Chapters 8-9 begin Russell's account of a priori knowledge.

• He starts with Kant, naturally enough, and outlines points of agreement (¶¶ 8.1-8.5) before turning to criticisms of Kant's view (¶¶ 8.5-8.9). There is a terminological oddity about this discussion. Although Russell, like Frege, reduced arithmetic to logic, he does not regard arithmetic as analytic (as Frege had). The reason is that Russell, while he adopts Frege's approach to logic, retains Kant's characterization of the analytic, so most of the truths of Russell's logic would not count as "analytic" in the way he uses the term here. Chapter 8 concludes (¶¶ 8.10-8.14) with two further comments on what the a priori is not that point to Russell's platonist approach to this sort of 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 Although Russell's initial historical references (¶¶ 9.1-9.4) are to Plato, much of the metaphysical scheme and the terminology he uses in his summary at the end of the chapter (¶ 9.17) has its sources in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 the case of 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, 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.