By this point, Russell has established a rational basis for our ordinary belief in "the existence of something independent of us and our experiences." We recognize the belief that the table persists when we close our eyes and that our sense-data are apparent signs of that table. In the third chapter, Russell addresses the fundamental question postponed from the first chapter. He asks us to consider what the nature of that independent something, the real table, might be.
First, he examines the hypothetical answer offered by physical science. Physical science reduces natural phenomena like light, heat, and sound to "wave- motions." A body consisting of matter emits a wave, which travels to an observer. It is important to note, as Russell does, that the only properties attributed to the emitting body are "position in space, and the power of motion according to the laws of motion." Now Russell introduces a comparison between this scientific view and our natural view of light, heat, and sound. What we "know directly by means of our senses is not a form of wave motion;" rather, what we know directly produces our natural view. In the case of light, our natural view consists in our experience, something knowable to any but a blind man. Russell holds that the experience of light essentially differs from anything that we might describe in an effort to convey light to a blind man. Of course, it is possible to imagine a blind man grasping the scientific definition of wave-motion. He might have knowledge of space through touch, and he might board a boat and perceive wave-motion. Yet, he cannot know what we know directly, that which cannot be captured in words. Authentic understanding emerges as a prominent criterion basic to our account of the nature of things.
Russell elucidates this separation between the scientific view and the one derived from direct experience. On the scientific view, what we might be said to "know directly" is not really a case of knowing the external world. The phenomena of light that we experience cannot be found in the external world. Instead it is caused by it, by the "action of certain waves upon the eyes and nerves and brain of the person who sees the light." The statement that "light is waves" really means that waves cause our experience of light. Waves exist in a world independent of our senses, and the notion of light is somehow composed in our experience of the waves. Russell suggests that a similar relation holds for all other sensations. Colors and sounds are the phenomena of experience and are "absent from the scientific world of matter."
Space, as we know it, is also absent. Russell claims that the space known by sight and the space known by touch differ. Our experience of either is discrete in infancy, and we learn to align them into the appearance of a unified space (we learn how to touch what we see and to recognize that something touches us). However, the space of science is a unified space, which is, as Russell puts it, "neutral" with respect to touch or sight" and thus cannot be identical with what he calls our "private spaces." To better understand the distinction at issue, Russell gives a spatial example. A coin that is known to be circular will always appear as a mere oval from all perspectives except that of directly facing it. Understanding that the coin is circular is an inference that different people make from different perspectives. The inference is based on knowing the shape of most coins but not on any direct knowledge of this particular coin. All that is readily available to the percipient is the apparent shape in an apparent space. The scientific understanding of a coin consists of its real shape in a real space. While private spaces offer different representations of the same coin, the public space only offers a consistent one. Though different, Russell concludes, the two kinds of space seem connected.
Working to clarify the connection between a real space and apparent ones, and between real objects and how they appear to us, Russell reviews the fruits of his preceding arguments. So far, in this chapter, we have gained a better understanding that physical objects do not seem exactly like our sense-data, yet the physical world seems to cause sense-data and private experience. Since physical objects occupy physical space, it seems reasonable now to grant that our sense organs, when in contact with these objects, also occupy the same physical space. One example is that we see an object when there is nothing opaque between the object and the eyes. Also, we sense touch when in direct contact with an object. In all cases, including sound and smell and taste, it seems that we perceive something when our body is in some suitable position in space relative to the object; our sensations depend on the relative positions of ourselves and the object.
Scrutinizing this relation, Russell reminds us of the assumption usually entertained both by science and by the common sense view that there is "one public all-embracing physical space in which physical objects are." Thus we construct a map of the external world from our private experience, which corresponds with an outer physical space. We usually believe that spatial relations in real space correspond with what we know from private experience. Given our belief, it is important to note that we can only know about the physical space in its sense of correspondence, not in itself. Though we can know "properties of the relations required to preserve the correspondence with sense-data," we "cannot know the nature of the terms between which the relations hold."