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

THE MATHEMATICS OF PSYCHOLOGY 367
I will begin with the mathematics of psychology and
will in the main confine my remarks to its most famous
achievement, which is also, I believe, its most important
one-the so-called Psychophysical Law of Weber and
Fechner. When the law was duly announced in its mathematical form, it aroused much interest among psychologists, evoked much admiration, and stimulated research
and discussion; at the same time it produced something
like fright or consternation for it began to seem that one
could not be a scientific psychologist without being a
mathematician, and that was a fearful thought. But the
"interest," the "admiration" and the "fright" were destined to pass or, at least, to suffer much mitigation. A
generation ago the law had been often presented and
elaborately discussed. At length it was handled by William James in The Principles of Psychology. After presenting it with characteristic honesty and with quite as
much accuracy as could be expected from one who not
only was not a mathematician but knew and owned that
he was not, James proceeds to examine the claims that
had been made in behalf of the law and then, with absolute candor and great confidence, to estimate its significance. And what is the estimate? It is this: "Fechner's
book, Psychophysik, was the starting point of a new department of literature, which it would be perhaps impossible to match for the qualities of thoroughness and subtlety, but of which, in the humble opinion of the present
writer, the proper psychological outcome is just nothing"
(Vol. I, p. 534). Again: "The Fechnerian Maasformel
and the conception of it as an ultimate 'psychophysic law'
will remain an 'idol of the den,' if there ever was%'one"
(p. 549). Of that judgment, right or wrong,p'ronounced
by so great an authority, it may not be said that its psycho