Thus if we are to say, as Miss Jones does, that "Scott is the author of Waverley" a.s.serts an ident.i.ty of denotation, we must regard the denotation of "the author of Waverley" as the denotation of what is _meant_ by "the author of Waverley." Let us call the meaning of "the author of Waverley" M. Thus M is what "the author of Waverley" means.

Then we are to suppose that "Scott is the author of Waverley" means "Scott is the denotation of M." But here we are explaining our proposition by another of the same form, and thus we have made no progress towards a real explanation. "The denotation of M," like "the author of Waverley," has both meaning and denotation, on the theory we are examining. If we call its meaning M', our proposition becomes "Scott is the denotation of M'." But this leads at once to an endless regress. Thus the attempt to regard our proposition as a.s.serting ident.i.ty of denotation breaks down, and it becomes imperative to find some other a.n.a.lysis. When this a.n.a.lysis has been completed, we shall be able to reinterpret the phrase "ident.i.ty of denotation," which remains obscure so long as it is taken as fundamental.

The first point to observe is that, in any proposition about "the author of Waverley," provided Scott is not explicitly mentioned, the denotation itself, i.e. Scott, does not occur, but only the concept of denotation, which will be represented by a variable. Suppose we say "the author of Waverley was the author of Marmion," we are certainly not saying that both were Scott--we may have forgotten that there was such a person as Scott. We are saying that there is some man who was the author of Waverley and the author of Marmion. That is to say, there is some one who wrote Waverley and Marmion, and no one else wrote them. Thus the ident.i.ty is that of a variable, i.e. of an indefinite subject, "some one." This is why we can understand propositions about "the author of Waverley," without knowing who he was. When we say "the author of Waverley was a poet," we mean "one and only one man wrote Waverley, and he was a poet"; when we say "the author of Waverley was Scott" we mean "one and only one man wrote Waverley, and he was Scott." Here the ident.i.ty is between a variable, i.e. an indeterminate subject ("he"), and Scott; "the author of Waverley" has been a.n.a.lysed away, and no longer appears as a const.i.tuent of the proposition.[48]

The reason why it is imperative to a.n.a.lyse away the phrase "the author of Waverley" may be stated as follows. It is plain that when we say "the author of Waverley is the author of Marmion," the _is_ expresses ident.i.ty. We have seen also that the common _denotation_, namely Scott, is not a const.i.tuent of this proposition, while the _meanings_ (if any) of "the author of Waverley" and "the author of Marmion" are not identical. We have seen also that, in any sense in which the meaning of a word is a const.i.tuent of a proposition in whose verbal expression the word occurs, "Scott" means the actual man Scott, in the same sense (so far as concerns our present discussion) in which "author" means a certain universal. Thus, if "the author of Waverley"

were a subordinate complex in the above proposition, its _meaning_ would have to be what was said to be identical with the _meaning_ of "the author of Marmion." This is plainly not the case; and the only escape is to say that "the author of Waverley" does not, by itself, have a meaning, though phrases of which it is part do have a meaning.

That is, in a right a.n.a.lysis of the above proposition, "the author of Waverley" must disappear. This is effected when the above proposition is a.n.a.lysed as meaning: "Some one wrote Waverley and no one else did, and that some one also wrote Marmion and no one else did." This may be more simply expressed by saying that the propositional function "_x_ wrote Waverley and Marmion, and no one else did" is capable of truth, i.e. some value of _x_ makes it true, but no other value does. Thus the true subject of our judgment is a propositional function, i.e. a complex containing an undetermined const.i.tuent, and becoming a proposition as soon as this const.i.tuent is determined.

We may now define the denotation of a phrase. If we know that the proposition "_a_ is the so-and-so" is true, i.e. that _a_ is so-and-so and nothing else is, we call _a_ the denotation of the phrase "the so-and-so." A very great many of the propositions we naturally make about "the so-and-so" will remain true or remain false if we subst.i.tute _a_ for "the so-and-so," where _a_ is the denotation of "the so-and-so." Such propositions will also remain true or remain false if we subst.i.tute for "the so-and-so" any other phrase having the same denotation. Hence, as practical men, we become interested in the denotation more than in the description, since the denotation decides as to the truth or falsehood of so many statements in which the description occurs. Moreover, as we saw earlier in considering the relations of description and acquaintance, we often wish to reach the denotation, and are only hindered by lack of acquaintance: in such cases the description is merely the means we employ to get as near as possible to the denotation. Hence it naturally comes to be supposed that the denotation is part of the proposition in which the description occurs. But we have seen, both on logical and on epistemological grounds, that this is an error. The actual object (if any) which is the denotation is not (unless it is explicitly mentioned) a const.i.tuent of propositions in which descriptions occur; and this is the reason why, in order to understand such propositions, we need acquaintance with the const.i.tuents of the description, but do not need acquaintance with its denotation. The first result of a.n.a.lysis, when applied to propositions whose grammatical subject is "the so-and-so," is to subst.i.tute a variable as subject; i.e. we obtain a proposition of the form: "There is _something_ which alone is so-and-so, and that _something_ is such-and-such." The further a.n.a.lysis of propositions concerning "the so-and-so" is thus merged in the problem of the nature of the variable, i.e. of the meanings of _some_, _any_, and _all_. This is a difficult problem, concerning which I do not intend to say anything at present.

To sum up our whole discussion. We began by distinguishing two sorts of knowledge of objects, namely, knowledge by _acquaintance_ and knowledge by _description_. Of these it is only the former that brings the object itself before the mind. We have acquaintance with sense-data, with many universals, and possibly with ourselves, but not with physical objects or other minds. We have _descriptive_ knowledge of an object when we know that it is _the_ object having some property or properties with which we are acquainted; that is to say, when we know that the property or properties in question belong to one object and no more, we are said to have knowledge of that one object by description, whether or not we are acquainted with the object. Our knowledge of physical objects and of other minds is only knowledge by description, the descriptions involved being usually such as involve sense-data. All propositions intelligible to us, whether or not they primarily concern things only known to us by description, are composed wholly of const.i.tuents with which we are acquainted, for a const.i.tuent with which we are not acquainted is unintelligible to us. A judgment, we found, is not composed of mental const.i.tuents called "ideas," but consists of an occurrence whose const.i.tuents are a mind[49] and certain objects, particulars or universals. (One at least must be a universal.) When a judgment is rightly a.n.a.lysed, the objects which are const.i.tuents of it must all be objects with which the mind which is a const.i.tuent of it is acquainted. This conclusion forces us to a.n.a.lyse descriptive phrases occurring in propositions, and to say that the objects denoted by such phrases are not const.i.tuents of judgments in which such phrases occur (unless these objects are explicitly mentioned). This leads us to the view (recommended also on purely logical grounds) that when we say "the author of Marmion was the author of Waverley," Scott himself is not a const.i.tuent of our judgment, and that the judgment cannot be explained by saying that it affirms ident.i.ty of denotation with diversity of meaning. It also, plainly, does not a.s.sert ident.i.ty of meaning. Such judgments, therefore, can only be a.n.a.lysed by breaking up the descriptive phrases, introducing a variable, and making propositional functions the ultimate subjects. In fact, "the so-and-so is such-and-such" will mean that "_x_ is so-and-so and nothing else is, and _x_ is such-and-such" is capable of truth. The a.n.a.lysis of such judgments involves many fresh problems, but the discussion of these problems is not undertaken in the present paper.

FOOTNOTES:

[40] See references later.

[41] _Philosophical Essays_, "The Nature of Truth." I have been persuaded by Mr. Wittgenstein that this theory is somewhat unduly simple, but the modification which I believe it to require does not affect the above argument [1917].

[42] Cf. Meinong, _Ueber Annahmen_, _pa.s.sim_. I formerly supposed, contrary to Meinong's view, that the relationship of supposing might be merely that of presentation. In this view I now think I was mistaken, and Meinong is right. But my present view depends upon the theory that both in judgment and in a.s.sumption there is no single Objective, but the several const.i.tuents of the judgment or a.s.sumption are in a many-term relation to the mind.

[43] This view has been recently advocated by Miss E.E.C. Jones. "A New Law of Thought and its Implications," _Mind_, January, 1911.

[44] I should now exclude "I" from proper names in the strict sense, and retain only "this" [1917].

[45] Meinong, _Ueber Annahmen_, 2nd ed., Leipzig, 1910, p. 141.

[46] _Mind_, July, 1910, p. 380.

[47] _Mind_, July, 1910, p. 379.

[48] The theory which I am advocating is set forth fully, with the logical grounds in its favour, in _Principia Mathematica_, Vol. I.

Introduction, Chap. III; also, less fully, in _Mind_, October, 1905.

[49] I use this phrase merely to denote the something psychological which enters into judgment, without intending to prejudge the question as to what this something is.