We think of relations as holding between two terms. However, Russell points out that certain relations call for three, four or more terms. The relation "between" is only possible when three terms are present; it would not be possible if only two places existed. "Jealousy" also requires three terms. Four terms are required in the proposition "A wishes to B to promote C's marriage with D." In order to allow for falsehood, the relation involving "judging" or "believing" calls for several terms. In Othello's case, a relation between his mind and a single object, "Desdemona's love for Cassio," does not exist. What does exist is a "relation in which the mind and the various objects concerned all occur severally; that is to say, Desdemona and loving and Cassio must all be terms in the relation," a relation of four terms, including Othello.
Believing is the relation that Othello may be said to have to all the terms together, not to each individually. His actual belief knits together the four terms into one complex whole. Our belief is this knitting, which "relates a mind to several things other than itself." Before we may better understand the distinction between a true judgment and a false one, we must understand Russell's adopted terminology. The mind which judges in the act of judgment is the subject. The terms about which it judges are the objects. Othello is the subject of the above proposition while Desdemona, loving, and Cassio are the objects. All of these terms together are the constituents of the judgment. There is also a "sense" or "direction" which orders the objects, represented by the words in the sentence. This is obvious because the relation of judging in "Cassio loves Desdemona" obviously orients the terms in a different direction than "Desdemona loves Cassio."
Russell states: "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." Believing and judging are relations and, like all other relations, they share the property of having a "sense," and the action of uniting terms into a whole. Wherever there is a relation between some certain terms, it unites them into a complex object. Also, conversely, wherever there is a complex object, there exists some relation at work.
In the proposition "Othello believes that Desdemona loves Cassio," it is clear that one of the objects is the relation, "loving." In Othello's act of belief, loving is not the relation which forms the complex unity between subject and objects. Russell writes, "(loving) is a brick in the structure, not the cement." Here the relation "believing" is the cement. In a case where "the relation which was one of the objects relates the other objects," then there is another complex unity and the belief is true. If, for instance, Othello believed truly that Desdemona loves Cassio, then there is a complex object, "Desdemona's love for Cassio," which unites the individual objects of the belief in the same order as in the belief. This complex object truly corresponds to the belief.
"Thus," Russell concludes, "a belief is true when it corresponds to a certain associated complex, and false when it does not." This is the meaning of truth. Terms are put into a certain order in a belief. That belief is true if the terms in that order unite through a relation like loving which is also an object of the belief, to form a complex object. Russell restates the theory thus: "If we take such a belief as 'Othello believes that Desdemona loves Cassio', we will call Desdemona and Cassio the object- terms, and loving the object relation. If there is a complex unity 'Desdemona's love for Cassio', consisting of the object-terms related by the object-relation in the same order as they have in the belief, then this complex unity is called the fact corresponding to the belief." A belief is true when a corresponding fact exists.
The key to understanding Russell's theory of truth is to grasp the difference between two things, a belief and the belief that has a complex object that exists as a fact. When discovering a belief to be true, the relation which was just one of the objects is seen as the relation that cements all the other objects together. "Loving" becomes the apparent relation doing the work between the other objects. It is important to recognize the double role of the object- relation. It can hold between the objects and form a complex unity that also corresponds to fact, in which case the belief will be true. Or, it can merely unite the relations into a complex object that does not correspond to fact, in which case the belief will be false.