On Denoting and its history

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On Denoting and its history Harm Boukema
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Everyone agrees that the golden mountain does
not exist is a true proposition. But it has,
apparently, a subject, the golden mountain, and
if this subject did not designate some object,
the proposition would seem to be meaningless.
Meinong inferred that there is a golden mountain,
which is golden and a mountain, but does not
exist. He even thought that the existent golden
mountain is existent, but does not exist. This
did not satisfy me, and the desire to avoid
Meinongs unduly populous realm of being led me
to the theory of descriptions. What was of
importance in this theory was the discovery that,
in analysing a significant sentence, one must not
assume that each separate word or phrase has
significance on its own account. The golden
mountain can be part of a significant sentence,
but is not significant in isolation. It soon
appeared that class-symbols could be treated like
descriptions, i.e., as non-significant parts of
significant sentences. This made it possible to
see, in a general way, how a solution of the
contradictions might be possible. My Mental
Development (1944)
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In the belief that propositions must, in the last
analysis, have a subject and predicate, Leibniz
does not differ either from his predecessors or
from his successors. Any philosophy which uses
either substance or the Absolute will be found,
on inspection, to depend on this belief. Kants
belief in an unknowable thing-in-itself was
largely due to the same theory. It cannot be
denied, therefore, that the doctrine is
important. Philosophers have differed, not so
much in respect of belief in its truth, as in
respect of their consistency in carrying it out.
In this latter respect, Leibniz deserves
credit. The Philosophy of Leibniz (1900)
Section 10
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Next after subject-predicate propositions come
two types of propositions which appear equally
simple. These are the propositions in which a
relation is asserted between two terms, and those
in in which two terms are said to be two. The
Principles of Mathematics (1903) 94
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Indeed it may be said that the logical purpose
which is served by the theory of denoting is, to
enable propositions of finite complexity to deal
with infinite classes of terms this object is
effected by all, any, and every, and if it were
not effected, every general proposition about an
infinite class would have to be infinitely
complex. Now, for my part, I see no possible way
of deciding whether propositions of infinite
complexity are possible or not but this at least
is clear, that all the propositions known to us
(and, it would seem, all propositions that we can
know) are of finite complexity. It is only by
obtaining such propositions about infinite
classes that we are enabled to deal with
infinity and it is a remarkable and fortunate
fact that this method is successful. Thus the
question whether or not there are infinite
unities must be left unresolved the only thing
we can say, on this subject, is that no such
unities occur in any department of human
knowledge, and therefore none such are relevant
to the foundation of mathematics. The Principles
of Mathematics (1903) 141
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The use of inverted commas may be explained as
follows. When a concept has meaning and
denotation, if we wish to say anything about the
meaning, we must put it in an entity-position
but if we it itself in an entity-position, we
shall be really speaking about the denotation,
not the meaning, for that is always the case when
a denoting complex is put in an entity-position.
Thus in order to speak about the meaning, we must
substitute for the meaning something which
denotes the meaning. Hence the meanings of
denoting complexes can only be approached by
means of complexes which denote those meanings.
This is what complexes in inverted commas are. If
we say any man is denoting a complex, any
man stands for the meaning of the complex any
man, which is a denoting concept. But this is
circular fir we use any man in explaining any
man. And the circle is unavoidable. For if we
say the meaning of any man, that will stand for
the meaning of the denotation of any man, which
is not what we want. On Fundamentals (1905)
35
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It might be supposed that the whole matter could
be simplified by introducing a relation of
denoting instead of all the complications about
C and C, we might try to put x denotes y. But
we want to be able to speak of what x denotes,
and unfortunately what x denotes is a denoting
complex. We might avoid this as follows Let C be
an unambiguously denoting complex (we may now
drop the inverted commas) then we have (?y) C
denotes y C denotes z.?z.zy Then what is
commonly expressed by ?C will be replaced
by (?y) C denotes y C denotes z.?z.zy
?y On Fundamentals (1905) 40
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The most convenient view might seem to be to take
everything and anything as primitive ideas,
putting (x). ? x.. ? (everything) (x). ?
x.. ? (anything). But it seems that on this
view everything and anything are denoting
concepts involving all the difficulties
considered in 35-39, on account of which we
adopted the theory of 40. We shall have to
distinguish between everything and everything,
i.e. we shall have everything is not
everything, but only one thing. Also we shall
find that if we attempt to say anything about the
meaning of everything, we must do so by means
of a denoting concept which denotes that meaning,
and which must not contain that meaning occurring
as entity, since when it occurs as entity it
stands for its denotation, which is not what we
want. These objections, to all appearance, are as
fatal here as they were in regard to the. Thus it
is better to find some other theory. On
Fundamentals (1905) 44
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The interesting and curious point is that, by
driving denoting back and back as we have been
doing, we get it all reduced to the one notion of
any, from which I started at first. This one
notion seems to be presupposed always, and to
involve in itself all the difficulties on account
of which we have rejected other denoting
concepts. Thus we are left with the task of
concocting de novo a tenable theory of any, in
which denoting is not used. The interesting point
which we have a elicited above is that any is a
genuinely more fundamental than other denoting
concepts they can be explained byit, but not it
by them. And any itself is not fundamental in
general, but only in the shape of anything. On
fundamentals (1905) 47
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The above gives a reduction of all propositions
in which denoting phrases occur to forms in which
no such phrases occur. Why it is imperative to
effect such a reduction, the subsequent
discussion will endeavour to show. The evidence
for the above theory is derived from the
difficulties which seem unavoidable if we regard
denoting phrases as standing for genuine
constituents of the propositions in whose verbal
expressions they occur. Of the possible theories
which admit such constituents the simplest is
that of Meinong. On Denoting (1905) p. 428
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The interpretation of such phrases is a matter of
considerable difficulty indeed, it is very hard
to frame any theory not susceptible of formal
refutation. All the difficulties with which I am
acquainted are met, so far as I can discover, by
the theory which I am about to explain. On
denoting (1905) p. 479
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Of the many other consequences of the view I have
been advocating, I will say nothing. I will only
beg the reader not to make up his mind against
the view as he might be tempted to do, on
account of its apparently excessive complication
until he has attempted to construct a theory of
his own on the subject of denotation. This
attempt, I believe, will convince him that,
whatever the true theory may be, it cannot have
such a simplicity as one might have expected
beforehand. On Denoting (1905) p. 493
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The relation of the meaning to the denotation
involves certain rather curious difficulties,
which seem in themselves sufficient to prove that
the theory which leads to such difficulties must
be wrong. On Denoting (1905) p. 485
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Thus all phrases (other than propositions)
containing the word the (in the singular) are
incomplete symbols they have a meaning in the
use, but not in isolation. For the author of
Waverley cannot mean the same as Scott, or
Scott is the author of Waverley would mean the
same as Scott is Scott, which it plainly does
not nor can the author of Waverly mean
anything other than Scott, or Scott is the
author of Waverley would be false. Hence the
author of Waverley means nothing. Principia
Mathematica (1910) p. 67