106 THE FACTORS OF THE MIND

no subsequent ' rotating of the axes? will guarantee the
emergence ofc psychological meaning.'

(ii) With this proviso, the order as well as the pregnancy
of the several principles will be ensured, if we extract our
factors in such a way that each accounts for a maximum
amount of the variance available at each stage, and then
arrange them in order of their contributions to the
variance. The principle is perhaps most familiar from the
parlour game ofc Animal, Vegetable, or Mineral,' where an
unknown object has to be identified after a minimum of
guesses; the guesser has to proceed by dichotomous
questions—c Is it alive or dead ?' c plant or animal ?? . . .
—and the expert so chooses his alternatives, that at each
successive step he eliminates the largest number of erroneous
possibilities. In serious scientific attempts at classification
or diagnosis, precisely the same procedure—the principle of
c progressive delimitation,' as I have called it ([53], p. 81)
—is more or less explicitly adopted,

(iii) The completeness of the list will be guaranteed if
the items selected for analysis consist either of the complete
population of items with which we are concerned (impos-
sible when the items are traits and hardly practicable when
tluey are persons), or else a random, i.e. an unbiased and
representative sample of that population, and if we then
extract, for n correlated traits, n uncorrelated factors (if our
data are free from error), or (if errors are inevitable) as many
factors as the margin of error permits.

The factorization of a number of traits into the same number of
factors has frequently been criticized. Thurstone lays down the
* postulate' that " the number of reference abilities in a test-
battery must be less than the number of tests," and regards any
other mode of factorization as uneconomical and useless.1 The

1 [84], p. 75. He argues that " the solution in which r — n violates the
fundamental postulate of science that every valid hypothesis should be over-
determined by the data. The only allowable case is that in which r <n"
To secure this he requires that r, the number of common factors, shall be
identical with the minimal rank of R, the correlation matrix.

Actually the total number of factors in Thurstone's initial * factorial
matrix' is not less than the number of tests, but more, since he, like Spear-
man, begins by assuming that each test will have its own * specific factor9 in
addition to the r common factors (p. 59), I agree that in practice specific