difference between
nominative and accusative.) Othello's judgement that Cassio loves
Desdemona differs from his judgement that Desdemona loves Cassio, in
spite of the fact that it consists of the same constituents, because the
relation of judging places the constituents in a different order in the
two cases. Similarly, if Cassio judges that Desdemona loves Othello,
the constituents of the judgement are still the same, but their order is
different. This property of having a 'sense' or 'direction' is one which
the relation of judging shares with all other relations. The 'sense'
of relations is the ultimate source of order and series and a host of
mathematical concepts; but we need not concern ourselves further with
this aspect.

We spoke of the relation called 'judging' or 'believing' as knitting
together into one complex whole the subject and the objects. In this
respect, judging is exactly like every other relation. Whenever a
relation holds between two or more terms, it unites the terms into a
complex whole. If Othello loves Desdemona, there is such a complex whole
as 'Othello's love for Desdemona'. The terms united by the relation may
be themselves complex, or may be simple, but the whole which results
from their being united must be complex. Wherever there is a relation
which relates certain terms, there is a complex object formed of the
union of those terms; and conversely, wherever there is a complex
object, there is a relation which relates its constituents. When an act
of believing occurs, there is a complex, in which 'believing' is the
uniting relation, and subject and objects are arranged in a certain
order by the 'sense' of the relation of believing. Among the objects,
as we saw in considering 'Othello believes that Desdemona loves Cassio',
one must be a relation--in this instance, the relation 'loving'. But
this relation, as it occurs in the act of believing, is not the relation
which creates the unity of the complex whole consisting of the subject
and the objects. The relation 'loving', as it occurs in the act of
believing, is one of the objects--it is a brick in the structure, not
the cement. The cement is the relation 'believing'. When the belief is
_true_, there is another complex unity, in which the relation which was
one of the objects of the belief relates the other objects. Thus, e.g.,
if Othello believes _truly_ that Desdemona loves Cassio, then there is
a complex unity, 'Desdemona's love for Cassio'