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

426 MATHEMATICAL PHILOSOPHY
and the author's closely allied notion of "Dimensions."
Let me say at the outset that one who would read
the book understandingly must come to it prepared to
grapple with a central concept, a concept whose rôle
among the other ideas in the work is like that of the sun
in the solar system. It happens, therefore, that readers
of the book, or of any other book built about a central
concept, fall into three mutually exclusive classes:
(I) The class of those who miss the central concept
-(I have known a learned historian to miss it)-not
through any fault of their own,-they are often indeed
well meaning and amiable people,-but simply because
they are not qualified for conceptual thinking save that
of the commonest type.
(II) The class of those who seem to grasp the
central concept and then straightway show by their
manner of talk that they have not really grasped it but
have at most got hold of some of its words. Intellectually such readers are like the familiar type of undergradumte who "flunks" his mathematical examinations but may
possibly "pull through" in a second attempt and so is
permitted, after further study, to try again.
(III) The class of those who firmly seize the central
concept and who by meditating upon it see more and
more clearly the tremendous reach of its implications. If
it were not for this class, there would be no science in the
world nor genuine philosophy. But the other two classes
are not aware of the fact for they are merely "verbalists."
In respect of such folk, the "Behaviorist" school of
psychology is right for in the psychology of classes (I)
and (II) there is no need for a chapter on "Thought
Processes"-it is sufficient to have one on "The Language
Habit."