Our common view with respect to any of our beliefs is that, when challenged, we can show them to be supported by a base of reason. Russell holds that we usually infer our common beliefs from instances and then forget our process of inference. Then, when asked why it is that we believe the food we are eating to be healthy instead of poisonous, our reason at first hidden from us. Though we are often justified in our common beliefs, Russell posits an "insistent Socrates, who, whatever reason we give him, continues to demand a reason for the reason." It is probable that at some point, we would be driven beyond our grounds for reason and would finally admit some general principle as the basis for our belief. Though such principles are "luminously evident," we cannot cite a qualification for our belief in these principles.
In the case of poisonous food, and in many everyday cases, we find ourselves using the inductive principle (chapter 6) as our primary resource. The inductive principle, though frequently used in reasoning, cannot be derived from any clearer self-evident principle; it cannot be the conclusion of any proof. It is one of a set of truths that is perfectly self-evident as it expresses a demonstration but cannot be demonstrated itself. Self-evidence is an interesting feature of logical principles in that it is as apparent in derivative propositions as it is in those given. Arithmetic is deducible from logic, yet the proposition "two and two are four" is as self-evident as any logical principle.
It is easier to recognize self-evidence in particular things than in general principles. For instance, we know from the law of contradiction that a particular rose cannot be both red and not red. It is easier to understand the law through the particular rose than through an abstract statement of the law in itself. This is because we usually grasp general principles through instances. Of course, to someone practiced in dealing with abstraction, it might be easier to grasp the law itself without considering a set of instances.
In addition to general principles, another sort of self-evident truth exists, "truths of perception." We use these to make judgments about perception. Yet, one should be careful with language involving sense and truth because there is no case where a sense-data could be true or false. Russell writes, "It is not the sort of thing that is true or false." The patch of color that one sees is radically different from things that could be said to be true or false. Self- evident truths of perception are obtained from our senses; they are not identical with the sense-data. One kind of this truth "simply asserts the existence of the sense-datum, without in any way analyzing it." Another kind of truth is when an object of perception is complex and our mind subjects it to analysis. If we see a round patch of red, a sense-datum containing color and shape, our judgment separates the color from the shape and allows us to recognize a proposition like "the red color is round in shape." This judgment asserts the relations between the constituents of the sense-datum. Both these kinds of truths of perception, that which asserts existence and that which analyzes, are "intuitive judgments of perception." A distinct but related group of self-evident intuitive judgments are those that come from memory. The nature of the memory is confusing as a memory of an object is often associated with an image. Yet, we can compare our image with "the object remembered" and tell differences. The mere possibility of such comparison suggests that the object itself is somehow "before the mind" and necessary to the "essence of memory." The fact of memory permits all of our knowledge of the past.
Memory is "notoriously fallacious" and motivates a skepticism with regard to our intuitive judgments. Russell describes our certainty of memory as "trustworthy in proportion to the vividness of the experience and to its nearness in time." He believes that if lightning struck half a minute ago, then he would still be keenly aware of it in the present. It would be ridiculous to doubt things so near in time, like the fact that one is sitting in the same chair now that one was sitting half a minute ago. He admits that, reviewing his day, some things seem more certain than others. He remembers breakfast, and some of the conversation at breakfast, and cannot recall other things. Russell writes that "there is a continual gradation in the degree of self-evidence of what I remember." This gradation corresponds to how trustworthy our perception of events vivid and recent.
The problem of fallacious memory arises in cases where a memory of which we are certain is also independently certifiably false. George IV finally believed, after lying about it sufficiently often, that he was at the battle of Waterloo. In such cases, it seems clear that the object remembered is falsely believed in, and real experience is not the proper object immediately before the mind. They are "not cases of memory in the strict sense at all."
The case of memory makes it clear that there are degrees of gradation in self- evidence; it is a quality that is "more or less present." The highest degree of self-evidence belongs to truths of perception and some truths of logic. Almost comparable are truths of immediate memory. The self-evidence of memories diminishes as they grow more remote and fainter. Principles of logic and math are less (obviously) self-evident as they grow in complexity. Russell also notes that ethical and aesthetic judgments have some indeterminate amount of self- evidence. These degrees of self-evidence are significant to a theory of knowledge because it becomes unnecessary to demand absolute certainty from our propositions. Propositions may be valuable as more self-evident than others. This point suggests that the concept of self-evidence posits a double standard, one by which propositions may be guaranteed true, and the other which offers "a greater or less presumption" of truth.
The figure of the "insistent Socrates," refers to the Socratic method of questioning. Russell imagines that an interlocutor like Socrates would put question after question to his student, until the student grasped the general proposition upon which his so-called "knowledge" was based. Russell skips the steps that a Socrates might have taken and proposes his theory of general principles and their self-evidence. His theory accounts for the sense in which we believe in our "knowledge" of truths. We practice belief in these truths, like the self-evident principle of induction (examined in chapter six), when we practice the everyday habit of "believing." Russell identifies a basis for our knowledge of truths that is patently natural and intuitive.