THE LOGICAL STATUS OF MENTAL FACTORS 115

methods. We are forced first of all to measure the traits
and persons, thus starting with c variables ' formed by the
numerical measurements, instead of with mere * attributes'x
named in verbal terms ; then to measure their resemblances.,
thus obtaining their covariability or correlation; and so
ultimately to measure (i) first, the diagnostic importance of
the traits—which we can specify by the ' saturation co-
efficients ' for traits when correlating traits, and (ii) secondly,
the closeness with which the individual approximates to a
typical member of his class—which, we can specify by the
< factor measurements ' for persons when correlating traits,
and by the saturation coefficients for persons when cor-
relating persons. It is for this reason, therefore, that what
is essentially a logical analysis masquerades as an arithmetical
analysis.

The logician, however, will at once inquire whether this
step is justified. No doubt, he will argue, it will be easier
to ' factorize ' our phenomena if we first substitute figures
for facts; but is such a substitution valid ? As a logician,
he will remind us, he has laid down the postulates to which
measurable quantities must logically conform.2 Has anyone
formally demonstrated that these postulates are satisfied
by the factorist's material ? The factorist, we have seen,
sets out with an additive equation. Has he ever shown that
mental abilities, mental performances, or mental character-
istics generally are really additive, or is this a gratuitous
assumption ?

The Postulates of Mental Measurement.—In view of cur-

1 As before, I use the terms * attributes' and c variables' as defined by
Yule ([no] pp. it, 82). A friendly critic maintains that my statement
" seems to obliterate the insuperable distinction between the statistical theory
of attributes and the statistical theory of variables." My reply is that Yule
and Kendall have already sought to " remove any possible idea that the theory
of attributes is concerned solely with qualitative classification and is not
also appropriate to the more precise data given by a numerically assessable
attribute " (p, 78).

2 Cf. Conrad and Nagel, Introduction to Logic, chap, xv; Stebbing,
Modern Introduction to Logic, chap, xviii, § 5 ; Johnson, Logic, Pt. II, chap,
vii. The possibility of measurement in general psychology has, of course,
been very fully discussed; here I am referring to the measurement of the
mental performances or qualities of individuals.