Chapters 9-10 provide Russell’s own account of a priori knowledge.

Chapter 9 combines an account of the nature of universals with arguments for their reality. Although Russell’s initial historical references (¶¶9.1-9.4) are to Plato, much of the metaphysical scheme and the terminology he uses in his summary at the end of the chapter (¶9.17) has its sources in medieval discussions of the “problem of universals.” Russell is also not far here from Locke, and he replies to criticisms of “abstract ideas” that were directed at Locke’s view (¶¶9.11-9.12). The importance Russell places on relations (¶¶9.9-9.15) partly reflects the innovations of Frege’s logic (whose advance over Aristotle’s centered on its ability to capture the logical properties of relations) and the criticisms offered by Russell (and G. E. Moore) of the British Idealists. The latter were followers of Hegel who formed the dominant philosophical movement in Britain at the end of the 19^th century; F. H. Bradley (1846-1924), who Russell mentions in ¶9.10, was the most important of the group.

Chapter 10 completes Russell’s account of the a priori. The heart of the chapter is his solution to the problem it poses (¶10.7), but he leads up to that by completing his account of knowledge by acquaintance (¶¶10.2-10.6) and follows it with a series of points about the relation of this knowledge to experience (¶¶10.8-10.14), each of which is interesting and potentially controversial. The chapter concludes (¶¶10.15-10.16) with a general account of his scheme of knowledge. Here he summarizes things he has said and points towards topics in the following chapters.