Now, if nothing that can be said significantly about a thing can be said significantly about a class of things, it follows that classes of things cannot have the same kind of reality as things have; for if they had, a class could be substituted for a thing in a proposition predicating the kind of reality which would be common to both. This view is really consonant to common sense. In the third or fourth century B.C. there lived a Chinese philosopher named Hui Tzŭ, who maintained that "a bay horse and a dun cow are three; because taken separately they are two, and taken together they are one: two and one make three."[53] The author from whom I quote says that Hui Tzŭ "was particularly fond of the quibbles which so delighted the sophists or unsound reasoners of ancient Greece," and this no doubt represents the judgment of common sense upon such arguments. Yet if collections of things were things, his contention would be irrefragable. It is only because the bay horse and the dun cow taken together are not a new thing that we can escape the conclusion that there are three things wherever there are two. [53] Giles, _The Civilisation of China_ (Home University Library), p. 147. When it is admitted that classes are not things, the question arises: What do we mean by statements which are nominally about classes? Take such a statement as, "The class of people interested in mathematical logic is not very numerous." Obviously this reduces itself to, "Not very many people are interested in mathematical logic." For the sake of definiteness, let us substitute some particular number, say 3, for "very many." Then our statement is, "Not three people are interested in mathematical logic." This may be expressed in the form: "If _x_ is interested in mathematical logic, and also _y_ is interested, and also _z_ is interested, then _x_ is identical with _y_, or _x_ is identical with _z_, or _y_ is identical with _z_." Here there is no longer any reference at all to a "class." In some such way, all statements nominally about a class can be reduced to statements about what follows from the hypothesis of anything's having the defining property of the class. All that is wanted, therefore, in order to render the _verbal_ use of classes legitimate, is a uniform method of interpreting propositions in which such a use occurs, so as to obtain propositions in which there is no longer any such use. The definition of such a method is a technical matter, which Dr Whitehead and I have dealt with elsewhere, and which we need not enter into on this occasion.[54] [54] Cf. _Principia Mathematica_, § 20, and Introduction, chapter iii.