THE LOGICAL STATUS OF MENTAL FACTORS 101

mathematical dress, are nothing more than a resuscitation
of the ancient logical and metaphysical disputes, which
arose out of the problem of scientific classification, and
which, at any rate for the case of qualitative attributes,
have already been fairly thoroughly thrashed out.

How Many Kinds of Factors are There ?—Let us begin
with what would seem to be the most fundamental question
of all—the issue that has been the main source of dissension
—namely, how many kinds of factors are we to postulate ?
Spearman based his original analysis of cognition on a
c theory of two factors '—i.e. two kinds of factors, one general
factor and a number of specific factors. Some of his fol-
lowers have reduced this to a theory of a single general
factor only. On the other hand, many of his critics have
contended that the mind and its workings cannot be
adequately described unless we invoke three kinds of factor
—general, group, and specific. Others again have argued
that the only set of factors that can have a real * psycho-
logical meaning ? must consist in an indefinite number of
common factors, each conforming to certain limiting,
requirements, such as those of Thurstone's * simple
structure.'

Now, if the position maintained in the preceding pages
be accepted, it seems clear that, in the first instance, the
issues thus raised are points to be decided, not by con-
sidering the general nature of the mind, but rather by exam-
ining a little more closely the logical basis on which factor-
analysis rests. If our factors are logical principles rather
than psychological principles, we should be able to state,
a priori and in advance, how many kinds we may in theory
expect, though whether all the kinds will be found in this
particular table or in that must depend upon the traits or
tests actually selected for study, i.e. upon the experimental
design.

The Four-factor Theory : (a) In Correlating Tests.—Con-
sider any set of measurements obtained by testing a number
of individuals for a number of mental capacities or traits.
The factorist's problem, we have seen, is to classify the
traits and the persons. From this standpoint it is evident
that one or more of the following propositions can be asserted