DERIVATION OF CHIEF THEORIES 161

hypothesis in its baldest form is adequate to cover all the
facts, if, indeed, he ever meant to do so. The logical
implications of the theory, which are unexpectedly sug-
gestive, I shall take up later on.

(g) The Multiple-factor Theory.—When we pass from
abstract mathematical deductions to concrete psycho-
logical demonstrations, it is evident that neither Thomson
nor Thurstone would admit that the * universal presence
of the hierarchy' had been empirically established. As an
explanation of the facts, therefore, they would neither of
them accept a reduction of the two-factor theory to a single-
factor theory : they would rather drop the general factor,
and reinstate the group-factors. Thomson, it is true, is not
prepared to deny all possibility of a general intellectual
factor ; but he regards such a factor as unproven and super-
fluous. To explain the appearance of group-factors, he
modifies the sampling theory so as to admit the existence of
c sub-pools' within the ' total pool' of elementary com-
ponents ([132], p. 283) ; and, once group-factors are
admitted, then, he urges, a general factor is no longer
necessary, for it is possible to c produce a hierarchical order '
(or at any rate a very close approximation to it)4 by random
overlap of group-factors, without any general factor
whatever ' ([39], pp. 175, 189).

Thurstone, in his more recent work ([122], p. vii), declares
that " so far we have not found any conclusive evidence
for a general common factor in Spearman's sense " ; yet he,
too, seems to concede it as a bare possibility. Actually,
however, his method of analysis virtually precludes any such

latter looks upon g as being part of the test, while the former looks upon the
test as being part of g." May I rephrase this as follows ? If we take a set
of tests (or rather a set of processes tested by cognitive tests) and consider
them in extension, we shall say that each of these processes is included in a
wider class which is defined as being cognitive : i.e. the special test-processes
are included in the same general class, labelled g. If we consider the same
processes in intension, we shall say that the concept of any particular cognitive
process is a complex concept, which contains as its generic constituent the
notion of being cognitive, i.e. the generic quality of g is included in the
specialized concept of each tested process. Thus the two theories really make
the same statement, for, if the sub-class is part of the class, the class-concept
must be part of the sub-class-concept,

II