162 THE FACTORS OF THE MIND

factor. His interpretation of the ' law of parsimony in
scientific description' requires, not (as mine does) that each
factor in turn should account for the greatest possible
amount of the variance, but that (a) the total number of
factors entering into the whole set of traits and (£) the
number of factors entering into each single trait should
be as small as possible ([122), p. 150 /.). He therefore seeks
a factorial matrix in which every factor shall have at least
one zero coefficient for at least one of the tests : i.e. no
factor is allowed to enter into all the tests ; each can enter
into a limited group alone.

If, then, from the four-factor theory we omit the general
factor as unproven, and if we regard the specific and the
chance factors as devoid of real psychological significance,
we are left with nothing but common factors confined each
to its own particular group. Such group-factors, however,
will now of necessity be numerous, or at any rate plural,
since their overlapping has to do the work of the general
factor. The number of positive general factors is in any
single investigation necessarily only one ; the number of
specific factors would, by definition, be equal to the number
of correlated tests ; but if there is no general factor what-
ever, the number of group or partly common factors must
certainly be more than one, but should on Thurstone's
principles be certainly less than the total number of the
tests (as we have seen, it should be about two-thirds with
a small battery, or less by V2^ if n is large).1 Accordingly,
this view, which prefers to look for a plurality of group-
factors rather than for a single general factor, has come to
be known as the * multiple-factor theory.' To distinguish
it from the earlier views of those who, like myself, are
prepared to recognize two kinds of c common factor '—
a positive general factor, common to all the tests, as well as
numerous group-factors, common to some of the tests only
(or, what amounts to the same thing, two kinds of general
factor—positive and bipolar)2—it should perhaps be termed

1 See above, p. 109.

2 In earlier writings I used the phrase * multiple-factor hypothesis' to
describe this view, because the test results were expressed in terms of a
multiplicity of factors by means of a multiple regression equation. But with