VARIOUS USES OF FACTORS 69

position, to consider whether the concrete correlational
results (i) tend to verify, or (ii) are inconsistent with, or (iii)
are completely independent of such causal theories. And
this aspect of the problem will evidently have to be dis-
cussed in the light of metaphysical rather than of empirical
considerations.1

In support of this contention it will perhaps be sufficient to
appeal to the favourite logician of the factorist—J. S. Mill. Mill
recognized, it may be remembered, * uniformities of coexistence'
as well as c uniformities of causation,5 2 For Mill a causal uniform-
ity is not a mere empirical relation, but a necessary relation. A
cause, as distinct from a mere invariable coexistence, he defines as
" the antecedent, or concurrence of antecedents, on which a
phenomenon is invariably and unconditionally consequent "3 : such
uniformities, he seeks to show, can be proved by inductive arguments
to be both certain and universally true. But with these universal
causal certainties he explicitly contrasts what he describes as
" approximate generalizations "—conclusions which are only prob-
able, or only true (so far as we know) in some instances and not in
all. Unless they in turn depend on causation, uniformities of
coexistence are not necessary, but at most merely invariable.
Hence they cannot as such be established with certainty by inductive
arguments : for * there is no general axiom standing in the same
relation to the uniformities of coexistence as the law of causation
does to those of succession.' * Consequently, they have the status
of * approximate generalizations' only. Now it is with these
empirical * uniformities of coexistence,' not with any alleged causal
certainties, that factor-analysis, to my mind, is primarily concerned.

As the chief examples of uniformities of coexistence, Mill cites the
regular conjunction of specific attributes or properties in what he
calls c Natural Kinds': e.g. (to take one of his instances) the
coexistence of such characteristics as blackness of skin and woolli-
ness of hair in most negroes. More particularly, he asserts, when
he comes to discuss the logic of psychological inquiries, that the
apparent uniformities discerned in human nature can never be any
more than mere * approximate generalizations,' upon whose lack of
certainty he has so strongly insisted : * as a scientific proposition'
we can only assert that * bodily strength tends to make men cour-

1 See below, pp. 218 f.

* System of Logic, Bk. Ill, chap, rdi, § 2, pp. 106 et seq.

* Ibid., Bk, III, chap, v, § 5, p. 377 (Mill's italics).
' * Ibid., p. 109,