METAPHYSICAL STATUS OF FACTORS 213

sum up the position by declaring that " the object of factor-
analysis is to discover the mental faculties." 1

Let us then proceed to inquire in what sense the factors
disclosed by such analysis can claim both reality and causal
efficacy.

(i) The Reality of Factors.—In spite of the apparent
unanimity which the foregoing descriptions reveal, perhaps
indeed because of it, more than one voice in recent discus-
sions has warned the factorist against the temptation to

* reify and deify his factors.' With such a caution, I am in
close sympathy. Yet, being addressed exclusively to the
psychologist, it may seem to deny to his working concepts a
validity allowed to those of other sciences. Thomson, for
example, writes : " My contention is that no degree of real
existence need attach to statistical entities like g ... I do
not think that g has any more real existence than a standard
deviation ; I do not believe that it is mental energy or any
of the other things it has been guessed to be." He points
out, rightly enough, that, if a mathematician claims to have
proved " the existence of a g which is real," he merely means
that g ' exists ' as a solution to a certain algebraic equation,
and that it is ' real ' inasmuch as it does not contain the
factor V — I ; on the other hand, the "ordinary non-
mathematical reader interprets this phraseology as meaning
that . . . he, like everybody else, possesses a g, just as he
possesses a liver." z

1 [84], p. 53. Again at the very outset of his first chapter he proposes to
postulate " abilities and their absence as primary causes of individual
differences," and adds : " this implies that individuals will be described in
terms of a limited number of faculties " (lac. cit^ pp. 45-6). Spearman, on
the other hand, explicitly insists that factors must not be identified with

* faculties ' or even with c abilities ' ([56], pp. 40, 222 et al.).

2 [87], pp. 64, 84, 90. The mathematical theory of quantum physics
would take a different criterion for existence. " The structural concept of
existence is represented by an idempotent symbol" (Eddington, The
Philosophy of Physical Science, p. 162 ; cf. id.9 The Relativity Theory of Protons
and Electrons, chap. xvi). In factorial work it can be shown that the selective
operator representing a pure and independent factor is an idempotent symbol
([113], p. 160; cf. p. 264 below): and it is suggestive to recall that the
equation of idempotency (E2 = E) appears as a fundamental postulate at the
outset of Boole's Laws of Thought. But, of course, the idempotency of a