THE LOGICAL STATUS OF MENTAL FACTORS 119

possible members of the class, the requisite conditions may
be formulated as follows :

(i) Connexive Postulate.—If x and y both < z or both
> z, then either x < y9 y < xy or x = y.

(ii) Postulate of Asymmetry.—If x < y, then neither
y < x nor y = x.

(iii) Postulate of Transitivity.—If x < y and y < z, then

X < Z.

Here = does not necessarily mean c equals,' but merely
' may always be interchanged in the argument ' ; and <
does not necessarily mean ' is less than ' but merely stands
for any relation obeying the conditions specified (e.g. such
a relation as " precedes," " is nearer than," " more difficult
than," " preferable to," " commoner than," " happier
than," " redder than," " more beautiful than," etc.).

Having established the existence of such a relation
between all the members of our psychological class, we may
employ any convenient set of symbols to represent the series
thus constructed—the numerals or the letters of the alphabet
in their conventional order or position along a line or down
a column. All these are characterized by order as above
defined ; and we can apply them by a one-one correlation
to the members of any given class that can be c linearly
ordered/ without introducing the ' rules of arithmetic,' or
any of the ' notions of numerical magnitude' to which
intuitionists so strongly object. For example, in the Report
on Mental and. Scholastic Tests there is a scale of 10 drawings,
purporting to be arranged in an c order of merit.' A few
minutes only are needed for the experimental check; and
practically every observer will agree at once that the
arrangement fulfils each of the simple requirements enumer-
ated above. A scale so defined forms only the beginning of
a scheme of mental measurement; yet, so far as it goes, it
seems every whit as valid and as useful as Mohs' well-known
scale of < hardness' used by mineralogists (" diamond — 10,
ruby = 9, . . ., talc = I ") or Beaufort's familiar scale for
reporting the strength of winds (" calm — o, light air — i,
. . ., whole gale = 10 ").

The construction of such a scale, however, is by no means
so easy as its verification. In practice, when the psychologist