The Principles of Mathematics (1903)

§ 483

It remains to discuss afresh the question whether concepts can be made into logical subjects without change of meaning. Frege's theory, that when this appears to be done it is really the name of the concept that is involved, will not, I think, bear investigation. In the first place, the mere assertion not the concept, but its name is involved, has already made the concept a subject. In the second place, it seems always legitimate to ask: what is it that is named by this name? If there were no answer, the name could not be a name; but if there is an answer, the concept, as opposed to its name, can be made a subject. (Frege, it may be observed, does not seem to have clearly disentangled the logical and linguistic elements of naming: the former depend upon denoting, and have, I think, a much more restricted range than Frege allows them.) It is true that we found difficulties in the doctrine that everything can be a logical subject: as regards any a, for example, and also as regards plurals. But in the case of any a, there is ambiguity, which introduces a new class of problems; and as regards plurals, there are propositions in which the many behave like a logical subject in every respect except that they are many subjects and not one only (see §§ 127, 128). In the case of concepts, however, no such escapes are possible. The case of asserted propositions is difficult, but is met, I think, by holding that an asserted proposition is merely a true proposition, and is therefore asserted wherever it occurs, even when grammar would lead to the opposite conclusion. Thus, on the whole, the doctrine of concepts which cannot be made subjects seems untenable.(§ 483 ¶ 1)