156	THE  FACTORS OF THE MIND
£ specific factor ' could be identified with some ' specific
ability/ it could obviously appear in more than one test of
that ability,1 and so would really cease to be a strictly
' specific factor ? : it thus becomes, potentially at any rate,
a c group-factor '—i.e. a factor common to a group of two
or more tests.
This view is confirmed by the low degree of stability that the
alleged specific factors show from one investigation to another.
The simplest test for stability is the symmetry of the product matrix
obtained by multiplying the correlation or covariance matrices
deduced from the successive sets of measurements. For this
purpose the principal diagonals should contain the complete com-
munalities—i.e. the sums of the squares of the saturation coefficients
for all the common factors, but for common factors only. If the
1 The case is perhaps a little different in dealing with correlations between
persons: to the logician, the * specific factor' for each person then becomes
almost an attempt to state his frincipium individualonis. But in that case
the * specific factor' can no longer be regarded as on the same footing as the
rest. The relation of an individual to his class and the relation of a sub-
ordinate class to a supraordinate (e.g. of species to genus), though treated as
identical from Aristotle to Frege and Peano, are now recognized as relations
of entirely different types; and to treat the c specific ' or individual factor
(which depends on the first relation) as a * factor' in the same sense as the
group and general factors (which depend on the second) is to commit the old
logical mistake.
So far as concerns factors for traits, it would be far better if the terms
* general' and * specific ' always referred to generality or specificity in the one
particular set of tests or traits under examination at the moment: i.e. the
word * general * should mean ' common to all these tests or traits' (not to all
conceivable tests or traits as seems at one time to have been maintained);
similarly, the word * specific ' should mean * peculiar to one of the tests as
used in this set'; (in that case, there would be no temptation to use the
phrase * specific ability '). Since, however, the looser usage has become so
well established, it might be well to adopt other terms to convey the narrower
meaning: elsewhere (e.g. [93]) I have proposed the terms of traditional
logic— * universal' (i.e. covering the universe of traits under examination
at the moment) and e singular * (i.e. peculiar to the measurement of this
single trait in this one set of data). It is, after all, solely with the latter
distinction that factor-analysis is concerned in any particular instance,
Only when the characteristics thus revealed have proved stable from one
battery to another can we pass to the broader usage ; and hitherto this transi-
tion has seldom been explicitly proved, but rather slurred over by the
ambiguous use of identical terms.