There are several ideas to watch for in ch. 13.
• Think about the example Russell uses to distinguish knowledge from true belief (¶13.2). A very similar example was offered fifty years after Russell to distinguish knowledge also from true justified belief, and it influenced discussions of knowledge for the next several decades.
• Although Russell’s prime topic is intuitive knowledge, his brief remarks on derivative knowledge (¶¶13.4-13.7) also address important issues.
• Russell’s account of intuitive knowledge (¶¶13.8-13.16) returns to and completes his discussion in chapter 11, now using ideas from chapter 12. The features Russell ascribes to intuitive knowledge make it an example of a sort of view we will later see Sellars describe as the “Myth of the Given.”
• Finally, think about Russell’s definitions of knowledge and related ideas (¶¶13.17-13.18). The definition of knowledge is not original; it is nearly identical with Locke’s and the basic idea goes back to Aristotle. But it is also not obviously correct (or even in agreement with Russell’s use of the word “knowledge” earlier in the book), and most recent philosophers interested in the concept of knowledge have taken different approaches. (The simplest of these approaches held that knowledge was true belief and were subject to the sort of counterexample mentioned above.)
Russell’s discussion of the problems of philosophy so far has focused on problems directly or indirectly concerning knowledge. But the nature of philosophy is itself one of the problems of philosophy and, as Russell’s addresses it in chapters 14 and 15, he has more to say about knowledge.
You should, of course, think about the broad topic of chapter 14 (and especially the discussion of the relation between philosophy and science at the end, ¶¶14.11-14.14), but give special attention two specific points which are part of Russell’s efforts to set limits on philosophy.
• The first is his discussion of Hegelian holism and the associated conception of relations (¶¶14.2-14.5)—especially points (1) and (2) of ¶14.4.
• The second is his claim that there can be no a priori knowledge of existence (¶14.10), which he had stated in a different context earlier (in ¶7.12).
In ch. 15, it is the broad ideas that you should look to. Russell’s account of the value of philosophy is not uncontroversial and is an expression of the spirit of its era. It seems to be influenced by G. E. Moore’s ethical ideas and is in keeping with ideas about literary and artistic modernism beginning to appear in Russell’s day (in particular, the ideas associated with what is known as the “Bloomsbury group,” which was also influenced by Moore’s views).