So far as logic goes, this is the same proposition as might be expressed by "some 's are 's"; but rhetorically there is a difference, because in the one case there is a suggestion of singularity, and in the other case of plurality. This, however, is not the important point. The important point is that, when rightly analysed, propositions verbally about "a so-and-so" are found to contain no constituent represented by this phrase. And that is why such propositions can be significant even when there is no such thing as a so-and-so. The definition of existence, as applied to ambiguous descriptions, results from what was said at the end of the preceding chapter. We say that "men exist" or "a man exists" if the [Pg 171] propositional function " is human" is sometimes true; and generally "a so-and-so" exists if " is so-and-so" is sometimes true. We may put this in other language. The proposition "Socrates is a man" is no doubt equivalent to "Socrates is human," but it is not the very same proposition. The is of "Socrates is human" expresses the relation of subject and predicate; the is of "Socrates is a man" expresses identity. It is a disgrace to the human race that it has chosen to employ the same word "is" for these two entirely different ideas—a disgrace which a symbolic logical language of course remedies. The identity in "Socrates is a man" is identity between an object named (accepting "Socrates" as a name, subject to qualifications explained later) and an object ambiguously described. An object ambiguously described will "exist" when at least one such proposition is true, i.e. when there is at least one true proposition of the form " is a so-and-so," where "" is a name. It is characteristic of ambiguous (as opposed to definite) descriptions that there may be any number of true propositions of the above form—Socrates is a man, Plato is a man, etc. Thus "a man exists" follows from Socrates, or Plato, or anyone else. With definite descriptions, on the other hand, the corresponding form of proposition, namely, " is the so-and-so" (where "" is a name), can only be true for one value of at most. This brings us to the subject of definite descriptions, which are to be defined in a way analogous to that employed for ambiguous descriptions, but rather more complicated.