THE LOGICAL STATUS OF MENTAL FACTORS 125

Distensive Magnitude.—The dilemma can be solved by
recognizing a mode of measurement which is not extensive,
but is yet additive. Relations themselves may have mag-
nitude. Thus, as Russell points out, " the difference or
resemblance of two colours is a relation, and is a magnitude;
for it is greater or less than other differences or resem-
blances." l We are thus led to the concept of what has been
called ' distensive magnitude.5 " By distensive magnitude
is meant degree of difference, more particularly between
distinguishable qualities ranged under the same deter-
minable." 2

Thus the difference, interval, or ' distance ' between the first and
last in our scale of children's drawings is plainly far greater than that
between the first and the second. We can symbolize the difference
by writing (10 — i) > (2 — i). And, if the initial items can be
arranged to form a transitive asymmetrical series, then differences
between them can also be arranged to form such a series : e.g.
(10 — i) > (9 — i) > . . . > (2 — i) > (i — i). Here > now
means ' perceptibly greater than ' ; and we are thus dealing directly
with magnitude in the literal sense. In theory, we should be able
to proceed step by step from these differences to differences of
higher orders, until at last we reach equal differences, whose differ-
ences in their turn would vanish. In practice such a proceeding is
scarcely feasible ; and a more reasonable plan is to begin with
differences that are barely perceptible, and, as it were, work back-
wards.

It will be observed that zero for a distensive magnitude indicates
equality, e.g. (10 — 10) = o, whereas zero for an intensive magni-
tude (with which it is currently confused) indicates non-existence.
This distinction will save many common fallacies. To distinguish
distensive from extensive magnitude is still more important. The
interval between the notes C and E is not formed by literally adding
more notes to the interval between C and D ; and the interval of
* a third' is not really measured by the three notes that it com-
prises, but by the two whole tones (a tone being not a note, but an

1 Principles of Mathematics, p. 171. This view is at least as old as Leibniz.
" As for the objection that, although space and time are quantities, order
and position are not, I answer : order also has its quantity. Relative things
have their quantity as well as absolute tilings. There is distance or interval."
(Philosoph. Werke, VII, p. 404).

2 Johnson, loc. cit.y p. 169.