Analytic Philosophy - Movement inaugurated by Bertrand Russell, together with G.E. Moore, which is sometimes called Oxford Philosophy. The practice of analytic philosophy is broadly defined as an enterprise that uses "analysis." Russell used it to expose what an essentially logical form of reality.
Appearance - Appearance is defined against reality in Russell's first chapter. He distinguishes our first impressions of our surroundings and how things appear to be, from the way that they actually are—their reality.
Idealism - Russell was educated in this tradition of thought, which held that "whatever exists, or at any rate, whatever can be known to exist, must be in some sense mental." Russell rejects Berkelian idealism in this work, although he is known to have been more influenced by the version of idealism advocated by his tutor, Bradley.
Deduction - A process of reasoning that gathers information from general principles and allows one to deduce things about other general principles or particular instances.
Empiricists - The empiricists are represented in this work by the British thinkers, Locke, Berkeley, and Hume. Their epistemic contribution is the steadfast belief that our knowledge comes from experience.
Induction - A process of reasoning that gathers information from particular instances and allows one to draw inferences concerning other particulars or general propositions.
Knowledge by Acquaintance - Knowledge by acquaintance is one of the ways Russell distinguishes that we can have knowledge of things. We have knowledge by acquaintance when we are directly aware of a thing, without any inference. We are immediately acquainted with our sense-data. Knowledge by acquaintance is logically independent of any knowledge of truths.
Knowledge by Description - Knowledge by description is the other way, together with acquaintance, that allows us to have knowledge of things. Knowledge by description is predicated on something with which we are acquainted, sense-data, and some knowledge of truths, like knowing the description: "such-and-such sense-data are caused by the physical object." Thus, knowledge by description allows us to infer knowledge about the actual world via the things that can be known to us, things with which we must have direct acquaintance. Russell's famous example of knowledge by description is his discussion of Bismarck, a physical entity with which we may either have acquaintance, or knowledge by the description: "the first Chancellor of the German Empire."
Neo-Platonic Realism - Russell's neo-Platonism is palpable in his substantial defense of the reality of universals. Russell's sense of the universal is like the Platonic ideal form. Like Plato's "ideas," universals are the abstract essences in which particulars participate for their being.
Particular - Particulars are objects in the physical world, like Russell's table, which Russell believes to be composed of matter. Particulars are in one place at any given time and exemplify universals. A white sheet of paper is a particular that exemplifies the universal "whiteness."
Proposition - A proposition is a complex philosophical expression of meaning. Russell's usage usually associates propositions as statements about objects and their relations.
Radical Doubt - This is the methodological doubt that Descartes first conceived in his Meditations. Descartes refused to accept anything as true unless it struck him as clearly and distinctly true, in itself. Russell revives this method in his first chapter's account of the dubious nature of our so-called "knowledge." He prompts us to doubt and reconsider our everyday conception of reality.
Rationalists - The rationalists relevant in Russell's regard were the Continental philosophers Descartes, Leibniz, and Kant. They believed that in addition to what we learn from experience, we have independent knowledge of "innate principles." Russell locates the concept of a priori knowledge in this latter criterion.
Reality - As opposed to appearance, reality comes to be defined as the way things really are in themselves. Russell believes in an independent reality, especially concerning universals and particulars.
Sense-data - Sense-data are the impressions that the appearance of reality offers our senses. We have a sensation of a piece of sense-data. For instance, we have a sensation of redness when we see a patch of red. Sense-data is an important concept distinguished from the physical world full of physical objects. Sense-data is unique in that it is the only part of the world with which we have direct acquaintance.
Universal - The universal is an ideal from which particulars derive their common essence. "Whiteness" is the universal property common to all white things. We come to understand universals by a process of abstraction; we practice induction about particulars that we encounter. Russell allows relations the same universal status as the traditional universals—qualities and properties.