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

224 MATIEMATICAL PHILOSOPHY
understand its meaning. And they should lead you to
surmise-what is true-that answers like the foregoing
ones are available for similar questions regarding all
geometries of a space of any number of dimensions and
-what is more-regarding mathematical doctrines in
general. Whatsoever things are invariant under all and
only the transformations of some group constitute the
peculiar subject-matter of some (actual or potential)
branch of knowledge. And you see that every such groupdefined science views its subject matter under the aspect of
eternity.
A Question for Psychologists.-Before closing this
lecture, I desire to speak briefly of two additional matters
connected with the notion of group: one of the matters
is psychological: the other is historical. Being students
of philosophy, you are obliged to have at least a good
secondary interest in psychology. I wish to propose for
your future consideration a psychological question-one
which psychologists (I believe) have not considered and
which, though it has haunted me a good deal from time
to time in recent years, I am not yet prepared to answer
confidently. The question is: Is mind a group? Let us
restrict the question and ask: Is mind a closed systemthat is, has it the group property? Some of the difficulties
are immediately obvious. In order that the question
shall have definite meaning, it is necessary to think of
mind as a system composed of a class of things and a rule,
or law, of combination by which each of the things can be
combined with itself and with each of the other things.
We may make a beginning by saying that the required
class is the class of mental phenomena. But what does
the class include? What phenomena are members of it?
Some phenomena,-feeling, for example, seeing, hearing,