THE LOGICAL STATUS OF MENTAL FACTORS 129

of addition itself must be physical, as those who are pre
occupied with physical measurement are prone to suppose.1

The general procedure may be illustrated by a tentative study
carried out at my suggestion by W. E. Craven on the measurability
of children's handwriting.2 A specimen script was obtained from

1 If a draughtsman wants to determine whether one side of an oblong
is twice the length of the other, he may find it easier to manipulate the paper,
by folding or the like, so as to get one length exactly beneath the other.
Similarly, in comparing e distances' between two pairs of pictures, the person
judging usually likes to bring the two pairs side by side. But neither action
makes the comparison itself a physical operation.

It is, only fair to observe that the view I am criticizing is by no means
confined to physicists. Thus Conrad and Nagel (Introduction to Logic,
1934, p. 297) explicitly declare that, unless we can demonstrate a " -physical
operation of addition " (their italics) corresponding to the process of arith-
metical addition, we cannot treat the measurements obtained as additive.
" It is nonsense," they maintain, " to say that one person has twice the intelli-
gence of another, because no operation has been found for adding intelli-
gence " : any such statement would be " strictly without meaning." " When
we assert that one man has an I.Q. of 150 and another one of 75, all we can
mean is that in a specific scale of performance . . . one man stands e higher '
than the other " (pp. 294, 298).

Now, if it could be shown that performance in the intelligence tests could
be ascribed to the same general factor at every age, and that the curve of
growth in that factor was linear, then I should reply that it was by no means
'* without meaning " to say that a normal child with a mental age of lo had
twice as much £ intelligence ' as one with a mental age of 5. More generally,
it would seem quite permissible to say that one person had twice the capacity
for mental work as another. However, with this mode of multiplication the
correlationist is not concerned. On an I.Q. scale the true zero is not an
I.Q. of zero, as the criticism cited presupposes, but an I.Q. of 100. The
correlationist when he multiplies (for weighting and the like) works always
with differences or with ' deviations,' as he calls them, not with absolute
figures. The form of statement whose validity he has to vindicate is not
2 X 75= 150, but 2 X (125 — 100) = (150 — loo). Whether lie starts
by calculating correlations or covariances, his initial measurements are first
expressed in a 6 distensive ' form : he takes, not the figures that specify the
observed positions, but the distances or intervals between them.

2 The general procedure was based upon a rough set of experiments
attempted by Miss Felling and myself when endeavouring to select a series
of pictures for testing pictorial preferences. Our object was to test the
postulates of addition and linearity, not for a sample of the entire ' field,'
but only for specimens selected to form a would-be linear scale. We found
that with widely spaced scales (like the age-scales in the L,C.C. Re-port) the
postulates were adequately satisfied ; but, for testing preferences, the coarser