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

THE PSYCHOLOGY OF MATHEMATICS 411
matical instruction from one in whose teaching the logic,
the philosophy, the psychology, and the poetry of the
subject mingled together and fortified each other like the
parts of an orchestra. I refer to Professor William
Benjamin Smith, now of world-wide fame as a Biblical
scholar and critic. I am not going to enlarge here upon
this important matter of making the psychology of
mathematics effective in mathematical instruction, but will
merely refer you, for some relevant suggestions, to the
earlier lectures where distinctions of logical and psychological were repeatedly indicated and where, especially
in Lecture VII, in connection with the psychological discrimination of logically identical doctrines, was introduced the important notion of "excessive meaning."
We have been talking about the neglect and backwardness of the psychology of mathematics. Thus far
we have referred mainly to the neglect of it by mathe.
maticians. What are we to say of its neglect by professional psychologists? I have no desire to be fault-finding,
querulous or unjust. I am well aware that psychologists
have many things to occupy their attention-that their
field is vast, diversified and complicate. I know that,
like other scientific folk, they are obliged to select. I
know that for an outsider to attempt to dictate or prescribe their choice would be presumptuous. At the risk,
however, of seeming impertinent,-which usually means
a little too pertinent,-I venture, as an interested layman,
to suggest that, in neglecting the psychology of mathematics, professional psychologists not only neglect an
obligation to mathematics and natural science but also
neglect an exceedingly interesting subdivision of their
own proper field. For their field is Mind,-psychology,
we are told, is the study of mind, the study of mental