Introduction to Mathematical PhilosophyRussell, Bertrand
Philosophy
Introduction to Mathematical Philosophy
Russell, Bertrand
Mathematics -- Philosophy
"The term satisfying the function exists" means:
"There is a term such that is always equivalent
to ' is .'"
In order to define "the author of Waverly was Scotch,"
we have still to take account of the third of our three propositions,
namely, "Whoever wrote Waverly was Scotch." This
will be satisfied by merely adding that the in question is to
be Scotch. Thus "the author of Waverly was Scotch" is:
"There is a term such that (1) ' wrote Waverly' is always
equivalent to ' is ,' (2) is Scotch."
And generally: "the term satisfying satisfies " is
defined as meaning:
"There is a term such that (1) is always equivalent to
' is ,' (2) is true."
This is the definition of propositions in which descriptions occur.
It is possible to have much knowledge concerning a term
described, i.e. to know many propositions concerning "the so-and-so,"
without actually knowing what the so-and-so is, i.e.
without knowing any proposition of the form " is the so-and-so,"
where "" is a name. In a detective story propositions about
"the man who did the deed" are accumulated, in the hope
that ultimately they will suffice to demonstrate that it was
who did the deed. We may even go so far as to say that,
in all such knowledge as can be expressed in words—with the
exception of "this" and "that" and a few other words of
which the meaning varies on different occasions—no names,
in the strict sense, occur, but what seem like names are really
descriptions. We may inquire significantly whether Homer
existed, which we could not do if "Homer" were a name. The
proposition "the so-and-so exists" is significant, whether
true or false; but if is the so-and-so (where "" is a name),
the words " exists" are meaningless. It is only of descriptions—definite
[Pg 178]
or indefinite—that existence can be significantly
asserted; for, if "" is a name, it must name something: what
does not name anything is not a name, and therefore, if intended
to be a name, is a symbol devoid of meaning, whereas a description,
like "the present King of France," does not become incapable
of occurring significantly merely on the ground that it
describes nothing, the reason being that it is a complex symbol,
of which the meaning is derived from that of its constituent
symbols. And so, when we ask whether Homer existed, we are
using the word "Homer" as an abbreviated description: we
may replace it by (say) "the author of the Iliad and the Odyssey."
The same considerations apply to almost all uses of what look
like proper names.
Public-domain text, read in full here on John Shaqi.
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