VARIOUS USES OF FACTORS 33

rather than probable generalizations ; secondly, it is
treated as a positive rather than as a negative procedure—
as being based on the agreement1 of positive instances
instead of on elimination by means of negative instances.
These misconceptions are so common in factorial work
that I may be pardoned for exposing them in some detail:
for unless we can fit factor-analysis in its true logical setting,
we shall, I am convinced, utterly misconstrue its nature, and
be continually led astray.

Where, as in psychology, the issue is somewhat involved,
it is, I think, a helpful practice to encourage the young
research student to outline for himself the successive steps
in his argument so that the formal aspect of his reasoning
shall be obvious at a glance. Any illicit transition will then
leap to the eye. Here, assuming for the moment that the
generalization to be proved is a certain and not a probable
proposition, the essential premisses and conclusions may be
set out schematically as follows. The writer begins with a
hypothetical syllogism.

" If relation-finding is the cause of educational progress
in these children, then their performances in the two types
of test should agree ;

" The correlations show that they do agree ;

" Therefore, relation-finding is the cause of their pro-
gress."

The fallacy is plain. It could be succinctly if somewhat
pedantically pinned down with the labels of scholastic logic :
the writer argues in the modus fonendo fonens (and commits
the fallacy of affirming the consequent), whereas he ought

1 The * method of agreement/ to which the writer (like so many other
factorists) more than once appeals, is somewhat deceptively named. It
assumes, not merely (as correlationists who cite Mill appear to suppose) that
" the instances have one factor in common," but that (in Mill's own words)
they have " only one circumstance in common " (System of Logic, Bk. Ill,
chap, viii, p. 428). Its value therefore depends more on disagreement than
on agreement. As Mill himself admits, the method " is an inferior resource "
(p. 433), and the required assumption cannot be made unless we show we have
" excluded all other causes," In other words, it is only valid when the c rele-
vant known positive analogy' (to use the terminology adopted below) is
equal to the' total analogy *; and this can hardly ever be the case in psycho-
logy, though it may seem to be the case in elementary mechanics.