The Principles of Mathematics (1903)

§ 67

When an object is unambiguously denoted by a concept, I shall speak of the concept as a concept (or sometimes, loosely, as the concept) of the object in question. Thus it will be necessary to distinguish the concept of a class from a class-concept. We agreed to call man a class-concept, but man does not, in its usual employment, denote anything. On the other hand, men and all men (which I shall regard as synonyms) do denote, and I shall contend that what they denote is the class composed of all men. Thus man is the class-concept, men (the concept) is the concept of the class, and men (the object denoted by the concept men) are the class. It is no doubt confusing, at first, to use class-concept and concept of a class in different senses; but so many distinctions are required that some straining of language seems unavoidable. In the phraseology of the preceding chapter, we may say that a class is a numerical conjunction of terms. This is the thesis which is to be established.(§ 67 ¶ 1)