• Section I is primarily an introduction but is does touch on some ideas that will be at least in the background throughout the paper. Williamson will define “factive” in §V; until then, you can take it to capture the idea that the object of knowing-that (or seeing-that, etc.) must be a fact. You have seen “internalism” and “externalism” distinguished with regard to justification, and I’ve noted that the same distinction can be applied to views on the question whether meanings are “in the head.” The sense in which Williamson uses the terms is related: interalism is the view that mental content must be “narrow” in the sense of being limited to what is “in the head” while externalism allows content that is “wide” in the sense of including features of the external environment that people may not be aware of.

• According to Williamson, §II is designed to introduce the idea of knowing being a mental state, with the next two sections developing it further. In each case, he addresses arguments against his view. In §II these are based on what he calls “Transparency,” in §III on various assumptions about the analyzability of knowledge, and in §IV on internalism.

• Section V is Williamson’s presentation of his own account of knowledge, which he does not regard as an analysis. He states it in summary on p. 556. The concluding §VI then discusses what this account implies for the relation between knowledge and belief.