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."