Mysticism and Logic and Other EssaysRussell, Bertrand
Philosophy
Mysticism and Logic and Other Essays
Russell, Bertrand
Mathematics; Philosophy; Science
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.
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