Platonic philosophy first expressed the world of universals. Here, Russell gives an account of the Platonic "theory of ideas." Understanding the universal or what Plato referred to as an "idea," helps in understanding Russell's broader discussion. From the previous chapter, we saw relations emerge as important considerations in a theory of knowledge. Russell concluded that relations have a being that is not physical, mental, or like sense-data. He considers what positive kind of being they might indeed have and what kinds of objects have this being.
The "theory of ideas" addresses how we come to understand relations. Deriving his theory, Plato first considered the concept of justice. To find out what justice is in itself, Plato looked at some just acts with the view to discovering what common essence they shared; this, he reasoned, must be justice itself. This method can be applied to any other abstract entity, like whiteness. The fact of whiteness, being white, can be applied to innumerable, particular white things. These things would be said to participate in a common essence, which is Plato's "idea" or "form." An idea is not identical with anything illustrated in particular; justice is not identical with a just act. The idea is not a piece of the world that we can sense. It is "eternally itself, immutable and indestructible."
Russell renames the Platonic "idea" as the "universal," since using "idea" is misleading (as we saw in chapter four, with Berkeley's idealist appeal to the sense of "idea" that exists in the mind.). The meaning of Plato's "idea" is a concept defined against a particular thing, given in sensation.
For Plato, the real world was the one of universals. Whatever we could declare about a perceived reality is only accurate by virtue of perceiving that a particular participates in universals. Russell writes, "Plato is led to a supra-sensible world, more real than the common world of sense, the unchangeable world of ideas, which alone gives to the world of sense whatever pale reflection of reality may belong to it." Russell sidesteps the issue of mysticism as it arises from Plato's theory of perceiving a universal like an object, and investigates the theory's logical basis.
With an analysis of ordinary language, Russell explores how we normally think of common words. He claims, "proper names stand for particulars while other substantives, adjectives, prepositions, and verbs stand for universals." He also claims that human speech habitually involves at least one word denoting a universal in each sentence. All of this is to say that all truths necessarily involve universals and our knowledge of those truths involves an acquaintance with universals.
Why, then, if so much depends on universals, do we usually ignore them? Russell answers that they seem to us "incomplete and insubstantial; they seem to demand a context" before we can utilize a particular meaning. Russell claims that the verb and preposition have been overlooked in philosophy and that analyses of the adjective and substantive have determined metaphysics since Spinoza. Russell outlines the consequence of this mistake: "Adjectives and common nouns express qualities or properties of single things, whereas prepositions and verbs tend to express relations," between things. Failing to recognize the significance of the verb and prepositions results in a preoccupation with attributing one property to a single thing. Ignoring relations leads to the belief that they are impossible and thus, that there is only one thing in the universe, a doctrine called "monism," held by Spinoza and later Bradley. An alternative doctrine, "monadism," held by Leibniz, claimed that if there is more than one thing in the universe, the things could not interact together because they would then be related and relations are impossible.
Russell acknowledges that we cannot prove there are qualities, the universals represented by adjectives and substantives, whereas we can prove the existence of relations. If we believe in whiteness, a universal, we say that white things are so because they share an abstract quality of whiteness. The empiricists Berkeley and Hume denied the existence of "bstract ideas."They suggested that what really happens when we choose to think of whiteness is that we isolate an image of a particular white thing and reason from it, "taking care not to deduce anything concerning it which we cannot see to be equally true of any other white thing." Russell compares this example to reasoning about a triangle in geometry. We reason as Berkeley and Hume prescribe. However, as soon as we wonder how we know that something we have chosen is white or a triangle, then we must choose something else white or triangular and use it as a criterion, saying that one "must have the right sort of resemblance to our chosen" other particular. Thus, resemblance is presupposed in the choosing of one particular and resemblance is a universal. It is a relation that holds for all pairs that are white; the empiricist alternative indirectly appeals to the abstract universal.
The relation of resemblance is a true universal. It transcends expression in any single particular. Having admitted this, it is faulty reasoning to deny universals about qualities, like whiteness and triangularity. Having proved that universals do exist, next Russell sets the discussion towards proving that universals are not mental in nature. He holds that they are independent of thought or apprehension.
He considers the proposition "Edinburgh is north of London." This relation between two places seems clearly independent of our knowing it. Our knowing it does not make it true; rather, we just "apprehend a fact" that existed prior to us. Even if no one existed, the place where Edinburgh is would still be in a relation north of the place where London is. It seems true, then, that nothing mental is assumed in the fact about these two places. Yet, this fact involves the relation called "north of," a universal. Since the proposition above does not involve anything mental, "north of" must be non-mental as well. We can therefore state that the relation is like the "terms it relates," independent of thought. "North of" is independent of thought and yet it cannot be said to exist exactly in the way that London and Edinburgh exist. There is no place or time in which the relation exists. Since "everything that can be apprehended by the sense or by introspection exists at some particular time," Russell concludes that the relation "north of" is something radically different from these other things; it is not physical or mental.
Russell concludes this chapter with a note on terminology. "Thoughts and feelings, minds and physical objects" exist "in time," in our normal sense. However, universals do not; they "subsist or have being. Being is timeless. Russell divides the world of existence from the world of being. The latter, he writes, is delightfully precise and exact, "unchangeable, rigid," to "all those who love perfection more than life." Comparatively, the world of existence is "fleeting, vague," a jumble of physical and mental things, and contains "everything that makes any difference to the value and life of the world."
This idiosyncratic type of being, not apparently physical or mental, has led to previous philosophical confusion that the universal is really mental in nature. Thinking about universals exists in the mind of course, and in that sense it may be mental. This argument depends on an equivocation similar to Berkeley's ambiguous "idea" discussed in chapter four. Think of whiteness. If we call the action of thought "whiteness," we can say that it is mental by this argument. However, the sense of the universal that we think of is the sense that denotes an object, the idea of whiteness. Russell claims that thought is necessarily differentiable from the universal because taking the universal to be identical with thought robs it of its essential universality. Since "one man's act of thought is necessarily a different thing from another man's," the idea of whiteness cannot be identical between them. What is common between their thought is an abstract object called "whiteness."
Russell's philosophy is most conspicuously neo-Platonic with respect to universals. The metaphysical dichotomy of the world is in complete harmony with Platonic metaphysics. The concrete world we know directly is like a collection of imperfect shadows of the world of ideals or universals. Since Russell also holds that we cannot directly access most of the world, but can only be acquainted with sense-data, universals neatly contain the counterpart essences after which we grope blindly. Neo-Platonic realism is essentially indirect realism, the theory that our understanding of reality is mediated by the veil of our senses. We access reality indirectly, gathering a muddy picture from what we can perceive and our reasoning about it.