Russell begins by asking his reader to consider what knowledge exists that can be known beyond reasonable doubt. His purpose is to produce the realization that radical doubt soon brings even the most self-evident assumptions in our everyday lives under reconsideration. In this beginning chapter, Russell describes a scene: "I am now sitting in a chair, at a table of a certain shape, on which I see sheets of paper with writing or print." All of these "facts" are easily called into question. Russell engages in his discussion to find out how knowledge of such things is possible at all.

In order to lay bare the ordinary assumptions at issue, Russell concentrates on one example, the table before him. Walking around the table, he discerns different colors from different points of view: in places seeming to reflect more light, a brighter shade of brown appears. In reality we assume that there is only one color of the table, yet the appearance of many colors contradicts our assumption. The color seems to be a relation depending on the observer, his point of view, and conditions like "the way the light falls on the table."

Since it seems clear that no two people could share one identical point of view, Russell registers a doubt as to whether one real color of the table even exists. Russell continues his investigation of color by reasoning that in ordinary language usage, when we refer to the color of an object, we actually refer to something perceived from the usual perspective of observer. However, he continues, there is no reason to assume that the usual perspective should be considered real and other perspectives, under other conditions, be considered less real. Russell does not think that the most usual brown should be considered the brown of the table, to the exclusion of other apparent browns.

As with color, the existence of just one texture of the table is ambiguous, because "to the naked eye, the table appears to be smooth and hard. Aided by microscope, the grain of the wood enlarges to appear as a mountainous range of different roughnesses and textures." Russell argues that one cannot consider one texture more real than another. The shape of the table, a rectangle, also changes immediate shape as one walks around it. Sensation of pressure depends on the force we exert on the table, as does the production of sound when we rap on the wood. Thus, the sensations of touch and sound, like sight, are not fixed by a reality; they are apparent possibilities and each depends on the conditions of observation. These observations lead to Russell's first distinction between appearance and reality, "between what things seem to be and what they are." Russell proposes that we are not struck with these discontinuities in our daily life because in practical experience, one learns "to construct the 'real' shape from the apparent shape." The real shape exists in so much as we infer it from our senses.

He writes, "the real table, if there is one, is not immediately known to us at all, but must be an inference from what is immediately known." The reality of the table, in the sense that there is a table, depends on a process of inference based on a knowable part of reality, the part Russell calls "sense-data". Sense-data are not the same as our sensations. Sense-data are "the things that are immediately known to us in sensation." Variations in our sensations indicate that sensation does not directly reveal the reality of an object like the table. Instead, it is probable that our sensations are "signs of some property which perhaps causes all the sensations." To fully grasp Russell's distinction, consider sensation as an act belonging to the realm of experience and consider the object of that direct experience to be sense-data. The object, a patch of red, produces the sensation or experience of redness. Since we have seen that certain knowledge of the table's reality is not available through the senses, Russell asks how we can know that a real table exists at all and what kind of certainty we can have. It remains clear that we do have an experience of awareness where we recognize colors and other properties as part of the table. While we may doubt the existence of a real table, it is harder to doubt our awareness of our own sensations. Therefore, we can regard our confidence in the sense-data of our everyday experiences as safe.

The next problem that arises is one of understanding how the real table, if there is one, relates to our sense-data. Russell states that it is impossible to understand, in this stage of the discussion, if or how the relation would work. The questions we must first approach are: "is there a real table at all" and "if so, what sort of object can it be?" This relation, between sense-data and the real table, is a substantial concern for Russell's enquiry. Returning to his table, he admits that when we have been saying the "real table," we have meant the "physical object." Physical objects may be understood as "matter." The questions at issue become: "is there any such thing as matter" and "if so, what is its nature?"