Introduction to Mathematical PhilosophyRussell, Bertrand
Philosophy
Introduction to Mathematical Philosophy
Russell, Bertrand
Mathematics -- Philosophy
We come now to the main subject of the present chapter,
namely, the definition of the word the (in the singular). One
very important point about the definition of "a so-and-so"
applies equally to "the so-and-so"; the definition to be sought
is a definition of propositions in which this phrase occurs, not a
definition of the phrase itself in isolation. In the case of "a
so-and-so," this is fairly obvious: no one could suppose that
"a man" was a definite object, which could be defined by itself.
[Pg 172]
Socrates is a man, Plato is a man, Aristotle is a man, but we
cannot infer that "a man" means the same as "Socrates"
means and also the same as "Plato" means and also the same
as "Aristotle" means, since these three names have different
meanings. Nevertheless, when we have enumerated all the
men in the world, there is nothing left of which we can say,
"This is a man, and not only so, but it is the 'a man,' the quintessential
entity that is just an indefinite man without being anybody
in particular." It is of course quite clear that whatever
there is in the world is definite: if it is a man it is one definite
man and not any other. Thus there cannot be such an entity
as "a man" to be found in the world, as opposed to specific
man. And accordingly it is natural that we do not define "a
man" itself, but only the propositions in which it occurs.
In the case of "the so-and-so" this is equally true, though
at first sight less obvious. We may demonstrate that this must
be the case, by a consideration of the difference between a name
and a definite description. Take the proposition, "Scott is the
author of Waverley." We have here a name, "Scott," and a
description, "the author of Waverley," which are asserted to
apply to the same person. The distinction between a name and
all other symbols may be explained as follows:—
Public-domain text, read in full here on John Shaqi.
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