THE LOGICAL STATUS OF MENTAL FACTORS 137

ignorance in this respect alone would not deprive them of
their usefulness : for we might be able to establish that,
though the operations themselves are unknown, they never-
theless form a ' group ? ; and thence an analysis on the lines
of group theory would still be attainable. Three kindred
points may be noted which seem to be overlooked by most
critics. The critics insist, as we have seen, that " no one can
safely assign a figure to a mental quality or a mental product."
In reply it may be said : (i) the requisite process of addition
may be defined without introducing the notion ofc figures' ;
(2) most of the demonstrations on which factor-analysis is
based hold good if the law of combination is not addition
at all; (3) many of them hold good even when the elements
of the matrix are not figures.

However, so long as our efforts at mental measurement
remain at an inchoate and tentative stage, it wj.ll be wiser
to avoid referring the resulting estimates to remote and
hypothetical entities, whose mode of interaction is beyond
conjecture. Let us keep to the empirical figures and their
weighted combinations. Book-keepers and accountants do
not wait till the theorists have formally demonstrated that
exchange values obey the postulates of addition, and that
costs and prices are valid modes of measurement; nor,
when the householder receives an invoice from his grocer,
does he argue that the pleasures of cheese and chocolate are
commensurable neither with each other nor yet with a
magnum of champagne, and that consequently the addition
exhibited on his bill contains * a fundamental flaw/

I am therefore far from supposing that factor-measure-
ments by themselves can yield an adequate picture of the
c living personality' that stands behind the measurable
performances. For such a reconstruction a factor-measure-
ment is about as helpful as the barring and metronome-
figures are in indicating the changing rhythm of a symphony.
A complete set of factor-measurements for a sample popula-
tion, with no comments and no case-histories, would be as
informative as the bare notes on an orchestral score with
no marks of expression and no concert-goer's notes. To
translate a musical experience into black dots on a number of
parallel staves is indeed to c disrupt a living whole into little