METAPHYSICAL STATUS OF FACTORS 239

describing a pattern or a system of relations, without
specifying what is the nature of the terms related. To the
contemporary psychologist who believes that conscious
phenomena are best described in terms of the patterns or
Gestalten that they display, rather than in terms of atomistic
sensations held together by c laws of association,5 matrix
algebra should obviously appear the appropriate quantitative
tool.

The Ultimate Inadequacy of all Purely Quantitative
Statement.—Yet even matrix algebra has limitations which
in the end may prove an encumbrance. The introduction of
numerical quantities, though scarcely avoidable in applied
psychology, raises difficulties in pure psychology, and even
in applied psychology may lead us astray unless supple-
mented by other modes of statement. It is these difficul-
ties, as we have already seen, that excite the protests of the
intuitionist school. What schedule of measurements, they
ask, can possibly describe the mind of a Leonardo or a
Cezanne ? How can we assess their unique accomplish-
ments as the sum of so many units, or multiply this set of
achievements by that set of figures so as to obtain a true
weighted average ? Even the substitution of a matrix for
a single figure does not dispose of the objection ; for in
matrix algebra we are still condemned to cross-multiply and
add : and every form of factor-analysis hitherto employed
by psychologists has treated all operations as reducible to
summation, weighted or otherwise. Yet why should we
always proceed by addition ? Suppose for the sake of
argument that (as the factorist assumes) a child's perform-
ance at English composition can be expressed as the
* product9 of two ' factors ?—his general intelligence, say,
and his verbal ability—why not take the two terms literally,
and find the * product? of the * factors? ? Why not
multiply his performances together instead of summing
them ? To which, of course, another critic may retort,
why proceed by multiplication ? Why not square, or take
higher powers still ? Why not, in short, seek some subtler
mathematical function, more complex, and therefore more
elastic, and so capable of supplying, if necessary, different
expressions for different mental processes. ?