136	THE  FACTORS OF THE  MIND
classification ; and your classifications are based, not on one
type of performance, but on many, not on a single observa-
tion, but on a system. How then is it possible to add and
subtract a set of complex systems f " In replying, I must
anticipate the sequel. Briefly, I shall maintain that any
such system can be adequately represented by a matrix of
figures ; and it is then a simple matter to show that the
matrices employed fit the necessary postulates. From this
standpoint, the very object of factor-analysis is to deduce
from an empirical set of test measurements a single
figure for each single individual which will plant him on a
linear scale for one of a number of independent classifying
principles, although each principle of classification embodies
a highly complex system.
The remaining objections urged against factorial measure-
ment turn for the most part on the dubious assumption—
commonly accepted by the psychometrist himself—that the
factor measurement he deduces is a measurement of some
isolated entity—an * ability,' an ^c instinct,' a ^c sensation,' a
' capacity for sensory discrimination,' or the like. With
perfect justice it is urged that no one has succeeded in
demonstrating that these ulterior psychological entities
conform to the postulates of addition ; " we cannot pile
up the intelligences of 50 imbeciles to make the intelligence
of a single Shakespeare." But to show that literal summa-
tion is impossible no more refutes psychometry than it
refutes thermometry. Such contentions are like assuming
that the thermometer is designed to measure an entity called
temperature, and then arguing that, since two temperatures
cannot be superposed to make a third, the measurement of
temperature is a sheer delusion.
No doubt, the psychologist's conclusions would be of
greater value to the teacher and the psychotherapist if he
could phrase his results in terms of constant properties—
permanent abilities, permanent predispositions, permanent
subjective attitudes, and so on. Ultimately, indeed, our
theories may lead us to envisage certain derived concepts,
stable and enduring, obedient to some law of conservation.
True, we cannot pretend to guess what operations such
concepts can legitimately be supposed to admit* But