The Problems of Philosophy is an introduction to the discipline of philosophy, written during a Cambridge lectureship that Russell held in 1912. In it, Russell asks the fundamental question, “Is there any knowledge in the world which is so certain that no reasonable man could doubt it?” Russell sketches out the metaphysical and epistemological views he held at the time, views that would develop and change over the rest of his career.

Russell begins by exploring the twin concepts of appearance and reality. Empiricists like Russell believe that all knowledge is ultimately derived from our sensory perceptions of the world around us. Individual perception, however, is easily affected and prone to error. If three people—one who’s had three martinis, one with a heavy fever, and one who’s color-blind—look at the same table, chances are they’ll each see the same object somewhat differently. Submerge the same table underwater, or set it behind a wavy pane of glass, and once again the table will look different. There is, then, a distinction to be made between appearance and reality. If perception is so variable, what can it actually tell us about the stable, real object we assume lies behind it?

Russell coined the term “sense-data” in his attempt to discern the relationship between appearance and reality. Sense-data are the particular things we perceive during the act of sensation. When you walk into a café, the smell of the coffee, the redness of the awning, and the heat from the radiator are all examples of sense-data. Sense-data are the mental images (visual as well as auditory, olfactory, tactile, and gustatory) we receive from a given object in the physical world. As we can see from the table example, the same object can produce variable sense-data. Sense-data are related to the physical objects they represent, but the exact nature of this relationship is unclear. The skeptical argument contends that sense-data tell us nothing about the reality of the object. Russell had a commonsense take on the matter: while he understood the skeptical arguments, he found no reason to believe them. A hundred different viewers may have a thousand different kinds of sense-data for a given table, yet each agrees that they are looking at the same table. This consistency suggests, to Russell, that we must at least believe in the existence of a single, particular, real table. To this “instinctive” belief, Russell also adds the hypothesis that physical objects cause the sense-data we receive and therefore correspond to them in some significant way.

During the act of sensation (i.e., the exercising of our five senses), we receive and process the sense-data produced by physical objects in our vicinity. The knowledge we gain during this process Russell calls “perceptual knowledge”—knowledge gained through experience. In contrast, Russell believes we are also in possession of certain kinds of a priori knowledge. These include the self-evident rules of logic, most important, and those of mathematics. Perceptual knowledge (the knowledge of things) and a priori knowledge (the knowledge of truths) work in concert: the first gives us empirical data, and the second tells us how to process that data.

Russell further divides human knowledge into knowledge by acquaintance and knowledge by description. To be acquainted with something is to be directly and immediately aware of it, without the action of an intermediary. When you sit on a red plastic chair, you become acquainted with lots of sense-data associated with that chair. You know its redness, its smoothness, its coolness, and its hardness. But to know that this thing is called a “chair” and that it’s often found in the company of other “chairs” and something called a “table” requires more than just direct, immediate acquaintance with the physical object. To know all that requires us to make inferences, based on our general knowledge of facts and on our acquaintance with other similar objects. This kind of knowledge is derivative, and Russell terms it “knowledge by description.” For instance, most of us know only by description that Everest is the tallest mountain in the world. Few of us have actually been there, so we have to rely on the testimony of others to “know” that fact. Indeed, to truly be acquainted with the fact of Everest’s superior height, one would have to visit and measure all the mountains in the world. It’s probably safe to say, then, that no one is truly acquainted with that particular piece of knowledge.

Just as we can know objects either immediately or derivatively, we can also know truths immediately or derivatively. Russell defines immediate knowledge of truths as intuitive truths. These are concepts that, to Russell, are so clearly self-evident that we just know they must be true. “1 + 1 = 2” is an example of such a self-evident truth. Derivative knowledge of truths involves deduction and inference from immediate, self-evident truths.