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

882 MATHEMATICAL PHILOSOPHY
admits is finite. It follows that the total number of
different sensations of which a human being is capable
is a finite number. I am not aware that this important
consideration has been recognized in the literature of
psychology. It would not be strange if it has not, for
the distinction of finite and infinite, though it is very important scientifically and in some of its connections is
awe-inspiring, has not yet gained much intelligent recognition outside the circle of mathematicians. What I wish
to signalize here is this: the fact that the ensemble of
possible concepts is infinite and the fact that the ensemble
of possible sensations or percepts is finite together confront
with a difficult and important problem those psychologists
who hold that our mental life is based on sensation in
the sense that all ideas arise out of sensation. For
others the problem does not exist. Plato, for example, held ideas to be eternal, existing before, during
and after sensation or perception, and that the world
of sensation or perception is only an imperfect and
transitory imitation of the eternal world of ideas or
concepts.
Sense Continua.-We have seen that the results of
experiment do not warrant us in saying that sensation is
a continuous function of stimulus in the mathematical
sense of the term. Nevertheless, it will be convenient to
speak of physical or experiential or sensible or sense
"continua" and we shall do so but we shall thereby
mean merely that to any amount of stimulus between the
initial and terminal thresholds of a sense department
there corresponds a sensation in the department. We
must at no time confound this meaning of continuous with
the mathematical meaning of the term. With this understanding we will speak of the " continuum" of pres