Chapters 6-8 begin a series in which Russell’s attention turns from sensation to our grasp of concepts. The first of the these chapters is devoted to the puzzles about inductive reasoning posed by Hume, and the next two concern the idea of a priori knowledge.

• Russell initial discussion of induction in chapter 6 (¶¶6.1-6.14) recalls Hume’s discussion of problem of causality. But Russell’s distinction between causes of beliefs and reasons for them (¶¶6.6-6.8) points to a criticism of Hume’s solution.

• Russell’s own solution lies in part in the principles stated in ¶¶6.15 and 6.16; think about the differences between the two and between the two parts of each. The remainder of his solution lies in what he says about the grounds for our belief in these principles; he begins to discuss that in ¶¶6.18-6.20.

• Ch. 6 concludes with an argument for the importance of our knowledge of general principles. Notice that the description “knowledge which, on a basis of experience tells us something about what is not experienced” (¶6.20) must, for Russell, apply to all our empirical knowledge of the external world.

Chapter 7 moves from the principles of induction to other examples of general principles, and Russell addresses a variety of different topics.

• Russell’s list of logical principles on ¶7.7 is a traditional list that he chooses for expository purposes. His own approach to logic was quite different. The Problems of Philosophy appeared in the midst of the publication of the Principia Mathematica, three volumes in which he (along with Alfred North Whitehead) worked out a way of founding mathematics on symbolic logic.

• Think about Russell’s views concerning the empiricist/rationalist dispute (¶¶7.10-7.12) and notice in particular his claim about knowledge of existence (¶7.12).

• The remainder of the chapter adds further examples of a priori knowledge. The most distinctive part of this discussion is Russell’s account of the utility of deduction (¶¶7.18-7.19); in ch. 10, he will return to the examples he uses here and the point he makes about them.

In chapter 8, Russell begins his discussion 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 the platonist approach Russell will take to this sort of knowledge.