In this chapter, Russell continues his discussion of knowledge of truths. He has just established a criterion for what we mean by truth and now turns to the more interesting question concerning how we can know what is true from what is false. Since it is plain that some of our beliefs are erroneous, it becomes difficult to regard any unexamined belief with certainty. What we must ask ourselves now is: "can we ever know anything at all"? So, Russell sets out first to define "knowing" and "knowledge."
He begins by positing "true belief" as a definition for knowledge. Although it sometimes happens that we believe something that happens to be true, we engage the word "know" in everyday language in a way that prohibits us from saying matter-of-factly that we have knowledge of this belief. In one instance a man might claim that he knows that the last Prime Minister's last name started with 'B'. He might believe correctly since the last prime minister (in Russell's 1912 example) was Sir Henry Campbell Bannerman. However, if this particular man holds his belief because he believes the minister's name was Mr. Balfour, then his belief could not be granted as proper knowledge. Russell states "a true belief is not knowledge when it is deduced from a false belief." Analogously, a true belief does not constitute knowledge when one deduces it by a "fallacious process of reasoning." The premises "All Greeks are men; Socrates was a man" are true. The inferred conclusion that "Socrates was a Greek" is true in itself but does not follow from the premises. Thus, this process of inference cannot be said to lead to knowledge.
The remaining alternative seems to be that "nothing is knowledge except what is validly deduced from true premises." Russell cannot accept this because it is not enough that premises are true; they must be known as well. However, if we change the alternative from "true premises" to "known premises," the definition becomes circular, assuming one has knowledge before the act of deducing knowledge. Russell allows that this definition at best defines "derivative knowledge," that which is "validly deduced from premisses known intuitively." Russell briefly postpones his discussion of intuitive knowledge to consider this definition.
One objection to the definition is that "it unduly limits knowledge." Russell claims that it frequently comes about that a person will hold a true belief, not because she has validly inferred it, but because she has been familiar with some piece of intuitive knowledge. Consider the beliefs created in the act of reading. If the newspapers announce that a king has died, then upon reading it our belief is justified, as the papers are usually correct when making such statements. However, our belief is based on knowledge that a sense-data exists, that of print which delivers news. Comprehension of meaning occurs, but not realization from direct experience. Although the reader could theoretically draw an inference from printed letters to meanings, she does not perform that act; she reads and associates an act of inference. Still, we would say that she "know(s) that the newspaper announces the King's death." Therefore, Russell admits derivative knowledge to be "the result of intuitive knowledge even if by mere association." Logical processes of reasoning are not required for such knowledge though there must be such a connection possible. Reading print is just one example of a "psychological inference," a process by which we often pass from one belief to another.
At this point Russell declares that the major difficulty that arises with respect to knowledge does not involve the derivative kind, rather the intuitive. One may use intuitive knowledge to test the derivative, but there is no known criterion for testing the intuitive. Russell maintains that "all our knowledge of truths (are) infected with some degree of doubt." However, the earlier established notion of self-evidence does something to diminish this difficulty.
The possibility for self-evidence in our truths contains a sense in which a truth may be judged infallible. "When a belief is true," Russell reminds from the previous chapter, "there is a corresponding fact, in which the several objects of the belief form a single complex." The belief then constitutes "knowledge of this fact." Besides knowledge from corresponding fact, we may also entertain knowledge of facts "constituted by perception." This method, by way of knowledge of things, allows for a case where one looks west, sees the setting sun, and knows a fact that the sun is setting. The same fact, that the sun is setting, can be known by way of knowledge of truths, a belief corresponding to fact. If the hour of sunset is known, then wherever one is at that hour, one can know that the sun is setting. There are thus two theoretical ways in which the same complex fact can be known, by acquaintance or by judgment.
Knowledge by acquaintance with perception is only possible "when there really is such a fact," when the parts of a complex whole really are present in the appropriate relation to form the whole. By comparison, the knowledge of truths by judgment only demands the "reality of the parts and the relation: the relation may not relate those parts in that way, and yet the judgment may (erroneously) occur."
The double-standard of self-evidence, discussed in chapter 11, suggested two kinds of evidence, one which gave "an absolute guarantee of truth," the other truth in degrees. Russell further distinguishes the two. The first absolute sense occurs when we "have acquaintance with the fact which corresponds to the truth," knowledge of a truth of perception. The fact involved in "Othello believes that Desdemona loves Cassio" is "Desdemona's love," a fact with which only Desdemona could have direct acquaintance. Thus, she is the only one who could regard this truth (if it were true) as self-evident. This is an example of a mental fact; the same privacy holds for facts known through sense-data. Each fact about particular sense-data can only be self-evident in this absolute sense to one person. (It is important to note that although our knowledge of the truth of a complex fact can be absolutely self-evident, we do not have the guarantee that a certain judgment concerning that fact is true. For we analyze the complex fact in passing from perception to judgment. "We have to separate out 'the sun' and 'shining' as constituents of the fact." We might make a judgment that does not correspond to fact.)
The second sense of self-evidence accompanies judgments not based in perception. This kind has degrees, from a high degree of certainty to "a bare inclination in favor of the belief." Consider cases of gradation, not in the sense-data themselves, but in the self-evidence of our judgments based on them. When a horse trots away from us, our certainty of hearing the rap of hooves is first clear, then "there comes a moment when we think perhaps it was imagination then we think we no longer hear anything, and at last we know we no longer hear anything." Russell offers other illustrations of degree-valued phenomena, resolving that we can trust the higher degrees more than the lower ones.
In our deductions from derivative knowledge, the premises must have some clear degree of self-evidence and this degree must be present at each stage of reasoning. As with derivative knowledge, intuitive knowledge is reliable in a proportion to its degree of certainty. Sense-data and truths of logic and arithmetic may be taken as examples of the high certainty end of the gradation, while judgments "only just more probable than their opposites" exemplify the other end.
When we firmly believe in something intuitive or something inferred from the intuitive, and it is true, then we have knowledge. When we firmly believe in the above and it is false, we are in error. And when we believe something "that is neither knowledge or error" hesitatingly because it has a lower degree of self- evidence, then what we believe "may be called probable opinion." Most of what would pass for knowledge, before Russell's enquiry, ends up being describable as probable opinion. The test of coherence (which failed as a definition of truth) is useful with respect to probable opinions in that a body of coherent opinions are more probable than one probable opinion in isolation. Some scientific hypotheses acquire recognition in this way. Russell notably cites the distinction between waking life and dreaming; "if our dreams, night after night, were as coherent one with another as our days, we should hardly know whether to believe the dreams or the waking life." But the test of coherence "condemns the dreams and confirms the waking life."
The content of this chapter, concerning derivative and intuitive knowledge of truths, is the height of Russell's technical outline of knowledge. It contains an echo of the Platonic dialogue "Protagoras," which also asks the question: How can we know anything at all? Russell's answer may be abridged as follows: Derivative knowledge is knowledge from known premises where the known premises are known intuitively. Psychological inference is an unclearly developed middle factor that partially explains our capacity for derivative knowledge. The only qualification for intuitive knowledge is a degree of self-evidence. We have highly self-evident intuitions from our knowledge of perception, our acquaintances with sense-data (fact). As we saw in the previous chapter, belief corresponding to fact is an ideal criterion for truth. We can make judgments, without being acquainted with fact, which may be true and leave room for error. These judgments are removed from our direct perception and may have a low degree of self-evidence. Probable opinion is the last category of self-evident truths, which have the lowest degree of self-evidence.