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

412 MATHEMATICAL PHILOSOPHY
phenomena,-and I believe we may assume that, where
there is mathematics, there is some manifestation of mind,
-that mathematics, regarded as an enterprise, is an
enterprise of mind,-that, regarded as a body of achievements, it is a body of mental achievements,-that, regarded as a mode of life, it is a mode of mental life,
-that, in a word, mathematical phenomena represent
mental phenomena and are unsurpassed as means in the
study of mind. I do not mean that all kinds of mental
phenomena are thus represented. Lust, for example, is
not, nor fear, nor anger, nor hate, nor malice, nor envy,
nor many another such amiable propensity of unregenerate souls-of course I am speaking here of mathematics and not of mathematicians, who have many interesting qualities that their science has not. But perception
- discrimination - imagination - fantasie - conception - judgment - analysis - synthesis - reasoning -
generalization - the energy of will - the restraint of
passion-the sensibility and daring of genius-the sense
for order, for symmetry, for harmony, for intellectual
beauty, for cogency and clarity of thought,-where outside of mathematics do such mental phenomena, which it
is the psychologist's profession to examine, show themselves in so clear a light? It is indeed obvious that the
whole literature of mathematics may be read and interpreted as a commentary upon the nature of the
human mind. Select, for example, a well-wrought demonstration and examine it. What can you say of it?
You can say this: A normal human mind is such that,
if it begin with such-and-such principles or premises and
with such-and-such ideas and if it combine them in suchand-such ways, moving from step to step in such-and-such
an order, it will find that it has thus passed from dark