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

THE MATHEMATICS OF PSYCHOLOGY 881
like phenomena are, of course, observed in the behavior
of a pair of scales for weighing. It is evident that, owing
to friction, the tangent of the needle's angle with the
meridian plane, though it is a function of the current's
strength, is not a continuous function of it. It is common,
however, to idealize the situation, by disregarding the
frictional effect, and to say that the function is continuous,
though as a matter of fact it is not. Misled by such
considerations certain psychologists have argued fallaciously as follows: The tangent of the needle's angle really
is, they say, a continuous function of the current's
strength. They admit that it does not appear to be so,
but that, they say, is because the fact or the law is
" masked " by the presence of friction. And then they
contend that the situation is essentially the same in the
case of sensation. Sensation, they say, is indeed a continuous function of stimulus, though it does not appear
to be such. For, they say, the continuity is " masked "
by what they call the " frictional effect " or the opposition
of some chemical or mechanical or physical resistance
offered by the sensorium to the action of stimulus. The
fallacy is obvious. It consists in ignoring some of the
facts. The question is not whether the functions under
consideration would be continuous if there were no
friction or " frictional effects," but whether they are in
fact continuous in a world where friction and " frictional
effects " persist as part of reality.
The Number of Possible Sensations Finite.-How many
different sense departments are there? I know of no way
to prove that the number is finite, but the assumption
that the number is finite seems to be very probably correct.
Let us make the assumption. We know that the number
of discernibly different sensations that any department