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.