When we say “the so-and-so exists,” we mean that there is just one object which is the so-and-so. The proposition “ a is the so-and-so” means that a has the property so-and-so, and nothing else has. “ Mr. A. is the Unionist candidate for this constituency” means “ Mr. A. is a Unionist candidate for this constituency, and no one else is.” “The Unionist candidate for this constituency exists” means “someone is a Unionist candidate for this constituency, and no one else is.” Thus, when we are acquainted with an object which is the so-and-so, we know that the so-and-so exists; but we may know that the so-and-so exists when we are not acquainted with any object which we know to be the so-and-so, and even when we are not acquainted with any object which, in fact, is the so-and-so.
Common words, even proper names, are usually really descriptions. That is to say, the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description. Moreover, the description required to express the thought will vary for different people, or for the same person at different times. The only thing constant (so long as the name is rightly used) is the object to which the name applies. But so long as this remains constant, the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears.
Let us take some illustrations. Suppose some statement made about Bismarck. Assuming that there is such a thing as direct acquaintance with oneself, Bismarck himself might have used his name directly to designate the particular person with whom he was acquainted. In this case, if he made a judgement about himself, he himself might be a constituent of the judgement. Here the proper name has the direct use which it always wishes to have, as simply standing for a certain object,