Here, Russell analyzes the kinds of claims that many philosophers "profess to be able to prove, by a priori metaphysical reasoning, such things as the fundamental dogmas of religion, the essential rationality of the universe, the illusoriness of matter, the unreality of all evil, and so on." Russell holds that such attempts at reasoning are in vain, that metaphysics cannot obtain knowledge about the universe as a whole. He devotes this chapter to examining such hypothetical views and reasoning about the limits to understanding that confront philosophy.

The thought of German philosopher Friedrich Hegel (1770–1831) is the major modern representative of these remarkable metaphysics. Russell's interpretation is that Hegel's "main thesis is that everything short of the Whole is obviously fragmentary, and obviously incapable of existing without the complement supplied by the rest of the world." The philosopher, according to Hegel, takes one piece of reality and reconstructs the whole from it. Each piece has "hooks which grapple it to the next piece; the next piece in turn has fresh hooks." It is thus that the Whole can be generated from a piece. The idea of an essential incompleteness emerges, in the world of thought and of things.

In the world of thought, one abstract, incomplete thought soon loses its essential incompleteness and becomes embroiled in contradictions, which turn the idea into its antithesis, or opposite. In order to escape contradictions, we find a new, "less incomplete idea, which is the synthesis of our original idea and its opposite." The new synthesis, still incomplete, develops contradictions and regenerates the cycle. Hegel progresses on this picture, finally reaching the "Absolute Idea," which is totally complete as a description of "Absolute Reality." This whole reality is timeless and not in space, "not in any degree evil," and "wholly rational." Our beliefs to the contrary are owing to our fragmentary view of the Whole. Hegel believes in the possibility of a God's-eye view of "an eternal perfect unchanging spiritual unity."

While Russell admires the sublime aspect of the picture, he finds that the arguments underpinning it are confused and participant in indefensible assumptions. He claims that the foundation of Hegel's thought is the belief that "what is incomplete" needs the support of "other things before it can exist." It is implied that a thing that is related to other things must contain some "reference" to those other things inside "its own nature" in order to be what it is. If the objects of his likes and dislikes constitute a man's nature, then he could not exist as he does without their mutual existence. Taken by himself, as a fragment in Hegel's sense, he "would be self-contradictory." Russell exposes that Hegel's view depends on the definition of "nature" as "all the truths about a thing." On this view, we cannot know the nature of something unless we know all of its relations to other things.

Russell isolates a confusion in Hegel's reasoning. It is possible, after all, to have knowledge of a thing by acquaintance without knowing propositions about it. The thing's nature is not involved. Russell writes, "Acquaintance with a thing does not logically involve a knowledge of its relations," and furthermore "knowledge of its relations does not involve a knowledge of all of its relations nor a knowledge of its 'nature'." One may have a complete acquaintance with one's toothache without knowing all about its nature, as a dentist might. Just because a thing has relations does not mean that they are "logically necessary." Just because a thing is what it is, we cannot know that it must have those relations to be what it is.

It follows from this objection to the use of the term "nature" that we cannot prove Hegel's hypothesis of a harmonious whole, nor can we believe in the characteristics of timelessness and the unreality of evil that he deduced. With Russell, we return to "the piecemeal investigation of the world," with no extra knowledge gained about those parts of the universe outside our experience. He points out that this return is confluent with "the inductive and scientific temper of (his) age" and with his examination of knowledge in The Problems of Philosophy.