I formerly supposed,
contrary to Meinong's view, that the relationship of supposing might
be merely that of presentation.
contrary to Meinong's view, that the relationship of supposing might
be merely that of presentation.
Mysticism and Logic and Other Essays by Bertrand Russell
" The word "German" will again
have different meanings for different people. To some it will recall
travels in Germany, to some the look of Germany on the map, and so on.
But if we are to obtain a description which we know to be applicable,
we shall be compelled, at some point, to bring in a reference to a
particular with which we are acquainted. Such reference is involved in
any mention of past, present, and future (as opposed to definite
dates), or of here and there, or of what others have told us. Thus it
would seem that, in some way or other, a description known to be
applicable to a particular must involve some reference to a particular
with which we are acquainted, if our knowledge about the thing
described is not to be merely what follows logically from the
description. For example, "the most long-lived of men" is a
description which must apply to some man, but we can make no judgments
concerning this man which involve knowledge about him beyond what the
description gives. If, however, we say, "the first Chancellor of the
German Empire was an astute diplomatist," we can only be assured of
the truth of our judgment in virtue of something with which we are
acquainted--usually a testimony heard or read. Considered
psychologically, apart from the information we convey to others, apart
from the fact about the actual Bismarck, which gives importance to
our judgment, the thought we really have contains the one or more
particulars involved, and otherwise consists wholly of concepts. All
names of places--London, England, Europe, the earth, the Solar
System--similarly involve, when used, descriptions which start from
some one or more particulars with which we are acquainted. I suspect
that even the Universe, as considered by metaphysics, involves such a
connection with particulars. In logic, on the contrary, where we are
concerned not merely with what does exist, but with whatever might or
could exist or be, no reference to actual particulars is involved.
It would seem that, when we make a statement about something only
known by description, we often _intend_ to make our statement, not in
the form involving the description, but about the actual thing
described. That is to say, when we say anything about Bismarck, we
should like, if we could, to make the judgment which Bismarck alone
can make, namely, the judgment of which he himself is a constituent.
In this we are necessarily defeated, since the actual Bismarck is
unknown to us. But we know that there is an object B called Bismarck,
and that B was an astute diplomatist. We can thus _describe_ the
proposition we should like to affirm, namely, "B was an astute
diplomatist," where B is the object which was Bismarck. What enables
us to communicate in spite of the varying descriptions we employ is
that we know there is a true proposition concerning the actual
Bismarck, and that, however we may vary the description (so long as
the description is correct), the proposition described is still the
same. This proposition, which is described and is known to be true, is
what interests us; but we are not acquainted with the proposition
itself, and do not know _it_, though we know it is true.
It will be seen that there are various stages in the removal from
acquaintance with particulars: there is Bismarck to people who knew
him, Bismarck to those who only know of him through history, the man
with the iron mask, the longest-lived of men. These are progressively
further removed from acquaintance with particulars, and there is a
similar hierarchy in the region of universals. Many universals, like
many particulars, are only known to us by description. But here, as in
the case of particulars, knowledge concerning what is known by
description is ultimately reducible to knowledge concerning what is
known by acquaintance.
The fundamental epistemological principle in the analysis of
propositions containing descriptions is this: _Every proposition which
we can understand must be composed wholly of constituents with which
we are acquainted. _ From what has been said already, it will be plain
why I advocate this principle, and how I propose to meet the case of
propositions which at first sight contravene it. Let us begin with the
reasons for supposing the principle true.
The chief reason for supposing the principle true is that it seems
scarcely possible to believe that we can make a judgment or entertain
a supposition without knowing what it is that we are judging or
supposing about. If we make a judgment about (say) Julius Caesar, it is
plain that the actual person who was Julius Caesar is not a constituent
of the judgment. But before going further, it may be well to explain
what I mean when I say that this or that is a constituent of a
judgment, or of a proposition which we understand. To begin with
judgments: a judgment, as an occurrence, I take to be a relation of a
mind to several entities, namely, the entities which compose what is
judged. If, e. g. I judge that A loves B, the judgment as an event
consists in the existence, at a certain moment, of a specific
four-term relation, called _judging_, between me and A and love and B.
That is to say, at the time when I judge, there is a certain complex
whose terms are myself and A and love and B, and whose relating
relation is _judging_. My reasons for this view have been set forth
elsewhere,[41] and I shall not repeat them here. Assuming this view of
judgment, the constituents of the judgment are simply the constituents
of the complex which is the judgment. Thus, in the above case, the
constituents are myself and A and love and B and judging. But myself
and judging are constituents shared by all my judgments; thus the
_distinctive_ constituents of the particular judgment in question are
A and love and B. Coming now to what is meant by "understanding a
proposition," I should say that there is another relation possible
between me and A and love and B, which is called my _supposing_ that A
loves B. [42] When we can _suppose_ that A loves B, we "understand the
proposition" _A loves B_. Thus we often understand a proposition in
cases where we have not enough knowledge to make a judgment.
Supposing, like judging, is a many-term relation, of which a mind is
one term. The other terms of the relation are called the constituents
of the proposition supposed. Thus the principle which I enunciated may
be re-stated as follows: _Whenever a relation of supposing or judging
occurs, the terms to which the supposing or judging mind is related by
the relation of supposing or judging must be terms with which the mind
in question is acquainted. _ This is merely to say that we cannot make
a judgment or a supposition without knowing what it is that we are
making our judgment or supposition about. It seems to me that the
truth of this principle is evident as soon as the principle is
understood; I shall, therefore, in what follows, assume the principle,
and use it as a guide in analysing judgments that contain
descriptions.
Returning now to Julius Caesar, I assume that it will be admitted that
he himself is not a constituent of any judgment which I can make. But
at this point it is necessary to examine the view that judgments are
composed of something called "ideas," and that it is the "idea" of
Julius Caesar that is a constituent of my judgment. I believe the
plausibility of this view rests upon a failure to form a right theory
of descriptions. We may mean by my "idea" of Julius Caesar the things
that I know about him, e. g. that he conquered Gaul, was assassinated
on the Ides of March, and is a plague to schoolboys. Now I am
admitting, and indeed contending, that in order to discover what is
actually in my mind when I judge about Julius Caesar, we must
substitute for the proper name a description made up of some of the
things I know about him. (A description which will often serve to
express my thought is "the man whose name was _Julius Caesar_. " For
whatever else I may have forgotten about him, it is plain that when I
mention him I have not forgotten that that was his name. ) But although
I think the theory that judgments consist of ideas may have been
suggested in some such way, yet I think the theory itself is
fundamentally mistaken. The view seems to be that there is some
mental existent which may be called the "idea" of something outside
the mind of the person who has the idea, and that, since judgment is a
mental event, its constituents must be constituents of the mind of the
person judging. But in this view ideas become a veil between us and
outside things--we never really, in knowledge, attain to the things we
are supposed to be knowing about, but only to the ideas of those
things. The relation of mind, idea, and object, on this view, is
utterly obscure, and, so far as I can see, nothing discoverable by
inspection warrants the intrusion of the idea between the mind and the
object. I suspect that the view is fostered by the dislike of
relations, and that it is felt the mind could not know objects unless
there were something "in" the mind which could be called the state of
knowing the object. Such a view, however, leads at once to a vicious
endless regress, since the relation of idea to object will have to be
explained by supposing that the idea itself has an idea of the object,
and so on _ad infinitum_. I therefore see no reason to believe that,
when we are acquainted with an object, there is in us something which
can be called the "idea" of the object. On the contrary, I hold that
acquaintance is wholly a relation, not demanding any such constituent
of the mind as is supposed by advocates of "ideas. " This is, of
course, a large question, and one which would take us far from our
subject if it were adequately discussed. I therefore content myself
with the above indications, and with the corollary that, in judging,
the actual objects concerning which we judge, rather than any supposed
purely mental entities, are constituents of the complex which is the
judgment.
When, therefore, I say that we must substitute for "Julius Caesar" some
description of Julius Caesar, in order to discover the meaning of a
judgment nominally about him, I am not saying that we must substitute
an idea. Suppose our description is "the man whose name was _Julius
Caesar_. " Let our judgment be "Julius Caesar was assassinated. " Then it
becomes "the man whose name was _Julius Caesar_ was assassinated. " Here
_Julius Caesar_ is a noise or shape with which we are acquainted, and
all the other constituents of the judgment (neglecting the tense in
"was") are _concepts_ with which we are acquainted. Thus our judgment
is wholly reduced to constituents with which we are acquainted, but
Julius Caesar himself has ceased to be a constituent of our judgment.
This, however, requires a proviso, to be further explained shortly,
namely that "the man whose name was _Julius Caesar_" must not, as a
whole, be a constituent of our judgment, that is to say, this phrase
must not, as a whole, have a meaning which enters into the judgment.
Any right analysis of the judgment, therefore, must break up this
phrase, and not treat it as a subordinate complex which is part of the
judgment. The judgment "the man whose name was _Julius Caesar_ was
assassinated" may be interpreted as meaning "one and only one man was
called _Julius Caesar_, and that one was assassinated. " Here it is
plain that there is no constituent corresponding to the phrase "the
man whose name was _Julius Caesar_. " Thus there is no reason to regard
this phrase as expressing a constituent of the judgment, and we have
seen that this phrase must be broken up if we are to be acquainted
with all the constituents of the judgment. This conclusion, which we
have reached from considerations concerned with the theory of
knowledge, is also forced upon us by logical considerations, which
must now be briefly reviewed.
It is common to distinguish two aspects, _meaning_ and _denotation_,
such phrases as "the author of Waverley. " The meaning will be a
certain complex, consisting (at least) of authorship and Waverley with
some relation; the denotation will be Scott. Similarly "featherless
bipeds" will have a complex meaning, containing as constituents the
presence of two feet and the absence of feathers, while its denotation
will be the class of men. Thus when we say "Scott is the author of
Waverley" or "men are the same as featherless bipeds," we are
asserting an identity of denotation, and this assertion is worth
making because of the diversity of meaning. [43] I believe that the
duality of meaning and denotation, though capable of a true
interpretation, is misleading if taken as fundamental. The denotation,
I believe, is not a constituent of the proposition, except in the case
of proper names, i. e. of words which do not assign a property to an
object, but merely and solely name it. And I should hold further that,
in this sense, there are only two words which are strictly proper
names of particulars, namely, "I" and "this. "[44]
One reason for not believing the denotation to be a constituent of the
proposition is that we may know the proposition even when we are not
acquainted with the denotation. The proposition "the author of
Waverley is a novelist" was known to people who did not know that "the
author of Waverley" denoted Scott. This reason has been already
sufficiently emphasised.
A second reason is that propositions concerning "the so-and-so" are
possible even when "the so-and-so" has no denotation. Take, e. g. "the
golden mountain does not exist" or "the round square is
self-contradictory. " If we are to preserve the duality of meaning and
denotation, we have to say, with Meinong, that there are such objects
as the golden mountain and the round square, although these objects do
not have being. We even have to admit that the existent round square
is existent, but does not exist. [45] Meinong does not regard this as a
contradiction, but I fail to see that it is not one. Indeed, it seems
to me evident that the judgment "there is no such object as the round
square" does not presuppose that there is such an object. If this is
admitted, however, we are led to the conclusion that, by parity of
form, no judgment concerning "the so-and-so" actually involves the
so-and-so as a constituent.
Miss Jones[46] contends that there is no difficulty in admitting
contradictory predicates concerning such an object as "the present
King of France," on the ground that this object is in itself
contradictory. Now it might, of course, be argued that this object,
unlike the round square, is not self-contradictory, but merely
non-existent. This, however, would not go to the root of the matter.
The real objection to such an argument is that the law of
contradiction ought not to be stated in the traditional form "A is not
both B and not B," but in the form "no proposition is both true and
false. " The traditional form only applies to certain propositions,
namely, to those which attribute a predicate to a subject. When the
law is stated of propositions, instead of being stated concerning
subjects and predicates, it is at once evident that propositions about
the present King of France or the round square can form no exception,
but are just as incapable of being both true and false as other
propositions. Miss Jones[47] argues that "Scott is the author of
Waverley" asserts identity of denotation between _Scott_ and _the
author of Waverley_. But there is some difficulty in choosing among
alternative meanings of this contention. In the first place, it should
be observed that _the author of Waverley_ is not a _mere_ name, like
_Scott_. _Scott_ is merely a noise or shape conventionally used to
designate a certain person; it gives us no information about that
person, and has nothing that can be called meaning as opposed to
denotation. (I neglect the fact, considered above, that even proper
names, as a rule, really stand for descriptions. ) But _the author of
Waverley_ is not merely conventionally a name for Scott; the element
of mere convention belongs here to the separate words, _the_ and
_author_ and _of_ and _Waverley_. Given what these words stand for,
_the author of Waverley_ is no longer arbitrary. When it is said that
Scott is the author of Waverley, we are not stating that these are two
_names_ for one man, as we should be if we said "Scott is Sir Walter. "
A man's name is what he is called, but however much Scott had been
called the author of Waverley, that would not have made him be the
author; it was necessary for him actually to write Waverley, which was
a fact having nothing to do with names.
If, then, we are asserting identity of denotation, we must not mean by
_denotation_ the mere relation of a name to the thing named. In fact,
it would be nearer to the truth to say that the _meaning_ of "Scott"
is the _denotation_ of "the author of Waverley. " The relation of
"Scott" to Scott is that "Scott" means Scott, just as the relation of
"author" to the concept which is so called is that "author" means this
concept. Thus if we distinguish meaning and denotation in "the author
of Waverley," we shall have to say that "Scott" has meaning but not
denotation. Also when we say "Scott is the author of Waverley," the
_meaning_ of "the author of Waverley" is relevant to our assertion.
For if the denotation alone were relevant, any other phrase with the
same denotation would give the same proposition. Thus "Scott is the
author of Marmion" would be the same proposition as "Scott is the
author of Waverley. " But this is plainly not the case, since from the
first we learn that Scott wrote Marmion and from the second we learn
that he wrote Waverley, but the first tells us nothing about Waverley
and the second nothing about Marmion. Hence the meaning of "the author
of Waverley," as opposed to the denotation, is certainly relevant to
"Scott is the author of Waverley. "
We have thus agreed that "the author of Waverley" is not a mere name,
and that its meaning is relevant in propositions in which it occurs.
Thus if we are to say, as Miss Jones does, that "Scott is the author
of Waverley" asserts an identity 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 asserting
identity of denotation breaks down, and it becomes imperative to find
some other analysis. When this analysis has been completed, we shall
be able to reinterpret the phrase "identity 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 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? , 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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have different meanings for different people. To some it will recall
travels in Germany, to some the look of Germany on the map, and so on.
But if we are to obtain a description which we know to be applicable,
we shall be compelled, at some point, to bring in a reference to a
particular with which we are acquainted. Such reference is involved in
any mention of past, present, and future (as opposed to definite
dates), or of here and there, or of what others have told us. Thus it
would seem that, in some way or other, a description known to be
applicable to a particular must involve some reference to a particular
with which we are acquainted, if our knowledge about the thing
described is not to be merely what follows logically from the
description. For example, "the most long-lived of men" is a
description which must apply to some man, but we can make no judgments
concerning this man which involve knowledge about him beyond what the
description gives. If, however, we say, "the first Chancellor of the
German Empire was an astute diplomatist," we can only be assured of
the truth of our judgment in virtue of something with which we are
acquainted--usually a testimony heard or read. Considered
psychologically, apart from the information we convey to others, apart
from the fact about the actual Bismarck, which gives importance to
our judgment, the thought we really have contains the one or more
particulars involved, and otherwise consists wholly of concepts. All
names of places--London, England, Europe, the earth, the Solar
System--similarly involve, when used, descriptions which start from
some one or more particulars with which we are acquainted. I suspect
that even the Universe, as considered by metaphysics, involves such a
connection with particulars. In logic, on the contrary, where we are
concerned not merely with what does exist, but with whatever might or
could exist or be, no reference to actual particulars is involved.
It would seem that, when we make a statement about something only
known by description, we often _intend_ to make our statement, not in
the form involving the description, but about the actual thing
described. That is to say, when we say anything about Bismarck, we
should like, if we could, to make the judgment which Bismarck alone
can make, namely, the judgment of which he himself is a constituent.
In this we are necessarily defeated, since the actual Bismarck is
unknown to us. But we know that there is an object B called Bismarck,
and that B was an astute diplomatist. We can thus _describe_ the
proposition we should like to affirm, namely, "B was an astute
diplomatist," where B is the object which was Bismarck. What enables
us to communicate in spite of the varying descriptions we employ is
that we know there is a true proposition concerning the actual
Bismarck, and that, however we may vary the description (so long as
the description is correct), the proposition described is still the
same. This proposition, which is described and is known to be true, is
what interests us; but we are not acquainted with the proposition
itself, and do not know _it_, though we know it is true.
It will be seen that there are various stages in the removal from
acquaintance with particulars: there is Bismarck to people who knew
him, Bismarck to those who only know of him through history, the man
with the iron mask, the longest-lived of men. These are progressively
further removed from acquaintance with particulars, and there is a
similar hierarchy in the region of universals. Many universals, like
many particulars, are only known to us by description. But here, as in
the case of particulars, knowledge concerning what is known by
description is ultimately reducible to knowledge concerning what is
known by acquaintance.
The fundamental epistemological principle in the analysis of
propositions containing descriptions is this: _Every proposition which
we can understand must be composed wholly of constituents with which
we are acquainted. _ From what has been said already, it will be plain
why I advocate this principle, and how I propose to meet the case of
propositions which at first sight contravene it. Let us begin with the
reasons for supposing the principle true.
The chief reason for supposing the principle true is that it seems
scarcely possible to believe that we can make a judgment or entertain
a supposition without knowing what it is that we are judging or
supposing about. If we make a judgment about (say) Julius Caesar, it is
plain that the actual person who was Julius Caesar is not a constituent
of the judgment. But before going further, it may be well to explain
what I mean when I say that this or that is a constituent of a
judgment, or of a proposition which we understand. To begin with
judgments: a judgment, as an occurrence, I take to be a relation of a
mind to several entities, namely, the entities which compose what is
judged. If, e. g. I judge that A loves B, the judgment as an event
consists in the existence, at a certain moment, of a specific
four-term relation, called _judging_, between me and A and love and B.
That is to say, at the time when I judge, there is a certain complex
whose terms are myself and A and love and B, and whose relating
relation is _judging_. My reasons for this view have been set forth
elsewhere,[41] and I shall not repeat them here. Assuming this view of
judgment, the constituents of the judgment are simply the constituents
of the complex which is the judgment. Thus, in the above case, the
constituents are myself and A and love and B and judging. But myself
and judging are constituents shared by all my judgments; thus the
_distinctive_ constituents of the particular judgment in question are
A and love and B. Coming now to what is meant by "understanding a
proposition," I should say that there is another relation possible
between me and A and love and B, which is called my _supposing_ that A
loves B. [42] When we can _suppose_ that A loves B, we "understand the
proposition" _A loves B_. Thus we often understand a proposition in
cases where we have not enough knowledge to make a judgment.
Supposing, like judging, is a many-term relation, of which a mind is
one term. The other terms of the relation are called the constituents
of the proposition supposed. Thus the principle which I enunciated may
be re-stated as follows: _Whenever a relation of supposing or judging
occurs, the terms to which the supposing or judging mind is related by
the relation of supposing or judging must be terms with which the mind
in question is acquainted. _ This is merely to say that we cannot make
a judgment or a supposition without knowing what it is that we are
making our judgment or supposition about. It seems to me that the
truth of this principle is evident as soon as the principle is
understood; I shall, therefore, in what follows, assume the principle,
and use it as a guide in analysing judgments that contain
descriptions.
Returning now to Julius Caesar, I assume that it will be admitted that
he himself is not a constituent of any judgment which I can make. But
at this point it is necessary to examine the view that judgments are
composed of something called "ideas," and that it is the "idea" of
Julius Caesar that is a constituent of my judgment. I believe the
plausibility of this view rests upon a failure to form a right theory
of descriptions. We may mean by my "idea" of Julius Caesar the things
that I know about him, e. g. that he conquered Gaul, was assassinated
on the Ides of March, and is a plague to schoolboys. Now I am
admitting, and indeed contending, that in order to discover what is
actually in my mind when I judge about Julius Caesar, we must
substitute for the proper name a description made up of some of the
things I know about him. (A description which will often serve to
express my thought is "the man whose name was _Julius Caesar_. " For
whatever else I may have forgotten about him, it is plain that when I
mention him I have not forgotten that that was his name. ) But although
I think the theory that judgments consist of ideas may have been
suggested in some such way, yet I think the theory itself is
fundamentally mistaken. The view seems to be that there is some
mental existent which may be called the "idea" of something outside
the mind of the person who has the idea, and that, since judgment is a
mental event, its constituents must be constituents of the mind of the
person judging. But in this view ideas become a veil between us and
outside things--we never really, in knowledge, attain to the things we
are supposed to be knowing about, but only to the ideas of those
things. The relation of mind, idea, and object, on this view, is
utterly obscure, and, so far as I can see, nothing discoverable by
inspection warrants the intrusion of the idea between the mind and the
object. I suspect that the view is fostered by the dislike of
relations, and that it is felt the mind could not know objects unless
there were something "in" the mind which could be called the state of
knowing the object. Such a view, however, leads at once to a vicious
endless regress, since the relation of idea to object will have to be
explained by supposing that the idea itself has an idea of the object,
and so on _ad infinitum_. I therefore see no reason to believe that,
when we are acquainted with an object, there is in us something which
can be called the "idea" of the object. On the contrary, I hold that
acquaintance is wholly a relation, not demanding any such constituent
of the mind as is supposed by advocates of "ideas. " This is, of
course, a large question, and one which would take us far from our
subject if it were adequately discussed. I therefore content myself
with the above indications, and with the corollary that, in judging,
the actual objects concerning which we judge, rather than any supposed
purely mental entities, are constituents of the complex which is the
judgment.
When, therefore, I say that we must substitute for "Julius Caesar" some
description of Julius Caesar, in order to discover the meaning of a
judgment nominally about him, I am not saying that we must substitute
an idea. Suppose our description is "the man whose name was _Julius
Caesar_. " Let our judgment be "Julius Caesar was assassinated. " Then it
becomes "the man whose name was _Julius Caesar_ was assassinated. " Here
_Julius Caesar_ is a noise or shape with which we are acquainted, and
all the other constituents of the judgment (neglecting the tense in
"was") are _concepts_ with which we are acquainted. Thus our judgment
is wholly reduced to constituents with which we are acquainted, but
Julius Caesar himself has ceased to be a constituent of our judgment.
This, however, requires a proviso, to be further explained shortly,
namely that "the man whose name was _Julius Caesar_" must not, as a
whole, be a constituent of our judgment, that is to say, this phrase
must not, as a whole, have a meaning which enters into the judgment.
Any right analysis of the judgment, therefore, must break up this
phrase, and not treat it as a subordinate complex which is part of the
judgment. The judgment "the man whose name was _Julius Caesar_ was
assassinated" may be interpreted as meaning "one and only one man was
called _Julius Caesar_, and that one was assassinated. " Here it is
plain that there is no constituent corresponding to the phrase "the
man whose name was _Julius Caesar_. " Thus there is no reason to regard
this phrase as expressing a constituent of the judgment, and we have
seen that this phrase must be broken up if we are to be acquainted
with all the constituents of the judgment. This conclusion, which we
have reached from considerations concerned with the theory of
knowledge, is also forced upon us by logical considerations, which
must now be briefly reviewed.
It is common to distinguish two aspects, _meaning_ and _denotation_,
such phrases as "the author of Waverley. " The meaning will be a
certain complex, consisting (at least) of authorship and Waverley with
some relation; the denotation will be Scott. Similarly "featherless
bipeds" will have a complex meaning, containing as constituents the
presence of two feet and the absence of feathers, while its denotation
will be the class of men. Thus when we say "Scott is the author of
Waverley" or "men are the same as featherless bipeds," we are
asserting an identity of denotation, and this assertion is worth
making because of the diversity of meaning. [43] I believe that the
duality of meaning and denotation, though capable of a true
interpretation, is misleading if taken as fundamental. The denotation,
I believe, is not a constituent of the proposition, except in the case
of proper names, i. e. of words which do not assign a property to an
object, but merely and solely name it. And I should hold further that,
in this sense, there are only two words which are strictly proper
names of particulars, namely, "I" and "this. "[44]
One reason for not believing the denotation to be a constituent of the
proposition is that we may know the proposition even when we are not
acquainted with the denotation. The proposition "the author of
Waverley is a novelist" was known to people who did not know that "the
author of Waverley" denoted Scott. This reason has been already
sufficiently emphasised.
A second reason is that propositions concerning "the so-and-so" are
possible even when "the so-and-so" has no denotation. Take, e. g. "the
golden mountain does not exist" or "the round square is
self-contradictory. " If we are to preserve the duality of meaning and
denotation, we have to say, with Meinong, that there are such objects
as the golden mountain and the round square, although these objects do
not have being. We even have to admit that the existent round square
is existent, but does not exist. [45] Meinong does not regard this as a
contradiction, but I fail to see that it is not one. Indeed, it seems
to me evident that the judgment "there is no such object as the round
square" does not presuppose that there is such an object. If this is
admitted, however, we are led to the conclusion that, by parity of
form, no judgment concerning "the so-and-so" actually involves the
so-and-so as a constituent.
Miss Jones[46] contends that there is no difficulty in admitting
contradictory predicates concerning such an object as "the present
King of France," on the ground that this object is in itself
contradictory. Now it might, of course, be argued that this object,
unlike the round square, is not self-contradictory, but merely
non-existent. This, however, would not go to the root of the matter.
The real objection to such an argument is that the law of
contradiction ought not to be stated in the traditional form "A is not
both B and not B," but in the form "no proposition is both true and
false. " The traditional form only applies to certain propositions,
namely, to those which attribute a predicate to a subject. When the
law is stated of propositions, instead of being stated concerning
subjects and predicates, it is at once evident that propositions about
the present King of France or the round square can form no exception,
but are just as incapable of being both true and false as other
propositions. Miss Jones[47] argues that "Scott is the author of
Waverley" asserts identity of denotation between _Scott_ and _the
author of Waverley_. But there is some difficulty in choosing among
alternative meanings of this contention. In the first place, it should
be observed that _the author of Waverley_ is not a _mere_ name, like
_Scott_. _Scott_ is merely a noise or shape conventionally used to
designate a certain person; it gives us no information about that
person, and has nothing that can be called meaning as opposed to
denotation. (I neglect the fact, considered above, that even proper
names, as a rule, really stand for descriptions. ) But _the author of
Waverley_ is not merely conventionally a name for Scott; the element
of mere convention belongs here to the separate words, _the_ and
_author_ and _of_ and _Waverley_. Given what these words stand for,
_the author of Waverley_ is no longer arbitrary. When it is said that
Scott is the author of Waverley, we are not stating that these are two
_names_ for one man, as we should be if we said "Scott is Sir Walter. "
A man's name is what he is called, but however much Scott had been
called the author of Waverley, that would not have made him be the
author; it was necessary for him actually to write Waverley, which was
a fact having nothing to do with names.
If, then, we are asserting identity of denotation, we must not mean by
_denotation_ the mere relation of a name to the thing named. In fact,
it would be nearer to the truth to say that the _meaning_ of "Scott"
is the _denotation_ of "the author of Waverley. " The relation of
"Scott" to Scott is that "Scott" means Scott, just as the relation of
"author" to the concept which is so called is that "author" means this
concept. Thus if we distinguish meaning and denotation in "the author
of Waverley," we shall have to say that "Scott" has meaning but not
denotation. Also when we say "Scott is the author of Waverley," the
_meaning_ of "the author of Waverley" is relevant to our assertion.
For if the denotation alone were relevant, any other phrase with the
same denotation would give the same proposition. Thus "Scott is the
author of Marmion" would be the same proposition as "Scott is the
author of Waverley. " But this is plainly not the case, since from the
first we learn that Scott wrote Marmion and from the second we learn
that he wrote Waverley, but the first tells us nothing about Waverley
and the second nothing about Marmion. Hence the meaning of "the author
of Waverley," as opposed to the denotation, is certainly relevant to
"Scott is the author of Waverley. "
We have thus agreed that "the author of Waverley" is not a mere name,
and that its meaning is relevant in propositions in which it occurs.
Thus if we are to say, as Miss Jones does, that "Scott is the author
of Waverley" asserts an identity 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 asserting
identity of denotation breaks down, and it becomes imperative to find
some other analysis. When this analysis has been completed, we shall
be able to reinterpret the phrase "identity 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 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? , 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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