THE LOGICAL STATUS OF MENTAL FACTORS 131

intervals is, for the majority of the observers (84 per cent.), unique,
e.g. the result of adding (8 — 7) or (8' — 7') to (7 — 6) yields an
interval that appears the same, i.e. (8 — 6) = (8' — 6).

(ii) Law of Equality (Addition of Equals yields Equals). —
Assuming that all just perceptible intervals are equal, we have
(IPO — 10-9) = (10-9 ~io-8) and (10-9 — 10-8) = (10-8 — 10-7).
Then on adding the two sides of the two equations we should have
(n-o — 10-8) = (10-9 — 10-7). As a corollary (n-o — 10-0) =
(lo-o — 9-0), (ii-o — 9-0) = (8-0 — 6-0), etc. On an average, 76
per cent, of the observers agreed with these statements ; but with
more than two-year intervals, the percentage of those agreeing
diminished appreciably.

(iii) Monotonic Postulate (Law of Increase). — Starting with any
pair of equal intervals, e.g. (10 — 9) = (7 — 6) and adding (say)
(ii — 10) > o to the first, the majority of observers (82 per cent.)
agreed that (ii — 9) > (7 — 6).

(iv) Commutative Law. — Assuming, according to the definition
given above, that (8 — 7) + (7 — 6) = (8 — 6), 92 per cent, agreed
that (7 — 6) + (8 — 7) = (8 — 6) ; i.e. the order of addition makes
little difference. With some, however, a slight constant error was
noticeable.

(v) Associative Law. — Nearly all (98 per cent.) agree that

In all such inquiries, the approximate verification of the
simple, formal postulates proves to be the least interesting
outcome. It is clear that the postulates are not wholly
inapplicable ; but the margin of error is very much larger
than that obtaining in fields where they have been accepted
almost without question. What is far more suggestive,
however, are the cases where the postulates do not apply
— particularly the introspections of the subjects and
their discussion of the investigator's injunctions, when
decision on the postulates is difficult. Flagrant inconsis-
tencies1 not infrequently occur. But instead of forming

1 The most striking are the following, (i) It is easy to find a series of
scripts in which the consecutive members are indistinguishable according to
our statistical standard, while the end-members are perceptibly different.
This is like the old paradox relating to * infinitesimals.' An c infinitesimal.5
magnitude was equated to zero ; yet a finite sum of such * infinitesimals '
was held to yield a finite magnitude. With ' fundamental measurements '
the most familiar illustration is the schoolboy's game of watching the
minute-hand of a clock, which seems to be still in the same position after an