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

378 MATHEMATICAL PHILOSOPHY
contrast with the "night view" of materialism. It is
not to small men, but to great ones, that this sublime conception of our universe appeals. Even so hard-headed
a scientific man as Bernhard Riemann, whose philosophic
Fragments I have already alluded to, there speaks of the
conception with deep interest and grave respect. And,
as you may be interested to know, Professor William James
has dealt with the same subject in one of his latest writings.
I refer to an article, entitled "The Earth Soul," which
appeared in the Hibbert Journal, January, I909.
Fechner's view that a given sensation is a sum of
sensation units has not ultimately found favor with
psychologists. Why not? Mainly because a sensation
is not felt or sensed as a sum of sensations or of sensation
units, and the question relates to sensations, not as they
may appear mediately in our reflection upon them, but as
they appear immediately in feeling. A sensation of brightness, for example, is not felt to be composed of so-and-so
many units of brightness. A feeling of pink, says James,
is surely not a portion of our feeling of scarlet.
And so the question recurs: What is it that the experiments have measured? Or approximately measured, as
we ought to say, for it is evident that nothing ever is or
can be measured with absolute precision experimentally.
Perhaps we may say that what is measured is a human
sensorium's discriminative sensibility to stimulus. Our
sensibility does not detect every difference of stimulus.
It does detect some differences. By experiment these have
been approximately ascertained for several departments
of sense, and the psychophysical law is an approximately
accurate statement of the way in which they are related.
Sensation as a Function of Stimulus.-In the mathematical meaning of the term " function," sensation is a