. Whoso loves them is free. Logic is the muse of
Thought."

No doubt mathematics is truly impersonal in method; too impersonal maybe
to please the sentimentalists before they take the time to think;
mathematical analysis of life phenomena elevates our point of view above
passion, above selfishness in any form, and, therefore, it is the only
method which can tell us genuine truths about ourselves. Spinosa even in
the 17th Century had well realized this fact and although imperfect in
many ways, his was an effort in the right direction and this quoted
conclusion may well be a conclusion for ourselves in the 20th century:

"The truth might forever have remained hid from the human race, if
mathematics, which looks not to the final cause of figures, but to