With respect to knowledge of things, our immediate acquaintance can never be "wrong" or mistaken. Yet, in the pursuit of knowledge by description, wrong inferences are, of course, possible. When Russell begins discussing knowledge of truths, it becomes clear that this type of knowledge, as opposed to knowledge of things, has a problematic opposite called error. There exists a dualism; we believe things falsely as well as truly. Since many people hold different and incompatible beliefs, some of them must be erroneous. The urgent question on this issue is how to distinguish truly held beliefs from those falsely held. Russell claims that no satisfactory answer is possible, but before approaching possible answers at all, there must first be an investigation into the meaning of the concepts of truth and falsehood. He stresses that this chapter is only concerned with "what is meant by the question (of) whether a belief is true or false," not with identifying which beliefs are true or false.
Russell lists three requisite features for a theory of truth:
1) The theory must take its opposite, falsehood, into account. 2) Since it is evident that if there were no beliefs there could be no truth or falsehood, then in a world of mere matter, which contained only fact and not belief, truth and falsehood would be impossible. Thus it seems clear that "truth and falsehood are properties of beliefs and statements." 3) "Truth or falsehood of a belief always depends upon something which lies outside the belief itself." Believing that Charles I died on the scaffold is a true belief because it is based on an actual event, not owing to anything intrinsic to the thought. Believing that he died in bed would be a false belief as it contradicts fact. Truth and falsehood are properties dependent on the relation of the belief to something not contained in the belief.
The third of these is the least self-evident and leads to the view, common among other philosophical systems, "that truth consists in some form of correspondence between belief and fact." Since an absolute form of such a correspondence with an outside factor has been hard to discern, some philosophers have rejected the correspondence criterion in favor of the theory that "truth consists in coherence."
Russell explains two objections to this latter theory. The first asserts that there is no good reason to suppose that one coherent set of beliefs is all that exists. There could be more than one. This is made clear by scientific and philosophic methodology in which more than one hypothesis fits the given facts. Although, scientists and philosophers seek one ultimate hypothesis, there is no reason that more than one should not apply. The second objection to coherence theory is that it "assumes the meaning of "coherence" known," when really "coherence presupposes the truth of the laws of logic." In order to use the coherence test at all, to see if two propositions are coherent, then the law of contradiction must be in place. For example: "this tree is a beech" is incoherent with "this tree is not a beech." It is clear that logical principles provide the framework for the test of coherence and "they themselves cannot be established by this test." Thus, though sometimes an important test of truth, coherence does not in itself give the meaning of truth.
Returning to the notion of "correspondence with fact" as a criterion for the theory of truth, and keeping the three requisite features in mind, Russell analyzes the meaning of "fact" and "correspondence." He posits, for the sake of argument, that it might be possible to regard correspondence "as a relation of the mind to a single object." But, like knowledge by acquaintance, this picture does not admit the truth/falsehood opposition; the belief would always be true. We know that Othello holds the false belief that Desdemona loves Cassio. The object of Othello's belief in this case is "Desdemona's love for Cassio." Since no such object does in fact exist (because she does not love Cassio), then Othello cannot have a relation to that object (unless one allows for objective falsehoods, which Russell does not). Yet, Othello does have a relation to something and we may still say that his belief does not consist in a relation to one object. Russell next seeks a theory that "does not make (belief) exist in the mind's relation to a single object."
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.
Here, Russell has established a structured basis for our reasoning, a criterion distinguishing truth from falsehood. It takes the form of a complex,grammatical form against which we can measure our beliefs. Thus, Russell's criterion for truth is essentially a correspondence between belief and fact. His next chapter will undertake the separate question as to which of our beliefs are true or false.