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 identity 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 identity is between a variable,
i.e. an indeterminate subject ("he"), and Scott; "the author of
Waverley" has been analysed away, and no longer appears as a
constituent of the proposition.[48]
The reason why it is imperative to analyse 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
identity. We have seen also that the common _denotation_, namely
Scott, is not a constituent 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 constituent 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 analysis of the above proposition, "the author of
Waverley" must disappear. This is effected when the above proposition
is analysed 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 constituent, and becoming a
proposition as soon as this constituent 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
substitute _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 substitute 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 constituent of propositions in which descriptions occur;
and this is the reason why, in order to understand such propositions,
we need acquaintance with the constituents of the description, but do
not need acquaintance with its denotation. The first result of
analysis, when applied to propositions whose grammatical subject is
"the so-and-so," is to substitute 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
analysis 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 constituents with which we are acquainted, for a constituent
with which we are not acquainted is unintelligible to us. A judgment,
we found, is not composed of mental constituents called "ideas," but
consists of an occurrence whose constituents are a mind[49] and
certain objects, particulars or universals. (One at least must be a
universal.) When a judgment is rightly analysed, the objects which are
constituents of it must all be objects with which the mind which is a
constituent of it is acquainted. This conclusion forces us to analyse
descriptive phrases occurring in propositions, and to say that the
objects denoted by such phrases are not constituents 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 constituent of our
judgment, and that the judgment cannot be explained by saying that it
affirms identity of denotation with diversity of meaning. It also,
plainly, does not assert identity of meaning. Such judgments,
therefore, can only be analysed 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 analysis 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_, _passim_. 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 assumption there is no single
Objective, but the several constituents of the judgment or assumption
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.
INDEX
Achilles and the tortoise, 80 ff, 89 ff
Acquaintance, the relation of, 209 ff
Alexander, 125
American Realists, the, 134
Aristotle, 42, 76, 97
Bacon, 41
Bergson, 14 ff, 22, 105, 128, 185 ff, 203
Berkeley, 97, 132
Blake, 1
Bosanquet, 99
Broad, 89 _n_
Calculus, the, 82
Cantor, Georg, 64, 81 ff, 85, 91
Carlyle, 50, 82
Cause, the conception of, 135 _n_, 180 ff
Christianity and renunciation, 51
Chuang Tz[)u], 106
Construction of permanent things and matter, 169 ff
Constructions, logical, 155 ff
Darwin, 15, 23, 43
Dedekind, 64, 81 ff, 85
Descartes, 97, 126
Descriptions, 175, 214 ff
Education, 37 ff
Euclid, 62, 92, 94
Evolutionism, 23 ff, 28
Fano, 93
Faraday, 34
Free will, 205 ff
Frege, 78 _n_
Galileo, 42
Gladstone, 177
Good and evil, 26 ff
Hegel, 8, 10, 18, 85, 97, 105 ff
Heine, 113
Heraclitus, 1 ff, 10
Hertz, 34
Holt, 177 _n_
Hume, 1, 97
Infinite, the mathematical, 84 ff
James, William, 100
Jones, Miss E.E.C., 224 _n_, 225
Judgment, 219 ff
Kant, 85, 96, 97, 99, 118 ff
Knowledge by acquaintance, 209 ff;
by description, 214 ff
Laplace, 23
Leibniz, 76, 79, 82 ff, 97, 126, 144, 160
Locke, 97
Logic, the laws of, 68 ff
Macaulay and Taylor's theorem, 95
Malthus, 43
Mathematics, 58 ff;
and the Metaphysicians, 74 ff;
and logic, 75 ff;
and the infinitesimal, 82 ff
Matter, the nature of, 125 ff;
definition of, 164 ff
Maxwell, 34
Meaning and denotation, 223 ff
Meinong, 174, 220 _n_, 225
Militarism, 50
Mill, 185, 193 ff
Mysticism and logic, 1 ff
Necessity, the notion of, 207 ff
Nietzsche, 22, 50
Nunn, 125, 137 _n_, 153
Parmenides, 7 ff, 18, 21
Particulars, awareness of, 210 ff
Peano, 78 ff, 93 ff
Perspectives, 139 ff;
the space of, 158 ff
Philosophy and logic, 111
Physics, sense-data and, 145 ff
Pierce, 76 _n_
Plato, 1 ff, 10, 30, 60, 97
Pragmatism, 22, 105
Realism and the analytic method, 120 ff
Reason and intuition, 12 ff
Relatives, the logic of, 76
Robb, 167 _n_
Santayana, 20
Sense-data, 147, 210 ff;
and physics, 145 ff
Sensibilia, 148 ff
Space, 138 ff;
private, 158 ff;
the logical problem, 114 ff;
the problem in physics, 115 ff;
the epistemological problem, 118 ff
Systems, deterministic, 199;
practically isolated, 198;
relatively isolated, 197;
mechanical, 201
Time, 10, 21 ff, 141 ff, 167 ff
Tristram Shandy, the paradox of, 90 ff
Unity and Plurality, 18 ff
Universals, awareness of, 212 ff
Ward, 180
Weierstrass, 80, 82, 95
Whitehead, 117, 157, 175
Wolf, 173
Zeno the Eleatic, 64, 80, 84, 89 ff
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