DERIVATION OF CHIEF THEORIES 143

indications. The modern version of the doctrine of
faculties has shown itself none the happier for discarding
the old name while retaining the old fallacy " ([56], p. 241).
If with Spearman we drop the group-factors, but retain
the specific, our four-factor theory is still reduced to two.
The outcome is the famous ' theory of two factors ' [24],
[28]. We may express it algebraically by writing —

Put into concrete terms the two-factor theory maintains
that " all branches of intellectual activity have in common
one fundamental function " (the general factor), " whereas
the remaining or specific elements seem in every case to be
different from that of the others." l

(e) The Single-factor Theory. — Suppose, however, we
admit that the status of the specific factors is at least as
dubious as that of group-factors, then we evidently shall be
left with a single factor only. Both before and since the
advent of factor analysis, many writers have attempted to
maintain that all mental life, or at least all cognitive activity,
can in fact be interpreted by a single unifying principle.
Several commentators, for example, have contended that,

abilities ' is inappropriate (cf . [56], p. 222). With that I agree ; but, when
I first used it (in my Child Study paper of 1909), I was endeavouring to find
a terminology that would be intelligible to teachers to whom the whole
notion of mental factors was entirely new : and the same reason led me to
retain it in the Board of Education Report.

1 c Theory of Two Factors,' Psychological Review^ 1914, XXI, pp. 101-15,
Spearman, it should be noted, does not deny the 'possibility that group -
factors may exist ; he merely considers that there is little or no convincing
evidence for the empirical fact. When two (or more) tests are very similar,
he admits that * overlapping specific factors * can be recognized. We are
tempted to ask why he is unwilling to treat the overlapping part as distinct
from the specific parts, i.e. as constituting a separate group-factor by itself ;
and the reason appears to be that in his view the so-called group-factors
" indicate no particular characters in any of the abilities themselves "
([56], p. 82). Here the word * overlapping ' describes the fact that a specific
factor may overlap more than one ability or test, viz. all those that are
similar (p. 223). The overlapping of one group-factor by another group-
factor appears to be definitely excluded. On the other hand, the group-
factors revealed in my educational tests showed a definite overlapping,
usually in f cyclic ' fashion ([35], p. 59)-

I am tempted to suggest that Spearman's more extended form of his