In the spirit of argument against idealistic assumptions, Russell also tackles the common impression that whatever is "relevant to our experience must be capable of being known by us" and that "what can have no importance for us cannot be real." One immediate reason for rejecting this false impression is man's natural interest in both "practical" and "theoretical" knowledge. Everything that is real is naturally relevant to the intellect "desirous of knowing the truth about the universe." Thus there is no reason to suppose that man's interest in knowledge confines itself to the things in his experience. Whatever can be known is relevant the practice of knowing, not the converse.

By considering the statement "we cannot know anything that exists that we do not know," Russell discriminates two ordinary language senses of the word "know." The first is the sense in which we know something to be true—knowledge of truths, which concerns our judgments and beliefs. The other sense of knowing that Russell discerns from the statement is our knowledge of things, in which case we are acquainted with our sense-data.

Yet, it is possible to have another kind of knowledge—it is possible that I can know of the existence of something of which no one else has knowledge or has acquaintance. If I am acquainted with something, then I have knowledge that it exists; however, it is not the case that "whenever I know can know that a thing of a certain sort exists, I or someone else must be acquainted with the thing." It is possible rather, Russell contends, that I have a kind of knowledge by description. Here, Russell formulates a hypothesis that will occupy him for the next few chapters. He proposes, "in virtue of some general principle, the existence of a thing answering to this description can be inferred from the existence of something with which I am acquainted." In the following chapters, Russell will explain knowledge by acquaintance and knowledge by description.

The practice of analytic philosophy emerges in view of Russell's analysis of what we mean by "idea" or "know." Like modern day ordinary language philosophers, Russell focuses on the role that the words at issue play in the lives of their ordinary speakers. His analysis, especially in the case of Berkeley's idealism, escapes philosophical confusion by exposing the tendency to be misled by the grammatical form of a question or phrase. In so doing, he gains meaningful insight about the structure of the world through the structure of language.