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.
Similar to Hegel, other metaphysicians have attempted to prove the unreality of parts of the apparent actual world by finding them self-contradictory. Yet, now the "tendency of modern thought" is "in the direction of showing that the supposed contradictions were illusory, and that very little can be proved a priori from considerations of what must be." Space and time bear out his view. They have formerly appeared to be "infinite in extent," as we believe when we find it incredibly difficult to imagine reaching the beginning or end of a continuous straight line or of continuous time, and "infinitely divisible," which seems evident from the consideration that any distance between two points or two moments could be halved ad infinitum. Some arguments in philosophy attempted to prove these properties illusory, to show that infinite collections were impossible. Kant first called attention to the contradiction between these arguments and the apparently infinite nature of space and time; he found space and time to be "purely subjective." Belief that space and time are only apparent, not real, has been a rich source for "metaphysical constructions."
Yet, in the present, advances in mathematics have proven that the "impossibility of infinite collections was a mistake," because they are only contradictory of certain mental prejudices. Mathematician went further and proved the possibility of many other kinds of space other than Euclidean space. The quality of necessity associated with some of Euclid's axioms has been traced to "our mere familiarity with actual space, and not from any a priori logical foundation." Logic has shown these possibilities by imagining other worlds, which are not based on experience. "While our knowledge of what is" has diminished, our sense of "what may be" has expanded.
In accord with this intellectual development with regards to time and space, other attempts to "prescribe to the universe by means of a priori principles (have) broken down." Logical possibilities and imaginary world hypotheses have replaced them. Our knowledge has thus become limited to "what we can learn from experience" not just to "what we can actually experience." This is evident from Russell's discussion of knowledge by description. Our sense-data enable us to infer implicit physical objects. This principle is a connection between universals, which describes how we learn about the physical world through indirect experience.
Russell does not continue with illustrations here; he draws conclusions that culminate in the apex of his enquiry into knowledge of truths. He writes, "our intuitive knowledge, which is the source of all our other knowledge of truths, is of two sorts: pure empirical knowledge, which tells us of the existence of some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connexions between universals, and enables us to draw inferences from the particular facts given in empirical knowledge." Derivative knowledge, in turn, depends in part on some a priori knowledge and also on some empirical knowledge.
The enterprise of philosophy is similar to science in this methodological regard and the results of both are "not radically different." What is essentially different in the pursuit of philosophy is criticism. Philosophy reviews accepted principles and only accepts them when no inconsistencies or reasons for rejecting them have become obvious. As a "criticism of knowledge," Russell insists on the imposition of limit where the skeptic is concerned. The influence of the skeptic is always productive, except in the case of the "absolute skeptic." No argument can be advanced against "blank doubt." Russell calls this kind of skepticism "destructive" and "unreasonable," as opposed to the Cartesian example of methodical doubt, which he calls the "essence of philosophy" (see chapters 1 and 2). Through such doubt, philosophy may rightly claim that it reduces the "risk of error" in knowledge (though knowledge will always be prone to error because humans are fallible).
Russell hints that Hegel's system is an attempt to overthrow and transcend the limitations of private experience. The upshot of Hegel's philosophy is the philosophical posture of being able to access a complete and public space. While this picture is attractive, it rests on unproven assumptions. Russell examines Hegel's arguments before finding them logically insufficient. Instead of lofty metaphysical systems, he discusses the merits and habits of being a "prudent advocate of philosophy." We have seen the success of "methodical doubt" with respect to sense-data and physical objects. Upon reflection, we retained our belief in the integrity of sense-data, but not our prior belief that physical objects exactly corresponded to that sense-data. According with this example, Russell's method is modest, even though his metaphysics are ultimately profoundly systematic and complex.