28 THE FACTORS OF THE MIND

exists; using the latter, we could almost always demonstrate,
even with the same set of data, that it does not exist. The
economy animating such inventions seems to be an economy
in the number of samples quite as much as an economy in the
number of factors: the factorist has in effect asked himself,
what method can I apply so as to reach a unique conclusion
on the basis of one correlation table only? But that, as it
seems to me, is to misconceive the requirements of inductive
arguments.

(K) The Appeal to the Positive Analogy.—There is thus a
second way in which reliance on simplicity seems often to
mislead the factorist. In physical inquiries, when an
investigator obtains a simple pattern of figures from a single
set of observations (as he does, for example., in observing
the acceleration of a dropped weight), the simplicity of the
resulting formula is held to absolve him from the need for
repeating his experiment over and over again before he
begins to generalize. Similarly in psychological inquiries,
when a simple pattern has been obtained, the factorist is
usually ready to generalize from one or two correlation
tables only.

Once again he forgets the wide differences between the
two sciences : the physicist^ can generally assume in
advance that a simple analysis will fit his simple material
and that in his experiments he is really varying one factor
only at a time; usually, indeed, he has deliberately selected
a factor whose relation to the effects he is studying is likely
to be expressible by some simple mathematical function.

1 This is rather the physicist of the elementary textbook (who Is held up
in other sciences as a model investigator), not the actual research worker,
It is quite exceptional for an experimenter in the research laboratory to vary
only one factor at a time or to imagine that he is doing so. All that the
textbook means is that, for purposes of simple exposition, his logical argument
can be stated as if he had actually varied the factors one at a time, and that
a rough demonstration can be arranged in the schoolroom to illustrate the
main principle. Observe that the schoolboy, knowing nothing of the
irrelevant factors, accepts a single instance as conclusive, and the proof as he
understands it involves an * intuitive * rather than a * statistical * induction ;
but even in physical research experiments are multiplied more to reduce
errors of measurement than because a mere increase of number leads to greater
generality (cf. Johnson, Logic, Pt. II, chap, x, p. 216).