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.