104 THE FACTORS OF THE MIND -

where m$ denotes z's measurements in test j, the fs denote
the weights or factor-loadings, them's, j>?s, j's, and ^3s denote
the four kinds of factor—general, group, specific, and error
factors respectively, and the summations indicate that more
than one factor of each kind may conceivably be present
in each test.1 Since, however, the kinds of factors are
being defined solely according to the number of traits and
occasions into which they enter, we can usually amalgamate
factors of the same kind entering into the same trait or set
of traits into one. Thus, as we shall see in a moment, except
for the group-factors, all the summations may be dropped;
mathematically, indeed, with only a single correlation
table, it is impossible to distinguish more than one specific
factor for each test, or more than one positive general factor
for the whole table, or even error factors from specific.

The Need for Relevance in the Correlated, Traits.—The
foregoing definitions of the various kinds of factors reveal
at once what a heavy onus is placed upon the initial selection
of the traits. Evidently if the general factor were defined
simply as that particular characteristic (or set of charac-
teristics) that is common to all the traits selected for com-
parison, it could possess little or no stable meaning, unless
those traits had already been selected according to some
provisional principle. Much the same holds good of the
so-called group-factors. At the same time, the definitions
need not be taken to imply that any feature that is common
to all the traits in a haphazard batch becomes ipso facto
a general factor, or that any feature which is shared by some
but not all of them becomes ipso facto a group-factor. We
may call them * general features' or ' group features,' but
the term * factor ' usually suggests something more.

A factor we have described, not as any characteristic that
may be observed or named, but as one which can serve as a
principle of classification, i.e., as it were, a stable nuclear
feature, which may be conceived as implying, in a wide
variety of instances and under various changes of conditions,
the numerous attributes that it synthesizes. As Aristotle
pointed out, there are three things we must look to in
seeking principles for systematic classification : the terms
1 Marks of Examiners, p. 258, eq. (v).