THE REAL ERROR OF CYRIL BURT 339
vidual test would always record the same PMA's only in simple
structures that are "complete and overdetermined" (1947, p.
363)—in other words, only when all the vectors of mind have been
properly identified and situated. Indeed, if there really are only a
few vectors of mind, and if we can know when all have been iden-
tified, then any additional test must fall into its proper and
unchanging position within the invariant simple structure. But
there may be no such thing as an "overdetermined" simple struc-
ture, in which all possible factor axes have been discovered. Per-
haps the factor axes are not fixed in number, but subject to
unlimited increase as new tests are added. Perhaps they are truly
test-dependent, and not real underlying entities at all. The very
fact that estimates for the number of primary abilities have ranged
from Thurstone's 7 or so to Guilford's 120 or more indicates that
vectors of mind may be figments of mind.
If Spearman attacked Thurstone by supporting his beloved g,
then Burt parried by defending a subject equally close to his
heart—the identification of group factors by clusters of positive
and negative projections on bipolar axes. Thurstone had attacked
Spearman and Burt by agreeing that factors must be reified, but
disparaging the English method for doing so. He dismissed Spear-
man's g as too variable in position, and rejected Burt's bipolar fac-
tors because "negative abilities" cannot exist. Burt replied, quite
properly, that Thurstone was too unsubtle a reifier. Factors are not
material objects in the head, but principles of classification that
order reality. (Burt often argued the contrary position as well—see
p. 318-322.) Classification proceeds by logical dichotomy and
ntithesis (Burt, 1939). Negative projections do not imply that a
~rson has less than zero of a definite thing. They only record a
relative contrast between two abstract qualities of thought. More of
mething usually goes with less of another—administrative work
d scholarly productivity, for example.
As their trump card, both Spearman and Burt argued that
lurstone had not produced a cogent revision of their reality, but
nly an alternative mathematics for the same data.
We may, of course, invent methods of factorial research that will always
ield a factor-pattern showing some degree of "hierarchical" formation of
if we prefer) what is sometimes called "simple structure." But again the
ults will mean little or nothing: using the former, we could almost