Russell analyzes an example of a moving and hungry cat in order to show the importance that simplicity plays in our reasoning. If a cat appears in one place in a room, then in the next moment it appears in another place, it is "natural," Russell says, to believe that the cat has moved. Yet, on the view of private experience that solely endorses sense-data, the cat could not have been in any other places besides where one sees him. He simply does not exist when one doesn't see him. Now, another possibility is that the cat does exist when one sees him and when one does not see him. He persists, and it is easy to infer that he becomes hungry between one meal and the next. Yet, Russell continues, if he does not exist when he is not observed, then it is harder to imagine him becoming hungry when he does not exist. Further still, if he does not exist independently and only exists as a piece of sense-data, then the idea of his being hungry is unintelligible anyway. On this view, one can only experience one's own hunger as a piece of sense-data. Russell writes that the "expression of hunger becomes utterly inexplicable when (the cat is) regarded as mere movements and changes of patches of color," as sense-data.
Russell then extends his cat example to other people. When watching someone speak, we perceive sense-data like moving lips and uttered sounds, and we naturally believe that another person is expressing his thoughts, much as we would if we acted in a similar way. We draw an unconscious analogy between how we think of our own behavior and how we perceive the behavior of others. That is, it is difficult to imagine that the person does not exist independently.
Here Russell discards the hypothesis that our notion of reality is just a case of dreaming. We know that in dreams one perceives the presence of other people and realizes this later to be a mistake. Russell claims that dreams are suggested by "waking life" and can be "accounted for on scientific principles if we assume there is a physical world," that is, we assume that our dreams are patterned on a reality where we probably do perceive real people. Though he admits that the dreaming case will always pose a "slight doubt," he reasons by that independent reality is the simpler hypothesis. It is the "natural view" urged by "every principle of simplicity," that we are experiencing real, physical objects that exist outside ourselves and do not depend on our perception for their existence.
Russell concludes his assertion of simplicity with a look at why the view seems natural in the first place. We do not first adopt the view that there are other people beside ourselves because someone has successfully argued the case before us. The independent existence of reality is a natural belief because "we find this belief ready in ourselves as soon as we start to reflect." Russell calls it an instinctive belief. He points out that we have only doubted the external world because it failed to be identical with our sense-data. Yet, physical objects still seem to correspond to our sense-data. This instinctive belief simplifies our thinking about our experiences, rather than complicating it, and thus there seems to be no reason not to accept the common sense hypothesis over the dreaming hypothesis.
He ends the chapter acknowledging that the argument for simplicity is perhaps weaker than we would have it but typical of most philosophical argument. Briefly, he conceives a theory about the hierarchical character of knowledge. He writes, "all knowledge, we find, must be built up upon our instinctive beliefs, and if these are rejected, nothing is left. But among our instinctive beliefs some are much stronger than others, while many have, by habit and association, become entangled with other beliefs, not really instinctive, but falsely supposed to be part of what is believed instinctively."
In the course of his discussion Russell offers a very brief but sophisticated reading of Cartesian certainty. He poses the classic problem of understanding personal identity examining the "I" of Descartes' famous "I think, therefore I am." His speculation that the "real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to immediate experiences (sense-data)," posits a fundamental doubt that we are the same person today as we were the day before. The passage is an example of The Problems of Philosophy in its capacity as introduction; however the problem of personal identity is a side issue.