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?"
Russell considers one possible answer to the first question with the thought of British philosopher Bishop Berkeley (1685–1753). Berkeley brought out the position that the immediate objects, which we call physical objects, do not exist independently of us. Rather, they depend on our minds. On his view, matter does not exist. What we call physical objects are really just ideas, mental products that we project onto the world. The existence of objects that appear to correspond to our sensations is dubious on this view. Russell's contemplation of the table shares Berkeley's spirit of enquiry insomuch as he agrees with Berkeley that "if there are any things that exist independently of us they cannot be the immediate objects of our sensations." However, Berkeley's arguments offer a more extreme philosophical view, belief in the impossibility of a reality independent of man.
At this point, Russell integrates an important distinction between meanings packed in the word "matter." A common conception of matter is something opposed to mind, something that takes up space in the physical world and is absolutely incapable of consciousness. Berkeley denies this sense of matter. He does not deny matter in the sense of things like sense-data, which signify an existence of something independent of ourselves. According to Berkeley, this independence is possible; he believes that there is something that persists when we close our eyes or walk out of a room. However, he believes that this something depends for its existence on a mind, that it may be independent but must be mental. It must not be "independent of seeing altogether, though it must be independent of our seeing." Thus, Berkeley regards the reality of the table and other such physical objects as ideas in the mind of God. Things can exist independently as long as they are not things essentially unknowable.
Berkeley's view is just one example of idealism, the view that there is "nothing acceptable as real except minds and their ideas." Argument supporting this view maintains that "whatever can be thought of is an idea in the mind of the person thinking it; therefore nothing can be thought of except ideas in minds; therefore anything else is inconceivable, and what is inconceivable cannot exist." Other philosophers held that the physical objects of the world merely depend on being observed by some entity, not necessarily God. Leibniz (1646–1716) thought that physical objects existed because they were observed by some conceptually collective mind, like the universe itself. These philosophers denied matter "as opposed to mind."
Russell also accepts the version of matter that they do not deny. By reiterating his initial question: "Is there a real table at all?" Russell points out his agreement with Berkeley and Leibniz in believing that there is a real table. However, Russell disagrees with the idealists over the question of the nature of the real table, the latter question "what sort of object can it be?" Russell continues that "almost all philosophers agree that there is a real table" and that our sense-data are signs of something that exists independent of us, something that may be said to cause the "sense-data whenever we are in a suitable relation to the real table." Before going on to an analysis of matter, Russell recognizes the positive agreement to his first question as conspicuously important and plans, in the next chapter, to investigate the reasons why anyone should believe thus. Russell concludes by reemphasizing that what we gather from our senses directly in terms of "appearance" are but signs from which we infer "reality."
Russell's method of approaching his subject embraces the Cartesian technique of radical doubt. Rene Descartes (1596–1650) first employed it in his Meditations on First Philosophy. Upon discovering his philosophical confusion about ordinary things, Descartes decided to believe in nothing that he did not discern as clearly and distinctly true. Descartes imagined the possibility of a mischievous demon, who disordered reality in order to deceive humans; anything was possible if he could not prove that it wasn't the case. Russell acknowledges his debt to Descartes in his second chapter when he makes explicit use of Cartesian philosophy to support the idea that "subjective things are the most certain." Russell's first chapter uses radical doubt to separate reality from illusory appearance, a distinction not motivated by a demon, but by the suggestion that reality is simply ordered in a way that is not immediately present to our senses.
Russell takes issue with the authority of common sense by showing that the appearances of the table are numerous and contradictory and cannot be said to suffice as a description of one reality. Confusion about the table's color, texture, and shape, are sufficient to prompt doubt as to whether or not the table exists at all. Belief in the table remains dubious until Russell creates a distinction between the table and sense-data representing the table. Engaging Russell's language allows us to separate our experience of the table, which becomes confusing, from an idea of a real table removed from our perception.
At the end of chapter 1, Russell writes, "Philosophy, if it cannot answer so many questions as we could wish, has at least the power of asking questions which increase the interest of the world, and show the strangeness and wonder lying just below the surface even in the commonest things of daily life." This philosophic capacity to ask questions finds thematic expression throughout the work. Here, the sudden way that reflective questioning can contradict our ordinary view of the world makes clear the necessity of Russell's project. He identifies a need for a theory of knowledge that will reconcile what appears to be from what really is. Russell also appeals to an urge to practice knowledge responsibly, that in order to make statements or hold beliefs about knowledge, we must be able to substantiate that our knowledge is faithful to reality.
Russell's sense-data terminology endures as a helpful reference throughout the work and also as a touchstone of modern philosophy. His table is the illustrative case of sense-data, famous from this popular work, and used as a staple of contemporary philosophical discussion. Among the philosophers who have responded to it in their own works, Hilary Putnam notably identifies Russell's table in his most recent work The Threefold Cord. Putnam discusses the notion of sense-data as a mistaken conceptualization of reality, which Russell developed as a result of the limitations of his scientific age. The mistake does not necessarily rest on an issue of perspective, because the table still might be one color, just affected by a force of nature not identified, not taken into account; if it were, then the table's color would be constant, and still independent of the observer.