If we were concerned to examine fully the relation of idea and object, we should have to enter upon a number of psychological and logical inquiries, which are not relevant to our main purpose. But a few further points should be noted. If "idea" is to be understood logically, it may be identical with the object, or it may stand for a description (in the sense to be explained in a subsequent chapter). In the former case the argument fails, because it was essential to the proof of reflexiveness that object and idea should be distinct. In the second case the argument also fails, because the relation of object and description is not [Pg 139] one-one: there are innumerable correct descriptions of any given object. Socrates (e.g.) may be described as "the master of Plato," or as "the philosopher who drank the hemlock," or as "the husband of Xantippe." If—to take up the remaining hypothesis—"idea" is to be interpreted psychologically, it must be maintained that there is not any one definite psychological entity which could be called the idea of the object: there are innumerable beliefs and attitudes, each of which could be called an idea of the object in the sense in which we might say "my idea of Socrates is quite different from yours," but there is not any central entity (except Socrates himself) to bind together various "ideas of Socrates," and thus there is not any such one-one relation of idea and object as the argument supposes. Nor, of course, as we have already noted, is it true psychologically that there are ideas (in however extended a sense) of more than a tiny proportion of the things in the world. For all these reasons, the above argument in favour of the logical existence of reflexive classes must be rejected.